find the coordinate of W' after a 90° rotation of the triangle about the origin and then a reflection about the line y= -3
Answers
Answer:
(4, -8).
Step-by-step explanation:
If point W were to be rotated 90 degrees, it would rotate 90 degrees clockwise. The current point of W is (-2, 4). After a 90 degree rotation about the origin, the point will be (4, 2).
y = -3 is a horizontal line where y = -3. The y-value of the newly rotated point is 2. That is five units above the line where y = -3. So, a reflection would result in a y-value of y = -3 - 5 = -8. The x-value does not change.
So, the coordinate of W' is (4, -8).
Hope this helps!
Related Questions
what is the constant of proportionality for 4y=16
Answers
Answer:
Step-by-step explanation:
y=4x
A data set is summarized in the frequency table below. Using the table, determine the number of values less than or equal to 6.
Answers
Answer:
18
Step-by-step explanation:
Given the above table of the data set, the number of values less than or equal to 6 would be the sum of the frequencies of all values that is equal to or less than 6.
From the table above, we would add up the frequencies of the values of 6 and below, which is:
2 + 3 + 6 + 4 + 3 = 18
Answer = 18
The number of values less than or equal to 6 is 18
Calculation of the number of values:Here the number of values should be less than or equivalent to 6 represent the sum of the frequencies i.e. equal or less than 6
So, here the number of values should be
= 2 + 3 + 6 + 4 + 3
= 18
Hence, we can conclude that The number of values less than or equal to 6 is 18
Learn more about frequency here: https://brainly.com/question/20875379
1. An architect is designing a house for the Mullet family. In the design he
must consider the desires of the family and the local building codes. The
rectangular lot on which the house will be built has 91 feet of frontage
on a lake and is 158 feet deep.
Answers
Answer:
An architect is designing a house for the Frazier family. In the design he must consider the desires of the family and the local building codes. The rectangular lot on which the house will be built has 91 feet of frontage on a lake and is 158 feet deep.
The building codes states that one can build no closer than 10 ft. to the lot line. Write an inequality and solve to see how long the front of the house facing the lake may be.
------
length = 91 - 2*10 = 71 ft.
-------------------------------
The Fraziers requested that the house contain no less 2800 ft square and no more than 3200 ft square of floor sample. Write an inequality to represent the range of permissible widths for the house.
---------
2800 <= area <= 3200
2800 <= (length)(width) <= 3200
2800 <= 71w <= 3200
39.44 <= width <= 45.07
hope it helpsss
Step-by-step explanation:
Answer: An architect is designing a house for the Frazier family. In the design he must consider the desires of the family and the local building codes. The rectangular lot on which the house will be built has 91 feet of frontage on a lake and is 158 feet deep.
The building codes states that one can build no closer than 10 ft. to the lot line. Write an inequality and solve to see how long the front of the house facing the lake may be.
------
length = 91 - 2*10 = 71 ft.
-------------------------------
The Fraziers requested that the house contain no less 2800 ft square and no more than 3200 ft square of floor sample. Write an inequality to represent the range of permissible widths for the house.
---------
2800 <= area <= 3200
2800 <= (length)(width) <= 3200
2800 <= 71w <= 3200
39.44 <= width <= 45.07
xdy+ydx= ? (a) d(x+y) (b) d(x/y) (c) d(x-y) (d) d(xy)
Answers
Answer:
d) d(x)
Step-by-step explanation:
Derivative Rules
Product Rule xy -> d(xy) = xdy + ydxExplain how estimating the quotient helps you place the first
digit in the quotient of a division problem.
Answers
Step-by-step explanation:
look at the picture and if you still need help let me know or if this doenst help then well im sorry lol
The principal P is borrowed at a simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume there are 360 days in a year. P = $7000, r = 0.2%, t = 6months
Answers
Answer:
$7
Step-by-step explanation:
Simple interest formula:
I = Prt
6 months = 6 * 30 days = 180 days
1 year = 360 days
t = (180 days)/(360 days) = 0.5
I = $7000 * 0.002 * 0.5
I = $7
Answer:
$7
Step-by-step explanation:
Recall that simple interest is given by
I = Prt,
Where :
I = interest (we are asked to find this)
P = principal amount = given as $7000
r = rate = given as 0.2% = 0.002
t = time in years = given as 6 months = 0.5 years
SImply substitute the known values into the equation above:
I = Prt
= (7000)(0.002)(0.5)
= $7
hellllllllppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answers
Answer:
see below.
Step-by-step explanation:
1st row has four small boxes
2nd row has three big boxes
big box 1 has no items ragged in it.
big box 2 has small box 1 and also small box 1 dragged into it.
big box 3 has small box 3 and small box 4 dragged into it.
A hypothesis will be used to test that a population mean equals 9 against the alternative that the population mean is less than 9 with known variance . What is the critical value for the test statistic for the significance level of 0.020
Answers
Answer:
-2.05
Step-by-step explanation:
From the given information,
Let consider [tex]\mu[/tex] to represent the population mean
Therefore,
The null and alternative hypothesis can be stated as :
[tex]H_o :\mu=9[/tex]
[tex]H_1 :\mu<9[/tex]
From the hypothesis , the alternative hypothesis is one tailed (left)
when the level of significance = 0.020, the Z- critical value can be determined from the standard normal distribution table
Hence, the Z-critical value at ∝ = 0.020 is -2.05
25 POINTS
Examine the following solution to a conversion problem. Do you see a mistake? If so, identify the location of the first mistake and explain why it is incorrect.
Original Problem: Convert 3.25 kg to mg
(1) 3.25 kg
(2) 1 kg = 1000 g
(3) 1000 mg = 1g
= (4) 3.25 mg
A) The conversion is not possible.
B) The first problem occurs in column (1). The problem should begin with mg.
C) The first problem occurs in column (2). 1 kg is not equal to 1000 g, so that should not be used as the conversion factor.
D) The first problem occurs in column (2). The conversion factor is upside down (grams should be on top, and kg should be on bottom).
E) The first problem occurs in column (4). The multiplication and division was performed incorrectly.
F) No mistakes.
Thanks a bunch!
Answers
Answer:
[tex]\boxed{\sf Option \ E}[/tex]
Step-by-step explanation:
(1) 3.25 kg
(2) 1 kg = 1000 g
(3) 1000 mg = 1g
= (4) 3.25 mg
The first problem occurred in column (4) where we actually had to multiply it by 1000 but we divided it by 1000 and so our conversion was incorrect.
The correct form of it is:
1) 3.25 kg
2) 1 kg = 1000 g ; 3.25 kg = 3250 g
3) 1 g = 1000 mg ; 3250 * 1000 = 3,250,000 mg
4) Answer = 3,250,000 mg
Answer:
[tex]\boxed{\sf Option \ E}[/tex]
Step-by-step explanation:
1 kg = 1000 g
1000 mg = 1g
3.25 kilograms is to be multiplied by 1000 to get the value in grams. Then the result should be multiplied again by 1000 to get the value in milligrams.
3.25 kg ⇒ 3250 g ⇒ 3250000 mg
The first problem occurs in column (4). The multiplication and division was performed incorrectly.
im not sure what it is asking me to do
Answers
Explanation:
Find the probability that x is smaller or equal to 0
In the table the number that are smaller or equal to 0 are -5,-3,-2,0
And we are given the probability of each number
So all you have to do is add all the probability of the number that are smaller or equal to 0:
0.17 + 0.13 + 0.33 + 0.16 = P
0.79 = P
Answer:
0.79Step-by-step explanation:
[tex]p(x \leqslant 0) = p( - 5) + p( - 3) + p( - 2) + p(0)[/tex]
[tex] = 0.17 + 0.13 + 0.33 + 0.16 [/tex]
[tex] = 0.79[/tex]
Hope this helps...
Best regards!!
Change Y - 4X = 0 to the slope-intercept form of the equation of a line.
Answers
Answer:
y=4x
Step-by-step explanation:
Add 4x to both sides to get y=mx+b
0 is y-intercept.
4x is the slope.
Point C is on the graph of the function y = x2 – 3. Its x-coordinate is 4. Which ordered pair gives the location of point C? A.(4, 42 – 3) B.(4, 2 + 3) C.(42, 42 – 3) D.(4, 42)
Answers
Answer:
B (4, 2+3)
Step-by-step explanation:
To do this you fill in x with 4 so the equation becomes y = (4)2 - 3
You then solve to y = 8 - 3
then 8 - 3 is 5.
Making the coordinates (4, 5) and in this case with the answers (4, 2+3)
Answer:
A. (4, 4^2 – 3)
A line passes through the points ( – 4, – 2) and ( - 1, - 2). Determine the slope of the line.
Answers
Answer: -4/3
Step-by-step explanation:
Formula to find a slope of two given points is
y(sub2) - y(sub1) / x(sub2) - x(sub1)
Plug the values in to get the answer.
-2 - 2 / -1 - (-4)
-4/3
objective: central limit theorem assumptions. the factor(s) to be considered when assessing if the central theorem holds is/are
Answers
Answer:
Sample size
Step-by-step explanation:
Central Limit Theorem states that population with mean and standard deviation and if the sample size is large then the distribution of sample mean will be will be normally distributed. The central limit theorem holds assumptions that the factors to be considered when assessing central limit theorem is sample size.
The CLT is the factor(s) to be considered when assessing if the central theorem holds are sample.
It is given that the objective that central limit theorem assumptions. the factor(s) to be considered when assessing if the central theorem holds.
It is required to describe the above theorem.
What is the central limit theorem?It is defined as the in statistics the assumption holds that the sample means distribution of arbitrary variables follows a normal distribution or close to normal distribution if the sample size is big.
We have an objective:
The CLT is the factor to be considered when assessing if the CLT holds a large sample size.
If we draw the random sample data and its measures, the Central limit theorem explains the distribution will explain the normal bell curve, the mean of the parameters and the distribution will be the same.
Thus, the CLT is the factor(s) to be considered when assessing if the central theorem holds are sample.
Learn more about the Central limit theorem here:
https://brainly.com/question/5027686
Ten thousand raffle tickets are sold for $1 each. One first prize of $2000, 4 second prizes of $700 each, and 8 third prizes of $300 each are to be awarded, with all winners selected randomly. If you purchase one ticket, what are your expected winnings? 132 cents -$0.28 72 cents -$0.88
Answers
Answer:
72 cents.
Step-by-step explanation:
The expected winnings is the amount times the probability that you will get that amount.
2,000 * (1/10,000) = 2,000 / 10,000 = 2 / 10 = 0.2.
700 * (4 / 10,000) = 2,800 / 10,000 = 28 / 100 = 0.28.
300 * (8 / 10,000) = 2,400 / 10,000 = 24 / 100 = 0.24.
0.2 + 0.28 + 0.24 = 0.72.
Hope this helps!
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A car manufacturer is reducing the number of incidents with the transmission by issuing a voluntary recall. During week 3 of the recall, the manufacturer fixed 391 cars. In week 13, the manufacturer fixed 361 cars. Assume that the reduction in the number of cars each week is linear. Write an equation in function form to show the number of cars seen each week by the mechanic. f(x) = 3x + 400 f(x) = 3x + 391 f(x) = −3x + 391 f(x) = −3x + 400
Answers
Answer:
f(x)= -3x + 400
Step-by-step explanation:
[tex]\frac{x-x_{1} }{x_{2}-x_{1} } = \frac{y-y_{1} }{y_{2}-y_{1} }[/tex]
[tex]\frac{x-3}{13-3} =\frac{y-391}{361-391}[/tex]
-3 ( x-3 ) = (y - 391 )
-3x + 400
Answer:
he is correct
Step-by-step explanation:
A local Internet provider wants to test the claim that the average time a family spends online on a Saturday is at least 7 hours. To test this claim, the Internet provider randomly samples 30 households and finds that these families' mean number of hours spent on the Internet on a Saturday was 6 hours with a standard deviation of 1.5 hours. At a level of significance of 0.05, can the Internet provider's claim be supported?
A) Fail to Reject the Null Hypothesis
B) Reject the Null Hypothesis
C) Reject The Alternative Hypothesis
D) Fail to Reject the Alternative Hypothesis
E) Accept the Null Hypothesis
F) Accept the Alternative Hypothesis
Answers
Answer:
A) Fail to Reject the Null Hypothesis
Step-by-step explanation:
Given that:
A local Internet provider wants to test the claim that the average time a family spends online on a Saturday is at least 7 hours.
sample size = 30
sample mean [tex]\bar x[/tex] = 6
standard deviation [tex]\sigma[/tex] = 1.5
level of significance ∝ = 0.05
The null hypothesis and the alternative hypothesis can be computed as:
[tex]\mathbf{ H_o: \mu \leq 7}[/tex]
[tex]\mathbf{ H_i: \mu \geq 7}[/tex]
The test statistic can be computed as:
[tex]z = \dfrac{\bar x - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \dfrac{6 -7} {\dfrac{1.5}{\sqrt {30}}}[/tex]
[tex]z = \dfrac{-1} {\dfrac{1.5}{5.477}}}[/tex]
[tex]z = \dfrac{-5.477} {1.5}[/tex]
z = -3.65
Given that ;
level of significance of 0.05;
z = -3.65
degree of freedom = 30 - 1 = 29
The p-value = P([tex]t_{29}[/tex] > - 3.65)
= 0.9998
Decision Rule: Reject [tex]H_o[/tex] if p-value is less than the level of significance
But since the p -value is greater than the level of significance, we conclude that There is no enough evidence to support the Internet provider claim, Therefore;
Fail to Reject the Null Hypothesis
You weigh six packages and find the weights to be 26, 18,58,22,54,and 50 ounces. If you include a package that weighs 66 ounces, which will increase more, the median or the mean?
Answers
Answer:
Step-by-step explanation:
The mean which is also known as the average is determined by dividing the sum of the weight of the packages by the total number of packages. From the information given,
Mean = (26 + 18 + 58 + 22 + 54 + 50)/6 = 38
If you include a package that weighs 66 ounces, the new mean would be
New mean = (26 + 18 + 58 + 22 + 54 + 50 + 66)/7 = 42
For the median, we would rearrange the weights in ascending order. It becomes
18, 22, 26, 50, 54, 58
Median = (26 + 50)/2 = 38
By adding the new weight, it becomes
18, 22, 26, 50, 54, 58, 66
New median = 50
It can be seen that both the median increased by more. It increased by 12 while the mean increased by 4
Answer: The mean which is also known as the average is determined by dividing the sum of the weight of the packages by the total number of packages. From the information given, Mean = (26 + 18 + 58 + 22 + 54 + 50)/6 = 38If you include a package that weighs 66 ounces, the new mean would be New mean = (26 + 18 + 58 + 22 + 54 + 50 + 66)/7 = 42For the median, we would rearrange the weights in ascending order. It becomes18, 22, 26, 50, 54, 58Median = (26 + 50)/2 = 38By adding the new weight, it becomes18, 22, 26, 50, 54, 58, 66New median = 50It can be seen that both the median increased by more. It increased by 12 while the mean increased by 4
Step-by-step explanation:
A group of children is trying to share a pile of stickers. If every
child gets two stickers, there will be 7 stickers left over. If two
children do not get any stickers, then each of the remaining
children will get exactly 3 stickers.
How many children are in the group?
Answers
Answer:
7 children
Step-by-step explanation:
Answer:
7 children is the correct answer
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The rate of earnings is 6% and the cash to be received in four years is $20,000. The present value amount, using the following partial table of present value of $1 at compound interest, is
Answers
Answer:
$15,842
Step-by-step explanation:
We use the Present value formula
Present Value = Future value/(1 + r)ⁿ
r = 6% = 0.06
n = 4 years
Future value = $20,000
Present value = 20,000/(1 + 0.06)⁴
= $15841.873265
≈ $15,842
A manufacturing company has an old machine which produces 25 components per hour. The company has recently installed a new machine which produces 35 components per hour. Yesterday, both machines were in operation for different periods of time. If 430 components were produced when the total number of hours of operation was 14 hours, determine for how many hours each machine was in operation
Answers
Answer: old machine 150, new machine 280
Step-by-step explanation:
given data:
Old machine = 25t
New machine = 35t
where t = hrs
we dont know the time for old machine so we assume it to be ( t ),
while that of the new machine is ( 14-t ) hours for new machine, and sum of 430 components.
therefore;
25t +490 - 35t = 430
-10t = -60
divide both sides by -10
t = 6 hours for the first machine.
6hrs * 25 components /hr
= 150 component parts For old machine.
for new machine
= 14 - t ........... eq1.
where ( t = 6 ), substitute t into the equation
= 14 - 6
= 8 hours for the second machine
= 8 * 35
= 280 components parts
Please explain this to me If f(x)=4x-2 than f(x-1)= A. 4x^2-6x+2 B. 4x^2+2x+2 C. 4x+2 D. 4x-6 E. 4x-1
Answers
Answer:
D. 4x − 6
Step-by-step explanation:
f(x) = 4x − 2
f(x−1) = 4(x−1) − 2
f(x−1) = 4x − 4 − 2
f(x−1) = 4x − 6
This table shows values that represent an exponential function. What is the average rate of change for this function for the interval from x=3 to x=5?
Answers
Answer: The average rate of change for this function for the interval from x=3 to x=5 is 12.
Step-by-step explanation:
Complete question is provided in the attachment below.
Formula: The average rate of change for this function y=f(x) for the interval from x= a to x= b :
[tex]Rate =\dfrac{f(b)-f(a)}{b-a}[/tex]
Let y= f(x) for the given table:
At x= 3 , f(3)=8 and f(5)=32
Then, the average rate of change for this function for the interval from x=3 to x=5:
[tex]Rate=\dfrac{f(5)-f(3)}{5-3}\\\\=\dfrac{32-8}{2}\\\\=\dfrac{24}{2}=12[/tex]
Hence, the average rate of change for this function for the interval from x=3 to x=5 is 12. (Option A is correct.)
During a camping trip, a group went one -third of the total distance by boat, 10km by foot and One – sixth of it by riding horses. Find the total distance of the trip.
Answers
Explanation:
Let d be the total distance
d = (1/3)d + 10 + (1/6)d
(6/6)d = (2/6)d + 60/6 + (1/6)d
6d = 2d + 60 + d
6d = 3d + 60
3d = 60
d = 60/3 = 20
in the diagram ,a and 46° are complementary angles. It is given that a and b are supplementary angles and the angle conjugate to c is 283°. Calculate the values of a,b,c and d. pleaseeeee answer soonn
Answers
Answer:
[tex]a=44^{\circ},b=136^{\circ},c=77^{\circ},d=57^{\circ}[/tex].
Step-by-step explanation:
It is given that a and 46° are complementary angles.
[tex]a+46^{\circ}=90^{\circ}[/tex]
[tex]a=90^{\circ}-46^{\circ}[/tex]
[tex]a=44^{\circ}[/tex]
It is given that a and b are supplementary angles.
[tex]a+b=180^{\circ}[/tex]
[tex]44^{\circ}+b=180^{\circ}[/tex]
[tex]b=180^{\circ}-44^{\circ}[/tex]
[tex]b=136^{\circ}[/tex]
Angle conjugate to c is 283°.
[tex]c+283^{\circ}=360^{\circ}[/tex]
[tex]c=360^{\circ}-283^{\circ}[/tex]
[tex]c=77^{\circ}[/tex]
Sum of all angles at a point is 360 degrees.
[tex]a+b+c+d+46^{\circ}=360^{\circ}[/tex]
[tex]44^{\circ}+136^{\circ}+77^{\circ}+d+46^{\circ}=360^{\circ}[/tex]
[tex]d+303^{\circ}=360^{\circ}[/tex]
[tex]d=360^{\circ}-303^{\circ}[/tex]
[tex]d=57^{\circ}[/tex]
Therefore, [tex]a=44^{\circ},b=136^{\circ},c=77^{\circ},d=57^{\circ}[/tex].
Suppose that the local sales tax rate is 6% and you purchase a computer for $1260.
a. How much tax is paid?
b. What is the computer’s total cost?
Answers
Answer:
a. $75.60
b. $1335.60
Step-by-step explanation:
A. First convert the percentage to a decimal.
6% = 0.06
Multiply the cost of the computer by the decimal to find the tax paid.
$1260 × 0.06 = $75.60
B. To find the total cost, add the cost of the computer with the tax.
$1260 + $75.60 = $1335.60
B: $1335.60
A rectangular piece of sheet metal has an area of 1200 in2. It is going to be bent into a cylinder with volume 600 in3. What are the dimensions of rectangular piece of sheet metal
Answers
Answer:
x=6.28 inches
y=191.08 inches
Step-by-step explanation:
Let the dimensions of the rectangle be x and y
Area of the rectangular sheet
x*y=1200 in^2}
x = circumference of the cylinder
This means x=2πr
Volume of a cylinder=πr^2h
h=y
Volume of the cylind=πr^2(y)=600 in^3
From x=2πr
r=x/2π
Substitute r=x/2π into Volume=πr^2(y)=600 in^3
We have,
Volume of the cylinder=πr^2(y)=600 in^3
π*(x/2π)^2(y)=600
(x^2/4π)y=600
Recall, x*y=1200
y=1200/x
Substitute y=1200/x into (x^2/4π)y=600
(x^2/4π)y=600
(x^2/4π)(1200/x)=600
1200x/4π=600
Multiply both sides by 4π
(x^2/4π)(1200/x)(4π)=600*4π
1200x=2400π
Divide both sides by 1200
1200x/1200 = 2400π/1200
x=2π
Substitute x=2π into y=1200/x
We have,
y=1200/2π
y=600/π
The dimensions are x=2π and y=600/π
Let π=3.14
x=2π
=2(3.14)
=6.28 inches
y=600/π
=600/3.14
=191.08 inches
Part A Each time you press F9 on your keyboard, you see an alternate life for Jacob, with his status for each age range shown as either alive or dead. If the dead were first to appear for the age range of 75 to 76, for example, this would mean that Jacob died between the ages of 75 and 76, or that he lived to be 75 years old. Press F9 on your keyboard five times and see how long Jacob lives in each of his alternate lives. How long did Jacob live each time? Part B The rest of the potential clients are similar to Jacob, but since they’ve already lived parts of their lives, their status will always be alive for the age ranges that they’ve already lived. For example, Carol is 44 years old, so no matter how many times you press F9 on your keyboard, Carol’s status will always be alive for all the age ranges up to 43–44. Starting with the age range of 44–45, however, there is the possibility that Carol’s status will be dead. Press F9 on your keyboard five more times and see how long Carol lives in each of her alternate lives. Remember that she will always live to be at least 44 years old, since she is already 44 years old. How long did Carol live each time? Part C Now you will find the percent survival of each of your eight clients to the end of his or her policy using the simulation in the spreadsheet. For each potential client, you will see whether he or she would be alive at the end of his or her policy. The cells in the spreadsheet that you should look at to determine this are highlighted in yellow. Next, go to the worksheet labeled Task 2b and record either alive or dead for the first trial. Once you do this, the All column will say yes if all the clients were alive at the end of their policies or no if all the clients were not alive at the end of their policies. Were all the clients alive at the end of their policies in the first trial? Part D Next, go back to the Task 2a worksheet, press F9, and repeat this process until you have recorded 20 trials in the Task 2b worksheet. In the Percent Survived row at the bottom of the table on the Task 2b worksheet, it will show the percentage of times each client survived to the end of his or her policy, and it will also show the percentage of times that all of the clients survived to the end of their respective policies. Check to see whether these percentages are in line with the probabilities that you calculated in questions 1 through 9 in Task 1. Now save your spreadsheet and submit it to your teacher using the drop box. Are your probabilities from the simulation close to the probabilities you originally calculated?
Answers
Step-by-step explanation:
brain list me please......
Answer:
Jacob:
Alive 69-70
alive 79-80
alive 62-63
alive 73-74
alive 78-Died 79
Carol:
alive 88-89
alive 67-68
alive 99-100
alive 73-74
alive 94- Died 95
Step-by-step explanation:
Suppose that Vera wants to test the hypothesis that women make less money than men doing the same job. According to the Bureau of Labor Statistics (BLS), the median weekly earnings for men in the professional and related occupation sector in 2015 was $1343. Vera collected median weekly earnings data for women in 2015 from a random subset of 18 positions in the professional and related occupation sector. The following is the sample data. $1811, $728, $1234, $966, $953, $1031, $990, $633, $796, $1325, $1448, $1125, $1144, $1082, $1145, $1256, $1415, $1170 Vera assumes that the women's median weekly earnings data is normally distributed, so she decides to perform a t-test at a significance level of α = 0.05 to test the null hypothesis, H0:µ=1343H0:μ=1343 against the alternative hypothesis, H1:µ<1343H1:μ<1343 , where µμ is the population mean. If the requirements for performing a t-test have not been met, only answer the final question. Otherwise, answer all five of the following questions. First, compute the mean, x⎯⎯⎯x¯ , of Vera's sample. Report your answer with two decimals of precision.
Answers
Answer:
There is sufficient evidence to conclude that women make less money than men doing the same job.
Step-by-step explanation:
The hypothesis for the test can be explained as follows:
H₀: Women does not make less money than men doing the same job, i.e. [tex]\mu\geq \$1343[/tex].
Hₐ: Women make less money than men doing the same job, i.e. [tex]\mu<\$1343[/tex].
From the provided data compute the sample mean and standard deviation:
[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{18}[1811+728+...+1170]=1125.11\\\\s=\sqrt{\frac{1}{n-1}\sum (X-\bar x)^{2}}=\sqrt{\frac{1}{18-1}\times 1322541.86}=278.92[/tex]
Compute the test statistic as follows:
[tex]t=\frac{\bar x-\mu}[\s/\sqrt{n}}=\frac{1125.11-1343}{278.92/\sqrt{18}}=-3.143[/tex]
The test statistic value is -3.143.
Compute the p-value as follows:
[tex]p-value=P(t_{n-1}<-3.143)=P(t_{17}<-3.143)=0.003[/tex]
*Use a t-table.
The p-value of the test is 0.003.
The p-value of the test is very small for all the commonly used significance level. The null hypothesis will be rejected.
Conclusion:
There is sufficient evidence to conclude that women make less money than men doing the same job.
Tensile strength tests were performed on two different grades of aluminum spars used in manufacturing the wing of a commercial transport aircraft. From past experience with the spar manufacturing process and the testing procedure, the standard deviations of tensile strengths are assumed to be known. The data obtained are as follows:
n_1 = 10
x_1 = 87.6
σ_1 = 1
n_2 = 12
x^2 = 74.5
σ_2 = 1.5.
Required:
If μ _1 and μ _2 denote the true mean tensile strengths for the two grades of spars. Construct a 90 percentage confidence interval on the difference in mean strength.
Answers
Answer:
(12.141, 14.059)
Step-by-step explanation:
Explanation is provided in the attached document.