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2 years ago

Given that

Mathematics

1 answer:

BaLLatris [955]2 years ago

8 0

Answer:

x=21/5

Step-by-step explanation:

5x:9 = 7:3

Turn the ratios into fractions:

5x/9 = 7/3

Then cross mutiply

15x=63

x=21/5

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Experian would like to test the hypothesis that the average credit score for an adult in Virginia is different from the average

aliya0001 [1]

Answer:

a. We fail to reject the hypothesis that the average credit score for an adult in Virginia is different from the average credit score for an adult in North Carolina at the significance level of 0.05.

b. The 95% confidence interval for the true difference of means is -2.2468 and 36.2468. There is a probability of 95% that the true difference of means $\mu_{1}-\mu_{2}$ is between -2.2468 and 36.2468. This confidence interval contains the number 0, this is consistent with the results we got in a. Because we fail to reject the hypothesis that the average credit score for an adult in Virginia is different from the average credit score for an adult in North Carolina at the significance level of 0.05.

Step-by-step explanation:

Let $\mu_{1}-\mu_{2}$ be the true difference between the average credit score for an adult in Virginia and the average credit score for an adult in North Carolina. We have the large sample sizes $n_{1} = 40$ and $n_{2} = 35$ , the unbiased point estimate for $\mu_{1}-\mu_{2}$ is $\bar{x}_{1} - \bar{x}_{2}$ , i.e., 699-682 = 17.

The standard error is given by $\sqrt{\frac{\sigma^{2}_{1}}{n_{1}}+\frac{\sigma^{2}_{2}}{n_{2}}}$ , i.e.,

$\sqrt{\frac{(44)^{2}}{40}+\frac{(41)^{2}}{35}}$ = 9.8198.

a. We want to test $H_{0}: \mu_{1}-\mu_{2} = 0$ vs $H_{1}: \mu_{1}-\mu_{2} \neq 0$ (two-tailed alternative). The rejection region is given by RR = {z | z < -1.96 or z > 1.96} where -1.96 and 1.96 are the 2.5th and 97.5th quantiles of the standard normal distribution respectively. The test statistic is $Z = \frac{\bar{x}_{1} - \bar{x}_{2}-0}{\sqrt{\frac{\sigma^{2}_{1}}{n_{1}}+\frac{\sigma^{2}_{2}}{n_{2}}}}$ and the observed value is $z_{0} = \frac{17}{9.8198} = 1.7312$ . Because 1.7312 does not fall inside RR, we fail to reject the null hypothesis.

b. The endpoints for a 95% confidence interval for $\mu_{1}-\mu_{2}$ is given by $17\pm (z_{0.05/2})9.8198$ , i.e., $17\pm (z_{0.025})9.8198$ where $z_{0.025}$ is the 2.5th quantile of the standard normal distribution, i.e., -1.96, so, we have 17-(1.96)(9.8198) and 17+(1.96)(9.8198), i.e., -2.2468 and 36.2468. There is a probability of 95% that the true difference of means $\mu_{1}-\mu_{2}$ is between -2.2468 and 36.2468. This confidence interval contains the number 0, this is consistent with the results we got in a. Because we fail to reject the hypothesis that the average credit score for an adult in Virginia is different from the average credit score for an adult in North Carolina at the significance level of 0.05.

3 0

4 years ago

Four mathematicians, three physicists, and an engineer are to be seated equally spaced around a circular table. How many differe

Vesna [10]

First, we can choose the seats for the four mathematicians. Then we seat the physicits, then the engineer. There are 4! ways to seat the mathematicians, then 3! ways to seat the physicists, then 1! ways to seat the engineer. But then we must divide by 8, because we can rotate the table, so there are 8!*4!*3!/8 = 725760 ways to seat everyone.

3 0

3 years ago

2V2 km 2 km X A) 2V5 km C) 2 km B) 2V3 km D) 4 km HELP PLEASEE

Rasek [7]

Answer:

$x=2\sqrt3\ km$

Step-by-step explanation:

Given that,

The base of a triangle = 2 km

The perpendicular height of the triangle = $2\sqrt{2} \ km$

We need to find the value of x. It is the Hypotenuse of the triangle. It can be solved as :

$x=\sqrt{(2\sqrt{2})^2+2^2 } \\\\=2\sqrt{2+1 } \\\\=2\sqrt3\ km$

So, the value of x is equal to $2\sqrt3\ km$ .

3 0

3 years ago

Given two complementary angles, 3x and (x - 2). Find the value of x.

ohaa [14]

Answer:

x = 23°

Step-by-step explanation:

Note: Complementary angles measure 90°

3x + (x - 2)° = 90°

=> 3x + x - 2° = 90°

=> 4x - 2° = 90°

Add the additive inverse of -2 to both sides of the equation

i.e 4x - 2° + 2° = 90° + 2°

=> 4x = 92°

Divide both sides of the equation by the coefficient of x which is 4

=> 4x/4 = 92°/4

x = 23°

6 0

3 years ago

3/7 of which is 2 1/14

GarryVolchara [31]

Step-by-step explanation:

the answer is 14

3/7 • 2 1/14

=14

5 0

3 years ago