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

Answer: 0.36 = 0.6

Step-by-step explanation:

An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. Of particular interest was whether higher income would result in shoppers spending more on groceries. A random sample of shoppers at a local supermarket was obtained. A questionnaire was administered asking about the weekly income of each shopper's family and their grocery bill for that week. The explanatory variable is:

A. weekly income.

B. weekly expenditure.

C. gender.

D. None of the answer options is correct

Answer:

A. weekly income.

Step-by-step explanation:

Explanatory variables are variables that shows the difference in response variables, the explanatory variable influences the response variable. It is an independent variable that can be manipulated. The independent variable helps explain the response variable.

In this case, the explanatory variable is the weeky income because the respose variable (weekly expenditure) variation depends on it. The economist wants to use the weekly income of each shoppers family to determine how much they will spend on groceries. So, the weekly income is the explanatory variable.

The toxicity level of the lake water is calculated by dividing the current level of toxins (0.86 mg per liter) by the maximum safe level (1.04 mg per liter) and then converting to a percentage, which results in approximately 83%.

To determine the toxicity level of lake water, we need to divide the amount of dissolved toxins per liter by the maximum safe amount and convert it to a percentage.

Given that the lake currently has 0.86 milligrams of dissolved toxins per liter of water and the maximum safe level is 1.04 milligrams per liter, we calculate the toxicity level using the following steps:

Therefore, the correct answer is C. 83%.

Answer:

93.18 feet

Step-by-step explanation:

Given:

Length of backyard pool = 31.74 feet

Height of backyard pool = 14.85 feet

To find: Length of fencing bought by Mirele

Solution:

To find the length of fencing bought by Mirele, use the formula for the perimeter of a rectangular pool.

Length of fencing bought by Mirele = 2 ( length + height ) = 2 ( 31.74 + 14.85 ) = 2 ( 46.59 ) = 93.18 feet

Answer:

93.18 feet

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

The distance the lifeguard should run along the shore before jumping into the water, can be determined by minimizing the function of time, that is, the time it takes for the lifeguard to reach the child. This problem can be solved either by using calculus or the graphical method with a graphing tool.

This problem can be solved using optimization of functions, which is a part of calculus. We would let 'x' be the distance along the shore that the lifeguard runs before jumping into the water. Then the total time taken to reach the child is given by the formula T = x/4 + sqrt((60-x)² + 40²)/1.1. We are looking for the minimum of T as a function of x. However, it would require knowledge of calculus to solve this problem. As an alternative, one can also use a graphing calculator or similar tool to graph the time function and then determine the minimum on the graph.

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Final answer:

To save the child, you should run along the shore for approximately 15 seconds before jumping into the water.

Explanation:

To determine how far along the shore you should run before jumping into the water to save the child, you need to find the time it takes to run along the shore and then swim directly to the child.

First, calculate the time taken to run along the shore using the formula: time = distance / speed. In this case, the distance is 60 meters and the speed is 4 meters per second. So, the time taken to run along the shore is 60 / 4 = 15 seconds.

Next, calculate the time taken to swim directly to the child using the formula: time = distance / speed. In this case, the distance is 40 meters and the speed is 1.1 meters per second.

So, the time taken to swim directly to the child is 40 / 1.1 ≈ 36.364 seconds.

Therefore, the total time taken to save the child is the sum of the time taken to run along the shore and the time taken to swim directly to the child.

So, in order to save the child, you should run along the shore for approximately 15 seconds before jumping into the water.

9514 1404 393

Answer:

  2.6 cm

Step-by-step explanation:

The full circle is 360°, so an arc of 30° will have 30/360 = 1/12 of the measure of the circumference of the circle.

  arc length = πd/12 = π(10/12) ≈ 2.6 cm

Answer:

reflection over the y- axis is x=0

so x will be negative.

(4,-6) will be (-4,-6)

Answer:

divide 252 by 7 and you get 36

Step-by-step explanation:

Answer:

  65.3 cm

Step-by-step explanation:

The law of sines can be used for this.

  g/sin(G) = f/sin(F)

  g = (37 cm)sin(124°)/sin(28°) ≈ 65.3 cm . . . . multiply by sin(G)

The length of g is about 65.3 cm.

Answer:

Standard deviation = 7.76

Step-by-step explanation:

The formula for determining standard deviation when dealing with population proportion is expressed as

Standard deviation = √npq

Where

n represents the number of samples from the population.

p represents the probability of success.

q represents the probability of failure.

From the information given,

n = 500 policyholders

p = 14% = 14/100 = 0.14

q = 1 - 0.14 = 0.86

Standard deviation = √500 × 0.14 × 0.86 = 7.76

Answer: std dev = 0.01552

Step-by-step explanation:

we will solve this by taking a step by step analysis of the problem.

i hope at the end of this section, you will feel confident  to try out other questions.

given that the size of the sample (n) = 500

The Insurance company records indicate that 14% of its policyholders file claims involving theft or robbery of personal property from their homes.

hence sample proportion of policyholders filing claims involving theft or robbery from their homes (p) = 14% =0.14

let Z be the number of policyholders files involving theft or robbery of personal property from their homes.

so Z~Bin(500,0.14) and p=Z/500

we know from basic mathematics that standard deviation = √(variance)

so variance is  given thus;

V[Z] = 500*0.14*(1-0.14)

or V[p] = V[Z/500] = 500*0.14*0.86/500² = 0.14*0.86/500

so standard deviation is;

sqrt[V[p]]=sqrt(0.14*0.86/500) = sqrt(0.0002408) = 0.01552

∴ the standard deviation = 0.01552

cheers i hope this helps!!!!

Answer:121

Step-by-step explanation:

11 times 11.

Answer:

[tex]121[/tex]

Step-by-step explanation:

[tex]11^{2} \\ write \: the \: exponentiation \: as \\ multiplication. \\ \\ 11 \times 11 \\ multiply \\ \\ 121[/tex]

The 0 acres of crop A, 60 acres of crop B, and 40 acres of crop c each crop should be planted to maximize profit $26,000.

Given that,

A farmer owns a 100-acre farm and plans to plant at most three crops. The seed for crops A, B, and C costs $40, $20, and $30 per acre, respectively.

A maximum of $3200 can be spent on the seed. Crops A, B, and C require 1,2, and 1 workday per acre, respectively, and there are a maximum of 160 workdays available.

If the farmer can make a profit of $100 per acre on crop A, $300 per acre on crop B, and $200 per acre on crop C,

We have to find,

How many acres of each crop should be planted to maximize profit?

According to the question,

The farmer can make a profit of $100 per acre on crop A, $300 per acre on crop B, and $200 per acre on crop C,

[tex]\rm P = 100A + 300B + 200C[/tex]

The seed for crops A, B, and C costs $40, $20, and $30 per acre, respectively.

And A maximum of $3200 can be spent on the seed.

[tex]\rm 40A + 20B + 30C \leq 3200[/tex]

Then, Sum of seed for crops costs = area of the farm

[tex]\rm A + B + C \leq 100[/tex]

Crops A, B, and C require 1,2, and 1 workday per acre, respectively, and there are a maximum of 160 workdays available.

[tex]\rm A + 2B + C = 160[/tex]

Solving all the equations,

From equation 3,

[tex]\rm A = 100-B-C[/tex]

Substitute the value of A in equation 4,

[tex]\rm 100 - B - C+ 2B + C = 160\\\\100 + B = 160 \\\\B = 160 - 100\\\\B = 60[/tex]

Put B = 60 in the equation,

[tex]\rm A = 100-B-C\\\\A = 100-60-C\\\\A = 40-C[/tex]

Substitute the value of A in equation 2,

[tex]\rm 40(40-C) + 20\times 60 + 30C = 3200\\\\1600 - 40C + 1200 + 30C = 3200\\\\-10C + 2800 = 3200\\\\-10C = 3200-2800\\\\-10C = 400\\\\C = \dfrac{400}{-10}\\\\C = -40[/tex]

The area can not be negative then the value of C is +40.

And the value of A is,

[tex]A + B + C = 100\\\\A = 100 - 60 -40\\\\A = 100-100\\\\A = 0[/tex]

Then, Maximize profit is,

[tex]\rm P = 100A + 300B + 200C\\\\\rm P = 100(0) + 300(60) + 200(40)\\\\P =0+18000+8000\\\\P = 26000[/tex]

Hence, The 0 acres of crop A, 60 acres of crop B, and 40 acres of crop c each crop should be planted to maximize profit $26,000.

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Tbe confidence interval marked the range of values for which the true population mean is estimated to be given a certain level of confidence. Hence, the confidence interval is (0.6523, 0.7477)

Since the sample size is large enough, we use the the Z distributuon :

Confidence interval is defined thus :

Margin of Error :

Hence,

Lower confidence boundary = 0.7 - 0.0290 = 0.6523

Upper confidence boundary = 0.7 + 0.0290 = 0.7477

Therefore, the confidence interval is (0.6523, 0.7477)

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To construct a 90% confidence interval for the population proportion, calculate the sample proportion, the standard error, and use the confidence interval formula.

Step 1:

Calculate the sample proportion, which is X divided by n. In this case, it is 175 divided by 250, which gives us 0.7.

Step 2:

Calculate the standard error, which is the square root of (p*(1-p))/n, where p is the sample proportion. In this case, it is the square root of (0.7*(1-0.7))/250, which is approximately 0.0266.

Step 3:

Construct the confidence interval using the formula p ± z*(standard error), where p is the sample proportion and z is the z-score corresponding to the desired level of confidence. For a 90% confidence interval, the z-score is approximately 1.645. Therefore, the 90% confidence interval is 0.7 ± 1.645*0.0266, which becomes (0.658, 0.742).

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Answer:

no,

Step-by-step explanation:

1/4 of 40 is 10

40-10=30

It depends. The actual price would be $31.35. So it is not really reasonable since it is closer to the original price than it is to the discounted one... Just use your best judgement...

The X-intercept (-250, 0)

The Y-intercept (0, 100)

These are the Y and X intercepts because this the first time the line intercepts. I hope I explained it well...

Have a good day!

Answer:

-9 21/50

Step-by-step explanation:

Answer: 30

Step-by-step explanation:

By dividing 15 miles by 0.5 miles, we find that there are 30 segments. Since Nella and Lydia do not rest at the start, they take one rest less than the number of segments, resulting in 29 rests during their hike.

The student is trying to determine the number of times Nella and Lydia will rest during a 15 mile hike if they stop after every 0.5 mile. The calculation involves dividing the total distance (15 miles) by the distance between rests (0.5 miles).

To find the number of rests, we perform the following calculation:

However, we need to consider that they do not rest at the start, only after each 0.5 mile. Hence, the total number of rests would be one less than the total number of segments.

30 segments - 1 = 29 rests.

Therefore, Nella and Lydia will rest 29 times during their hike.

Answer: 2.6

Step-by-step explanation:

Step 1: Calculate the mean of Shade's plant heights.

= 7+12+12+8+9+8+8+8/8

= 72/8

=9

Step 2: Calculate the range of Shade's plant heights. Range is highest minus lowest number. This will be:

12 - 7 = 5

Step 3: Calculate the mean of Sun plant heights.

19+24+20+23+24+23+23+20/8

= 176/8

= 22

Step 4: Find the range of Sun plants height.

= 24 - 19 = 5

Step 5: Find the difference of means

= 22 - 9

= 13

Step 6: Divide the difference of means by the range.

= 13 ÷ 5

= 2.6

The difference in mean and range are 13 and 0 respectively.

We are to find the difference in mean and range of the plant height.

Given the Shade plant heights expressed as 7 12 12 8 9 8 8 8

Mean =  7 + 12+12+ 8+ 9+ 8+ 8+ 8

Mean = 72

Sample size = 8

Range = Highest value - Lowest value

Range = 21 - 7

Given the Sun plant heights expressed as 19 24 20 23 24 23 23 20

Mean =  19+ 24+ 20+ 23+ 24+ 23+ 23+ 20

Mean = 176

Sample size = 8

Range = Highest value - Lowest value

Range = 24 - 19

Evaluate the difference in mean

Difference in mean = 22 - 9

Difference in mean = 13

Evaluate the difference in range

Difference in range = 5 - 5

Difference in range = 0

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Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image for the step by step explanation of the answer to the question

The systematic sampling method that would result in the smallest sample size is A. Surveying each 50,000th number.

The sample size that is given will depend on the number that the systematic sampling model uses. The higher the number, the smaller the sample size.

If each 50,000th number is being surveyed then the sample size would be:

= 500,0000 / 50,000

= 10 users

This is the smallest sample size that can be acquired here.

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Answer:

$12 per foot

Step-by-step explanation:

$72.00 divided by 6 is $12

Answer:

The cost per foot of the sandwich is $12.

Step-by-step explanation:

You need to use division for this problem.

Pretend you are cutting the 6-foot sanwhich into 1-foot pieces. You will have 6 pieces. You have to give each piece an equal amount of money. Think about your 6-times tables. What times 6 = 72?

__ x 6 =72

or

72/6 = __

To calculate the difference between the expected reimbursements of insurance policies G and H for a given month, we need to find the expected reimbursement for each policy and then take the difference of the two values.

To calculate the difference between the expected reimbursements of insurance policies G and H for a given month, we need to find the expected reimbursement for each policy and then take the difference of the two values.

For policy G, there is a 45% chance of no claims, in which case the reimbursement is 0. If a claim is made, the loss amount follows an exponential distribution with a mean of 5. We need to find the expected value of the reimbursement in this case. Let X be a random variable representing the loss amount. The expected reimbursement for policy G is then given by:

Expected Reimbursement for Policy G = 0.45(0) + 0.55(0.8)(E(X) - 2)

Similarly, for policy H, there is a 35% chance of no claims and a 65% chance of a claim with a loss amount following an exponential distribution with a mean of 9. Let Y be a random variable representing the loss amount. The expected reimbursement for policy H is:

Expected Reimbursement for Policy H = 0.35(0) + 0.65(0.8)(E(Y) - 2)

To find the difference between the expected reimbursements, we subtract the expected reimbursement for policy H from the expected reimbursement for policy G:

Difference = Expected Reimbursement for Policy G - Expected Reimbursement for Policy H

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Answer: C

Step-by-step explanation: It divides the original segment into two equal pieces

The properties that do not apply for the perpendicular bisector should be option c. that it divides the original segment to two equal pieces.

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Answer:

There are 22 chickens and 8 rabbits

Step-by-step explanation:

1 chicken = 2 legs

1 rabbit = 4 legs

we need to do 2 equations to solve this problem

c + r = 30

c*2 + r*4 = 76

we clear c in the first equation

c + r = 30

c = 30 - r

we replace c with (30 - r) in the second equation

(30 - r) * 2 + r * 4 = 76

60 - 2r + 4r = 76

-2r + 4r = 76 - 60

2r = 16

r = 16/2

r = 8

now we replace r in the first equation

c = 30 - r

c = 30 - 8

c = 22

There are 22 chickens and 8 rabbits

Do  you know that you have the correct solution because you can verify it by multiplying

22 * 2 + 8 * 4 =

44 + 32 = 76

Answer:

Step-by-step explanation:

Let x represent the quantity of 80% solution. Then 130-x is the amount of 55% solution. The total amount of salt in the mix is ...

  0.80x +0.55(130 -x) = 0.75·130

  0.25x = 0.20·130 . . . . . . . subtract 0.55(130)

  x = 0.20/0.25(130) = 104

  130-x = 26

She should use 26 ounces of 55% solution and 104 ounces of 80% solution.

Final answer:

The scientist would need to use 26 ounces of Solution A and 104 ounces of Solution B to create 130 ounces of a 75% salt mixture.

Explanation:

To solve the problem of mixing two salt solutions of different concentrations to achieve a specific final concentration, we can set up a system of equations based on the amounts of salt and total solution. We know that Solution A is 55% salt and Solution B is 80% salt, and we want 130 ounces of a 75% salt mixture.

Let x be the amount of Solution A and y be the amount of Solution B. The first equation is based on the total amount of solution, and it is:

x + y = 130 ... (1)

The second equation is based on the amount of salt in the final mixture:

0.55x + 0.80y = 0.75(130) ... (2)

From equation (1), we can express y as y = 130 - x. Substitute this into equation (2) and solve for x:

0.55x + 0.80(130 - x) = 97.5

0.55x + 104 - 0.80x = 97.5

-0.25x = -6.5

x = 26 ounces (Solution A)

Substitute x back into equation (1) to find y:

x + y = 130

26 + y = 130

y = 104 ounces (Solution B)

So, to obtain 130 ounces of a 75% salt mixture, the scientist would use 26 ounces of Solution A and 104 ounces of Solution B.

Answer:

She still has 166.67 square feet does she have left to plant flowers

Step-by-step explanation:

The sum of total area planted, and the remaining area left to plant, is 100% = decimal 1.

She has planted 1/3 of the area. So

[tex]\frac{1}{3} + p = 1[/tex]

[tex]p =  1 - \frac{1}{3}[/tex]

[tex]p = \frac{3-1}{3}[/tex]

[tex]p = \frac{2}{3}[/tex]

So she still has to paint two thirds of the area.

The area is of 250 square feet.

2/3 of 250

[tex]250\frac{2}{3} = 166.67[/tex]

She still has 166.67 square feet does she have left to plant flowers

Answer:

Read below for the answer

Step-by-step explanation:

1 pound = 1/14 stone

[multiply by 14]

14 pounds = 1 stone

[multiply by 3]

42 pounds = 3 stone

[divide by 4]

42 / 4 pounds = 3/4 stone

[simplify]

21 /2 = 10.5 pounds = 3/4 stone

Answer:  i dont now

Step-by-step explanation:

Yes, a square can be considered as a rhombus and a rectangle both.

The square is a quadrilateral with all sides equal and all angles equals to 90° and having equal diagonals.

Square being a rhombus and a rectangle :-

Rhombus :-

It has it's all sides equal having their diagonals equal and intersect at right angle rhombus is a parallelogram so a square, all the properties that a rhombus holds are also the properties of a square, so we can say a square can be considered as a rhombus.

Rectangle :-

A square is always a rectangle because, it has all the properties of a rectangle, such as parallel and equal opposite sides, vertex angles being a right angle, diagonals being equal.

Hence, a square can be considered as a rhombus and a rectangle both.

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Final answer:

A square is both a rhombus and a rectangle because it has four equal sides and four right angles, fulfilling the criteria for both shapes.

Explanation:

A square indeed has all the properties of a rhombus, which is a parallelogram with four equal sides, and it also has the properties of a rectangle, which is a quadrilateral with four right angles. Since a square has four equal sides and four right angles, it satisfies the criteria to be called both a rhombus and a rectangle. Therefore, the answer is yes; a square is both a rhombus and a rectangle.