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2 years ago

7

One number is 2 less than 3 times another. If the sum of the two number is 14, find the numbers.One number is 2 less than 3 time

s another. If the sum of the two number is 14, find the numbers.

1 answer:

Serga [27]2 years ago

7 0

Answer:

Step-by-step explanation:

One number is 2 more than 3 times another. Their sum is 14.Find the numbers. 8, 14 5, 17 2, 20 4, 18 10, 12

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Josh is solving the equation 2 % + 2% and predicts that his

gregori [183]

4 5/6 Hope this helps.

You have to find the common denominator for 1/3 & 4/8. & it’s 24. By doing that you have to multiply 3x8, when you do that you also have to multiply 1x 8 so you get 8/24 , same with 4/8 but with three so you get 12/24. Then add your answer 20/24, which equals out to 20/24 which reduces to 5/6. Add 5/6 to 2+2 and you’re left with 4 5/6. Hope this helps.

4 0

3 years ago

A school flag poll casts a 16 foot shadow on the lawn. A teacher stood at the shadows edge and measure the angle of elevation to

vovikov84 [41]

Answer:

30.1 feet.

Step-by-step explanation:

We have been given that a school flag poll casts a 16 foot shadow on the lawn. A teacher stood at the shadows edge and measure the angle of elevation to the top of the poll at 62°. We are asked to find the height of the tall.

First of all, we will draw a diagram to represent our give scenario as shown in the attachment.

We can see that side length with 16 feet is adjacent side and height of the pole (h) is opposite side to angle of elevation.

We know that tangent relates opposite side of a right triangle to its adjacent side.

$\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}$

$\text{tan}(62^{\circ})=\frac{h}{16}$

$h=16\cdot \text{tan}(62^{\circ})$

$h=16\cdot 1.880726465346$

$h=30.0916234\approx 30.1$

Therefore, the poll is approximately 30.1 feet tall.

6 0

3 years ago

Suppose that a random sample of 10 newborns had an average weight of 7.25 pounds and sample standard deviation of 2 pounds. a. T

frosja888 [35]

Answer:

$z=\frac{7.25-7.5}{\frac{1.4}{\sqrt{10}}}=-0.565$

$p_v =P(Z$

a) If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true average is not significantly less than 7.5.

b) $\chi^2 =\frac{10-1}{1.96} 4 =18.367$

$p_v =P(\chi^2 >18.367)=0.0311$

If we compare the p value and the significance level provided we see that $p_v >\alpha$ so on this case we have enough evidence in order to FAIL reject the null hypothesis at the significance level provided. And that means that the population variance is not significantly higher than 1.96.

Step-by-step explanation:

Assuming this info: "Suppose birth weights follow a normal distribution with mean 7.5 pounds and standard deviation 1.4 pounds"

1) Data given and notation

$\bar X=7.25$ represent the sample mean

$s=1.2$ represent the sample standard deviation

$\sigma=1.4$ represent the population standard deviation

$n=10$ sample size

$\mu_o =7.5$ represent the value that we want to test

$\alpha=0.05,0.01$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

2) State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is less than 7.5, the system of hypothesis would be:

Null hypothesis: $\mu \geq 7.5$

Alternative hypothesis: $\mu < 7.5$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

3) Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{7.25-7.5}{\frac{1.4}{\sqrt{10}}}=-0.565$

4)P-value

Since is a left tailed test the p value would be:

$p_v =P(Z$

5) Conclusion

Part a

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true average is not significantly less than 7.5.

Part b

A chi-square test is "used to test if the variance of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test. The two-sided version tests against the alternative that the true variance is either less than or greater than the specified value"

$n=10$ represent the sample size

$\alpha=0.01$ represent the confidence level

$s^2 =4$ represent the sample variance obtained

$\sigma^2_0 =1.96$ represent the value that we want to test

Null and alternative hypothesis

On this case we want to check if the population variance increase, so the system of hypothesis would be:

Null Hypothesis: $\sigma^2 \leq 1.96$

Alternative hypothesis: $\sigma^2 >1.96$

Calculate the statistic

For this test we can use the following statistic:

$\chi^2 =\frac{n-1}{\sigma^2_0} s^2$

And this statistic is distributed chi square with n-1 degrees of freedom. We have eveything to replace.

$\chi^2 =\frac{10-1}{1.96} 4 =18.367$

Calculate the p value

In order to calculate the p value we need to have in count the degrees of freedom , on this case 9. And since is a right tailed test the p value would be given by:

$p_v =P(\chi^2 >18.367)=0.0311$

In order to find the p value we can use the following code in excel:

"=1-CHISQ.DIST(18.367,9,TRUE)"

Conclusion

If we compare the p value and the significance level provided we see that $p_v >\alpha$ so on this case we have enough evidence in order to FAIL reject the null hypothesis at the significance level provided. And that means that the population variance is not significantly higher than 1.96.

4 0

3 years ago

Substitution method need help for home work

Marizza181 [45]

-3y = x...so we sub in -3y for x in the other equation

-x + 7y = 70
-(-3y) + 7y = 70
3y + 7y = 70
10y = 70
y = 70/10
y = 7

so we sub in 7 for y in either of the original equations to find x
-3y = x
-3(7) = x
-21 = x

so ur solution is (-21,7)

6 0

3 years ago

Can anyone help me with number 7 a b and c?

Sonbull [250]

Answer:

7a........they are similar because none of the sides are equal

6 0

2 years ago