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2 years ago

48. Line h passes through the point (4, 12) and is parallel to line k.

Mathematics

1 answer:

Misha Larkins [42]2 years ago

4 0

Answer: y = 3/4 x + 8

Step-by-step explanation: First you must find the slope of line k.

y2 - y1

m = ----------- The slope is 3/4

x2 - x1

Since the two lines are paralell you know that line h has the same slope.

Next you must find the y-intercept by replacing x and y with the values given by the point.

y = 3/4x + ? -----> 12 = 3/4(4) + ?

12 = 3 + 8

The y-intercept is 8

Your equation for line h is y = 3/4 x +8

Hope this was helpful!

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An experimenter conducted a two-tailed hypothesis test on a set of data and obtained a p-value of 0.44. If the experimenter had

Lyrx [107]

Answer:

Correct option is (C).

The possible value of the p-value for a one-tailed test are 0.22 and 0.78.

Step-by-step explanation:

The p-value is the probability of acquiring a result as extreme as the observed result, assuming the null hypothesis statement is true.

The p value of a test is:

Left-tailed test: $P(TS$

Right-tailed test: $P(TS>ts) = 1- P(TS$ .

Here,

TS = Test statistic

ts = computed value of the test statistic.

The two-tailed p-value is: $2P(TS$ or $2P(TS>ts)$ .

The p-value of the two tailed test is, 0.44.

Compute the p-value for one-tailed test a follows:

For a left-tailed test:

$2P(TS$

For a right-tailed test:

$P(TS>ts) = 1- P(TS$

Thus, the possible value of the p-value for a one-tailed test are 0.22 and 0.78.

The correct option is (C).

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3 years ago

The sum of three consecutive even numbers is one hundred sixty-two. What is the smallest of the three numbers?

zepelin [54]

Since the numbers are consecutive, they must be near each other in size, and therefore near one-third of 168. And since the lower number is -2 off the middle, and the upper number is +2 from the middle, the middle number must be exactly one-third of 168—otherwise the sum of the three could never be 168. Labelling the three consecutive numbers as x, y, and z:

x + y + z = 168

(y-2) + y + (y+2) = 168.

3y = 168

y = 56

therefore the smallest number (x) = 54.
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A consumer group is testing camp stoves. To test the heating capacity of a stove, they measure the time required to bring 2 quar

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Answer:

The decision rule is

Reject the null hypothesis

The conclusion is

There is sufficient evidence to show that there is a difference between the performances of these two models

The 95% confidence interval is $0.224 < \mu_1 - \mu_2 < 2.776$

Step-by-step explanation:

From the question we are told that

The sample size is n = 36

The first sample mean is $\= x_1 = 11.4$

The first standard deviation is $s_1 = 2.5$

The second sample mean is $\= x_2 = 9.9$

The second standard deviation is $s_2 = 3.0$

The level of significance is $\alpha = 0.05$

The null hypothesis is $H_o : \mu_1 - \mu_2 = 0$

The alternative hypothesis is $H_a : \mu_1 - \mu_2 \ne 0$

Generally the test statistics is mathematically represented as

$z = \frac{ (\= x_1 - \= x_2 ) - (\mu_1 - \mu_2 ) }{ \sqrt{ \frac{s_1^2 }{n} + \frac{s_2^2 }{ n} } }$

=> $z = \frac{ ( 11.4 - 9.9) - 0 }{ \sqrt{ \frac{2.5^2 }{36} + \frac{ 3^2 }{36 } } }$

=> $z = 2.3$

From the z table the area under the normal curve to the left corresponding to 2.3 is

$P( Z > 2.3 ) = 0.010724$

Generally the p-value is mathematically represented as

$p-value = 2 * P( Z > 2.3 )$

=> $p-value = 2 * 0.010724$

=> $p-value = 0.02$

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

The decision rule is

Reject the null hypothesis

The conclusion is

There is sufficient evidence to show that there is a difference between the performances of these two models

Considering question b

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$\alpha = (100 - 95 ) \%$

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Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{s_1^2 }{n } + \frac{s_2^2}{n}}$

=> $E = 1.96 * \sqrt{ \frac{2.5^2 }{ 36 } + \frac{ 3^2}{36}}$

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Generally 95% confidence interval is mathematically represented as

$( \= x_1 - \= x_2) -E < \mu_1 - \mu_2 < ( \= x_1 - \= x_2) + E$

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