Answer:
i think its c
Step-by-step explanation:
Answer:
C: Columns: likes roller coasters, doesn’t like roller coasters; rows: likes water rides, doesn’t like water rides
Step-by-step explanation:
Like variables need to be together on the columns and rows
Jane moved from a house with 58 square feet of closet space to an apartment with 38.86 square feet of closet space. What is the percentage decrease of Jane's closet space?
Answer:
figure it out
Step-by-step explanation:
What is cot based on the image
the answer is b I'm sure
A researcher focusing on birth weights of babies found that the mean birth weight is 3370 grams (7 pounds, 6.9 ounces) with a standard deviation of 582 grams. Complete parts (a) through (c) below. a. Identify the population and variable. Choose the correct population below. A. The group of all babies ever born B. The group of researchers C. The number of babies born the year the research was performed D. The group of all of the babies whose recorded weights were examined Choose the correct variable below. A. The weights of the babies at birth B. The accuracy of the measurements of baby birth weights C. The number of babies that were born D. The number of births per capita b. For samples of size 175, find the mean mu Subscript x overbar and standard deviation sigma Subscript x overbar of all possible sample mean weights. mu Subscript x overbarequals nothing (Type an integer or a decimal. Do not round.) sigma Subscript x overbarequals nothing (Round to two decimal places as needed.) c. Repeat part (b) for samples of size 350. mu Subscript x overbarequals nothing (Type an integer or a decimal. Do not round.) sigma Subscript x overbarequals nothing (Round to two decimal places as needed.)
Answer:
a) D. The group of all of the babies whose recorded weights were examined
b) A. The weights of the babies at birth
c) i) Ux' = u = 3370;
s.d = 43.95
ii) Ux' = u = 3370
s.d = 35.109
Step-by-step explanation:
Given:
Mean, u = 3370
Standard deviation = 582
a) Population in statistics involves every member of the group in study.
Here, the correct population is the group of all of the babies whose recorded weights were examined.
b) In statistics, variable involves data collected.
The correct variable is the weights of the babies at birth
c)
i) at X' = 175
Sample mean:
Ux' = u = 3370
Standard deviation:
[tex] \sigma x' = \frac{\sigma}{\sqrt{n}} = \frac{582}{\sqrt{175}} = 43.995 [/tex]
ii) at X' = 175
Sample mean:
Ux' = u = 3370
Stanard deviation:
[tex] \sigma x' = \frac{\sigma}{\sqrt{n}} = \frac{582}{\sqrt{350}} = 35.109 [/tex]
a. The population includes all babies whose recorded weights were examined, and the variable is the birth weights of the babies.
b. For sample sizes of 175, the mean birth weight remains 3370 grams, with a standard deviation of approximately 43.96 grams.
c. For sample sizes of 350, the mean birth weight remains 3370 grams, with a standard deviation of approximately 31.15 grams.
Let's address each part of the question step-by-step to ensure clarity and accuracy.
Part (a): Identifying Population and Variable
To identify the correct population:
Population: The group of all of the babies whose recorded weights were examined.To identify the correct variable:
Variable: The weights of the babies at birth.Hence, the correct answers are:
Population: D. The group of all of the babies whose recorded weights were examined.Variable: A. The weights of the babies at birth.Part (b): Calculating Mean ([tex]\mu_\bar{x}[/tex]) and Standard Deviation ([tex]\sigma_\bar{x}[/tex]) for Sample Size 175
For samples of size 175, we need to find the mean and standard deviation of all possible sample means:
Mean ([tex]\mu_\bar{x}[/tex]) is the same as the population mean ([tex]\mu[/tex]): [tex]\mu_\bar{x}[/tex] = 3370 grams.Standard Deviation ([tex]\sigma_\bar{x}[/tex]):Part (c): Calculating Mean ([tex]\mu_\bar{x}[/tex]) and Standard Deviation ([tex]\sigma_\bar{x}[/tex]) for Sample Size 350
For samples of size 350, we perform similar calculations:
Mean ([tex]\mu_\bar{x}[/tex]) is the same as the population mean ([tex]\mu[/tex]): [tex]\mu_\bar{x}[/tex] = 3370 grams.Standard Deviation ([tex]\sigma_\bar{x}[/tex]):In summary, we have identified the population and variable, and calculated the mean and standard deviation for different sample sizes of 175 and 350.
Dozen cookies calls for 2/4 cup of flour. How much flour would be needed to triple the recipe
Answer:
1 2/4
Step-by-step explanation: 2/4 * 3 = 1 2/4
The editor of a textbook publishing company is deciding whether to publish a proposed textbook. Information on previous textbooks published show that 20 % are huge successes, 30 % are modest successes, 30 % break even, and 20 % are losers. Before a decision is made, the book will be reviewed. In the past, 99 % of the huge successes received favorable reviews, 70 % of the moderate successes received favorable reviews, 40 % of the break-even books received favorable reviews, and 20 % of the losers received favorable reviews. If the textbook receives a favorable review, what is the probability that it will be huge success?
Answer:
34.86% probability that it will be huge success
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Receiving a favorable review.
Event B: Being a huge success.
Information on previous textbooks published show that 20 % are huge successes
This means that [tex]P(B) = 0.2[/tex]
99 % of the huge successes received favorable reviews
This means that [tex]P(A|B) = 0.99[/tex]
Probability of receiving a favorable review:
20% are huge successes. Of those, 99% receive favorable reviews.
30% are modest successes. Of those, 70% receive favorable reviews.
30% break even. Of those, 40% receive favorable reviews.
20% are losers. Of those, 20% receive favorable reviews.
Then
[tex]P(A) = 0.2*0.99 + 0.3*0.7 + 0.3*0.4 + 0.2*0.2 = 0.568[/tex]
Finally
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)} = \frac{0.2*0.99}{0.568} = 0.3486[/tex]
34.86% probability that it will be huge success
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 18 cm
What is the volume of the sphere?
O 12 cm
O 24 cm
O 36 cm
Mark this and return
Save and Exit
Next
Sub
Answer: b
Step-by-step explanation: ik
evaluate 6+xwhen x=3
Answer:
9
Step-by-step explanation:
Plug in 3 for x, and the equation is 6 + 3, which is equal to 9.
Answer:
6 + x = 9
Step-by-step explanation:
If x equals 3
6 plus x (when x equals 3)
Thus, 6 plus 3
= 9
9 will be your answer
Completely factor this quadratic expression: 4x2 + 12x − 72.
Answer:
4(x-3)(x+6)
Step-by-step explanation:
Factor out the 4
4(x2 + 3x - 18)
what 2 numbers add to 3 and multiply to - 18?
-3 and 6
therefore 4x2 + 12x − 72 = 4(x-3)(x+6)
Answer:
(4x² + 24x)- (12x + 72)
4x( x+ 6)- 12(x + 6)
ans = (4x - 12)(x + 6)
What is the factorization of 121b4 − 49?
Answer:
( 11 b 2 + 7 ) ( 11 b 2 − 7 )
Step-by-step explanation:
Answer:
121b⁴ − 49 = (11b² + 7) • (11b² - 7)
Step-by-step explanation:
The difference of two squares.
Step 1: reformat equation
11²b² - 49
Step 2: Factoring: 121b⁴- 49
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A² - AB + BA - B² =
A² - AB + AB - B² =
A² - B²
Factorization is : (11b² + 7) • (11b² - 7)
The measure of an angle is 43.5 degrees . What is the complementary angle?
A complimentary angle has to add up two angles to equal 90 degrees.
We have one angle which is 43.5 degrees, so all we have to do is subtract 43.5 degrees from 90 degrees to find the missing angle.
90 degrees minus 43.5 degrees is 46.5 degrees.
That means the missing angle is 46.5 degrees.
It should be noted that the complementary angles is 46.5°.
From the information given, measure of an angle is 43.5 degree. It should be noted that the sum of the angles in complementary angles equal 90°.
Therefore, the value of the remaining angle will be:
= 90 - 43.5°
= 46.5°
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Consider rolling two 6-sided dice. One of them is a fair die. The other is unfair, where the numbers 1-4 are all equally likely to be rolled, but the number 5 is twice as likely as the number 1 to be rolled, and the number 6 is 3 times as likely as the number 1 to be rolled. What are these values from the probability distribution for the set of possible outcomes for the sum of the two dice
Answer:
is there a pic i need more info...
Step-by-step explanation:
Jade says that 8 divided by ½ means the same thing as ½ of 8, so the answer is 4. Do you agree with her? Why or why not?
Answer:
Jade's statement is incorrect because "8 divided by ½" does not mean the same thing as "½ of 8".
Explanation:
No, I don't agree with Jade's statement.
When we say "8 divided by ½", it means we are dividing 8 into two equal parts, each representing one-half. Mathematically, [tex]\(8 \div \frac{1}{2}\)[/tex] means we are dividing 8 by [tex]\(\frac{1}{2}\)[/tex] , which is equivalent to multiplying 8 by the reciprocal of [tex]\(\frac{1}{2}\)[/tex], which is 2. So:
[tex]\[ 8 \div \frac{1}{2} = 8 \times 2 = 16 \][/tex]
On the other hand, "½ of 8" means finding half of 8, which is indeed 4. However, this is not the same as "8 divided by ½".
A dealer bought a snowboard for E45 and sold it for E54. What was her percentage profit?
Answer:
20%
Step-by-step explanation:
(54/45) - 1 = 0.2 or 20%
need math help pls:))
Answer:
see below
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationships between triangle sides and trig functions. For the angle of interest, the diagram shows values for the Opposite side (12) and the Adjacent side (16.5). The mnemonic tells you that these are related to the Tangent of the angle:
Tan = Opposite/Adjacent
tan(θ) = (12/16.5)
Find the mean. Round to the nearest tenth. Help help?????
Answer:
(2). 26 (4). 547 (6). 3,132 (8). 46.1 (10). 10.6
Step-by-step explanation:
Una pileta se vacía con una bomba que extrae agua a razón de 400 litros por minuto. Al encender la bomba, en la pileta hay 30000 litros de agua.
a) Hallar la función que indica el caudal restante de agua en función del tiempo, y
representarla gráficamente.
b) Determinar la cantidad de agua que queda en la pileta luego de media hora de
comenzar a vaciarla.
c) Determinar el tiempo necesario para vaciar la pileta por completo.
Answer:
a) The function that represents the amount of water as a function of time is
f(x) = 30,000 - 400x
b) The amount of water left in the sink after half an hour of starting to empty it
= 18,000 litres
c) The time it will take to empty the sink completely = 75 minutes.
Step-by-step explanation:
English Translation
A sink is emptied with a pump that extracts water at the rate of 400 liters per minute. when turning on the pump in the sink there were 30000 liters of water.
a) The time (in minutes) from when the pump is turned on is called x. find the function that represents the amount of water left in the sink as a function of time
b) Determine the amount of water left in the sink after half an hour of starting to empty it.
c) Determine the time it will take to empty the sink completely?
a) Speed is a quantity that is described as the rate of change of another quantity with time.
So, the speed of emptying the sink is given as
Speed = (Amount of water emptied) ÷ (Time taken to empty that amount of water).
The Speed of emptying the sink is given as 400 litres/min
Time taken to empty the sink = x
Let the amount of water left in the sink, a function of the time taken to empty the sink, be f(x)
Amount of water emptied = 30,000 - f(x)
400 = [30000 - f(x)] ÷ x
30000 - f(x) = 400x
f(x) = 30,000 - 400x
b) Determine the amount of water left in the sink after half an hour of starting to empty it.
f(x) = 30000 - 400x
x = 30 mins
f(x) = 30000 - 400(30) = 18,000 litres
c) Determine the time it will take to empty the sink completely?
f(x) = 30000 - 400x
when the sink is completely empty, the amount of water left in the sink is 0 litres, that is, f(x) = 0 litres
0 = 30000 - 400x
400x = 30000
x = (30000/400) = 75 minutes.
Hope this Helps!!!
Q 3.19: In 2011 and 2015, the study was held to determine the proportion of people who read books. 948 people of 1200 said they read at least one book in the last 3 months in 2011. 1080 people of 1500 said they read at least one book in the last 3 months in 2015. Find the 95% confidence interval for the difference in proportions.
Answer:
[tex] (0.79-0.72) -1.96 \sqrt{\frac{0.79(1-0.79)}{1200} +\frac{0.72(1-0.72)}{1500}} =0.0376[/tex]
[tex] (0.79-0.72) +1.96 \sqrt{\frac{0.79(1-0.79)}{1200} +\frac{0.72(1-0.72)}{1500}} =0.1024[/tex]
And the 95% confidence interval for the difference of the two proportions is given by:
[tex] 0.0376 \leq p_1 -p_2 \leq 0.1024[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex] X_1 = 948[/tex] number of people that they read at least one book in the last 3 months in 2011
[tex]n_1 = 1200[/tex] the sample size selected for 2011
[tex] X_2 = 1080[/tex] number of people that they read at least one book in the last 3 months in 2015
[tex]n_2 = 1500[/tex] the sample size selected for 2015
The estimated proportions people that they read at least one book in the last 3 months for each year are given by:
[tex]\hat p_1 = \frac{948}{1200}= 0.79[/tex]
[tex]\hat p_2 = \frac{1080}{1500}= 0.72[/tex]
And the confidence interval for the true difference of proportions is given by:
[tex](\hat p_1 -\hat p_2) \pm z_{\alpha/2} \sqrt{\frac{\hat p_1 (1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}[/tex]
The confidence level is 95% so then the significance is 0.05 or 5% and [tex]\alpha/2 =0.025[/tex] and the critical value for this case using the normal standard distribution is:
[tex]z_{\alpha/2}=\pm 1.96[/tex]
And replacing into the confidence interval formula we got:
[tex] (0.79-0.72) -1.96 \sqrt{\frac{0.79(1-0.79)}{1200} +\frac{0.72(1-0.72)}{1500}} =0.0376[/tex]
[tex] (0.79-0.72) +1.96 \sqrt{\frac{0.79(1-0.79)}{1200} +\frac{0.72(1-0.72)}{1500}} =0.1024[/tex]
And the 95% confidence interval for the difference of the two proportions is given by:
[tex] 0.0376 \leq p_1 -p_2 \leq 0.1024[/tex]
A triangular pyramid has three dimensions.
-The sides of the base are 5 centimeters, 12 centimeters, and 13 centimeters.
-The height is 12 centimeters
What is the volume of the pyramid?
A) 120 cm^3
B) 360 cm^3
C) 240 cm^3
D)720 cm^3
Answer:
A) 120 cm^3
Step-by-step explanation:
area of triangle = 1/2 x 5 x 12 = 30
volume = 1/3 x 30 x 12 = 120
Answer:
A
Step-by-step explanation:
A line passes through the point (4, −9) and has a slope of 5/2.
Write an equation in slope-intercept form for this line.
The equation of the line that has a slope of 5/2 and passes through the point (4, -9) is y = 5/2x -19.
Explanation:The equation of a line in slope-intercept form is given by the formula y = mx + b, where m is the slope and b is the y-intercept. We're given that this line has a slope of 5/2 and it passes through the point (4, -9).
Plugging the known values into the equation, we get: -9 = (5/2) * 4 + b. By solving for b, we find the y-intercept of the line.
-9 = 10 + b --> b = -9 - 10 = -19
So the equation of the line in slope-intercept form is y= 5/2x - 19
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Find all the critical points of h(x) = x^3 − 3x^4 and categorize them as local
maximums, local minimums, or neither, using the first derivative test.
Answer:
0 is an inflection point
1/4 is a local maximum.
Step-by-step explanation:
To begin with you find the first derivative of the function and get that
[tex]h'(x) = 3x^2 - 12x^3[/tex]
to find the critical points you equal the first derivative to 0 and get that
[tex]3x^2 - 12x^3 = 0, x = 0,1/4[/tex]
To find if they are maximums or local minimums you use the second derivative.
[tex]h''(x) = 6x-36x^2[/tex]
since [tex]h''(0) = 0[/tex] is neither an inflection point, and since [tex]h''(1/4) = -3/4 <0[/tex] then 1/4 is a maximum.
Matthew invests $500 into an account with a 2.5% interest that is compounded quarterly. How much money will he have in this account if he keeps it for 10 years? Round your answer to the nearest cent. Do NOT round until you have calculated the final answer.
Answer:
Step-by-step explanation:
CORRECT ANSWER IS : $641.51
Use the compound interest formula and substitute the given values: A=$500(1+0.0254)4(10). Simplify using the order of operations: A=$500(1.00625)40=$500(1.283026821)≈ $641.51.
After ten years, Matthew will have $641.51 in the account, rounded to the closest penny.
What is compound interest?The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. [tex]A = P(1 + r/n)^{nt[/tex], where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.
We can use the formula for compound interest to calculate how much money Matthew will have in the account after 10 years:
[tex]A = P(1 + r/n)^{nt[/tex]
Where:
A = final amount
P = principal (initial amount invested) = $500
r = annual interest rate (as a decimal) = 0.025
n = number of times interest is compounded per year = 4 (quarterly)
t = time in years = 10
Plugging in the values, we get:
[tex]A = 500(1 + 0.025/4)^(4*10)\\A = 500(1.00625)^{40}\\A = 500(1.305011)[/tex]
A = $641.51
Therefore, Matthew will have $641.51 in the account after 10 years, rounded to the nearest cent.
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How many decimal places are in 0.0050
Answer:
HERE IS YOUR ANSWER
Step-by-step explanation:
4
The senior class at a very small high school has 25 students. Officers need to be elected for four positions: President, Vice-President, Secretary, and Treasurer. a. In how many ways can the four officers be chosen? b. If there are 13 girls and 12 boys in the class, in how many ways can the officers be chosen if the President and Treasurer are girls and the Vice-President and Secretary are boys?
Answer:
(a) The total number of ways to select 4 officers from from 25 students is 12,650.
(b) The total number of ways the four officers are selected such that the President and Treasurer are girls and the Vice-President and Secretary are boys is 5,148.
Step-by-step explanation:
(a)
It is provided that there are a total of n = 25 students.
Officers need to be elected for four positions:
President, Vice-President, Secretary, and Treasurer.
k = 4
In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.
The formula to compute the combinations of k items from n is given by the formula:
[tex]{n\choose k}=\frac{n!}{k!(n-k)!}[/tex]
Compute the number of ways to select 4 students from from 25 as follows:
[tex]{25\choose 4}=\frac{25!}{4!(25-4)!}[/tex]
[tex]=\frac{25!}{4!\times 21!}\\\\=\frac{25\times 24\times 23\times 22\times 21!}{4!\times 21!}\\\\=\frac{25\times 24\times 23\times 22}{4\times 3\times 2\times 1}\\\\=12650[/tex]
Thus, the total number of ways to select 4 officers from from 25 students is 12,650.
(b)
It is provided that of the 25 students, there are 13 girls and 12 boys in the class.
For the post of President and Treasurer only girls are selected.
For the post of Vice-President and Secretary only boys are selected.
Compute the number of ways to select 2 girls for the post of President and Treasurer as follows:
[tex]{13\choose 2}=\frac{13!}{2!(13-2)!}[/tex]
[tex]=\frac{13!}{2!\times 11!}\\\\=\frac{13\times 12\times 11!}{2!\times 11!}\\\\=\frac{13\times 12}{ 2\times 1}\\\\=78[/tex]
Compute the number of ways to select 2 boys for the post of Vice-President and Secretary as follows:
[tex]{12\choose 2}=\frac{12!}{2!(12-2)!}[/tex]
[tex]=\frac{12!}{2!\times 10!}\\\\=\frac{12\times 11\times 10!}{2!\times 10!}\\\\=\frac{12\times 11}{ 2\times 1}\\\\=66[/tex]
The number of ways the four officers are selected such that the President and Treasurer are girls and the Vice-President and Secretary are boys is:
[tex]{13\choose 2}\times {12\choose 2}=78\times 66=5148[/tex]
Thus, the total number of ways the four officers are selected such that the President and Treasurer are girls and the Vice-President and Secretary are boys is 5,148.
We have 50 video gamers who share information about their favorite games. 20 people say that Borderlands II is their favorite game. 33 say their favorite game is Fortnite, while 19 declare Minecraft as their favorite game (note that a single person can have several favorite games). 15 people say that Borderlands and Fortnite are both favorites, while 10 say that both Borderlands and Minecraft are their favorites. Finally, 5 people declare all 3 of the games as their favorites. How many people declared Minecraft and Fortnite (exclusively) as their favorites?
Answer:
2 people
Step-by-step explanation:
Total number of people (n) = 50
Borderlands II (B) = 20
Fortnite (F) = 33
Minecraft (M) = 19
Borderlands and Fortnite (B&F) = 15
Borderlands and Minecraft (B&M)= 10
All games (B&M&F) = 5
The number of people that claimed more than one game as their favorite (X) is given by:
[tex]X=M+B+F-n\\X=19+20+33-50\\X=22\ people[/tex]
Those people can be divided in B&F only, B&M only, M&F only and B&M&F:
[tex]X=(B\&M-B\&M\&F)+(B\&F-B\&M\&F)+(M\&F-B\&M\&F)+B\&M\&F\\X=B\&M+B\&F+M\&F-2*B\&M\&F\\22=10+15+M\&F-2*5\\M\&F=7\ people[/tex]
7 people claimed that Minecraft and Fortnite were their favorites however, 5 of those people claimed all of the games as their favorite. Therefore, only 2 people declared Minecraft and Fortnite (exclusively) as their favorites.
Answer:
2
Step-by-step explanation:
25y = 15y +75
y= 7.5
infinite solutions
no solution
y= 750
Answer:
y= 7.5
Step-by-step explanation:
25y = 15y +75
-15y -15y
10y = 75
÷10 ÷10
y = 7.5
The Harris family and the Baker family each used their sprinklers last summer. The water output rate for the Harris family's sprinkler was 20L per hour. the water output rate for the Baker family's sprinkler was 35L per hour. The families used their sprinklers for a combined total of 75 hours, resulting in a total water output of 2025L. How long was each sprinkler used?
Answer:40 hr and 35 hr
Step-by-step explanation:
Given
Harris family sprinkler output rate is [tex]20\ L/\text{per hour}[/tex]
and Baker family sprinkler output rate is [tex]35\ L/\text{per hour}[/tex]
Total output of two is [tex]2025\ L[/tex]
Suppose Harris family sprinkler used for [tex]t_1[/tex] time and Baker family for [tex]t_2 [/tex]time then
[tex]20\times t_1+35\times t_2=2025\quad \ldots(i)[/tex]
and [tex]t_1+t_2=75[/tex]
[tex]t_1=75-t_2[/tex]
Substitute the value in [tex](i)[/tex]
[tex]\Rightarrow 20\times (75-t_2)+35t_2=2025[/tex]
[tex]\Rightarrow 1500-20t_2+35t_2=2025[/tex]
[tex]\Rightarrow 15t_2=525[/tex]
[tex]\Rightarrow t_2=\frac{525}{15}[/tex]
[tex]\Rightarrow t_2=35\ hr[/tex]
[tex]\therefore \ t_1=75-35=40\ hr[/tex]
Therefore Harris family use [tex]40\ hr[/tex] of sprinkler and Baker family use [tex]35\ hr[/tex] of sprinkler
Which of the following statement is true? A. For any discrete random variable X and constants a and b, E(aX+b) = (a + b). E(X) B. For any discrete random variable X and constants a and b, V(aX+b) = . C. If a constant c is added to each possible value of a discrete random variable X, then the variance of X will be shifted by that same constant amount. D. If a constant c is added to each possible value of a discrete random variable X, then the expected value of X will be shifted by that same constant amount.
Answer:
A. False
B. False
C. False
D. True
Step-by-step explanation:
A. False
Remember that E[aX+b] = aE[X] + b, therefore the equality would be true only if E[X] = 1.
B. False
Remember that [tex]V[aX+b] = a^2 V[X][/tex].
C. False
In other words they are telling you in words that [tex]V[X+b] = V[X]+b[/tex], that is false because [tex]V[X+b] = V[X][/tex]
D. True
That is a property of the expected value E[X+b] = E[X]+b
Option D is correct in stating that adding a constant to each value of a random variable shifts the expected value of that variable by that same constant. Adding a constant does not alter the variance.
Explanation:The correct answer among the given options is D. This statement says that if a constant c is added to each possible value of a discrete random variable X, then the expected value of X will be shifted by that same constant amount. This is in accordance with the properties of expected value, where the expected value of (X + c) is E(X) + c. On the other hand, adding a constant does not affect the variance of a random variable. Variance measures the dispersion of a variable's possible values from its expected value, and adding a constant shifts every possible value, including the expected value, by the same amount, leaving dispersion unchanged.
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Expand. Your answer should be a polynomial in standard form. (x + 5)(x +3)
Answer: x^2+8x+15
Step-by-step explanation:
(x+5)(x+3)
x^2+3x+5x+15
x^2+8x+15
To expand the polynomial (x + 5)(x + 3), multiply each term from the first binomial by each term from the second binomial and combine like terms.
Explanation:
To expand the polynomial (x + 5)(x + 3), we need to use the distributive property. We multiply each term from the first binomial by each term from the second binomial. So, we have:
x * x = x^2x * 3 = 3x5 * x = 5x5 * 3 = 15Combining like terms, we get x^2 + 3x + 5x + 15. Simplifying further, we have the expanded polynomial:
x^2 + 8x + 15.
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"A public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes. Karen took bus number 14 during peak hours on 18 different occasions. Her mean waiting time was 7.3 minutes with a standard deviation of 1.5 minutes. At the 0.01 significance level, test the claim that the mean waiting time is less than 10 minutes. Use the P-value method of testing hypotheses."
Answer:
We conclude that the mean waiting time is less than 10 minutes.
Step-by-step explanation:
We are given that a public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes.
Karen took bus number 14 during peak hours on 18 different occasions. Her mean waiting time was 7.3 minutes with a standard deviation of 1.5 minutes.
Let [tex]\mu[/tex] = mean waiting time.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\geq[/tex] 10 minutes {means that the mean waiting time is more than or equal to 10 minutes}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 10 minutes {means that the mean waiting time is less than 10 minutes}
The test statistics that would be used here One-sample t test statistics as we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n}}}[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean waiting time = 7.3 minutes
s = sample standard deviation = 1.5 minutes
n = sample of occasions = 18
So, test statistics = [tex]\frac{7.3-10}{\frac{1.5}{\sqrt{18}}}[/tex] ~ [tex]t_1_7[/tex]
= -7.637
The value of t test statistics is -7.637.
Now, the P-value of the test statistics is given by the following formula;
P-value = P( [tex]t_1_7[/tex] < -7.637) = Less than 0.05%
Since, our P-values of test statistics is less than the level of significance as 0.05% < 1%, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the mean waiting time is less than 10 minutes.
In a boutique, a $14 scarf is marked, "20% off." What is the sale price of the scarf?
Answer:
11.2
Step-by-step explanation:
20 percent of 14 is 2.8 14 minus 2.8 is 11.2