Using the t-distribution, it is found that since the absolute value of the test statistic is less than the critical value for the two-tailed test, you cannot conclude that the mean sales differ between the two programs.
At the null hypothesis, it is tested if the mean sales do not differ between the two programs, that is, the subtraction of the means is 0, hence:
[tex]H_0: \mu_1 - \mu_2 = 0[/tex]
At the alternative hypothesis, it is tested if they differ, that is:
[tex]H_1: \mu_1 - \mu_2 \neq 0[/tex]
The mean and the standard errors for each sample are:
[tex]\mu_1 = 42, s_1 = 5.9675[/tex]
[tex]\mu_2 = 44.56, s_2 = 5.6177[/tex]
The distribution of the difference has mean and standard deviation given by:
[tex]\overline{x} = \mu_2 - \mu_1 = 44.56 - 42 = 2.56[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{5.9675^2 + 5.6177^2} = 8.1957[/tex]
The test statistic is:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.
Then:
[tex]t = \frac{2.56 - 0}{8.1957}[/tex]
[tex]t = 0.31[/tex]
The critical value for a two-tailed test, as we are testing if the mean is different of a value, with 9 + 9 - 2 = 16 df and a significance level of 0.05 is [tex]|t^{\ast}| = 2.12[/tex]
Since the absolute value of the test statistic is less than the critical value for the two-tailed test, you cannot conclude that the mean sales differ between the two programs.
A similar problem is given at https://brainly.com/question/13873630
500 children ages 5-11 were asked the following question:
"Do you read books for fun every day?"
Results are shown in the two-way table below.
Boy Girl Total
Yes 48 75
No 182 195
Total 500
a. In this sample, what proportion of children are boys? (Round your answer to the nearest hundredth)
b. What proportion of boys read books for fun every day? (Round your answer to the nearest hundredth)
c. What proportion of girls read books for fun every day? (Round your answer to the nearest hundredth)
d. Based on the findings, does the likelihood of reading books for fun depend on the gender of a child? Explain.
e. If a child is selected at random, find the probability that the child reads book for fun. (Round your answer to the nearest hundredth)
f. If a child is selected at random, find the probability that the child is a girl AND reads book for fun. (Round your answer to the nearest hundredth)
g. If a child is selected at random, find the probability that the child is a girl OR reads book for fun. (Round your answer to the nearest hundredth)
h. If a child is selected at random, find the probability that the child reads book for fun GIVEN that the child is a girl. (Round your answer to the nearest hundredth)
500 children ages 5-11 were asked the following question:
"Do you read books for fun every day?"
Results are shown in the two-way table below.
Boy Girl Total
Yes 48 75 123
No 182 195 377
Total 230 270 500
What are proportions?A proportion is the number of desired outcomes divided by the number of total outcomes.
a. Proportion of children that are boys.There are 500 children and 230 are boys.
230/500 = 0.46
b. Proportion of boys who read books for fun every day.There are 230 boys and 48 read books for fun every day.
48/230 = 0.21
c. Proportion of girls who read books for fun every day.There are 270 girls and 75 read books for fun every day.
75/270 = 0.28
d. Does the likelihood of reading books for fun depend on the gender of a child?Based on the results from b and c, it would seem more likely for a girl to read books for fun than for a boy.
e. For a child selected at random, what is the probability that the child reads books for fun?There are 500 children and 123 read books for fun.
P = 123/500 = 0.25
f. For a child selected at random, what is the probability that the child is a girl and reads books for fun?There are 500 children and 75 are girls who read books for fun.
P = 75/500 = 0.15
g. For a child selected at random, what is the probability that the child is a girl or reads books for fun?There are 500 children. The favorable cases are the girls (270) plus the children who read books for fun (123) minus the girls who read books for fun (75).
P = (270 + 123 - 75)/500 = 0.64
h. For a child selected at random, what is the probability that the child reads books for fun given that the child is a girl.There are 270 girls and 75 of them read books for fun.
P = 75/270 = 0.28
a. The proportion of children who are boys is 0.46.b. The proportion of boys who read books for fun every day is 0.21.c. The proportion of girls who read books for fun every day is 0.28.d. It would seem more likely for a girl to read books for fun than for a boy.e. For a child selected at random, the probability that the child reads books for fun is 0.25.f. For a child selected at random, the probability that the child is a girl and reads books for fun is 0.15.g. For a child selected at random, the probability that the child is a girl or reads books for fun is 0.64.h. For a child selected at random, the probability that the child reads books for fun given that the child is a girl is 0.28.Learn more about proportions here: https://brainly.com/question/25259185
If you earn both hourly wages and a commission at your job, your gross wages, w, can be calculated with the following equation:
cs + rh = w
where c is your commission rate, s is your total sales in dollars, r is your hourly rate, and h is your hours worked.
Solve for s to rewrite the equation for total sales.
Question 1 options:
s = c(w + rh)
s = c(w − rh)
s = w + rh/c
s = w − rh/c
The value of "s" as a function of other variables is s = (w - rh)/c
If you earn both hourly wages and a commission at your job, your gross wages, w, can be calculated with the following equation:
cs + rh = w
We will make "s" the subject of the formula:
Subtract rh from both sides
cs + rh - rh = w - rh
cs = w - rh
Divide both sides by c
cs/c = (w - rh)/c
s = (w - rh)/c
Hence the value of "s" as a function of other variables is s = (w - rh)/c
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NEED HELP ASAP (WILL GIVD BRAINELST)
Answer:
5
Step-by-step explanation:
The answer is 60/12 becuase we can simfly both of theese mixed numbers into an improper fraction, wich will be 4/3*15/4. We do the multiplication, and we get 60/12. 60/12 can be simplifed to 5 becuase 60 divided by 12 is 5
1. “Zoe and Toria are going into business. They need 80,000 to start the business. Their investment is 3:5, respectively.
a. What's Zoe & Ares individual investment amounts?
b. What percent did each person invest?
9514 1404 393
Answer:
a. Z: 30,000; T: 50,000
b. Z: 37.5%; T: 62.5%
Step-by-step explanation:
a. The "ratio units" add up to 3+5 = 8, so we can find the investment amounts by multiplying the ratio by 10,000
Z : T = 3 : 5 = 30,000 : 50,000
Zoe invested 30,000Toria invested 50,000__
b. Zoe's investment amount is 3/8 of the total, or ...
3/8 × 100% = 37.5%
Toria's percentage is the rest of it:
100% -37.5% = 62.5%
Zoe invested 37.5% of the total; Toria invested 62.5% of the total.
A patient has an illness that typically lasts about 24 hours. The temperature, T, in degrees Fahrenheit, of the patient t hours after the illness begins, is given by: T(t) = -0.013t^2 + 0.3172t +98.6. When does the patient reach its maximum value? what is the patient's maximum temp?
Answer:
no entiendo, perdóname, suerte
Please help me :0
What is the order of this matrix?
============================================================
Explanation:
The order of a matrix is a way of describing its size. Specifically, the order is represented in the form [tex]m \times n[/tex], where,
m = number of rowsn = number of columnsThe rows are laid out horizontally, and the columns are vertical.
In this case, we have 5 rows and 3 columns. Therefore, the answer is 5 x 3. The order is important because a 5 x 3 matrix is different from a 3 x 5 matrix.
HELP ASAP
In math class, the girl to boy ratio is 8 to 6. If there are 24 girls in the class, how many boys are there?
A
20
B
30
C
18
D
16
Answer:
C, 18.
Step-by-step explanation:
Since 24 divided by 8 is 3, which means that
8x3 = 24, then the amount of boys must be solved using the equation 6x3 which equals 18.
on a photograph an ant is enlarged at scale 25:1 In the photo the ant leg is 15 cm what is the actual length of the ants leg
Answer:
0.6 cm
Step-by-step explanation:
15/25=0.6
Answer:
0.6 Is the answer
Step-by-step explanation:
Hope this helped ¬∪ω∪¬
Solve for the value of q.
Answer:
q=13
Step-by-step explanation:
(8q-5)°+81°=180° (angles on a str line)
8q-5+81=180
8q=180+5-81
=104
q=104÷8
=13
Using supplementary angle theorem
[tex]\\ \sf\longmapsto 8q-5+81=180[/tex]
[tex]\\ \sf\longmapsto 8q+76=180[/tex]
[tex]\\ \sf\longmapsto 8q=104[/tex]
[tex]\\ \sf\longmapsto q=13[/tex]
Use an equation to find the value of k so that the line that passes through the given points has the given slope.
(−4,k), (6,−7); m=−15
Answer:
Step-by-step explanation:
(-7 - k)/(6 + 4) = -15
(-7 - k)/10 = -15
-7 -k = -150
-k = -143
k = 143
This diagram models 3 friends who are sharing 2 turkey sandwiches equally.
How much does each friend get?
1/3 sandwich
2/3 sandwich
11/3 sandwiches
11/2 sandwiches
Answer:
2/3 sandwich.
Step-by-step explanation:
No Explanation
What is the inequality shown?
-4<x>/=5
○ means either< or > but since the line is moving to the right it means that x is greater than -4 (<x)● means greater than or equal to since the line stoped at 5 it means x can be equal to 5 or less then 5
At a particular time, a tree casts a shadow 17 m long on horizontal ground. At the same time, a vertical pole 3 m high casts a shadow 4 m long. Calculate the height of the tree to the nearest tenth of a meter.
Using a system of equations, the height of the tree would be 12.80 meters.
Equating the height and shadows of the tree and pole :
Height of pole / shadow of pole = height of tree / shadow of tree
Representing the equation thus :
Let the height of the tree = h
3/4 = h/17
Cross multiply
4h = 17 × 3
4h = 51
Divide both sides by 4
h = 51/4
h = 12.75.
Hence, the height of the tree to the nearest tenth of a meter is 12.80 meters.
Learn more : https://brainly.com/question/25562438
Help me with question 9
Answer:
a) 5.25m^2
b) 1 can
Step-by-step explanation:
a)
area of a triangle = bh/2
=(4.2 x 4.5)/2
=18.9/2
=9.45m^2
area of a rectangle = 2(l+w)
=2 x (0.6 + 1.5)
=4.2m^2
9.45-4.2 = 5.25m^2
b) 1 can, you can't have a partial can of paint
7. Add [-6-2 2] + [-3 2 1].
A. [-9-3-5]
B. [-3 0 3]
C. [-6 0 3]
D. [-9 0 3]
What is the area of a rectangle with a length of 88 inches and width of 56 inches
Answer: 4928
Step-by-step explanation:
Area= LxW
88 x 56= 4928
Peter wins five sixth of his matches and loses the rest. What is the ratio of wins to losses?
BRAINLIEST
Answer:
5:1
Step-by-step explanation:
5/6 won
1/6 lost
5:1=6
Answer:
5:1
Step-by-step explanation:
Total numbers of match = 6
No. of matches Peter wins = 5
Ratio of wins to lose = 5:(6-5) = 5:1
Please, don't write the answer as 1:5. Because, 5:1 and !:5 both are different so don't be confused.
The rectangle shown has a perimeter of 64 cm and the given area. Its length is 8 more than five times its width. Write and solve a system of equations to find the dimensions of the rectangle.
Answer:
Length 28 cm, width 4 cmStep-by-step explanation:
Given:
P = 64 cmL = 5W + 8Simplify equation for perimeter and solve for W:
P = 2(L + W) = 2(5W + 8 + W) = 2(6W + 8) = 12W + 1612W + 16 = 6412W = 48W = 4 cmFind L:
L = 5*4 + 8 = 28 cmi really need help with this quition
Answer:
I really need help with this question.*
Answer:
There is no question
Step-by-step explanation:
Hope you have a great day!!
Find the absolute maximum and minimum values of the following function on the given region R. f(x,y)=5x2+5y2−10x+21; R=(x,y): x2+y2≤4, y≥0
We first compute the partial derivatives of f(x, y):
f(x, y) = 5x² + 5y² - 10x + 21
∂f/∂x = 10x - 10
∂f/∂y = 10y
The critical points of f occur where both ∂f/∂x and ∂f/∂y are equal to zero. This only happens at the point (x, y) = (1, 0). (And this point does lie inside R.)
Next, compute the Hessian matrix H(x, y) for f :
[tex]H(x, y) = \begin{bmatrix}\frac{\partial^2f}{\partial x^2} & \frac{\partial^2f}{\partial x\partial y} \\ \frac{\partial^2 f}{\partial y\partial x} & \frac{\partial^2f}{\partial y^2}\end{bmatrix} = \begin{bmatrix}10&0\\0&10\end{bmatrix}[/tex]
Since det(H(x,y)) = 100 is positive for all x and y, this means the critical point (1, 0) is a local minimum, and we have f(1, 0) = 16.
Next, we check for extrema along the boundary of R, which is comprised of a semicircle with radius 2 and the line segment connecting (-2, 0) and (2, 0).
• Parameterize the semicircular portion by
x(t) = 2 cos(t)
y(t) = 2 sin(t)
with 0 ≤ t ≤ π. Then
f(x(t), y(t)) = 20 sin²(t) + 20 cos²(t) - 20 cos(t) + 21
which is simplifies to a function of one variable t,
g(t) = 41 - 20 cos(t)
Find the extrema of g over the interval [0, π] : we have critical points when
g'(t) = 20 sin(t) = 0
which happens at t = 0 and t = π. At these points, we get local extreme values of
•• t = 0 => x = 2 and y = 0 => f(2, 0) = 21
•• t = π => x = -2 and y = 0 => f(-2, 0) = 61
• Over the line-segment portion, we take y = 0, so f(x, y) again reduces to a function of one variable:
f(x, 0) = 5x² - 10x + 21
Completing the square, we have
5x² - 10x + 21 = 5 (x - 1)² + 16
which has a maximum value of 16 when x = 1 (and this happens to be the critical point (1, 0) we found earlier).
So, over the region R, f(x, y) has
• an absolute maximum of 61 at the point (-2, 0), and
• an absolute minimum of 16 at (1, 0)
What is (−47)−(−107)=?
please help
60
Step-by-step explanation:
(-47)-(-107)
(-47)-1(-107)
-47+107
=60
Solve for k.
14k+3k–16k=5
k=
Answer:
5Step-by-step explanation:
Solve for k.
14k+3k–16k=5
17k - 16k = 5
k = 5
Dеtеrmіnе tһе range օf tһе fսnсtіօn f(х) = 2х + 1 ԝһеn tһе domain іѕ {-3, 9, 15}.
Answer:
{ - 5, 19, 31 }
Step-by-step explanation:
Substitute the values from the domain ( input) into f(x) to obtain range (output )
f(- 3) = 2(- 3) + 1 = - 6 + 1 = - 5
f(9) = 2(9) + 1 = 18 + 1 = 19
f(15) = 2(15) + 1 = 30 + 1 = 31
range is { - 5, 19, 31 }
PLS DO THE MATH INT HE PICTURE
Answer:
Area = 100cm²
Perimeter = 48cm
f/3 + 22 = 17.
» How can you isolate the variable f?
yeah
Answer:
subtract 22 from both sides then multiply 3 to both sides
Step-by-step explanation:
F/3+22=17
-22. -22
F/3 = -5
x3. x3
F= -15
Malachi has math, science, and language arts every day. How many different ways could the subjects be ordered? Explain.
City planners are planning to build a new community pool. They agree that the pool will be rectangular in shape, but the proposed dimensions changed. At the most recent meeting, it was determined that the width would remain at 11.6 meters but that the length would increase by 3.7 meters. So, the pool would now cover an area of 205.85 square meters.
Which equation can be used to determine the original length of the pool, l?
205.85=2(l+15.3)
205.85=11.6(l+3.7)
205.85=3.7(l+11.6)
The equation that can be used to determine the original length of the pool is 205.85 = 11.6(l + 3.7)
Let l be the original length of the pool.
Since the length of the pool is increased by 3.7 m, the new length L = l + 3.7.
Also, the area of the pool A = 205.85 square meter and it is a rectangle with width, W = 11.6 meters,
So, A = LW
Substituting the values of the variables into the equation, we have
A = LW
205.85 = (l + 3.7)11.6
So, the equation that can be used to determine the original length of the pool is 205.85 = 11.6(l + 3.7)
Learn more:
https://brainly.com/question/12932084
Answer:
Step-by-step explanation
205.85=11.6(l+3.7)
A business valued at $96 000 is purchased for a down payment of 25% and payments of $4000 at the end of every three months. If interest is 9% compounded monthly,
what is the size of the final payment?
Write your answer as 2,569.43.
Size of final payment is $6392.43
Given that formula for compound interest is P(1+r/n[tex])^{nt}[/tex]
where P is initial principal
r is interest rate
n is compound times per period
t is time in years
We find all the variables in the formula in order to get our answer.
Initial principal = 96000 less 25%= 72000
interest rate = 9%
number of compound times= 12
time in years =4.25 years (whole period is 4.5 years since number of payments to complete balance will take 54 months)
Hence principal and CI after 4 years and 3 months(the second to last payment)
72000(1+0.09/12)^12x4.25=$105,393.6
We use $105,393.6 as our principal to calculate the whole interest and principal for the period in order to find last payment
105393.6(1+0.09/12)^12x0.25=$107,786.03
interest for the final month = $107786.03-$105,393.6=$2392.43
To get our final payment, we add the principal payment of $4000 to final compounded interest =$6392.43
Please help pleasee right now
Ms. Mary spent $192 less than Ms.Mona on supplies for their class. Together they spent a total of $988. How much did each person spend?
Answer:
Mary:604
Mona:796
Step-by-step explanation:
Answer:
Ms. Mary spend $302
Ms. Mona spend $ 686
Step-by-step explanation: We know that Ms. Mary spend $192 less than Ms. Mona.
So we are to divide $988 by 2 which is 494
now both have $494 each but Ms. Mona spend 192 so we are to add 192 + 494 to get the right sum of how much money Ms. Mona have and take away 494-192 to get the right sum of how much money Ms. Mary spend.
192 + 494 = 686
494 - 192 = 302
Quotient of 0 and 15
Answer:
15Step-by-step explanation:
cause the first number is zero so the answer is 15 #happy learning