Math

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How do you find the height of a trapezoid?

The Pythagorean Theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the legs. This equation can be modified to find one of the legs if the hypotenuse and the other leg is known; in this case, the tall leg is the height of the trapezoid. The legs of a right triangle are defined as the sides of the triangle opposite from the acute angle and form the shorter two sides of the triangle. The equation that uses the area of the trapezoid is found by manipulating the original equation for the area of the trapezoid and solving it for the height. Tra..

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What is the volume of a sphere?

Geometrically, a sphere is defined as the set of all points equidistant from a given center point in three dimensions. Of all geometric solids, a sphere has the least amount of surface area for a given volume. For that reason, soap film tends to pull itself into a spherical bubble, because surface tension tends to minimize the surface area around the enclosed volume of air.

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What is a percentile in statistics?

For ease in reporting, percentiles are often broken into quartiles, with the 25th percentile known as the first quartile, the 50th percentile known as the median or second quartile, and the 75th percentile as the third quartile. Another option is demarcation of percentiles in 10 percent sets, known as deciles, where the 10th percentile is the first decile, and so on.

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How do you round to two decimal places?

Rounding is a simple process that involves looking one number to the right of the value to be rounded. A helpful phrase for this process is: "5 and above, give it a shove. 4 and below, let it go." For example, if the number to be rounded to two decimal places is 2.938, it is rounded to 2.94 because the third decimal place (8) is higher than 4. If the number is 2.931, it is rounded to 2.93 because the third decimal place (1) is lower than 5. If the third decimal place is 0, or there is no third decimal place, the number is already rounded to two decimal places.\nWhen rounding the number 9 up, e..

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How do you calculate contribution per unit?

Calculate the overall revenue of the productDiscover the revenue of the product by the sale price multiplied by the number of units sold. For instance, if your company sells 1,000 products at $100 each, the overall revenue is $100,000.Determine the variable costsCalculate the variable costs that go directly into the product, such as materials, supplies, wages and commissions. For example, the aforementioned 1,000 products include $40 of variable costs each. This means the variable costs totaled $40,000.Divide by units soldTake the overall calculations of revenue and costs, and then divide that..

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How do you find the percentage of two numbers?

Determine which number to divide byThe first step is determining which number should by divided by the other. Typically, the smaller number is divided by the larger number. For example, if you are trying to find the percentage of 135 out of 180, 135 would be divided by 180. If, however, you are trying to find what percentage 200 is out of 125, you would divide the larger number by the smaller number.\nDivide the two numbers togetherDividing 135 by 180 equals 0.75:\n135 / 180 = 0.75\n\nDividing 200 by 125 equals 1.6:\n200 / 125 = 1.6\n\nThis answer is the percentage in decimal form.\n\nMultiply..

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What contributions did Aryabhata make to math and science?

In addition to approximating Pi's value, Aryabhata is believed to have first defined the number as irrational. He also developed formulas for calculating the area of shapes like triangles, leaving a strong mark on geometry, and his trigonometric contributions include a sine table that, like his other work, was written in verse. Not only was Aryabhata a mathematician and scientist, but he also had a talent for words.\nAryabhata's contributions to astronomy are also significant; these contributions include counting solar days, determining the Earth's spherical shape and making a n..

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What is two-thirds in percent form?

If a given fraction has a denominator that one can multiply by another number that gives 100 in the denominator, then this is another method of finding a fraction in percent form. An example of this type of problem is the fraction one-half, or 1/2. One can multiply the numerator and denominator by 50 to get the answer 50/100. This fraction is equal to 0.50 percent. If one multiplies this by 100, one finds the answer 50 percent. In math, 50/100 is an equivalent fraction of 1/2.

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What are the notable mathematical problems that feature pi?

While the circle's circumference is given by the formula 2 x radius x pi, its area formula is pi x radius squared. Similarly, many of the area and volume formulas for different geometric solids were formulated with pi as a term in them. For example, the area of a sphere is 4 x pi x radius squared, and its volume formula is 4/3 x pi x radius cubed.The history of pi dates back to the ancient Babylonians and Egyptians. Babylonians estimated pi as 3.125, and the Egyptians approximated pi to be 3.1605. However, it was the Greek mathematician Archimedes that calculated pi to be between 223/71 a..

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What does domain mean in math?

An example in which the domain is not all real numbers is when a function results in an undefined number. For the function y= 3/(x-1), all real numbers work except for 1. When 1 is entered into the function, the end result is 3 divided by 0, which is an undefined number.

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