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bearhunter [10]
3 years ago
7

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? (
Mathematics
1 answer:
nataly862011 [7]3 years ago
4 0

Answer:

13%

Step-by-step explanation:

Given the two way frequency table :

Country Music Rock Total

West 26 15 41

East 24 22 46

South 7 33 40

North 41 25 66

Total 98 95 193

From. The table :

n(West n Country music) = 26

n(Total) = 193

P(West n Country music) = n(West n Country music) / n(Total)

P(West n Country music) = 26 / 193

= 0.1347

= 13.47%

= 13%

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3 years ago
The perimeter of a triangular field is 120m. Two of the sides are 21m and 40m.Calculate the largest angle of the field.
Mama L [17]

Answer:

the largest angle of the field is 149⁰

Step-by-step explanation:

Given;

perimeter of the triangular filed, P = 120 m

length of two known sides, a and b = 21 m and 40 m respectively

The length of the third side is calculated as follows;

a + b + c = P

21 m  + 40 m  + c = 120 m

61 m +  c = 120 m

c = 120 m - 61 m

c = 59 m

                         B

                     ↓            ↓  

                  ↓                          ↓

                ↓                                       ↓

            A →  →  → →  →  → →  → →    →    →  C

Consider ABC as the triangular field;

Angle A is calculated by applying cosine rule;

a^2 = b^2 + c^2 - 2bc \ Cos A\\\\Cos \ A = \frac{b^2 + c^2 - a^2}{2bc} \\\\Cos \ A = \frac{40^2 + 59^2 - 21^2}{2 \times 40 \times 59} \\\\Cos \ A = 0.983\\\\A = Cos ^{-1} (0.983)\\\\A = 10.6 \ ^0

Angle B is calculated as follows;

Cos \ B = \frac{a^2 + c^2 - b^2}{2ac} \\\\Cos \ B = \frac{21^2 + 59^2 - 40^2}{2 \times 21 \times 59} \\\\Cos \ B = 0.937\\\\B= Cos ^{-1} (0.937)\\\\B = 20.5 \ ^0

Angle C is calculated as follows;

Cos \ C = \frac{a^2 + b^2 - c^2}{2ab} \\\\Cos \ C = \frac{21^2 + 40^2 - 59^2}{2 \times 21 \times 40} \\\\Cos \ C = -0.857\\\\C = Cos ^{-1} (-0.857)\\\\C = 149\ ^0

Therefore, the largest angle of the field is 149⁰.

       

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3 years ago
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Step-by-step explanation:

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Nastasia [14]

Answer:

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Step-by-step explanation:

Step 1- Multiply

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Step 2- Add

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3 years ago
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