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Simora [160]
3 years ago
7

Given sin A = 12/13 and that angle A is in Quadrant 1,

Mathematics
1 answer:
UkoKoshka [18]3 years ago
5 0

We have been given that \text{sin}(A)=\frac{12}{13} and angle A is in quadrant 1. We are asked to find the exact value of \text{cot}(A) in simplest radical form.

We know that sine relates opposite side of right triangle with hypotenuse.

\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}

This means that opposite side is 12 units and hypotenuse is 13 units.

We know that cotangent relates adjacent side of right triangle with adjacent side.

\text{cot}=\frac{\text{Adjacent}}{\text{Opposite}}

Now we will find adjacent side using Pythagoras theorem as:

\text{Adjacent}^2=\text{Hypotenuse}^2-\text{Oppoiste}^2

\text{Adjacent}^2=13^2-12^2

\text{Adjacent}^2=169-144

\text{Adjacent}^2=25

Let us take positive square root on both sides:

\sqrt{\text{Adjacent}^2}=\sqrt{25}  

\text{Adjacent}=5

Therefore, adjacent side of angle A is 5 units.

\text{cot}(A)=\frac{5}{12}

Therefore, the exact value of cot A is \frac{5}{12}.

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Jason designs a rectangular sandbox. He models the perimeter of the sandbox using the expression 8l+2, where l is the length of
inn [45]

Answer:

A   .The expression 2l+2(3l+1) shows the width is 1 more than 3 times the length.

Step-by-step explanation:

p = 8l + 2

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2w = p - 2l

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3 years ago
Assume that the heights of women are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If
djyliett [7]

Answer:

Option a. 0.9811

Step-by-step explanation:

First, you need to use a normal distribution table to solve this. If you don't have it, then see the attached table so you can guide yourself.

Now, we want to know the probability of randomly select 75 women whose height have a mean between 63 and 65 inches, knowing that in general, the mean is 63.5 and standard deviation of 2.5

To do this, you should calculate first the Z score value for both heights, one for 63 inches and the other with 65 inches. Then, with those values, we'll look the table to get the area under the curve, and thus, the probability. To calculate Z use the following expression:

Z = x - μ / (σ/√n)

Where:

μ: mean height

σ: standard deviation

x: height required

n: sample population

We have all the data so let's calculate both values of Z:

Z1 = 63 - 63.6 / (2.5/√75) = -2.08

Z2 = 65 - 63.6 / (2-5/√75) = 4.85

With these Z score, let's watch the table, and see which area belongs to,

In the case of Z1, the area is 0.0188, while Z2 is 1.

To know the probability, all we need to do is substract those values:

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Option a) is the most accurate and closest result to this.

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True or false, If false replace the word
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Answer:

If quadrilaterals ABCD and WAYS have corresponding angles congruent and corresponding sides proportional, they are called cross products is

Step-by-step explanation:

True

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3 years ago
13. Mark has a board that is 12 feet long. He
horrorfan [7]

Answer:

1.5 feet

Step-by-step explanation:

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