Pythagoream Theorem Escape Room

lions [1.4K]

20 percent of 40 is 8. As a fraction that would be 8/1.

Hope this helps

6 0

3 years ago

According to the Bureau of Labor Statistics, citizens remain unemployed for an average of 15.9 weeks before finding their next j

Ahat [919]

Complete Question

According to the Bureau of Labor Statistics, citizens remain unemployed for an average of 15.9 weeks before finding their next job (June, 2008). Suppose you want to show that Louisiana has been effective in getting their unemployed back to work sooner. You take a random sample of 50 citizens who were unemployed six months earlier and ask them to report the duration. You find that the average time spent unemployed was 13.4 weeks with a sample standard deviation of the time unemployed is 6.7 weeks.

1 Which of the following statements is the correct alternative hypothesis?

2 The test statistic for testing the hypothesis is

a. -2.64

b. -2.32

c. -2.11

d. -1.28

e. none of these are correct

Answer:

1

The alternative hypothesis $H_a : \mu < 15.9$

2

The test statistics $z = -2.64$

Step-by-step explanation:

From the question we are told that

The population mean value for time citizens remain unemployed is $\mu = 15.9 \ weeks$

The sample size is n = 50

The sample standard deviation is 6.7 weeks.

The sample mean value for time citizens remain unemployed is $\mu = 15.9 \ weeks$

The null hypothesis is $H_o : \mu \ge 15.9$

The alternative hypothesis $H_a : \mu < 15.9$

Generally test statistics is mathematically represented as

$z = \frac{ \= x - \mu }{ \frac{s}{\sqrt{n} } }$

=> $z = \frac{13.4 - 15.9}{\frac{6.7}{\sqrt{50}}}$

=> $z = -2.64$

7 0

3 years ago

Please Hurryyy

Helga [31]

The measure of angle J is 19.8°, and the correct option is D.

<h3>What is the formula of cosine?</h3>

The law of cosine or cosine rule in trigonometry is a relation between the side and the angles of a triangle. Suppose a triangle with sides a, b, c and with angles cosC.

The following formula is used to find the angle j is;

$\rm j^2 = h^2 + i^2 -2hicosC$

Triangle HIJ has side lengths h=12, i = 17, j = 7.

Substitute all the values in the formula;

$\rm j^2 = h^2 + i^2 -2hicosJ\\\\(7)^2=(12)^2+(17)^2-2 \times 12 \times 17 cosJ\\\\49=144+289-408cosJ\\\\144+289 -49 =408cosJ\\\\384 =408cosJ\\\\cosJ=\dfrac{384}{408}\\\\cosj = 0.94\\\\J =cos^{-1}(0.94)\\\\J=19.8$