ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answers
Answer:
B. F(x) = 3(x - 2)² - 2
Step-by-step explanation:
→The function F(x) narrowed, meaning the absolute value being multiplied to the function is greater than 1.
→The function F(x) flipped over the x-axis, this means that the number being multiplied has to be a negative.
→The function F(x) shifted to the left 2 units, this means there needs to be a 2 being added.
→The function F(x) shifted downwards 2 units, meaning there needs to be a 2 being subtracted from the whole function.
This gives us the correct answer of "B. F(x) = 3(x - 2)² - 2."
Related Questions
The bottom of a ladder must be placed 3 ft. from a wall. The ladder is 12 feet long. How far above the ground does the ladder touch the wall? Round your answer to the nearest tenth.
Answers
Use the Pythagorean theorem to solve.
Height = sqrt(12^2 -3^2)
Height = sqrt(144-9)
Height = sqrt(135)
Height = 11.6189 = 11.6 feet
. A certain coin is a circle with diameter 18 mm. What is the exact area of either face of the coin in terms of p?
Answers
Answer:
[tex] r =\frac{D}{2}=\frac{18mm}{2}= 9mm[/tex]
The area is given by:
[tex]A= \pi r^2[/tex]
And replacing we got:
[tex] A=\pi (9mm)^2 =81\pi mm^2[/tex]
So then we can conclude that the area of the coin is [tex] 81\pi[/tex] mm^2
Step-by-step explanation:
For this case we know that we have a coin with a diamter of [tex] D =18mm[/tex], and by definition the radius is given by:
[tex] r =\frac{D}{2}=\frac{18mm}{2}= 9mm[/tex]
The area is given by:
[tex]A= \pi r^2[/tex]
And replacing we got:
[tex] A=\pi (9mm)^2 =81\pi mm^2[/tex]
So then we can conclude that the area of the coin is [tex] 81\pi[/tex] mm^2
Please help! Correct answer only, please! Find the following product if possible. Explain if it is not possible. A. B. C. D.
Answers
Answer: A
Step-by-step explanation:
To multiply matrices, multiply each term in Row 1 of the first matrix with each term in Column 1 of the second matrix and then find their sum. Repeat for Row1×Column2, Row2×Column1, and Row2×Column2.
[tex]\left[\begin{array}{ccc}1&4&-1\\3&2&2\end{array}\right] \times \left[\begin{array}{cc}2&-1\\0&3\\5&2\end{array}\right] \\\\\\=\left[\begin{array}{ccc}1(2)+4(0)-1(5)&1(-1)+4(3)-1(2)\\3(2)+2(0)+2(5)&3(-1)+2(3)+2(2)\end{array}\right] \\\\\\=\left[\begin{array}{cc}-3&9\\16&7\end{array}\right][/tex]
Older people often have a hard time finding work. AARP reported on the number of weeks it takes a worker aged 55 plus to find a job. The data on number of weeks spent searching for a job collected by AARP (AARP Bulletin, April 2008) Shows that the mean number of weeks a worker aged 55 plus spent to find a job is 22 weeks. The sample standard deviation is 11.89 weeks and sample size is 40.a) Provide a point estimate of the population mean number of weeks it takes a worker aged 55 plus to find a job.
b) At 95% confidence, what is the margin of error?
c) What is the 95% confidence interval estimate of the mean?
d) Discuss the degree of skewness found in the sample data. What suggestion would you make for a repeat of this study?
Answers
Answer:
Step-by-step explanation:
Hello!
Be the variable of interest:
X: Number of weeks it takes a worker aged 55 plus to find a job
Sample average X[bar]= 22 weeks
Sample standard deviation S= 11.89 weeks
Sample size n= 40
a)
The point estimate of the population mean is the sample mean
X[bar]= 22 weeks
It takes on average 22 weeks for a worker aged 55 plus to find a job.
b)
To estimate the population mean using a confidence interval, assuming the variable has a normal distribution is
X[bar] ± [tex]t_{n_1; 1-\alpha /2}[/tex] * [tex]\frac{S}{\sqrt{n} }[/tex]
[tex]t_{n-1; 1-\alpha /2}= t_{39; 0.975}= 2.023[/tex]
The structure of the interval is "point estimate" ± "margin of error"
d= [tex]t_{n_1; 1-\alpha /2}[/tex] * [tex]\frac{S}{\sqrt{n} }[/tex]= 2.023*[tex](\frac{11.89}{\sqrt{40} })[/tex]= 3.803
c)
The interval can be calculated as:
[22 ± 3.803]
[18.197; 25.803]
Using s 95% confidence level, you'd expect the population mean of the time it takes a worker 55 plus to find a job will be within the interval [18.197; 25.803] weeks.
d)
Job Search Time (Weeks)
21 , 14, 51, 16, 17, 14, 16, 12, 48, 0, 27, 17, 32, 24, 12, 10, 52, 21, 26, 14, 13, 24, 19 , 28 , 26 , 26, 10, 21, 44, 36, 22, 39, 17, 17, 10, 19, 16, 22, 5, 22
To study the form of the distribution I've used the raw data to create a histogram of the distribution. See attachment.
As you can see in the histogram the distribution grows gradually and then it falls abruptly. The distribution is right skewed.
Write the coordinates of the vertices of a triangle A'B'C' that results from a translation of triangle ABC two units to the right and four units down .
Answers
Answer:
A'(4,-6) , B'(0,1), C'(-2,-2)
Step-by-step explanation:
From the given graph the coordinates of ΔABC area A (2,-2), B(-2,5) and C(-4,2)
If a translation is applied on ΔABC two units to the right and four units down to create ΔA'B'C'.
Then to find the coordinates of ΔA'B'C' will be we need to apply the translation rule
[tex](x,y)\rightarrow(x+2,y-4)[/tex]
Now, [tex]A(2,-2)\rightarrow A'(2+2,-2-4)=A'(4,-6)[/tex]
[tex]B(-2,5)\rightarrow B'(-2+2,5-4)=B'(0,1)[/tex]
and [tex]C(-4,2)\rightarrow C'(-4+2,2-4)=C'(-2,-2)[/tex]
George and Paula are running around a circular track. George starts at the westernmost point of the track, and Paula starts at the easternmost point. The illustration below shows their starting positions and running directions. They start running toward each other at constant speeds. George runs at 9 feet per second. Paula takes 50 seconds to run a lap of the track. George and Paula pass each other after 14 seconds.
After running for 4 minutes, how far east of his starting point is George?
Answers
Answer:
George is 43.20 ft East of his starting point.
Step-by-step explanation:
Let Paula's speed be x ft/s
George's speed = 9 ft/s
Note that speed = (distance)/(time)
Distance = (speed) × (time)
George takes 50 s to run a lap of the track at a speed of y ft/s
Meaning that the length of the circular track = y × 50 = 50y ft
George and Paula meet 14 seconds after the start of the run.
Distance covered by George in 14 seconds = 9 × 14 = 126 ft
Distance covered by Paula in 14 seconds = y × 14 = 14y ft
But the sum of the distance covered by both runners in the 14 s before they first meet each other is equal to the length of the circular track
That is,
126 + 14y = 50y
50y - 14y = 126
36y = 126
y = (126/36) = 3.5 ft/s.
Hence, Paula's speed = 3.5 ft/s
Length of the circular track = 50y = 50 × 3.5 = 175 ft
So, in 4 minutes (240 s), with George running at 9 ft/s, he would have ran a total distance of
9 × 240 = 2160 ft.
2160 ft around a circular track of length 175 ft, means that George would have ran a total number of laps (2160/175) = 12.343 laps.
Breaking this into 12 laps and 0.343 of a lap from the starting point. 0.343 of a lap = 0.343 × 175 = 60 ft
So, 60 ft along a circular track subtends an angle θ at the centre of the circle.
Length of an arc = (θ/360°) × 2πr
2πr = total length of the circular track = 175
r = (175/2π) = 27.85 ft
Length of an arc = (θ/360) × 2πr
60 = (θ/360°) × 175
(θ/360°) = (60/175) = 0.343
θ = 0.343 × 360° = 123.45°
The image of this incomplete lap is shown in the attached image,
The distance of George from his starting point along the centre of the circular track = (r + a)
But, a can be obtained using trigonometric relations.
Cos 56.55° = (a/r) = (a/27.85)
a = 27.85 cos 56.55° = 15.35 ft
r + a = 27.85 + 15.35 = 43.20 ft.
Hence, George is 43.20 ft East of his starting point.
Hope this Helps!!!
Zelie planned for a square pool to have a side length of 28 ft but found that it needs to be 14 ft long to fit in her backyard. She found the change of scale below. Which is Zelie’s error? Zelie should have divided both numbers by 14. Zelie should have written the ratio as 28/7. Zelie should have written the ratio as 14/8. Zelie should have subtracted 14 from both numbers.
Answers
Answer:
Zelie should have divided both numbers by 14 to find the scale (2)
Step-by-step explanation:
Answer:
the answers A.
Step-by-step explanation:
I TOOK THE QUIZ edg 2020
How many real solutions does the function shown on the graph have?
Answers
Answer:
2 real solutions
Step-by-step explanation:
A company plans to manufacture a rectangular box with a square base, an open top, and a volume of 452 cm3. The cost of the material for the base is 0.4 cents per square centimeter, and the cost of the material for the sides is 0.6 cents per square centimeter. Determine the dimensions of the box that will minimize the cost of manufacturing it. What is the minimum cost
Answers
Answer:
The box has sides of 11.07 cm and height of 3.69 cm.
The cost (minimum) is 147 cents per box.
Step-by-step explanation:
We have a box with open top, with a volume of 452 cm^3.
Let x: base side of the box, in cm, and y: height of the box, in cm.
Then, the volume can be expressed as:
[tex]V=x^2\cdot y=452\\\\y=452x^{-2}[/tex]
This box has 4 sides and 1 base. The material cost is 0.4 cents/cm^2 for the base and 0.6 cents/cm^2 for the sides.
Then, we can write the cost as:
[tex]C=0.4\cdot 1\cdot (x^2)+0.6\cdot 4\cdot (xy)\\\\\\xy=x\cdot(452x^{-2})=452x^{-1}\\\\\\C=0.4x^2+2.4(452x^{-1})\\\\\\C=0.4x^2+1084.8x^{-1}[/tex]
The value for x that gives a minimum cost can be found deriving the function C and equal to 0:
[tex]\dfrac{dC}{dx}=0.4(2x)+1084.8(-1\cdot x^{-2})=0\\\\\\0.8x-1084.8x^{-2}=0\\\\0.8x=1084.8x^{-2}\\\\0.8x^{1+2}=1084.8\\\\x^3=1084.8/0.8=1356\\\\x=\sqrt[3]{1356}\\\\x=11.07[/tex]
The height can be calculated with the equation:
[tex]y=452x^{-2}=452(11.07^{-2})=452\cdot 0.00816 =3.69[/tex]
The minimum cost can be calculated as:
[tex]C=0.4x^2+1084.8x^{-1}\\\\C(11.07)=0.4(11.07)^2+1084.8(11.07)^{-1}\\\\C(11.07)=0.4\cdot 122.51+1084.8\cdot0.09\\\\C(11.07)=49+98\\\\C(11.07)=147[/tex]
What postulate would justify the following statement?
If D is between A and B, than AD+DB=AB
Answers
Answer:
A, D and B must be in a straight line.
Step-by-step explanation:
If D is between A and B, than AD+DB=AB
This would mean A, D and B would be in a straight line.
which set of sides make a right triangle
Answers
Answer:
A right triangle consists of two legs and a hypotenuse.
Step-by-step explanation:
The two legs meet at a 90° angle and the hypotenuse is the longest side of the right triangle and is the side opposite the right angle. There are a couple of special types of right triangles, like the 45°-45° right triangles and the 30°-60° right triangle.
Some have argued that throwing darts at the stock pages to decide which companies to invest in could be a successful stock-picking strategy. Suppose a researcher decides to test this theory and randomly chooses 250 companies to invest in. After 1 year, 135 of the companies were considered winners; that is, they outperformed other companies in the same investment class. To assess whether the dart-picking strategy resulted in a majority of winners, the researcher tested Upper H 0: pequals0.5 versus Upper H 1: pgreater than0.5 and obtained a P-value of 0.1030. Explain what this P-value means and write a conclusion for the researcher.
Answers
Answer:
The calculated value Z = 1.2903 < 1.96 at 0.05 level of significance
Null hypothesis is accepted at 0.05 level of significance
The population proportion is equal to 0.5
Step-by-step explanation:
Step (i):-
Given random sample size ' n' = 250
Sample proportion 'p'
[tex]p= \frac{x}{n} = \frac{135}{250} = 0.54[/tex]
Given Population proportion P = 0.5
Q = 1-P = 1-0.5 =0.5
Null Hypothesis : H₀ : P = 0.5
Alternative Hypothesis : H₁ : P≥ 0.5
Step(ii):-
Test statistic
[tex]Z = \frac{p - P}{\sqrt{\frac{PQ}{n} } }[/tex]
[tex]Z = \frac{0.54-0.5}{\sqrt{\frac{0.5 X 0.5}{250} } }[/tex]
Z = 1.2903
Level of significance α = 0.05
Z₀.₀₅ = 1.96
The calculated value Z = 1.2903 < 1.96 at 0.05 level of significance
Null hypothesis is accepted at 0.05 level of significance
Step(iii):-
P- value
The probability of test statistic
P(Z > 1.2903) = 0.5 - A ( 1.2903)
= 0.5 - 0.4015
= 0.0985≅ 0.10
i) P- value =0.10 > α = 0.05
null hypothesis is accepted
Conclusion:-
The population proportion is equal to 0.5
what are the answers to the following quadratic equation:
x^2-4x-12
Answers
Answer:
6 and -2
Step-by-step explanation:
x^2-4x-12
set up equal to zero
x^2-4x-12=0
lets factor:
(x-6)(x+2)=0
x-6=0
x=6
or
x+2=0
x=-2
Answer:
x=6 x=-2
Step-by-step explanation:
x^2-4x-12 = 0
Factor
What two numbers multiply to -12 and add to -4
-6*2 = -12
-6+2 = -4
(x-6)(x+2) =0
Using the zero product property
(x-6) =0 x+2 = 0
x=6 x=-2
luvenia can row 4mph in still water. She takes as long to row 7 mi upstream as 21 mi downstream. how
Answers
Answer:
The speed of the river is 2mph.
Step-by-step explanation:
I guess that we want to find the speed of the river.
First, remember the relation: speed*time = distance
If the speed of the river is Sr, when Luvenia moves downstream (in the same direction that the flow of the water) the total speed will be equal to the speed of Luvenia in still water plus the speed of the water:
Sd = 4mph + Sr
and at this speed, in a time T, she can move 21 miles, so we have:
Sd*T = (4mph + Sr)*T = 21 mi
When moving upstream, the speed will be:
Su = (4mph - Sr)
and in the same time T as before, she moves 7 miles, so we have the equation:
Su*T = (4mph - Sr)*T = 7 mi
Then we have two equations:
(4mph + Sr)*T = 21 mi
(4mph - Sr)*T = 7 mi
Now we can take the quotient of those two equations and get:
((4mph + Sr)*T)/((4mph - Sr)*T) = 21/7
The time T vanishes, and we can solve it for Sr.
(4mph + Sr)/(4mph - Sr) = 3
4mph + Sr = 3*(4mph - Sr) = 12mph - 3*Sr
4*Sr = 12mph - 4mph = 8mph
Sr = 8mph/4 = 2mph.
3.
B
С
A
D
E
How many rays intersect at point o?
Answers
80 81 82 83 84 85 86 87 88 89 90
Anika's test scores are shown below.
Anika's Test Scores
80 81 82 83 84 85 86 87 88 89 90
Which statement compares the shape of the two dot plots?
There is a gap in both plots.
There is a gap in Anika's scores, but not in Lorenzo's scores.
The data is widely spread across both plots.
The data is more widely spread for Lorenzo's scores than for Anika's.
Mark this and return
Save and Exit
Answers
Answer:
D :)
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Braily please
For a long-distance person-to-person telephone call, a telephone company charges $ 0.72 for the first minute, $ 0.42 for each additional minute, and a $ 1.85 service charge. If the cost of a call is $ 8.03 comma how long did the person talk?
Answers
Answer:
13 mins
Step-by-step explanation:
8.03- 1.85= 6.18
-.72=5.46
/.42=13
Please answer this correctly
Answers
Answer:
12 2/5 hours
Step-by-step explanation:
[tex]1+1+1\frac{1}{5} +1\frac{1}{5} +1\frac{1}{5} +1\frac{3}{5} +1\frac{3}{5} +1\frac{4}{5} +1\frac{4}{5} =\\\\2+3\frac{3}{5} +3\frac{1}{5} +3\frac{3}{5} =\\\\11\frac{7}{5} =\\\\12\frac{2}{5}[/tex]
12 2/5 hours have been logged in all.
Find the exact length of the third side. (Pythagorean Theorem)
Answers
Answer:
3 sqrt(5) =c
Step-by-step explanation:
We can use the pythagorean theorem
a^2 + b^2 = c^2
3^2 + 6^2 = c^2
9+36 = c^2
45 = c^2
Take the square root of each side
sqrt(45) = sqrt(c^2)
sqrt(9)sqrt(5) = c
3 sqrt(5) =c
Please show me how to solve 40% of X is 23?
NOT what is 40% of 23. But what number is 40% of to equal 23.
Thank you!!
Answers
Answer: The answers are in the steps hopes it helps.
Step-by-step explanation:
40% * x = 23 convert 40% to a decimal
0.4 * x = 23 multiply 0.4 is by x
0.4x = 23 divide both sides by 0.4
x= 57.5
Check:
57.5 * 40% = ?
57.5 * 0.4 = 23
Please answer...i always answer... please
Answers
Answer:
A) -x + y = 2
B) x + 2y = 4
we add both equations
3 y = 6
y = 2
We put y = 2 into equation B)
x + 2 * 2 = 4
x = 0
***********************************************
A) -2x + y = 6
B) x + y = 0
We multiply B) by 2
B) 2 x + 2 y = 0 then we add A)
A) -2x + y = 6
3y = 6
y = 2
Therefore x = -2
Step-by-step explanation:
I don’t know if it’s g(2(5)(3(5)^2-5-5
Answers
Answer:
B. 135
Step-by-step explanation:
For ...
f(x) = 3x^2 -xg(x) = 2x -5f(5) = 3·5^2 -5
= 3·25 -5 = 75 -5 = 70
Then g(f(5)) is ...
g(f(5)) = g(70) = 2·70 -5 = 140 -5
g(f(5)) = 135 . . . . . matches choice B
Eagle Outfitters is a chain of stores specializing in outdoor apparel and camping gear. They are considering a promotion that involves mailing discount coupons to all their credit card customers. This promotion will be considered a success if more than of those receiving the coupons use them. Before going national with the promotion, coupons were sent to a sample of credit card customers. Click on the datafile logo to reference the data.
a. Develop hypotheses that can be used to test whether the population proportion of those who will use the coupons is sufficient to go national.b. The file Eagle contains the sample data. Develop a point estimate of the population proportion.c. Use αα= .05 to conduct your hypothesis test. Should Eagle go national with the promotion?
Answers
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
Eagle Outfitters is a chain of stores specializing in outdoor apparel and camping gear. It is considering a promotion that involves mailing discount coupons to all its credit card customers. This promotion will be considered a success if more than 10% of those receiving the coupons use them. Before going national with the promotion, coupons were sent to a sample of 100 credit card customers. Out of the 100 customers, 13 customers said that they used the discount coupons to make a purchase at a Eagle Outfitters store. Use a 0.05 level of significance. (a) Develop the null and alternative hypotheses that can be used to test whether the population proportion of those who will use the coupons is sufficient to go national. (b) Compute the sample proportion. (c) Compute the test statistic. (d) Compute the critical value. (e) Based on the critical value, do we reject H0 or do we not reject H0? (f) Based on the result of the hypothesis test, should Eagle Outfitter go national with the promotion?
Solution:
a) We would set up the hypothesis test.
For the null hypothesis,
H0: p ≥ 0.1
For the alternative hypothesis,
Ha: p < 0.1
This is a left tailed test
Considering the population proportion, probability of success, p = 0.1
q = probability of failure = 1 - p
q = 1 - 0.1 = 0.9
b) Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 13
n = number of samples = 100
p = 13/100 = 0.13
c) We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.13 - 0.1)/√(0.1 × 0.9)/100 = 1
The calculated test statistic is 1 for the right tail and - 1 for the left tail.
d) Since α = 0.05, the critical value is determined from the normal distribution table.
For the left, α/2 = 0.51/2 = 0.025
The z score for an area to the left of 0.025 is - 1.96
For the right, α/2 = 1 - 0.025 = 0.975
The z score for an area to the right of 0.975 is 1.96
e) In order to reject the null hypothesis, the test statistic must be smaller than - 1.96 or greater than 1.96
Since - 1 > - 1.96 and 1 < 1.96, we would fail to reject the null hypothesis.
Therefore, based on the result of the hypothesis test, the Eagle Outfitter should go national with the promotion
2. {5.0A.A.1, 5.0A.A.2} Write an expression to show....the product of eight
and two, minus the product of three and four. *
Answers
Answer:
[tex]\left ( 8\times 2 \right )-\left ( 3\times 4 \right )[/tex]
Step-by-step explanation:
Given: The statement is ' the product of eight and two, minus the product of three and four'
To find: expression for the given statement
Solution:
An algebraic expression is an expression consists of coefficients, variables, and the arithmetic operations.
Product of eight and two = [tex]\left ( 8\times 2 \right )[/tex]
Product of three and four = [tex]\left ( 3\times 4 \right )[/tex]
Therefore,
Product of eight and two, minus the product of three and four = [tex]\left ( 8\times 2 \right )-\left ( 3\times 4 \right )[/tex]
Josslyn is thinking of a number, n and she wants her sister to guess the number. Her first clue is that seven less than six times her number is between negative one and twenty-nine (inclusive). Write a compound inequality that shows the range of number that Josslyn might be thinking of.
Answers
Answer:
1<X<=6
Step-by-step explanation:
seven less than six times her number is between negative one and twenty-nine (inclusive).
The above statement can be expressed mathematically thus;
Let the number be x
6x-7= (-1 ,29]
Hence 6x-7 = -1=>6x=6=>x=1 or
6x-7= 29=>6x=36=>x=6
Hence 1<X<=6
what is 12/5 as a mixed nunber
Answers
Answer:
2 2/5
Step-by-step explanation:
12/5
5 goes into 12 2 times
12 - 5*2
12-10 =2
There is 2 left over. This goes over the denominator
2 2/5
Please help ASAP thank you
Answers
Answer:
q
Step-by-step explanation:
Since AB is a transversal of the two parallel lines, the angle with measure 135 degrees and angle q are vertical angles. Therefore, their measure must be equal.
Hope this helps!
what is the dot product of vectors
Answers
Answer:
The dot product of vectors is the method used to "multiply" vecotrs since vectors aren't directly multiplieable
Step-by-step explanation:
In the diagram below, measure of arcABC = 230º.
What is the measure of
Answers
Answer:
65°
Step-by-step explanation:
Short arc AC is the difference between 360° and long arc ABC:
arc AC = 360° -230° = 130°
The inscribed angle ABC that intercepts this short arc will have half the measure of the arc:
∠ABC = 130°/2 = 65°
A manager records the repair cost for 4 randomly selected stereos. A sample mean of $82.64 and standard deviation of $14.32 are subsequently computed. Determine the 90% confidence interval for the mean repair cost for the stereos. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answers
Answer:
CI = (70.861 , 94.418)
Step-by-step explanation:
In order to determine the 90% confidence interval you use the following formula (for a population approximately normal):
[tex]CI=(\overline{x}-Z_{\alpha/2}\frac{\sigma}{\sqrt{n}},\overline{x}+Z_{\alpha/2}\frac{\sigma}{\sqrt{n}})[/tex] (1)
[tex]\overline{x}[/tex]: mean = 82.64
σ: standard deviation = 14.32
n: sample = 4
α: tail area = 1 - 0.9 = 0.1
Z_α/2 = Z_0.05: Z factor = 1.645
You replace these values and you obtain:
[tex]Z_{0.05}(\frac{14.32}{\sqrt{4}})=(1.645)(\frac{14.32}{\sqrt{4}})=11.778[/tex]
The confidence interval will be:
[tex]CI=(82.64-11.778,82.64+11.778)=(70.861,94.418)[/tex]
The 90% confidence interval is (70.861 , 94.418)