alpha = 25°

Step-by-step explanation:

The picture indicates a rectangle.

Alpha is in a straight corner of 90 °, so...

65 + alpha = 90

subtract 65 left and right of the = sign.

65 - 65 + alpha = 90 - 65

0 + alpha = 90 - 65

alpha = 25°

## Related Questions

The time needed for all college students to complete a certain paper-and-pencil maze follows a normal distribution with a population mean of 30 seconds and a population standard deviation of 3 seconds. You wish to see if the mean time μ (where μ stands for population mean) is changed by vigorous exercise, so you have a group of nine college students exercise vigorously for 30 minutes and then complete the maze. It takes them an sample average of 31.2 seconds to complete the maze. Use this information to test the hypotheses:

H0: μ = 30,

Ha: ≠30

at the significance level of 0.01.

You conclude:

a) There is not enough evidence to support the claim.

b) There is enough evidence to support the claim.

The correct option is a

Step-by-step explanation:

From the question we are told that

The population mean is

The standard deviation is

The sample size is  n  = 9

The null hypothesis is

The alternative hypothesis is

The level of significance is

The sample mean is

Generally the test statistics is mathematically represented as

=>

=>

From the z table  the area under the normal curve to the right corresponding to  1.2  is

Generally the p-value is mathematically represented as

=>

=>

From the value obtained w can see that

hence

The decision rule is

Fail to reject the null hypothesis

The conclusion is there is not enough evidence to support the claim

To test the hypotheses, use a one-sample t-test to compare the sample mean to the population mean. Calculate the t-value and compare it to the critical t-value at the significance level of 0.01. If the calculated t-value falls within the critical region, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

### Explanation:

To test the hypotheses, we can use a one-sample t-test since we know the population standard deviation and the sample size is small. The null hypothesis (H0) is that the population mean (μ) is equal to 30 seconds, while the alternative hypothesis (Ha) is that the population mean is not equal to 30 seconds.

Using the given information, we can calculate the t-value by using the formula:

t = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

Once we have the t-value, we can compare it to the critical t-value at the significance level of 0.01. If the calculated t-value falls within the critical region, we reject the null hypothesis. If not, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim.

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A manufacturer has a monthly fixed cost of $750 and a production cost of$15 for each item x that is produced. The product sells for \$37 per item.Write the equation of the total cost function, C(x), in terms of x.
Write the equation of the total revenue function, R(x), in terms of x.
Write the equation of the profit function, P(x), in terms of x. Simplify P(x) completely.

The cost function is C(x) = 14x + 100000,

the revenue function is R(x) = 20x,

the profit function is P(x) = R(x) − C(x) = 20x − 14x − 100000 = 6x − 100000.

Step-by-step explanation:

Reese read twice as many pages Saturday than she read Sunday. If she read a total of 78 pages over the weekend, how many pages did Reese read Sunday?

Reese read 26 pages on Sunday.

Step-by-step explanation:

If she read twice the amount on Saturday than she read on Sunday, then you can replace the days with variables. 2x for Saturday and x for Sunday. That leaves you with 2x + x = 78. This can be simplified to 3x = 78. We can solve this by dividing both sides by 3. This leaves you with x = 26. If x represents the pages read on Sunday then Reese read 26 pages on Sunday.

1. Two angles are supplementary. Angle 1 measures4x + 6 degrees and Angle 2 measures 38 degrees.
What is the value of x? *
doaroor​

34 degrees

Step-by-step explanation:

supplementary Angles are pair of angles whose sum is 180 degrees.

Given

Angle 1 =4x + 6 degrees

Angle 2 = 38 degrees

Condition : angles are supplementary Angles

therefore

Angle 1 + Angle 2 =180

4x+6+38 = 180

=>4x+44 = 180

=> 4x = 180-44

=> 4x= 136

=>x = 34

Thus value of x is 34 degrees.

2. You are in a car traveling an average speed of 60 km/hr. Thetotal trip is 240 km. How long does the trip take?

4 hours

Step-by-step explanation:

60*4=240