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Lapatulllka [165]

3 years ago

8

In a set of three lines, a pair of parallel lines is intersected by a transversal. The intersection forms eight special angles.

Two of the special angles, A and B, are corresponding angles.
For the set of parallel lines intersected by a transversal, A=4x and B=-5(x-18).

Part A: Write an equation to represent the corresponding relationship betweenA andB.
Part B: Use the equation to find the measures of A and B.

1 answer:

My name is Ann [436]3 years ago

7 0

Answer:

Part A: 4x = -5(x-18)

Part B: A and B both = 40 degrees

Step-by-step explanation:

Ok, corresponding angles are in the same position on the two parallel lines cut by the transversal. And they are equal in measure. So, upper right = upper right.

So A = B

4x = -5(x -18)

4x = -5x + 90

9x = 90

x = 10

Angle A = 4x = 40 degrees, which means angle B is also 40, but let's show the work:

Angle B = -5(x - 18) = -50 + 90 = 40

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A triangle has an area of 56 square units it's height is 14 units

kobusy [5.1K]

The formula for the area of a triangle is 1/2*b*h=a.
1/2*b*14=56
b*14=112
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7 0

3 years ago

Alexus [3.1K]

Answer:

1/8

Step-by-step explanation:

To simplify the expression √3/√8, we can first simplify the square root terms by finding the prime factorization of each number under the square root. The prime factorization of 3 is 3, and the prime factorization of 8 is 2 * 2 * 2.

We can then rewrite the square root terms as follows:

√3/√8 = √(3) / √(2 * 2 * 2)

Next, we can use the property of square roots that says that the square root of a number is equal to the square root of each of its prime factors. This means that we can rewrite the square root term as follows:

√(3) / √(2 * 2 * 2) = √(3) / √(2) / √(2) / √(2)

Since the square root of a number is the same as the number itself, we can simplify the expression further by removing the square root symbols from the prime numbers 2:

√(3) / √(2) / √(2) / √(2) = √(3) / 2 / 2 / 2

Finally, we can use the rules of division to simplify the expression even further:

√(3) / 2 / 2 / 2 = √(3) / (2 * 2 * 2)

Since any number divided by itself is equal to 1, we can simplify the expression one last time to get our final answer:

√(3) / (2 * 2 * 2) = 1/2 * 1/2 * 1/2 = 1/8

Therefore, the simplified form of the expression √3/√8 is 1/8.

6 0

1 year ago

Read 2 more answers

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

What is the derivative of w=(t^2+1)^100<br><br> How is it 200t(t^2+1)^99?

GuDViN [60]

(t^2+1)^100

USE CHAIN RULE

Outside first (using power rule)

100*(t^2+1)^99 * derivative of the inside

100(t^2+1)^99 * d(t^2+1)

100(t^2+1)^99 * 2t

200t(t^2+1)^99

6 0

3 years ago

Read 2 more answers

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zzz [600]

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6 0

3 years ago