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How To Pick The Right Patio Slabs For Your Garden

When you are looking to improve your garden, then you want to ensure that you pick the right patio slabs. After all, choosing the right patio slabs can make a substantial difference in the result that you get in the end. 

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Ultimately, when you are considering improving your garden and using patio slabs, you should have 4 main questions:

#1: The Style:

The truth is that in what concerns to gardens, you can adopt many different styles. However, it is important that you think about the house and the garden as one piece. Just to give you an overall idea, you can go for a traditional, rustic riven or a modern sawn faced type of stone. 

#2: The Color:

As you can imagine, the color of the pavers also plays an important role here. After all, you want to ensure that you look for a color that either contrasts or complements the existing house and garden. Some people prefer to use more that one color and it is perfectly fine. 

Check out our paver calculator.

#3: The Function:

When you are looking to choose the best patio slabs, then you need to consider the use that you will give to your garden. You need to think if there will be a lot of traffic, footfall as well as the weight. After all, you want to ensure that it lasts for a very long time in the best conditions. 

#4: The Cost:

Obviously, the costs also play a crucial role when you are picking the best patio slabs. You should keep in mind that the cost of the stone in a landscaping project is only about 20% of the total cost. The vast majority of the costs involved include other materials and labor. So, if you are planning on getting a more expensive stone, then this will definitely increase your overall costs. 

Looking for a complete paver calculator tool?

How To Pick The Right Patio Slabs For Your Garden

Now that you know that you need to find an answer to all these 4 questions, the first thing that you need to consider is the space that you have available. For example, in case you are designing a small place, then you should pick smaller stones or slabs. On the other hand, if you have a large place, then you should go for larger stones and slabs. 

Notice that an extra factor to consider is the weather conditions. The truth is that depending on where you live, some patio slabs are better than the others. Keep in mind that the more porous the stone, the more green with algae it will go. Generally, concrete stone tends to fade and natural stone tends to darken with weathering.

So, with this in mind, you have 3 main types of patio slabs to choose from: 

#1: Natural Stone:

This is the one that tends to look better since each stone has its own individuality, color, and texture. So, you can be sure that you will get an amazing result. Natural stone is also hard-wearing and high-quality. On the negative side, it is more expensive. 

Discover our paver pattern calculator.

#2: Reconstituted Stone:

The truth is that there are many different types of reconstituted stones available on the market:

Pressed Concrete Slabs: These are cheap and can give a very neat, uniform look.

Wet Cast: There is a wide variety to look at and one of the best things is that it tends to be weather slower. Besides, it has a smoother look.  

Impressed Concrete: When you don’t want to spend a lot of money, you can have a great garden looking like natural stone or slabs. 

Blocked Paviours: These are usually used for drives because they are so strong but can be used for patios due to their decorative effect. Concrete and clay forms in many different sizes, finishes, and colors.

#3: Porcelain Paving:

The last option that you have is porcelain paving. This is a relatively new product that is mainly designed for outside use. Available in multiple sizes, it is very robust and is less slippery than stone and concrete. Besides, it has lots of finishes from smooth to textured and is very resistant to staining. 

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6 Signs You Aren’t Ready To Retire

When you get to a certain age, it’s not easy to not think that maybe it’s time to retire. The truth is that when you listen to the alarm clock, you don’t get thrilled about going to work. But if this would mean that you would be ready to retire, then you could do it since you were 25 or 30 years old. 

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Ultimately, there are many different aspects to consider before you retire. After all, you need to ensure that you have a good monthly budget, a decent income coming in every month and that you have your debt under control. But there’s a lot more to think about. 

6 Signs You Aren’t Ready To Retire

#1: You Struggle To Pay Current Bills:

No matter how old you are, if you are still struggling to pay current bills, this means that you aren’t ready to retire. 

As a general rule, retirees may need about 75% of their pre-retirement income to enjoy a comfortable retirement. That income typically comes from Social Security, pensions, 401(k)s, IRAs, and other savings. 

Discover how much you need to save for retirement.

#2: You Have A High Level Of Debt:

The reality is that a high level of debt will steal your savings as soon as you retire. So, according to most specialists, you should retire when you still have car loans or credit card payments. In addition, and if you can, you should also consider downsizing or paying off your mortgage before you retire. While this may imply working more years, the positive side is that you won’t need to worry about these after retirement. 

Wondering about your mortgage?

#3: You Don’t Have A Plan For Future Major Expenses:

Life is unexpected and major expenses tend to appear when you don’t have such a good cash flow. With that said, before you retire, you should ensure that you have enough money to cover any of these unexpected expenses. These may include repaving your driveway, repairing or replacing your roof, or even buying a new car. 

Check out our hourly weekly yearly wage conversion calculator.

#4: You Don’t Have A Monthly Financial Plan:

One of the things that most people tend to forget is that when they retire, the paychecks will stop arriving but the bills will continue to arrive. Therefore, it is crucial that before you retire, you have a plan where you map out your monthly cash flow. 

#5: You Don’t Have A Long-Term Financial Plan:

Just as important as having a monthly financial plan is to have a long-term financial plan in place. The reality is that you need to have a clear picture of how long your savings will last and what should your spending level be. 

These business calculators can help you. 

#6: Don’t Forget About Inflation: 

While you may have done all the math so far and be ready for retirement, you need to ensure that you account for inflation. As you know, inflation will affect your daily expenses as well as the value of your life savings. 

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How To Lay Tarmac

When your home has a driveway, then you may be looking for a solution that looks not only good as it is also affordable. The reality is that while it is normal that your driveway suffers from wear and tear, it can certainly decrease both the value and look of your entire property. However, this doesn’t need to b like this when you find the right solution for your driveway such as a tarmac driveway. 

When you don’t choose a good material for your driveway, you may end up with an influx of weeds, among many others that just make this space ugly. 

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What Is Tarmac?

When you’re new to these things, then you may be wondering what tarmac is. So, simply put, tarmac is just concrete asphalt. And, ys, you probably already know what this is. 

Overall, tarmac is made form a composite mixture of some form of aggregate such as sand or stone, and mixed with asphalt. The entire mixture is then heated and transported up to the worksite so it can be laid and compacted into a strong and durable surface. 

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How To Lay Tarmac

Now that you already know what tarmac is and that a tarmac driveway cost is very affordable, it is time to discover how to lay tarmac.

#1: Excavation: 

Before you even start laying tarmac, you need to do some excavation first. The truth is that you need to create the formation level which is the surface level of the ground. 

Generally speaking, the formation level for driveways is about 175mm below the paving level. 

Discover how many pavers you need with our simple patio paver calculator.

#2: Edging: 

Simply put, edging is used to ensure that the tarmac is kept in its place. The truth is that when you don’t restrain tarmac, you may end up with the edges of the surface cracked and crumbled after repeated vehicle usage. So, since you want to ensure that your driveway lasts for a very long time, you can’t skip this step. In addition, you should use materials such as timber, for example.

#3: Protection:

As soon as the surface has been excavated, you will need to lay down a Geotextile woven membrane. This ensures that there is no weed growth as well as it also minimizes sinking. 

#4: Layering:

After placing the Geotextile membrane, you will need to place down Class 1 M.O.T crushed concrete. This will be then compacted and rolled up until it reached the final depth to be used for the driveway. 

Make sure to use our paver pattern calculator.

#5: Drainage:

No matter if you are using tarmac or any other material to build your own driveway, you need to keep in mind that drainage is crucial. Ultimately, it served to remove the excess water from the driveway. 

#6: Concrete Edgings:

At this point, you should install concrete edgings. 

#7: Apply Tarmac: 

Finally, it’s time to apply tarmac. Noice that while it seems that your driveway takes too many materials, a tarmac driveway cost is still pretty low when compared with other options. 

When applying tarmac, just keep in mind that you should add about 2 inches of this material as a base coat. Then, you should add a top coat that needs to be compacted using a roller. 

Bottom Line

While tarmacking a driveway is a process that requires different layers and precision, the reality is that the tarmac driveway cost is totally worth it. In addition, your driveway will look better than ever as well as it will last for a very long time. 

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Understanding Z Score Tables

When you are studying statistics, you will learn about the z score. But simply determining the z score using the formula won’t tell you much. The reality is that you will then need to check the z score tables to figure out its value and to b able to withdraw your conclusions. 

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What Are Z Score Tables?

Z score tables are simply tables with a wide range of numbers. When you use these tables, you will be able to know the percentage of values that are below a z score in a standard normal distribution. 

In case you don’t know or simply forgot about it, the z score or standard score is a value that indicates the number of standard deviations a raw score has either above or below the mean. 

Notice that the mean of the z score is always zero and its standard deviation or variance is always in increments of 1. 

Use our z score calculator for free.

One of the things that tend to cause a great deal of stress to many statistics students is actually using the z score tables. However, this is not difficult at all. You just need to understand whether you find the area to the left or to the right of a positive z score. So, let’s see the differences. 

Finding The Area To The Left Of A Positive Z Score

In most cases, the z score tables show you the percentage of values using a decimal figure. So, you know that when you have this decimal, you just need to multiply it by 100 to get the percentage. 

But how can you find the area to the left of a positive z score using z score tables?

Let’s say that you calculated the z score and you got 1.09. So, now you know that you will need to find this value in your z score tables. To do so, you will need to take a look at the side column located on the left. In this column, you will need to find the whole number first. 

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Since you got 1.09 as a result:

1.09 = 1 + 0.09

So, the value that you need to look for in the column is 1. Next, you will need to look for the 0.09 at the tip of the table. 

If you have your z score tables with you, then you can see that the corresponding area is 0.8621. As we already mentioned above, you just need to multiply it by 100 to get the percentage. In this case, you would get 86.21%. 

Confirm your z score results here.

Finding The Area To The Right Of A Positive Z Score

Since you know that the total area under the bell curve is always equal to 1 which is the same as saying that is 100%, then you will need to subtract the area from the z score table for normal distribution from 1. 

So, let’s say that you have again the same z score of 1.09. One of the biggest differences now that you are looking at the right of a positive z score is that you will need to:

1 – 0.8621. = 0.1379, since you already knew that 0.8621 was the area to the left of z = 1.09.

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6 Benefits Of Using Concrete Blocks In Construction

When you are looking for the right materials to start your own building projects, then you need to consider concrete blocks. The truth is that while you have a wide range of options on the market today, concrete blocks are one of the best choices. After all, they are not only affordable, easy to find, and they are strong which means they will last for a very long time. 

Find here all the calculators that you will ever need.

In case you still have some concerns about using concrete blocks for your building projects, then take a closer look at their main benefits below.

6 Benefits Of Using Concrete Blocks In Construction

#1: Very Versatile:

One of the best things about concrete blocks is that they are incredibly versatile. After all, you can use them throughout many different projects. You will also be glad to know that concrete blocks are available in a wide range of surface textures, shapes, and colors for both indoor and outdoor use.

Check out our concrete block calculator.

#2: Good Performance:

No matter if you are trying to do a big or small project, you want to ensure that it stands up for a very long time. 

In case you don’t know, the most fragile points on any structure are joints. So, you will be glad to know that since concrete blocks are available in different sizes, you can pick the larger ones and get fewer joints. This way, you’ll be minimizing the most vulnerable parts. 

#3: Very Affordable:

There’s no question that one of the most important factors, when you are determining the best materials to use in your building project, is the price. And you’ll be happy to know that concrete blocks are pretty affordable. 

Don’t know how many concrete blocks you need?

#4: Strength And Durability: 

When you are starting a DIY project or even if you have a construction company, you need to ensure that your project lasts for a very long time. And this can be done by using concrete blocks. 

The reality is that concrete blocks are not only strong as they can stand the test of time. One of the things that you may not know about concrete blocks is that concrete actually gets stronger over time. Besides, it’s not weakened by mold, pests or even by moisture. 

Use our concrete block calculator to determine how much they’re going to cost you.

#5: Good Insulator:

One of the main benefits of using concrete blocks in your building projects is the fact that they feature insulating properties. This means that these are great blocks to use when you want to keep outside temperatures from entering your home. Ultimately, this will lead to lower energy costs. 

Notice that not all concrete blocks have the same insulating properties. The truth is that these vary from manufacturer to manufacturer as well as it depends on their density. 

#6: Resistant To Fire:

When you use concrete blocks in your construction, you are actually protecting it against fire. While many DIYers prefer to use wood on their construction projects, it is a lot better to use concrete blocks. After all, concrete blocks are resistant to fire as well as they can also limit the fire’s ability to spread quickly. 

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Save Your Back With This Paver Patio Base

When you are thinking of building a new patio, then you want to ensure that you save your back a bit. The reality is that this can be a task that takes a lot of effort and you may hurt your back. 

One of the things that you can consider instead of building yourself a new patio just like the ones that you are used to seeing is to consider a paver patio base instead. 

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In case you don’t know, a traditional base for a paver patio is a deep layer of compacted gravel which is about 6 inches. If you think of the average patio which tends to be 10 X 12 ft, his means that you will need a lot of soil as well as a lot of gravel base. However, you have a different option now – you may use plastic panels instead of the traditional gravel base. 

Benefits Of Using A Paver Patio Base

While you may be wondering if a paver patio base is really the best option for you, then you need to take a look at some of its main benefits. These include:

Saving a lot of time

Eliminating heavy gravel fill

Less digging

Decreasing the cost of digging and hauling

Preventing damage to the landscaping caused by excavating equipment.

Protecting the screened sand while you’re installing pavers

Allowing patio installations in areas with limited access or in fenced areas. 

Check out how many pavers you need for your patio.

How Does The Paver Patio Base Actually Work?

One of the things that you need to understand is that this paver patio base is built with the best materials to ensure that your patio lasts for a very long time just like a traditional paver patio. However, instead of using that solid base with a lot of sand and gravel, you would only need to use paver patio base panels that are made from lightweight high-density polypropylene. 

One of the main advantages of using these panels is the fact that they include a tongue-and-groove system that allows them to flush with each other easily. 

Make sure to use our paver calculator with a pricing tool.

One of the questions that many homeowners tend to have is regarding about the weight. After all, how can these lightweight panels hold the weight as a 6 feet deep layer of gravel? Well, the straight answer is that they can hold that much weight. And the reason is that the panel spreads out the load. This means that the weight of someone walking on the patio will be widely distributed. So, ultimately, this ends up not putting so much pressure on the soil and will also prevent pavers from becoming uneven.  

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An extra advantage of using a paver patio base instead of the traditional base for your paver patio is the fact that it also delivers an insulated layer that substantially reduces the problems caused by soil that thaws and refreezes. Last but not least, paver patio base panels also come with built-in holes and channels to drain water to the sand layer below.

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Determining Z Score For A Normally Distributed Data

As you probably already know, the z score is also known as the standard score. Ultimately, this is a very important statistic that allows you to easily determine the probability of a score that occurs within your normal distribution. Besides, the z score also allows you to compare two different scores that have different normal distributions. 

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One of the things that you need to know about the z score is that it standardizes or converts scores in a normal distribution to z scores. So, when this occurs, it will turn into a standard normal distribution. 

How To Determine The Z Score?

While we find many statistics students who struggle whenever they need to determine the z score, the truth is that it isn’t hard at all. 

As you probably already read or heard all the theories and methods around this, we decided to take a more practical approach. So, instead of keep repeating what you need to do to determine the z score, we decided to show you how you can simply do it. 

Check out our z score calculator.

Let’s imagine that your English teacher decided to surprise the class and do a test. Let’s suppose that your class has 50 students. All students did the test and then the English teacher took the tests home to correct them. 

When he completed correcting the tests, he discovered that the mean score was 60 out of 100 and that the variation in scores, or the standard variation, was 15 marks.

On the next day, the teacher hands over the tests to students and you find out that you scored 70 out of 100. So, you asked him how you went. 

While at first sight, it appears that you did pretty well, after all, you scored 70 out of 100, looking closer to the data the teacher collected, he discovered that the mean score was 60. So, apparently, you did well. But you can not know for sure since this conclusion isn’t based on variations of scores of all the students in your class. So, what this means in terms of statistics is that it doesn’t consider the standard deviation. 

So, to know if you did well, you need to use the standard normal distribution and the z score. 

Make sure to use our z score online calculator.

The Standard Normal Distribution And The Z Score

One of the most important concepts that you need to know is that the standard normal distribution only converts the group of data in your frequency distribution. So, it always needs to consider that the mean is zero and that the standard deviation is 1. 

The Z Score Formula

As you know, when you want to calculate the z score, you need to use the following formula:

where:

– X = score

– µ = mean

– σ = standard deviation

If you remember, we were trying to determine how well you did on your English test. Remember that you scored 70 out of 100 and the mean score was 60. However, when you are trying to use the z score, you need to ask the question in a different way: What number (or percentage) of students scored higher than you and what number (or percentage) of students scored lower than you?

In case you don’t remember, we also mentioned that the standard deviation was 15. 

So, all you need to do is to replace the values that you have in the Z score formula that we showed you above. So:

Z Score = ( X – µ ) / σ 

Z Score = (70 – 60) /15 

Z Score = 10 / 15 

Z Score = 0.6667

Click here to confirm your results with our z score calculator.

So, you now know that your z score is 0.67. But to answer your question, you need to take an additional step – you need to use a z score table. 

You will see a value of 0.2514 which means that the probability of a score is greater than 0.67 is 0.2514. So, we can then say that about 25% of the students in your class got a better mark than you.

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The Advantages Of Paver Patios

No matter if you are thinking of building yourself your patio or hiring a company to do it for you, then you need to ensure that you pick the best materials. And while you have many options, you should definitely consider paver patios. 

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The truth is that when you have an outdoor area available, then you can make the most out of it. And a patio may be just what you need. 

The Advantages Of Paver Patios

As we already mentioned, there are many different materials that you can use in your patio. However, in our opinion, paver patios are the best ones. And if you don’t want to take our word for it, then just take a look at the advantages of paver patios.

#1: Affordable:

One of the main considerations that homeowners have in mind when they want to do some construction work or remodeling is the price. And in what concerns paver patios, they can be extremely affordable. And we are not only talking about the price of buying the pavers. We are also talking about the maintenance that paver patios require which is very low. 

Use our paver calculator with pricing tool to determine how much this will cost you.

#2: Very Durable:

When you decide to build a patio, you want it to last. After all, you are making an investment no matter if it is for you or if you’re simply trying to increase the value of your property to sell it. 

As w already said, you can use different materials in your patio, However, pavers last for a very long time. Besides, you will also be glad to know that this is the kind of material that can stand up to the wear and tear of the weather without a patio cover, for example. Another incredible advantage of paver patios is the fact that they are slip-resistant. So, you can walk outside without the risk of accidentally falling. 

Discover how much you can save with our free paver calculator.

#3: Aesthetics:

When you are considering building a patio, then you want to ensure that you can pick the right type. It’s important to consider that pavers are available in a wide range of shapes, styles, and even colors. Just as an idea, many people tend to like paver patios because they can get the look of natural stone. 

#4: Easy Installation:

No one likes their remodels to last forever. And in case you pick paver patios, then you won’t need to worry about it. The truth is that paver patios are incredibly easy to install. In fact, they are so easy that you can even do it all by yourself. 

Looking for a free online paver calculator with a pricing tool?

#5: Low Maintenance:

When you build a patio, you want to make the most out of it. You don’t want to simply build one to have just one more space to clean. And with paver patios, you will get a beautiful and affordable new space that you can enjoy at home. And it won’t be difficult to maintain. 

With paver patios, you don’t need to seal or stain them as you need to do with wood decks. When you don’t, your wood deck won’t last long since weather conditions will damage it. 

In case one of the pavers get damaged, you can also simply replace that piece without moving the other ones around it. And this is definitely a plus. 

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Jobs That Use the Pythagorean Theorem

As a math student, the Pythagorean Theorem shouldn’t be new to you. After all, this is one of the most popular and easiest theorems that serves a wide range of uses. 

Simply put, and according to the Pythagorean Theorem, the sum of the squares of the lengths of the two legs of a right triangle is equal to the square of the length of the hypotenuse. 

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The reality is that while some students love math, others simply hate it. That’s a fact. And if you belong to the latter group, then you may be wondering why you should learn this Pythagorean Theorem and how it may be useful for you in the future. 

One of the things that you need to know about the Pythagorean Theorem is that a lot of jobs actually use the Pythagorean Theorem. Unlike other topics that you need to learn at school, the Pythagorean Theorem is one that can serve you on your future depending on the carer that you choose. 

Jobs That Use the Pythagorean Theorem

#1: Jobs In Management:

In case you are considering a career in management, then you want to ensure that you understand the Jobs That Use the Pythagorean Theorem well. 

The reality is that the Jobs That Use the Pythagorean Theorem is very used by a wide range of managers including engineering managers, construction managers, information systems managers, and even natural science managers. 

Check out our Pythagorean Theorem calculator.

#2: Jobs In Agriculture:

While you may think that if you want a career in agriculture that you don’t need math at all, then you are wrong. The reality is that from farmers to environmentalists and even gardeners use maths a lot on a daily basis. 

Just think of the times when they need to draw precise lines to determine growing spaces, for example. And the truth is that no matter if you intend to work directly with trees, plants, animals or food crops, you need math and you need a good understanding of the Pythagorean Theorem.

Looking for the best Pythagorean Theorem calculator. 

#3: Cartographers And Surveyors Jobs:

These jobs are usually regarded as tasks that use a lot of mathematical tools. After all, you need to know how to determine distance and length. 

In case you don’t know, cartographers and surveyors are the ones that measure and map properties, they set official water, land, and air boundaries for the government, businesses, and homeowners. So, they want to make sure that they can do their work fast and this is why the Pythagorean Theorem and other math theorems and tools are needed. 

#4: Production Workers:

While this is a very wide field of jobs, the truth is that most production workers need to have a good grasp of math especially of the Pythagorean Theorem. For instance, when creating specialized items for a company that produces tractor parts, the ability to measure across both long and short distances makes the process that much easier.

Looking for the easiest Pythagorean Theorem calculator? 

#5: Architects:

As you probably already know, this is the type of job that uses a lot of math. After all, architects can’t deal with the risk of measuring things wrong and have a building collapse. 

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Understanding The Pythagorean Theorem

There’s no question that whether or not you like math, you already hard about the Pythagorean Theorem. After all, the Pythagorean Theorem is probably one of the most popular as well as one of the simplest math theorems. However, you shouldn’t think that just because it is simple, it doesn’t have too much use. In fact, it’s quite the opposite. 

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So, before we go ahead and show you the different perspectives about the Pythagorean Theorem as well as the different calculations this theorem can help you solve, it is better to start with the basics. So, let’s begin.

Understanding The Pythagorean Theorem

Simply put, the Pythagorean Theorem which is also known as Pythagoras’ Theorem os a relationship between the sides that you can find in a right triangle. 

In case you don’t know, a right triangle is a triangle where one of the three angles is a 90-degree angle. Besides, it is also important to keep in mind that when you are talking about a right triangle, the sides are called legs and hypotenuse.

The Pythagorean Theorem

In the image above, you can see a clear representation of the Pythagorean Theorem. As you can see, we have a right triangle and there is a relationship between the legs and the hypothenuse which are represented by: 

a^2+b^2=c^2

where a and b are the legs and c is the hypothenuse. 

So, when you are trying to calculate c or the hypothenuse, you can simply do the following math operation: 

c=√a^2+b^2

Check out our Pythagorean Theorem calculator.

A Brief History Of The Pythagorean Theorem

While you may think that Pythagoras was the one that proved the Pythagorean Theorem in the first place, there isn’t actually any evidence of it. In fact, no one knows this for sure. Yet, this theorem has always been credited to Pythagoras who was a Greek mathematician (c. 570–495 BC).

The truth is that Chinese and Babylonian mathematicians already knew this theorem before Pythagoras. It is yet to be discovered whether they discovered it first or if the theorem was discovered multiple times in different places. After all, at that time, people didn’t travel around the world with ease and it was completely possible for something like this to not be known in other parts of the world for centuries. 

One of the things that you may not know about the Pythagorean Theorem is the fact that its history is connected to the discovery of Pythagorean Triples. 

Simply put, the Pythagorean triples consist of 3 positive integers such as c^2 = a^2 + b^2. The 3 integers 3, 4, and 5 tend to be a well-known Pythagorean triple. Why?

5^2 = 3^2 + 4^2

Notice that Pythagorean triples were discovered by the Babylonians, from 2000 to 1786 BC. However, there isn’t any reference to triangles at that point. 

It is believed that either Pythagoras or his disciples may have built the first known algebraic proof of the theorem and that then other famous writers including Ciceron and Plutarch have acclaimed him for discovering this proof. And this is why the Pythagorean Theorem has always ben linked to Pythagoras as it can easily be seen by the name of the theorem itself. 

Examples Where The Pythagorean Theorem Is Used

While there are many different examples that we could show you about using the Pythagorean Theorem, we decided to share with you just 2 of them. We believe that they are more than enough to understand this theorem as well as its importance. 

Example #1: Find The Length of The Hypothenuse In A Right Triangle:

As you can easily understand, this is the basis of the theorem itself and this is where you usually start when you are learning the Pythagorean Theorem for the first time. 

So, let’s say that you have the following right triangle and that you want to find the length of the hypothenuse:

While you can see the x in the hypothenuse side, traditionally we call it c.

So, simply put, you want to calculate c. 

So, turning to the Find The Pythagorean Theorem that states that:

c^2 = a^2 + b^2

Replacing the values you got:

c^2 = 3^2 + 4^2

c^2 = 9 + 16

c^2 = 25

Taking the square root:

c = √25 = 5

So, the hypothenuse, in this case, is 5 (c = 5). 

In case you want to confirm your results, make sure to use our Pythagorean Theorem calculator.

Example #2: Find The Length Of A Leg In A Right Triangle:

Let’s now say that instead of the hypothenuse, you want to determine the leg of the right triangle that is above. 

So, in this case, you are trying to determine y. Notice that just as before, according to the terminology of the Pythagorean Theorem, you will be looking to determine b. 

So, turning to the Pythagorean Theorem again:

c^2 = a^2 + b^2

And replacing the values:

12^2 = 8^2 + b^2

144 = 64 + b^2

b^2 = 144-64

b^2 = 80

Taking the square root:

b = √80 = 8.94

So, the leg, in this case, is 8.94 (b = 8.94).

Confirm your results with our simple calculator. 

Example #3: Is It A Right Triangle?

Up until now, we have been looking at the easiest ways to determine the hypothenuse or one of the legs of a right triangle. However, you may also use the Pythagorean Theorem to discover if you are looking at a right triangle or not. 

So, how can you do this using the Pythagorean Theorem?

Let’s say that you’re in a math test and that one of the questions that you need to answer to is the following one: The sides in a triangle is 6, 12 and 13. Is it a right triangle?

When you are using the Pythagorean Theorem, you always need to keep in mind that the hypothenuse is the largest side of the right triangle. So, in this case, 13 would refer to the hypothenuse and, consequently, 6 and 12 are the legs of the right triangle. 

When you have this type of question, you just need to prove that: 

c^2 = a^2 + b^2

So, we already know that c = 13 and a and b are 6 and 12. Therefore:

13^2 = 6^2 + 12^2

169 = 36 + 144

169 = 170

Since this is not true, we can then state that a triangle with the sides of 6, 12, and 13 isn’t a right triangle. 

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8 Key Performance Indicators (KPIs) Defined

When you are a team manager, then Key Performance Indicators (KPIs) are not new to you. In case you aren’t, then it is important that you know what Key Performance Indicators (KPIs) are.

Simply put, Key Performance Indicators (KPIs) are some performance measurement indicators that can help you understand how your department or organization is performing. 

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One of the things that you should keep in mind is that a KPI should act as a compass. This means that it should help you and your team to better understand if you’re taking the right path toward your strategic goals. 

To ensure that a KPI is effective, a KPI must:

Be well-defined and quantifiable.

Be communicated throughout your organization and department.

Be crucial to achieving your goal. (Hence, key performance indicators.)

Be applicable to your Line of Business (LOB) or department.

One of the main problems with Key Performance Indicators (KPIs) is that there are a lot of them. So, when you choose the wrong KPI, then you might be measuring something that doesn’t align with your goals. 

Discover everything you ned to know about the IRR.

8 Key Performance Indicators (KPIs)

#1: Financial Metrics:

Profit: There’s no question that this is one of the most Key Performance Indicators (KPIs). However, you shouldn’t forget to analyze both net and gross profit margins as well to ensure that you can understand how your organization is at generating a high return. 

Cost: This one measures the cost-effectiveness and also finds the best ways to decrease and manage your costs.  Learn how to determine your working capital needs.

Cost Of Goods Sold: When you keep a good track of your production costs, you have a good idea about how your product markup should look like as well as your actual profit margin. 

LOB Revenue Vs. Target: In case you don’t know, this KPI refers to the comparison between your actual revenue and the revenue you projected. The truth is that when you check discrepancies, this should help you identify how your department is performing. 

LOB Expenses Vs. Budget: This KPI should help you compare your actual overhead with your forecasted budget.  

Check out how to determine the startup costs of opening a new business. 

#2: Customer Metrics:

Customer Lifetime Value (CLV): While you are always minimizing costs, this may not be your best option when you are looking to optimize your customer acquisition. The reality is that CLV helps you look at the value of your organization is getting from a long-term customer relationship. 

Customer Acquisition Cost (CAC): When you divide your total acquisition costs by the number of new customers in the time frame you are looking get, you will get the CAC. In case you have an e-commerce, then you need to know that this is one of the most important Key Performance Indicators (KPIs) that you can use. 

Customer Satisfaction & Retention: There are many different indicators that can help you determine how happy your customers are and that they will buy back from you again. These include customer satisfaction scores and the percentage of customers repeating a purchase.

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5 Different Types Of Mortgage For Homebuyers

There’s no question that buying a home is always exciting. However, you need to think about how you will be financing it. And the reality is that this may b a bit overwhelming. 

Take a look at the best free online calculators.

One of the things that you need to know os that you have different types of mortgage. So, today, we decided to take a look at the most important ones so that you can make a better decision. 

5 Different Types Of Mortgage For Homebuyers

#1: Traditional Mortgages:

Simply put, a traditional mortgage is the home loan that you can get which is not insured by the federal government. And within this category of mortgages, we can divide it into two different ones: conforming and non-conforming loans. 

A conforming loan simply means the loan amount falls within maximum limits set by Fannie Mae or Freddie Mac, government agencies that back most U.S. mortgages. On the other hand, loans that don’t meet these guidelines are considered non-conforming loans. 

Traditional mortgages are ideal for borrowers with strong credit, a stable income and employment history, and a down payment of at least 3 percent.

Looking for the top mortgage calculators?

#2: Jumbo Mortgages:

Jumbo mortgages are traditional loans that have non-conforming loan limits. This means that the home prices exceed federal loan limits. 

The truth is that these types of mortgage are very common in higher-cost areas and they tend to require more in-depth documentation to qualify. 

Jumbo loans make sense for more affluent buyers purchasing a high-end home. 

Should you get a second mortgage?

#3: Government-Insured Mortgages:

While the United States government is not a mortgage lender, the reality is that it does play an important role in helping more American citizens become homeowners. 

One of the things that you may not know is that there are 3 government agencies to back loans: the Federal Housing Administration (FHA loans), the U.S. Department of Agriculture (USDA loans) and the U.S. Department of Veterans Affairs (VA loans).

Ultimately, these types of mortgage are meant for people who have low cash savings, a not so great credit, and people who can’t qualify for a conventional loan. 

#4: Fixed-Rate Mortgages:

These types of mortgage are the ones that maintain the same interest rate over the life of your loan. So, this means that your monthly mortgage payment always stays the same. 

So, in case you are looking to stay in your home for at least 8 to 10 years, then this type of loan may be perfect for you since it delivers the stability with your monthly payments. 

Find out what you need to ask a potential mortgage lender.

#5: Adjustable-Rate Mortgages:

Unlike the previous type of mortgage, the adjustable-rate mortgages have fluctuating interest rates that can go up or down with market conditions. 

One of the things that you need to know about these types of mortgage is the fact that there are some mortgages that have a fixed interest rate for a couple of years and then the loan resets to a variable interest rate for the rest of the term. 

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How To Lose Weight Fast

While you know that losing weight fast isn’t probably the best way to introduce better daily habits to maintain a good health, sometimes, you just need to lose weight fast. So, what can you do? 

No matter if you need to attend an event and you need to fit in that beautiful dress you already bought or if you’re going on vacation, then you just know that you need to lose weight fast. Nevertheless, it is always wise to know your ideal weight before.

#1: Cut Back On Sugars And Carbs:

When you are looking to lose weight fast, then you want to ensure that you cut on sugars and carbs. In case you don’t know, when you do this, you will notice that your hunger levels will decrease and you’ll end up eating fewer calories. So, you will be able to lose weight at a fast rate and still be completely fulfilled and without being hungry all the time. 

#2: Eat Protein, Fat, And Vegetables:

Even when you are trying to lose weight fast, you still need to include a protein source, a fat source, and low-carb vegetables in each one of your meals. In case you need some ideas of sources of protein, here are some that you can use:

Meat: pork, chicken, beef, lamb

Fish and Seafood: shrimp, trout, salmon

Eggs: whole eggs with the yolk are the best. 

One of the things that you should keep n mind about protein is that high-protein diets can reduce cravings and thoughts about food by 60%. So, you won’t have that desire for late-night snacking most of the time. 

In terms of good sources of low-carb vegetables, you may go for brussels sprouts, cauliflower, broccoli, lettuce, spinach, cucumber, kale, tomatoes, swiss chard, among others. 

In what concerns to good fat sources, these include butter, avocado oil, coconut oil, and olive oil. 

#3: Lift Weights Regularly:

As you already know, when you are looking to lose weight, then you want to make sure that you also exercise. And lifting weights 3 times a week should be considered. Make sure that you do a warm-up before you start.

Besides the benefits of exercising for your overall health, the reason why we include weightlifting is due to the fact that this exercise allows you to burn a lot of calories as well as prevents your metabolism from slowing down. 

Discover your ideal weight using this ideal weight calculator.

#4: Looking At Calories And Portion Control:

When you are trying to lose weight fast, you won’t need to keep an eye on your calories or portion control. As long as you keep including on all your meals protein, fat, and low-carb vegetables, you won’t need to monitor these. 

Bottom Line

In any diet that you decide to use, you should always make sure that you know your ideal weight. And you can use our ideal weight calculator to know how it should be. Besides, you should also keep in mind that water plays a very important role and that it can also help you when you are feeling a bit hungry. So, make sure that you always keep a water bottle near you all the time. 

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4 Ways To Lose Weight Naturally

When you are trying to lose weight naturally, you will find that there is a wide range of meal replacement plans, supplements, and diets that state they can help you. However, and while some of them may actually work, they are spread out all over the Internet making it difficult for you to find the right way. 

Notice that before you start any diet, you should always make sure that you know your ideal body weight. You can use our body weight calculator here. 

4 Ways To Lose Weight Naturally

#1: Intermittent Fasting:

One of the most popular ways to lose weight naturally is through intermittent fasting. Simply put, this method involves regular short-term fasts and consuming meals within a shorter period of time during the day. 

According to some studies, intermittent fasting for up to 24 weeks has been showing positive results when you are overweight. 

#2: Monitoring Your Diet And Exercise:

The truth is that when you are looking to lose weight, you want to ensure that you keep track of what you eat and drink during the day. So, you can create a simple log system that allows you to always be in control. 

While you have a wide range of apps that allow you to do this, some of them only allow you to monitor your diet. However, you should make sure that the app you pick also allows you to keep track of your exercise routine. 

#3: Eating Mindfully:

One of the reasons why so many people is trying to lose weight naturally is because they don’t even eat mindfully. This simply means that you are not paying attention to what you eat or to how you eat. The truth is that most of us tend to eat quickly on the run, working at the desk, in the car or even watching TV. So, there are some things that you can do that prevent you from doing this. These include always sitting down to eat, preferably at a table, avoid any distractions when you are eating, make considered food choices, and eat slowly. With this, you will be actually enjoying and appreciating what you are eating and not to simply fill your stomach. 

Check out our ideal weight calculator. 

#4: Eat Protein For Breakfast:

As you probably already heard so many times, breakfast is the most important meal of the day. After all, after spending a lot of hours sleeping, your body needs the energy to get back on track. However, when you are trying to lose weight naturally, you may feel tempted to skip breakfast. Instead, you should rather include protein since protein can regulate appetite hormones to help you feel full. 

Good choices for a high-protein breakfast include eggs, oats, nut and seed butters, quinoa porridge, sardines, and chia seed pudding.

Bottom Line

As you can see, there are many things you ca do and change to ensure that you lose weight naturally. Notice that while it is always important to be aware of your ideal body weight, you should follow a plan and stick to it.

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Understanding Density, Volume, Mass

Density, volume, mass are the most basic properties of an object. After all, volume tells you how big the object is, mass tells you how heavy the object is, and density is mass divided by volume. 

The truth is that while you are used to dealing with volume and mass almost on a daily basis, the same can’t be said about density. 

Discover the best calculators online in 2019. 

So, let’s take a quick example to see how you can easily determine the density of an object. 

Let’s imagine that you ate looking at a lead brick that is 5 cm x 2 cm x 10 cm and weighs 1,134 g. 

As you can see, you already know the mass in grams which is 1,134 g. However, you don’t know the volume of the lead brick. But you do know its dimensions which allows you to easily determine its volume. 

So, we can then state that: 

Volume = 5 X 2 X 10

Volume = 100 cubic cm

As we already mentioned above, the formula to determine the density of an object is equal to the mass divided by the volume:

Density = Mass / Volume

By replacing the numbers:

Density = 1,134 / 100 

Density = 11.34 grams per cubic cm

Get your density results faster with our density calculator. 

What About Mass?

When we are talking about density, volume, mass, the one that arises more questions is, without any questions, density. However, do you really know what mass is? 

One of the things that you may not know about mass is that it can be defined in two different ways: 

inertial mass measures how strongly an object resists acceleration

gravitational mass measures how strongly an object attracts other things to itself.

To make things simpler, you just need to think of mass as weight. 

Looking to confirm your density results? Use our free online calculator.

What About Volume?

Simply put, volume measures the spacial size of an object. When you are trying to determine density, you need to ensure that you consider the shape of the object that you are using. Nevertheless, the volume tends to be thought and considered in a very simple way. The volume will be equal to width times height times length. 

When you can’t determine the shape of the object, one of the best things that you can do is to simply put it in a large container of water and just measure the rise in water level. 

What About Density?

As you already know and as we already showed you, density is calculated by dividing mass by volume of a specific object. 

Make sure to use our density calculator to determine density. 

While density can be less intuitive than mass or volume, the truth is that it is a matter of practice. After all, you already picked up two objects to determine which one is the heaviest. And you do this naturally. And while this may not mean anything to you, the reality is that you’re trying to conclude something about the density of the two different objects. 

Check out some practical samples here.

One of the key aspects of density is that it is not possible to measure it directly. Instead, it needs to be calculated after both mass and volume have been determined. 

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What Is The Density Of Water?

When you are trying to determine the density of a substance or object, you ar about to find out that if this substance is water, then it has some different characteristics. 

The Density Of Water

Simply put, the density of water is the weight of the water per its unit volume. However, this depends on the temperature of the water itself. 

As a rule of thumb, whenever you are told to consider the water density, you need to assume that it is 1 gram per milliliter (1 g/ml) or 1 gram per cubic centimeter (1 g/cm^3). 

Make sure to use our density calculator.

Understanding The Water Density

In case you’re still in school, you probably already heard that density is the mass per unit volume of a substance. But what does this mean? 

The reality is that density is just the weight for a specific amount or volume of material. 

The Water Density Isn’t Always The Same

The truth is that while you may assume that water always has a density of 1 gram per milliliter, the reality is that this isn’t exactly true. At least, for all temperatures. Just check the following table where you can see the different temperature measured in both Celsius and Fahrenheit degrees, its density and its weight.

Temperature (°F/°C) Density (grams/cm^3) Weight (Pounds/ft^3) 32°F/0°C 0.9998762.41639.2°F/4.0°C1.0000062.42440°F/4.4°C0.9999962.42350°F/10°C0.9997562.40860°F/15.6°C0.9990762.36670°F/21°C0.9980262.30080°F/26.7°C0.9966962.21790°F/32.2°C0.9951062.118100°F/37.8°C0.9931861.998120°F/48.9°C0.9887061.719140°F/60°C0.9833861.386160°F/71.1°C0.9772961.006180°F/82.2°C0.9705660.586200°F/93.3°C0.9633360.135212°F/100°C0.9586559.843

Ice Is Less Dense Than Water

If you add ice to a glass of water, you will see that part of it will be below the water level. And while this may be a surprise for you, the reality is that this happens dues to the density of the ice that is inferior to the liquid water’s density. Upon freezing, the density of ice decreases by about 9%. 

Check out our density calculator to determine water density. 

The best way that you can understand this is by actually doing some experiments and visualizing the results. Besides, you also need to keep in mind that the density of ice is about 90% that of water. However, it doesn’t remain constant. In fact, it varies because ice also contains air. This means that about 10% of an ice cube will be above the water line. 

Another important key aspects that you need to know about water density is that water at about 39°F (4°C) is denser than water at 32°F (0°C). 

Measuring A Liquid’s Density

The instrument that is used to measure the density of a liquid is called a hydrometer. While this is one of the simplest of scientific-measuring devices, it is an accurate instrument that you can use. 

Confirm your water density with our calculator. 

In order to determine the density of water with an hydrometer, you just need to gently lower it into the liquid until it can float freely. On the device, you will be able to see how high or low the hydrometer is floating through its marked lines. 

Learn more about water density. 

As a rule of thumb, whenever the hydrometer floats lower, it means that you are dealing with a less dense liquid. 

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How To Calculate Roof Pitch

When you are considering to build a new home, then choosing the best roof is definitely something that you need to consider. However, besides the materials that you will be using, it is also important to understand how to calculate roof pitch. 

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While many people tend to use both roof pitch and roof slope as similar concepts, this isn’t exactly right. So, in order to make things clear, you should keep in mind that while slope is used for steepness, pitch is used for the roof’s overall dimensions. 

So, How To Calculate Roof Pitch?

The truth is that you have more than one way to calculate roof pitch as well as there are also different ways on how to measure roof pitch. So, let’s check them out. 

Check out our roof pitch calculator.

Method #1: Measuring Slopes From The Rafters

So, if you are looking to measure the slope from the rafter, you need to make sure that you are measuring it from the underside of the roof. After all, this is the most accurate way that you have to find the slope. 

One of the things that you need to keep in mind is that you should position a level against the underside of the rafter. All you need to do is to place one end of a carpenter’s level against the underside of the rafter and then adjust it until you see the bubble centered between the two lines. 

The next thing that you will need to do is to find the 12 inches mark on the level. In case you don’t know, the 12 inches are the traditional measurement used in the United States. 

Learn hot to calculate roof pitch with our calculator.

With our tape extended, you will need to set it perpendicular to the level. As soon as you do it, you should make sure that you measure the distance from the 12 inches mark to the underside of the same rafter, that is directly above it. 

Finally, you just need to determine the slope. So, in case you don’t know, the slope of your roof is simply the ratio of the vertical distance (rise) to the horizontal distance (run). 

Here’s a practical example. Let’s say that you discovered that you see 4 inches of height with the tape measure at the 12 inched mark on the level. So, in this case, you can simply state that your slope is 4:12 or 4 in 12. 

Make sure to confirm your results using our roof pitch calculator. 

Method #2: Calculating Pitch From Slope:

So, how can you determine the pitch from slope? 

The truth is that while you have different methods that allow you to calculate pitch, one of the simplest and easiest ons is to simply determine it using some shortcuts instead of measuring the roof’s overall dimensions. Here are some tips that you can use:

In case you are looking for a roof with the ridge above one wall, then the span is the same then the run. This way, the slope and the pitch will be equal. 

Discover the different types of roofing materials.

In case you are looking for a simple gable roof, then the span (wall to wall) needs to be twice the size of the run (wall to ridge, horizontally. Then, you just need to divide the slope by two to determine the pitch. 

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