The mortgage department of a large bank is interested in the nature of loans of first-time borrowers. This information will be used to tailor their marketing strategy. They believe that 40% of first-time borrowers take out smaller loans than other borrowers. They perform a hypothesis test to determine if the percentage is the same or different from 40%. They sample 100 first-time borrowers and find 53 of these loans are smaller than the other borrowers. For the hypothesis test, they choose a 5% level of significance. What would be the null and alternative hypotheses

Answers

Answer 1

Answer:

Step-by-step explanation:

The null hypothesis is the statement or claim that is believed or assumed to be true. In this case, the null hypothesis is "They believe that 40% of first-time borrowers take out smaller loans than other borrowers". Since we are dealing with proportion, we will denote it with p. The null hypothesis would be

p = 0.4

The alternative hypothesis is what the researcher expects or predicts. It is the statement that is believed to be true if the null hypothesis is rejected. The alternative hypothesis is "They perform a hypothesis test to determine if the percentage is the same or different from 40%". It would be written as

p ≠ 0.4

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Does anyone wanna help

sarah can complete a project in 90 minutes and her sister betty can complete it in 120 minutes if they both work on the project at the same time how long will it take them to complete the project

Answers

Answer:

It will take them approximately 51.43 minutes to complete the project together

Step-by-step explanation:

This is what is called a "shared job" problem.

The best way to work on them is to start by finding the "portion" of the job done by each of the people in the unit of time.

So, for example, Sarah completes the project in 90 minutes, so in the unit of time (that is 1 minute) she completed 1/90 of the total project

Betty completes the project in 120 minutes, so in the unit of time (1 minute) she completes 1/120 of the total project.

We don't know how long it would take for them to complete the project when working together, so we call that time "x" (our unknown).

Now, when they work together completing the entire job in x minutes, in the unit of time they would have done 1/x of the total project.

In the unite of time, the fraction of the job done together (1/x) should equal the fraction of the job done by Sarah (1/90) plus the fraction of the job done by Betty. This in mathematical form becomes:

$(1)/(x) =(1)/(90) +(1)/(120)\n(1)/(x) =(4)/(360) +(3)/(360)\n(1)/(x) =(7)/(360) \nx=(360)/(7) \nx=51.43\,\,min$

So it will take them approximately 51.43 minutes to complete the project together.

A water tank leaked 14 gallons of water over eight hours at a constant rate what was the change in the amount of water in gallons in a tank each hour

Answers

Answer:

7/4 gallons per hour

Step-by-step explanation:

We have to divide the amount of water lost by the lapse of time. So we get

14/8= 7/4

Answer: the answer would be 1.75 gallons/hour

Step-by-step explanation: if you take the 14 gallons divided by the eight hours, you get 1.75

Circle R has a radius of line segment of QR and QP is a tangent to circle R at point Q.(Picture attached)

(a) What is the measure of RQP? Explain your answer.

(b) What is the value of x? Explain your answer with work.

(c) What is the measure of QRP? Explain your answer with work.

(d) What is the measure of RPQ? Explain your answer with work.

Answers

Answer:

(a) 90°

(b) 8.75

(d) 26.25°

Step-by-step explanation:

(a) A radius to a point of tangency is always perpendicular to the tangent line there. Q is the point of tangency of line PQ, so the segment RQ from the center of the circle, R, to that point makes a 90° angle with PQ. Angle RQP is 90°.

(b) The sum of the acute angles of a right triangle is 90°, so ...

(5x +20)° + (3x)° = 90° . . . . . the sum of the acute angles is 90°

8x + 20 = 90 . . . . . . . . . . . . simplify, divide by °

8x = 70 . . . . . . . . . . . . . . . . . subtract 20

70/8 = x = 8.75 . . . . . . . . . . . divide by the coefficient of x

(c) ∠QRP = (5x+20)° = (5·8.75 +20)° = 63.75° . . . . . use the value of x in the expression for the angle measure

(d) ∠RPQ = (3x)° = (3·8.75)° = 26.25° . . . . . use the value of x in the expression for the angle measure

A painter can finish painting a house in 3 hour

Answers

Answer:

cool

Step-by-step explanation:

Find the value of x in the triangle above Thank you to whoever helps

Answers

this is an isosceles triangle two sides are the same

so there are 180° in a triangle

180-58= 122 now divide this by two because the last two angles are equal

122/2=61° =x°

Some people take the early retirement option at age 62. According to the Social Security Administration, if you retire at age 62, your retirement benefits will be permanently reduced by 25%. If your monthly benefit, at full retirement age (67), would have been $1300 per month, and you retire at age 62, how much would you lose in total annual income over one year?