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2 years ago

14

The minute hand of a clock 7 inches long to the nearest 10th of an inch how far does the tip of the minute and trouble as time p

rogresses from 12:00 to 12:25

1 answer:

RSB [31]2 years ago

7 0

Answer:

The answer to the question is;

The distance the tip of the minute and travels as time progresses from 12:00 to 12:25 is 18.33 in.

Step-by-step explanation:

To solve the question, we note that

Number of minutes in one complete revolution of the clock = 60

Position travel of the minute hand = 12:00 to 12:25 = 25 minutes

Fraction of complete revolution traveled by minute hand = 25/60

Distance of one complete revolution = Circumference of circle = 2·π·r

Length of minute hand = 7 inches = r

Distance of one complete revolution = 2 × π × 7 = 43.98 in

Distance traveled by minute hand = 25/60×43.98 in = 18.33 in.

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An environmental engineer is tasked with determining whether a power plant cooling system is heating the water it uses more than

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Step-by-step explanation:

From the question we are told that

The sample size is n = 15

The difference in population proportion is $d = 6$

Generally the sample mean of the input temperature is

$\= x_1 = \frac{\sum x_i }{n}$

=> $\= x_1 = \frac{57.6 + 68.9 + \cdots +60.4 }{15}$

=> $\= x_1 = 62.57$

Generally the sample mean of the output temperature is

$\= x_2 = \frac{\sum x_i }{n}$

=> $\= x_2 = \frac{65.1 + 74.4 + \cdots +67.3 }{15}$

=> $\= x_2 = 55.97$

Generally the difference of the sample mean of the input temperature and that of the output temperature is

$\= d = \= x_1 - \= x_2$

=> $\= d = 62.57 -55.97$

=> $\= d = 6.6$

Generally the standard deviation is mathematically represented as

$s_d = \sqrt{\frac{\sum(d_1 - \= d )^2}{n} }$

=> $s_d = \sqrt{\frac{([57.6- 65.1]- 6.6)^2+ ([68.9 - 74.4]- 6.6)^2 + \cdots + ([60.4 - 67.3]- 6.6)^2 }{15} }$

=> $s_d = 1.732 [/texGenerally the test statistics is mathematically represented as [tex]t = \frac{ d - \= d }{ \frac{s_d}{\sqrt{n} } }$

=> $t = \frac{ 6-6.6 }{ \frac{1.732}{\sqrt{15} } }$

=> $t = 1.3417$

Generally the degree of freedom is mathematically represented as

$df = n - 1$

=> $df = 15 - 1$

=> $df = 14$

Generally the probability of t obtained from the t - distribution table at a degree of freedom of $df = 14$ is

$P(t >1.3417 ) = 0.10052569$

Generally the p-value is mathematically represented as

$p-value = 2 * P(t > 1.3417)$

=> $p-value = 2 * 0.10052569$

=> $p-value = 0.201$

From the values obtained we see that $p-value > \alpha$ hence

The decision rule is

Fail to reject the null hypothesis

The conclusion is

The cooling system changes the temperature of the water by 6 degrees.

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