Answer:
(4,-4)
Step-by-step explanation:
Diagonals of a rectangle share a common midpoint
(4-6)/2 , (0-4)/2 = (-6+x)/2, (0+y)/2
-2 = -6 + x
x = 4
-4 = y
We determined the fourth point of a rectangle by ensuring that the sides of the rectangle are parallel to the axes and the sides are equal in length. The fourth point of the rectangle formed by the points (4,0), (-6,0), and (-6,-4) is (4,-4).
Explanation:The fourth point of the rectangle should have the same x-coordinate as the point (4,0) and the same y-coordinate as the point (-6,-4). Therefore, the fourth point is (4,-4)
To better understand the reasoning, let's consider the points on a plane. We recall that rectangles have sides of equal length and parallel to the axes. Therefore, since the line connecting (4,0) and (-6,0) is parallel to the x-axis, the fourth point's x-coordinate has to be the same as the point on the opposite side of the rectangle, which is 4. Similarly, as the line connecting (-6,0) and (-6,-4) is parallel to the y-axis, the fourth point's y-coordinate has to equal the y-coordinate of the point on the opposite side (-6,-4), which is -4. Hence, the fourth point is (4,-4).
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The plot shows the temperatures (in ºF) for a group of children who visited a doctor’s office. A plot shows the temperature of children at a doctor's office. 1 child had a temperature of 96 degrees; 2, 97 degrees; 5, 98 degrees; 2, 99 degrees; 1, 100 degrees. What conclusions can be drawn from the data set? Check all that apply.
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
the four-digit numeral 3AA1 is divisible by 9. What digit does A represent?
Answer:
7
Step-by-step explanation:
Trial and error. Start with 1 and go to 9
The digit A in the numeral 3AA1, which is divisible by 9, represents the number 7. This is deduced by the rule that a number is divisible by 9 if the sum of its digits is also divisible by 9.
To find the digit that A represents in the four-digit numeral 3AA1 that is divisible by 9, we must remember that a number is divisible by 9 if the sum of its digits is divisible by 9. Let's denote A as a single digit, and since we know that 3 and 1 are already part of the sum, the equation we need to solve is:
3 + A + A + 1 = 3 + 2A + 1
Simplifying further:
2A + 4 must be divisible by 9. Since A is a digit, it can only be one of the following numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. We can now test these values:
For A = 0, the sum is 4 (not divisible by 9)
For A = 1, the sum is 6 (not divisible by 9)
For A = 2, the sum is 8 (not divisible by 9)
For A = 3, the sum is 10 (not divisible by 9)
For A = 4, the sum is 12 (not divisible by 9)
For A = 5, the sum is 14 (not divisible by 9)
For A = 6, the sum is 16 (not divisible by 9)
For A = 7, the sum is 18 (divisible by 9)
For A = 8, the sum is 20 (not divisible by 9)
For A = 9, the sum is 22 (not divisible by 9)
The only value for A that makes the sum divisible by 9 is 7. Therefore, A represents the digit 7.
What percentage of the data values falls between the values of 27 and 45 in the data set shown?
A box-and-whisker plot. The number line goes from 25 to 50. The whiskers range from 27 to 48, and the box ranges from 32 to 45. A line divides the box at 36.
25%
50%
75%
100%
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%.
What is a box plot?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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A 2010 estimate of Australia's population is 21,515,754.
Which is the best estimate of the number of Australians with type A blood in 2010?
Blood Types in Australia
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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Josh wants to download music online. He must buy a membership for $14.
Then he can download songs for 99 cents each. Josh has $20. How many
songs can Josh buy without spending more money than he has?
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.
8. A well-balanced stock market portfolio will often experience an exponential growth. A
particular investor with a well-balanced stock market portfolio records the portfolio balance
every month, in thousands of dollars, from the date of investment. The roughly exponential
growth can be transformed to a linear model by plotting the natural log of the balances
versus time, in months, where t - 0 represents the date the money was invested. The linear
regression equation for the transformed data is
In (balance)-5.550 + 0.052t.
Using this equation, what is the predicted balance of the portfolio after 2 years (24 months)?
(A) $5,654
(B) $6,798
(C) $285,431
(D) $896,053
(E) $948,464
Answer:
D) $896,053
Step-by-step explanation:
Write the equation for g(x)
Answer:
g-x=3
Step-by-step explanation:
The number of undergraduates at Johns Hopkins University is approximately 2000, while the number at Ohio State University is approximately 40,000. A simple random sample of 50 undergraduates at Johns Hopkins University will be obtained to estimate the proportion of all Johns Hopkins students who feel that drinking is a problem among college students. A simple random sample of 50 undergraduates at Ohio State University will be obtained to estimate the proportion of all Ohio State students who feel that drinking is a problem among college students. Answer Questions 4-5 below.
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.
g Exercise 6. Let X be a Gaussian random variable with X ∼ N (0, σ2 ) and let U be a Bernoulli random variable with U ∼ Bern(?) independent of X. Define V as V = XU. (a) Find the characteristic function of V , ϕV = E(e jsV ) = RfV (v)e jsv. Hint: use iterated expectation. (b) Find the mean and variance of V .
Answer:
Step-by-step explanation
question solved below
An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. These classes are open to any of the 86 students in the school. There are 38 in the Spanish class, 27 in the French class, and 16 in the German class. There are 14 students that in both Spanish and French, 6 are in both Spanish and German, and 5 are in both French and German. In addition, there are 2 students taking all 3 classes. If one student is chosen randomly, what is the probability that he or she is taking at least one language class
Answer: The required probability is 0.674.
Step-by-step explanation:
Since we have given that
Number of students in the Spanish class = 38
Number of students in the French class = 27
Number of students in the German class = 16
Number of students in both spanish and French = 14
Number of students in both Spanish and German = 6
Number of students in both French and German = 5
Number of students in all three class = 2
So, it becomes:
[tex]n(S\cup F\cup G)=n(S)+n(F)+n(G)-n(S\cap F)-n(G\cap F)-n(S\cap G)+n(S\cap F\cap G)\\\\n(S\cup F\cup G)=38+27+16-14-5-6+2=58[/tex]
So, Probability that he or she is taking at least one language class is given by
[tex]\dfrac{58}{86}=0.674[/tex]
Hence, the required probability is 0.674.
You and a friend go to the movies. You each buy a ticket for x dollars and a popcorn-and-drink combo for $5.25. Use the distributive property to find the total amount of money you and your friend spent using the following expression 2(x + 5.25)
Answer:
2x + 10.5.
Step-by-step explanation:
Multiply 2 by x and 5.25.
Answer:
.
Step-by-step explanation:
Is 26, 31, 36, 41, 46 an arithmetic sequence?
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
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.
p = −0.01x2 − 0.1x + 32
Determine the consumers' surplus if the market price is set at $2/cartridge. (Round your answer to two decimal places.)
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.
What do you mean by domain and range of a function?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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The U.S. Department of Agriculture claims that the mean cost of raising a child from birth to age 2 by husband-wife families in the United States is $13,120. A random sample of 500 children (age 2) has a mean cost of $12,925 with a standard deviation of $1745. At α=.10, is there enough evidence to reject the claim? (Adapted from U.S. Department of Agriculture Center for Nutrition Policy and Promotion).
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
A pair of snow boots at an equipment store in Big Bear that originally cost $60 is on sale for 40% off. Then, you have a coupon for 10% off. What is the final cost?
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
How many centimeter cubes will fill a box 20cm by 6cm by 3cm
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
Ali is riding his bicycle. He rides at a Speed of 12.8 kilometers per hour for 2 hours how many kilometers did he ride
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.
Explanation: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:
Use the formula: Distance = Speed x TimePlug in the given values: Distance = 12.8 km/h x 2 hCompute: Distance = 25.6 kmTherefore, Ali rode his bicycle for a distance of 25.6 kilometers.
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A rectangular plot of land is to be fenced in using two kinds of fencing. Two opposite sides will use heavy-duty fencing selling for $3 per foot, while the remaining two sides will use standard fencing costing $2 per foot. The budget that will be entirely used for fencing is $6000. In order to maximize the area of the plot, how many feet of standard fencing should be purchased for the project?
So, the required length of the sides that have standard fencing is 1500 ft.
Area of the rectangle: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.
Explanation: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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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 fve colors in equal proportions. Which of the following would represent the alternative hypothesis in a chi squared goodness-of-fost conducted to determine if the five colors of W&Ws occur in equal proportions? My: Al of the proportions are different from 0.20 MP1 P2 =3 =p4 P5 - 0.20 0 Hy: At least two of the mean number of colors differ from one another He the number of candies per bag and candy color are dependent Hy: At least one proportion is not equal to 0 20 5.5556
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
Carmen needs $3560 for future project. She can invest $2000 now at annual rate of 7.8%, compound monthly. Assuming that no withdrawals are made, how long will it take for her to have enough money for her project?
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.
The Wall Street Journal recently published an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked of both men and women was: "Do you think sexual harassment is a major problem in the American workplace?" 24% of the men compared to 62% of the women responded "Yes". Suppose that 150 women and 200 men were interviewed.
a) What are the null and alternative hypotheses that The Wall Street Journal should test in order to show that its claim is true?
b) For a 0.01 level of significance, what is the critical value for the rejection region?
c) What is the value of the test statistic? (hint: you need to find pbar)
d) What is the p-value of the test?
e) What conclusion should be reached?
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.
Let X and Y denote the values of two stocks at the end of a five-year period. X is uniformly distributed on the interval (0, 12). Given X = x, Y is uniformly distributed on the interval (0, x). Determine Cov(X, Y) according to this model.
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
the difference of two numbers is 1. their sum is 19. find the numbers.
Answer:
x = 10
y = 9
Step-by-step explanation:
First, you need to write two equations that represent the information given. I'm going to set the two numbers and x and y.
x - y = 1
x + y = 19
This turns it into a systems of equations. When you add the two equations, keeping everything on each side, you eliminate a variable, and solve for the other.
2x = 20
x = 10
Now, you'd plug x into either original equation.
(10) - y = 1
-y = -9
x = 10
I hope this helped!
Answer:
The numbers are 9 and 10. Add to get a sum of 19, but subtract to get a difference of 1.
Step-by-step explanation:
What is 3 to the 3rd power
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..
14.) Although most of us buy milk by the quart or gallon, farmers measure daily production in pounds. Ayrshire cows average 47 pounds of milk a day, with a standard deviation of 6 pounds. For Jersey cows, the mean daily production is 43 pounds, with a standard deviation of 5 pounds. Assume that Normal models describe milk production for these breeds.
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%
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. (7 points) What is the proportion of semester students returning to summer school
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
Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim.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. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.There is sufficient evidence to support the claim that the mean attendance is greater than than 694.There is sufficient evidence to support the claim that the mean attendance is less than 694.There is not sufficient evidence to support the claim that the mean attendance is less than 694.There is not sufficient evidence to support the claim that the mean attendance is greater than 694.
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!!!
The point (-3,1) is on the terminal side of the angle in standard position. What is tanθ
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]
A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. Of the 29 tires surveyed, the mean lifespan was 45,800 miles with a standard deviation of 9,800 miles. Using alpha = 0.05, is the data highly consistent with the claim?
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.
Suppose samples of size 100 are drawn randomly from a population that has a mean of 20 and a standard deviation of 5. What are the values of the mean and the standard deviation of the distribution of the sample means
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.