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Solnce55 [7]
4 years ago
13

A two-way frequency table is shown below that displays the relationship between the region of the country in which people live a

nd the type of music preferred. We took a sample of 193 people and recorded the following results:
              Country Music      Rock      Total
West               26                   15            41
East                24                   22            46
South              7                    33            40
North              41                   25            66
Total               98                   95           193


What is the probability (rounded to the nearest whole percent) that a randomly selected person is from the western region of the country if he or she prefers country music? A. 26%
B. 13%
C. 63%
D. 27%
Mathematics
1 answer:
djverab [1.8K]4 years ago
7 0
We are given the data for the number of persons from different areas versus their music preference. We are asked to determine the probability that a person likes country music if he selected is random from the western region.

The total number of persons in the West:

26 + 15 + 41 = 82

Number of persons who like country music = 26

Probability = 26/82 = 0.3171
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1+secA/sec A = sin^2 A / 1-cos A​
Fofino [41]

Answer:  see proof below

<u>Step-by-step explanation:</u>

\dfrac{1+\sec A}{\sec A}=\dfrac{\sin^2 A}{1-\cos A}

Use the following Identities:

sec Ф = 1/cos Ф

cos² Ф + sin² Ф = 1

<u>Proof LHS → RHS</u>

\text{LHS:}\qquad \qquad \dfrac{1+\sec A}{\sec A}

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\text{Simplify:}\qquad \qquad \dfrac{\frac{\cos A+1}{\cos A}}{\frac{1}{\cos A}}\\\\\\.\qquad \qquad \qquad =\dfrac{1+\cos A}{1}

\text{Multiply:}\qquad \qquad \dfrac{1+\cos A}{1}\cdot \bigg(\dfrac{1-\cos A}{1-\cos A}\bigg)\\\\\\.\qquad \qquad \qquad =\dfrac{1-\cos^2 A}{1-\cos A}

\text{Identity:}\qquad \qquad \dfrac{\sin^2 A}{1-\cos A}

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3 0
3 years ago
(w-2) (w+5) <br> I need help I don't understand ...
Phantasy [73]
<h3>Answer: w^2 + 3w - 10</h3>

===============================================

Work Shown:

Let x = w-2

This will allow us to replace the (w-2) with x to get...

(w-2)(w+5)

x(w+5)

x*w + x*5 ... distribute

w(x) + 5(x)

Now replace x with w-2 and distribute again

w(x) + 5(x)

w(w-2) + 5(w-2)

w*w + w*(-2) + 5*w + 5*(-2)

w^2 - 2w + 5w - 10

w^2 + 3w - 10

6 0
3 years ago
Read 2 more answers
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