What is the measure of side x in the isosceles triangle that is shown below

Answer:

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

Step-by-step explanation:

Since, point (-3, 1) is on the terminal side of the angle in standard position.

[tex] \therefore \: ( - 3, \: 1) = (x, \: y) \\ \therefore \:x = - 3 \: \: and \: \: y = 1 \\ \because \tan \theta = \frac{y}{x} \\ \therefore \:\tan \theta = \frac{1}{ - 3} \\ \\ \huge \red{ \boxed{\therefore \:\tan \theta = - \frac{1}{3} }}[/tex]

Question in order:

The exact numbers of each color of Umbrella Corporation's most popular candy, W&Ws, naturally vary from bag to bag, but the company wants to make sure that the process as a whole is producing the five colors in equal proportions. Which of the following would represent the alternative hypothesis in a chi-squared goodness-of-fit test conducted to determine if the five colors of W&Ws occur in equal proportions?

a. H1: All of the proportions are different from 0.20

b. HI: p1 = P2 = p3 =P4=p5 = 0.20

c. H1: At least one proportion is not equal to 0.20

d. H1: At least two of the mean number of colors differ from one another.

e. HI: the number of candies per bag and candy color are dependent

Answer:

option C

Step-by-step explanation:

H1: At least one proportion is not equal to 0.20

Answer:

25.6 kilometers

Step-by-step explanation:

12.8 km in an hour

he is riding for 2 hours

12.8 x 2 = 25.6

Using the formula 'Distance equals Speed times Time', we find that Ali rode a distance of 25.6 kilometers given that he rode his bicycle at a speed of 12.8 kilometers per hour for 2 hours.

To answer this question, you can use the formula to calculate distance, which is Speed multiplied by Time. In Ali's case, he's riding his bicycle at a speed of 12.8 kilometers per hour and for 2 hours. Using the formula, you'll multiply 12.8(km/h) by 2(h). Thus, Ali's distance covered would be 25.6 kilometers.

Here's how it works in a step-by step format:

Therefore, Ali rode his bicycle for a distance of 25.6 kilometers.

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Answer:

(a) H₀: P₂ - P₁ = 0 vs. Hₐ: P₂ - P₁ > 0.

(b) The critical value for the rejection region is 2.33.

(c) The calculated z-statistic value is, z = 7.17.

(d) The p-value of the test is 0.

(e) The proportion of women who view sexual harassment on the job is more than that for men.

Step-by-step explanation:

Here we need to test whether the proportion of women who view sexual harassment on the job is more than that for men.

(a)

Our hypothesis will be:

H₀: The difference between the proportions of men and women who view sexual harassment on the job as a problem is same, i.e. P₂ - P₁ = 0

Hₐ: The difference between the proportions of men and women who view sexual harassment on the job as a problem is more than 0, i.e. P₂ - P₁ > 0.

(b)

The significance level of the test is:

α = 0.01

The rejection region is defined as:

If test statistic value, z[tex]_{t}[/tex] > z₀.₀₁ then then null hypothesis will be rejected.

Compute the critical value of the test as follows:

[tex]z_{\alpha}=z_{0.01}=2.33[/tex]

*Use z-table.

Thus, the critical value for the rejection region is 2.33.

(c)

The z-statistic for difference of proportions is,

[tex]z=\frac{\hat p_{2}-\hat p_{1}}{\sqrt{P(1-P)\times (\frac{1}{n_{2}}+\frac{1}{n_{1}})}}[/tex]  

[tex]\hat p_{i}[/tex] = ith sample proportion,

P = population proportion

[tex]n_{i}[/tex] = ith sample size.

The given information is:

[tex]n_{1}=200\\n_{2}=150\\\hat p_{1}=0.24\\\hat p_{2}=0.62[/tex]

Since, there is no data about the population proportion the unbiased estimate of P is given by,

[tex]P=\frac{n_{1}\hat p_{1}+n_{2}\hat p_{2}}{n_{1}+n_{2}}=\frac{200\times 0.24+150\times 0.62}{200+150}=0.4029[/tex]

Using the given data we compute the z-statistic as:

[tex]z=\frac{\hat p_{2}-\hat p_{1}}{\sqrt{P(1-P)\times (\frac{1}{n_{2}}+\frac{1}{n_{1}})}}[/tex]

  [tex]=\frac{0.62-0.24}{\sqrt{0.4029(1-0.4029)\times (\frac{1}{150}+\frac{1}{200})}}[/tex]

  [tex]=7.17[/tex]

Thus, the calculated z-statistic value is, z = 7.17.

(d)

Compute the p-value of the test as follows:

[tex]p-value=P(Z>z_{t})[/tex]

               [tex]=P(Z>7.17)\\=1-P(Z<7.17)\\=1 -(\approx1)\\=0[/tex]

Thus, the p-value of the test is 0.

(e)

As stated in part (b), if z₀.₀₁ > z[tex]_{t}[/tex] then then null hypothesis will be rejected.

z[tex]_{t}[/tex] = 7.17 > z₀.₀₁ = 2.33

Thus, the null hypothesis will be rejected at 1% level of significance.

Conclusion:

The proportion of women who view sexual harassment on the job is more than that for men.

Answer:

The proportion of semester students returning to summer school

p = 0.35

Step-by-step explanation:

Explanation:-

Given data A university planner is interested in determining the percentage of spring semester students who will attend summer school.

She takes a pilot sample of 160 spring semester students discovering that 56 will return to summer school

Given the sample size 'n' = 160

let 'x' = 56

Sample proportion of semester students returning to summer school

[tex]p = \frac{x}{n} = \frac{56}{160}[/tex]

p = 0.35

Answer:

Option D is correct.

Failure to reject the null hypothesis means that there is not sufficient evidence to support the claim that the mean attendance is greater than 694.

Step-by-step explanation:

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

It usually maintains that random chance is responsible for the outcome or results of any experimental study/hypothesis testing.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

It usually maintains that other than random chance, there are significant factors affecting the outcome or results of the experimental study/hypothesis testing.

For this question, the owner of a football team claims that the average attendance at games is over 694, and he is therefore justified in moving the team to a city with a larger stadium.

So, the null hypothesis would be that there isn't enough evidence to support the claim that the mean attendance is greater than 694.

That is, the mean isn't greater than 694; the mean is less than or equal to 694.

While the alternative hypothesis would be that there is sufficient evidence to support the claim that the mean attendance is greater than 694.

Mathematically,

The null hypothesis is represented as

H₀: μ₀ ≤ 694

The alternative hypothesis is represented as

Hₐ: μ₀ > 694

Failure to reject the null hypothesis means that the null hypothesis is true. Hence, the answer choice picked is the obvious correct answer.

Hope this Helps!!!

Answer:

the answer is 75% hope that helps

Step-by-step explanation:

i did the test and i got it right

The required percentage of the data values falls between the values of 27 and 45 in the data set shown is 75%.

A straightforward method of expressing statistical data on a plot in which a rectangle is drawn to represent the second and third quartiles, with a vertical line inside to indicate the median value. Horizontal lines on both sides of the rectangle show the lower and upper quartiles.

Based on the box-and-whisker plot, we can see that the majority of the data values fall between the values of 32 and 45, and the median value is 36.

To find the percentage of data values that fall between 27 and 45, we can estimate by visually analyzing the plot. Since the whiskers go from 27 to 48, we can assume that all data values between 27 and 48 are included. Then, we need to estimate how much of the data falls between 32 and 45, which is the range of the box.

Since the box takes up most of the range of values between 32 and 45, we can estimate that around 75% of the data values fall within this range. Therefore, the percentage of data values that fall between 27 and 45 can be estimated as around 75%.

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Answer:

27

Step-by-step explanation:

3 x 3 x 3=27

Answer:

27

Step-by-step explanation:

you can just do 3x3x3 or 3^3 to figure it out.. 3x3=9 and 9x3= 27.. hope this helped..

Answer:

101.85ft

Step-by-step explanation:

We can use tan here

[tex]tan\theta=\frac{opp}{adj}\\adj = \frac{opp}{tan \theta} \\adj = \frac{74}{tan(36)} = 101.85[/tex]

The height should be 101.85 ft.

Since it casts a 74-ft shadow when the angle of elevation of the sun is 36°

So, the height should be

Here we can use tan

[tex]= 74\div tan\ 36[/tex]

= 101.85 ft

Therefore, we can conclude that The height should be 101.85 ft.

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The remaining part of Question:

4) what can we conclude about sampling variability in the sample proportion calculated in the sample at John Hopkins as compared to that calculated in the sample at Ohio State.

5) The number of undergraduates at Johns Hopkins is approximately 2000 while the number at Ohio State is approximately 40000, suppose instead that at both schools, a simple random sample of about 3% of the undergraduates Will be taken.

Answer:

4) The sample proportion from Johns Hopkins will have about the same sampling variability as that from Ohio State

5) The sample proportion from John Hopkins will have more sampling variability than that from Ohio State

Step-by-step explanation:

Note: The sampling variability in the sample proportion decreases with increase in the sample size.

4) since the sample size at both Johns Hopkins and Ohio State is the same (i.e. n = 50), the sample variability of the sample proportion will be the same for both cases.

5) 3% of the population are selected for the observation in both cases.

At Johns Hopkins, sample size, n = 3% * 2000

n = 60

At Ohio State, sample size, n = 3% * 40000

n = 1200

Since sampling variability in the sample proportion decreases with increase in the sample size, the sampling variability in sample proportion will be higher at Johns Hopkins than at Ohio State.

Answer:

6 songs

Step-by-step explanation:

It's best to start by setting up an equation equal to $20.

$14 + $.99s = $20

s being songs in this case.

First we add like terms by subtracting $14 from both sides.

$.99s = $6

Now we solve for s by dividing both sides by $.99

s = $6.06

Therefore, Josh can by 6 songs.

Final answer:

Josh can buy 6 songs with his remaining $6 after purchasing a $14 membership, since each song costs 99 cents.

Explanation:

Josh wants to download music online. With $20 to spend, he first needs to buy a membership for $14, leaving him with $6 to spend on songs. Each song costs 99 cents, so to determine how many songs Josh can purchase without exceeding his budget, we have to divide the remaining money by the cost per song.

Step 1: Calculate the remaining budget after membership: $20 - $14 = $6.

Step 2: Divide the remaining budget by the cost per song: $6 \(\div\) $0.99 ≈ 6 songs.

Thus, Josh can buy 6 songs without spending more than he has.

Answer:

$30 i think

Step-by-step explanation:

because %40+%10=%50

and %50 is half of %100 so 60-(60×(50%)=30

sorry is its wrong

Answer:

See explanation

Step-by-step explanation:

Solution:-

- A survey was conducted among the College students for their motivations of using credit cards two years ago. A randomly selected group of sample size n = 425 college students were selected.

- The results of the survey test taken 2 years ago and recent study are as follows:

                                           Old Survey ( % )            New survey ( Frequency )

                  Reward                 27                                              112

                  Low rate               23                                              96

                  Cash back           21                                              109

                  Discount              9                                               48

                  Others                  20                                             60

- We are to test the claim for any changes in the expected distribution.

We will state the hypothesis accordingly:

Null hypothesis: The expected distribution obtained 2 years ago for the motivation behind the use of credit cards are as follows: Rewards = 27% , Low rate = 23%, Cash back = 21%, Discount = 9%, Others = 20%

Alternate Hypothesis: Any changes observed in the expected distribution of proportion of reasons for the use of credit cards by college students.

( We are to test this claim - Ha )

We apply the chi-square test for independence.

- A chi-square test for independence compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each other.

- We will compute the chi-square test statistics ( X^2 ) according to the following formula:

                                [tex]X^2 = Sum [ \frac{(O_i - E_i)^2}{Ei} ][/tex]

Where,

 O_i : The observed value for ith data point

 E_i : The expected value for ith data point.

- We have 5 data points.

So, Oi :Rewards = 27% , Low rate = 23%, Cash back = 21%, Discount = 9%, Others = 20% from a group of n = 425.

     Ei : Rewards = 112 , Low rate = 96, Cash back = 109, Discount = 48, Others = 60.

Therefore,

                     [tex]X^2 = [ \frac{(112 - 425*0.27)^2}{425*0.27} + \frac{(96 - 425*0.23)^2}{425*0.23} + \frac{(109 - 425*0.21)^2}{425*0.21} + \frac{(48 - 425*0.09)^2}{425*0.09} + \frac{(60 - 425*0.20)^2}{425*0.20}]\\\\X^2 = [ 0.06590 + 0.03132 + 4.37044 + 2.48529 + 7.35294]\\\\X^2 = 14.30589[/tex]

- Then we determine the chi-square critical value ( X^2- critical ). The two parameters for evaluating the X^2- critical are:

                     Significance Level ( α ) = 0.10

                     Degree of freedom ( v ) = Data points - 1 = 5 - 1 = 4  

Therefore,

                     X^2-critical = X^2_α,v = X^2_0.1,4

                    X^2-critical = 7.779

- We see that X^2 test value = 14.30589 is greater than the X^2-critical value = 7.779. The test statistics value lies in the rejection region. Hence, the Null hypothesis is rejected.

Conclusion:-

This provides us enough evidence to conclude that there as been a change in the claimed/expected distribution of the motivations of college students to use credit cards.

Final answer:

To test for changes in credit card usage motivations among college students, calculate the expected frequencies from the old survey percentages, apply the chi-square goodness-of-fit test, and compare the statistic to the chi-square critical value at alpha = 0.10.

Explanation:

Understanding the Hypothesis Test for Changed Distribution

To determine whether there has been a shift in the distribution of college students' motivations for using credit cards since the previous survey, we conduct a hypothesis test for goodness of fit. The test will compare the observed frequencies from the new survey with the expected frequencies based on the old survey percentages.

First, calculate the expected frequency for each category using the formula: Expected Frequency = (Old Survey Percentage / 100) × Total Number of Students. Then, employ the chi-square goodness-of-fit test to analyze the data:

Reward: Expected = 0.27 × 425 = 114.75

Low rate: Expected = 0.23 × 425 = 97.75

Cash back: Expected = 0.21 × 425 = 89.25

Discount: Expected = 0.09 × 425 = 38.25

Others: Expected = 0.20 × 425 = 85.00

With the expected frequencies calculated, the chi-square statistic will be computed:

χ² = Σ((Observed - Expected) ² / Expected)

This statistic will be compared to a critical value from the chi-square distribution table with (n - 1) degrees of freedom, where n is the number of categories, at alpha = 0.10 to determine whether to reject the null hypothesis (no change in distribution).

Answer:

a) The mean of the sampling distribution of means μₓ = μ = 20

b) The standard deviation of the sample σₓ⁻ = 0.5

Step-by-step explanation:

Explanation:-

Given sample size 'n' =100

Given  mean of the Population 'μ' = 20

Given standard deviation of population 'σ' = 5

a) The mean of the sampling distribution of means μₓ = μ

                                                                                     μₓ = 20

b) The standard deviation of the sample σₓ⁻   =    [tex]\frac{S.D}{\sqrt{n} }[/tex]

    Given standard deviation of population 'σ' = 5

                                                                              = [tex]\frac{5}{\sqrt{100} } = 0.5[/tex]

Final answer:

The mean of the distribution of the sample means drawn from a population with a mean of 20 and a standard deviation of 5, using samples of size 100, is 20. The standard deviation of this distribution, also known as the standard error, is 0.5.

Explanation:

The question involves understanding the concept of the distribution of sample means, also known as the sampling distribution. When samples of size 100 are drawn from a population with a mean (μ) of 20 and a standard deviation (σ) of 5, the mean of the distribution of the sample means will be the same as the population mean, which is 20. However, the standard deviation of the distribution of sample means, known as the standard error (SE), will be the population standard deviation divided by the square root of the sample size (√n), which in this case is 5/√100 = 0.5.

Therefore, the mean of the distribution of the sample means is 20 and the standard deviation (standard error) of this distribution is 0.5. This is based on the central limit theorem which states that, for a sufficiently large sample size, the sampling distribution of the sample mean will be approximately normally distributed regardless of the population’s distribution, with these exact parameters of mean and standard deviation.

Answer:

2x + 10.5.

Step-by-step explanation:

Multiply 2 by x and 5.25.

Answer:

.

Step-by-step explanation:

Answer:

D) $896,053

Step-by-step explanation:

So, the required length of the sides that have standard fencing is 1500 ft.

The area of rectangle is the region covered by the rectangle in a two-dimensional plane. A rectangle is a type of quadrilateral, a 2d shape that has four sides and four vertices.

Let [tex]x[/tex] ft be the length of the sides that duty fencing and [tex]y[/tex] ft be the length of the sides that have standard fencing.

So, the area will be calculated by the above formula we get,

[tex]Area=xy[/tex]...(1)

Now, the cost of fencing is,

[tex]3x+2y=6000\\y=3000-\frac{3x}{2}[/tex]...(2)

Now, substituting equation (2) in equation (1) we get,

[tex]A=3000x-\frac{3x^2}{2}[/tex]

Now, differentiating the above equation we get,

[tex]\frac{dA}{dx} =3000-3x=0\\x=1000[/tex]

Substituting [tex]x=1000 ft[/tex] in equation (2) we get,

[tex]y=3000-\frac{3\times 1000}{2}\\=1500 ft[/tex]

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The question pertains to maximizing the area of a rectangular land plot within a fence budget. We derive a mathematical equation to fit the budget involving both types of fences and then maximize the equation to find the solution. It involves applications of maximization and differentiation.

The subject of this question is Mathematics, specifically problems involving equations and budgets. This problem can be solved by using the concept of maximization of areas in rectangle and budget calculations.

We know the total budget which is $6000, and costs of the two types of fencing. Let's denote the lengths of the heavy-duty fenced sides as H and the lengths of the standard fenced sides as S. The equation that describes the budget is 3H + 2S = 6000.

If we're maximizing area, we want to maximize S*H. Remember that the area of a rectangle is the product of its dimensions (length times width). Since H and S are lengths of sides of a rectangular plot, H*S will give us the area.

Replacing H from the budget equation we get H = (6000 - 2S) / 3. You can plug this into the area equation to get Area = S * (6000 - 2S) / 3. To find the maximum of this function, take its derivative and set it to zero, solve for S.

Doing this results in the required amount of standard fencing for the project, making it a solution to the question asked.

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Answer:

Yes, it is arithmetic sequence.

Step-by-step explanation:

31-26=5

36-31=5

41-36=5

46-41=5

Difference between consecutive numbers is the same, so we have arithmetic sequence.

Answer:

Yes it is an arithmetic sequence

26+5=31

31+5=36

36+5=41

41+5=46

Answer:

[tex]\mathrm{Number\:of\:Australians\:with\:type\:A\:Blood\:Group\:in\:2010}\:\approx\:8175987[/tex]

Step-by-step explanation:

[tex]\mathrm{Percent}:\\\\\mathrm{A\:ratio\:expressed\:as\:a\:fraction\:out\:of\:a\:hundred.}\\\\\mathrm{In\:order\:to\:convert\:a\:percent\:to\:a\:ratio,\:divide\:it\:by\:100}:\\\\38\%\:=\frac{38}{100}\\\\\mathrm{Percentage\:of\:population\:with\:A\:Blood\:Type}\:=\frac{38}{100}\times 21515754\\\\\approx8175987[/tex]

An estimated 8,175,987 Australians have Type A blood.

There were 21,515,754 in Australia in 2010. In the same year, it was estimated that 38% of people had Type A blood.

This means that the best estimate of people in Australia with Type A blood is:

= Percentage of people with type A blood x Number of people in Australia

= 38% x 21,515,754

= 8,175,986.52

= 8,175,987 people

In conclusion, approximately 8,175,987 Australians have Type A blood.

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Answer:

360

Step-by-step explanation:

formula is L x B x H so first layer would be 6 rows of 20 cubes which is 120cubes

H is 3cm so 120x3 = 360

or find out the volume of the box, 20x6x3 = 360

Answer:

Cov (X,Y) = 6

Step-by-step explanation:

hello,

Cov(X,Y) = E(XY) - E(X)E(Y)

we must  first find E(XY), E(X), and E(Y).

since X is uniformly distributed on the interval (0,12), then E(X) = 6.

next we find the joint density f(x,y) using the formula

[tex]f(x,y) = g(y|x)f_{X}(x)[/tex]

[tex]f_{X} (x) = \frac{1}{12} \ $for$\ 0<x<12[/tex] this is because f is uniformly distributed on the the interval (0,12)

also since the conditional probability density of Y given X=x, is  uniformly distributed on the interval [0,x], then

[tex]g(y|x)=\frac{1}{x}[/tex]  for 0≤y≤x≤12

thus

[tex]f(x,y)=\frac{1}{12x}[/tex].

hence,

[tex]E(X,Y)= \int\limits^{12}_{x=0} \int\limits^x_{y=o} xy\frac{1}{12x} \,dy dx[/tex]

[tex]E(X,Y)=\frac{!}{24} \int\limits^{12}_{x=0} x^2 \, dx = 24[/tex]

also,

[tex]E(Y) = \int\limits^{12}_{x=0} \int\limits^x_{y=0} y\frac{1}{12x} \, dydx[/tex]

[tex]E(Y)=\frac{1}{24}\int\limits^{12}_{x=0} {x} \, dx =3[/tex]

thus Cov(X,Y) = E(XY) - E(X)E(Y)

                      =  24 - (6)(3)

                      =     6

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 13120

For the alternative hypothesis,

µ ≠ 13120

This is a 2 tailed test

Since the population standard deviation is not given, the t test would be used to determine the test statistic. The formula is

t = (x - µ)/(s/√n)

Where

s = sample standard deviation

x = sample mean

µ = population mean

n = number of samples

From the information given,

µ = $13120

x = $12925

n = 500

s = $1745

t = (12925 - 13120)/(1745/√500) = - 2.5

Degree of freedom = n - 1 = 500 - 1 = 499

Using the t score calculator to find the probability value,

p = 0.012

Since α = 0.10 > p = 0.012, it means that there is enough evidence to reject the claim

Answer:

See below.

Step-by-step explanation:

1) the measure of center are the same  

3) there is little variability in the data

4) the average temperature is 98

5) the data is clustered around the mean

Answer:

The answer is Option E; both B and C are correct

Step-by-step explanation:

Both (b) and (c) are correct. Simpson's paradox is a paradox in which a trend that appears in different groups of data disappears when these groups are combined, and the reverse trend appears for the aggregate data. This result is often encountered in social-science and medical-science statistics, and is particularly confounding when frequency data are unduly given causal interpretations. Simpson's Paradox disappears when causal relations are brought into consideration.

Now, this question is an example of Simpsons paradox because the groups of collected data over a period of time from five major cities showed a trend that StatsAir does better overall, but this trend is reversed when the groups are studied separately to show that air median does better.

So, option B is correct.

Also, City is a variable that influences both the dependent variable and independent variable, causing a spurious association. That is it is the cause of why the 2 results are biased. Thus, city is a lurking variable.

So, option C is also correct

Answer:

g-x=3

Step-by-step explanation:

Demand function:  p = -0.01x^2-0.2x+13  (1).

The equation (2) is: CS = ∫ D(p) dp, where D is the demand curve expressed in terms of the price.  The bottom limit of the integrand is the market price given as $5 and the top limit is $13 found by setting x = 0 in (1) above. Equation (2) above requires we solve the original equation, (1) above, for x in terms of p.  The first step is (a) to multiply both sides of equation by -100 to clear decimals, then (b) place equation in standard quadratic form, namely, x^2 + 20x + 100p – 1300 = 0.  Step (c): Solve for x by applying quadratic formula, namely, x = (-b +- √(b^2 – 4ac)) / 2a to solve for x.  Use a = 1, b = 20, c = 100p – 1300. The new demand equation is: x = -10 +  10√(14 – p). Now calculate ∫ (-10 +  10(14 – p)^(1/2)) dp and evaluate at 5 and 13.   This gives: -10(13 – 5) – (2/3) (10) ((14 - 13)^(3/2) – (14 – 5)^(3/2)) .  This evaluates to: -80 – (20/3) + 180.   So, CS = $93.33.

The consumer surplus demanded will be 50 per week if the market price is set at $2/cartridge.

For any function y = f(x), Domain is the set of all possible values of [x] for which [y] exists. Range is the set of all values of [y] that exists for the given domain.

Given is the demand function for a certain make of replacement cartridges for a water purifier is given by the following equation where [p] is the unit price in dollars and [x] is the quantity demanded each week, measured in units of a thousand.

The demand function is -

p = − 0.01x² − 0.1x + 32

For p = 2, we can write -

− 0.01x² − 0.1x + 32 = 2

− 0.01x² − 0.1x + 30 = 0

Graph the equation and note the [x] intercepts. Taking the positive value of [x] intercept, we get 50.

Hence, the consumer surplus demanded will be 50 per week if the market price is set at $2/cartridge.

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Answer:

Step-by-step explanation

question solved below

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ ≥ 50000

For the alternative hypothesis,

µ < 50000

Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = lifetime of the tyres

µ = mean lifetime

σ = standard deviation

n = number of samples

From the information given,

µ = 50000 miles

x = 45800 miles

σ = 8000

n = 29

z = (50000 - 45800)/(8000/√29) = - 2.83

Looking at the normal distribution table, the probability corresponding to the z score is 0.9977

Since alpha, 0.05 < than the p value, 0.9977, then we would accept the null hypothesis. Therefore, At a 5% level of significance, the data is not highly consistent with the claim.

Answer:

  7.42 years (7 years 5 months)

Step-by-step explanation:

The future value of Carmen's account can be modeled by

  FV = P(1 +r/12)^(12t)

where P is the principal invested, r is the annual rate, and t is the number of years.

Solving for t, we have ...

  FV/P = (1 +r/12)^(12t)

  log(FV/P) = 12t·log(1 +r/12)

  t = log(FV/P)/(12·log(1 +r/12))

For FV = 3560, P=2000, r = 0.078, the time required is ...

  t = log(3560/2000)/(12·log(1 +.078/12))

  t ≈ 7.42

It will take Carmen about 7 years 5 months to reach her savings goal.

Answer:

69.50%

Step-by-step explanation:

Given:  

Ayrshire cows:  

E(X) =μ  = 47

SD(X) = σ = 6 Var (X) = 6^2 = 36  

Jersey cows:  

E(Y) = μ = 43

SD(Y) = σ  = 5 Var(Y) = 52 = 25

Properties mean, variance and standard deviation:  

E(X +Y) = E(X) E(Y)

V ar(X +Y) = Var(X) + Var(Y)

SD(X +Y) = √Var(X)+Var(Y)

X — Y represents the difference between Ayrshire and Jersey cows.  

E(X — Y) = E(X) — E(Y). 47 — 43 = 4

SD(X — Y) = √Var(X)+ Var(Y) =√36+ 25 = √61 = 7.8102

The z-score is the value decreased by the mean, divided by the standard deviation:  

z = x-μ /σ = 0-4/ 7.8102  = -0.51

Determine the corresponding probability using table Z in appendix F.  

P(X—Y [tex]\geq[/tex] 0) = P(Z > —0.51) = 1—P(Z < —0.51) = 1-0.3050 = 0.6950 = 69.50%