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Natali5045456 [20]
3 years ago
12

Point U is on line segment TV . given TU=4 UV=5x and TV=3x+6 determine the numerical lenth of TV

Mathematics
2 answers:
adelina 88 [10]3 years ago
6 0

TU=13; UV= 13; TV=26

Step-by-step explanation:

Hope this helped!

olga_2 [115]3 years ago
4 0

Answer:9

Step-by-step explanation:

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Refer to the following scenario:You want to see if there is a difference between the exercise habits of Science majors and Math
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Answer:

1. H0: P1 = P2

2. Ha: P1 ≠ P2

3. pooled proportion p = 0.542

4. P-value = 0.0171

5. The null hypothesis failed to be rejected.

At a signficance level of 0.01, there is not enough evidence to support the claim that there is significant difference between the exercise habits of Science majors and Math majors .

6. The 99% confidence interval for the difference between proportions is (-0.012, 0.335).

Step-by-step explanation:

We should perform a hypothesis test on the difference of proportions.

As we want to test if there is significant difference, the hypothesis are:

Null hypothesis: there is no significant difference between the proportions (p1-p2 = 0).

Alternative hypothesis: there is significant difference between the proportions (p1-p2 ≠ 0).

The sample 1 (science), of size n1=135 has a proportion of p1=0.607.

p_1=X_1/n_1=82/135=0.607

The sample 2 (math), of size n2=92 has a proportion of p2=0.446.

p_2=X_2/n_2=41/92=0.446

The difference between proportions is (p1-p2)=0.162.

p_d=p_1-p_2=0.607-0.446=0.162

The pooled proportion, needed to calculate the standard error, is:

p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{82+41}{135+92}=\dfrac{123}{227}=0.542

The estimated standard error of the difference between means is computed using the formula:

s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.542*0.458}{135}+\dfrac{0.542*0.458}{92}}\\\\\\s_{p1-p2}=\sqrt{0.001839+0.002698}=\sqrt{0.004537}=0.067

Then, we can calculate the z-statistic as:

z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.162-0}{0.067}=\dfrac{0.162}{0.067}=2.4014

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

\text{P-value}=2\cdot P(z>2.4014)=0.0171

As the P-value (0.0171) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

At a signficance level of 0.01, there is not enough evidence to support the claim that there is significant difference between the exercise habits of Science majors and Math majors .

We want to calculate the bounds of a 99% confidence interval of the difference between proportions.

For a 99% CI, the critical value for z is z=2.576.

The margin of error is:

MOE=z \cdot s_{p1-p2}=2.576\cdot 0.067=0.1735

Then, the lower and upper bounds of the confidence interval are:

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The 99% confidence interval for the difference between proportions is (-0.012, 0.335).

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