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4 years ago

5

First and second place in a contest use a ratio to share a cash prize.When first place pays $100 and second pays $60.how much do

es first place pay if second place pays $36?

2 answers:

Morgarella [4.7K]4 years ago

8 0

Ratio between first prize pay and second prize is 100/60=10/6

first/second=10/6
First=10/6 of second
so if second place pays 36 so first will be 60$

svlad2 [7]4 years ago

5 0

Let's make a proportion: 60/100 = 36/x. Cross multiply and find x. In this case, x would equal 60.

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3 years ago

What is the volume of the right triangular prism shown?

ollegr [7]

<u>Given</u>:

The sides of the base of the triangle are 8, 15 and 17.

The height of the prism is 15 units.

We need to determine the volume of the right triangular prism.

<u>Area of the base of the triangle:</u>

The area of the base of the triangle can be determined using the Heron's formula.

$S=\frac{a+b+c}{2}$

Substituting a = 8, b = 15 and c = 17. Thus, we have;

$S=\frac{8+15+17}{2}$

$S=\frac{40}{2}=20$

Using Heron's formula, we have;

$Area = \sqrt{S(S-a)(S-b)(S-c)}$

$Area = \sqrt{20(20-8)(20-15)(20-17)}$

$Area = \sqrt{20(12)(5)(3)}$

$Area = \sqrt{3600}$

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The volume of the right triangular prism can be determined using the formula,

$V=\frac{1}{2}A_b h$

where $A_b$ is the area of the base of the prism and h is the height of the prism.

Substituting the values, we have;

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3 years ago

What is the height of a pyramid (with a square base) whose side length is 12 cm and its slant

Bingel [31]

We have been given that side length of pyramid the square base is 12 cm and its slant height is 10 cm. We are asked to find the height of the pyramid.

We will use slant height of a pyramid formula to solve our given problem.

$s=\sqrt{h^2+\frac{1}{4}a^2}$ ,where,

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Upon substituting our given values in above formula, we will get:

$10=\sqrt{h^2+\frac{1}{4}\cdot 12^2}$

$10=\sqrt{h^2+\frac{1}{4}\cdot 144}$

$10=\sqrt{h^2+36}$

Switch sides:

$\sqrt{h^2+36}=10$

Let us square both sides:

$(\sqrt{h^2+36})^2=10^2$

$h^2+36=100$

$h^2+36-36=100-36$

$h^2=64$

Now we will take positive square root of both sides.

$\sqrt{h^2}=\sqrt{64}$

$h=8$

Therefore, the height of the pyramid is 8 cm and option 'b' is the correct choice.

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