Answer:
The answer is D. 4(sqrt(5))
Step-by-step explanation:
To find this we use the Pythagorean Theorem a^2+b^=c^2
So making 4 = to a, and 8 = to, and x = to, we do
4^2+8^2= 80
Then we take the square root of 80 to find the missing side, which is equal to 4(sqrt(5)
Good luck!
2 1/4 divided by 1 1/2
Answer: 3/2
Step-by-step explanation:
Answer:
3/2 or 1 1/2
Step-by-step explanation:
\(2\frac{1}{4}/1\frac{1}{2} \\\frac{9}{4}/\frac{3}{2} \\(\frac{9}{4})(\frac{2}{3})\\\frac{18}{12} \\\frac{3}{2} or 1\frac{1}{2}\)
70 points and brainliest if the answer is correct
5^4x5^7
A. 125^11
B. 15^11
C. 5^28
D. 5^11
Answer:
Option D
Step-by-step explanation:
If the bases are the same in a multiplication problem, then you can simply add the exponents. (i.e., a² × a⁶ = a²⁺⁶ = a⁸)
\(\bullet \rightarrow 5^4\times5^7\)
\(\bullet\rightarrow 5^{4 + 7}\)
\(\bullet \rightarrow \boxed{5^{11}}\)
Answer: D
Step-by-step explanation:
5^4 x 5^7
You will add the exponent 4 + 7 = 11
You will keep your base 5^11
60 rulers cost £9 how much does 1 cost
Answer:
the answer to your question is
6 2/3 if you were dividing 60 ÷ 9 that is
You want to take out a $219,000 mortgage (home loan). The interest rate on the loan is 4.5%, and the loan is for 30 years. Your monthly payments are $1,109.64. How much will still be owed after making payments for 15 years? Round your answer to the nearest dollar.
After making payments for 15 years, the amount still owed on the mortgage would be approximately $145052.36.
To determine how much will still be owed after making payments for 15 years, we can use the formula for the remaining balance on a mortgage:
Remaining balance = P ((1 + r)ⁿ - (1 + r)ᵇ) / ((1 + r)ⁿ - 1)
where:
P = the initial loan amount (in this case, $219,000)
r = the monthly interest rate (which is the annual interest rate divided by 12)
n = the total number of monthly payments (which is 30 years times 12 months per year, or 360 months)
b = the number of monthly payments made so far (which is 15 years times 12 months per year, or 180 months)
First, we need to calculate the monthly interest rate:
r = 4.5% / 12 = 0.00375 = 0.375%
Next, we can plug in the values to get:
Remaining balance = $219,000 ((1 + 0.00375)³⁶⁰- (1 + 0.00375)¹⁸⁰) / ((1 + 0.00375)³⁶⁰ - 1)
= $145052.36
To learn more about loan calculations;
https://brainly.com/question/28244942
#SPJ1
Same set up as the problem to the left. Fill in the blanks.
The blanks that are missing in the sequence are -3 and 11
How to fil in the blanks in the sequencefrom the question, we have the following parameters that can be used in our computation:
The blanks in the sequence
When listed out, we have
_, _, 25, 39
Assuming that the sequence, is an arithmetic sequence, then we have
Common difference = 39 - 25
Common difference = 14
This means that
Previous term = 25 - 14 = 11
Firs term = 11 - 14 = -3
So, the missing terms are -3 and 11
Read more about sequence at
https://brainly.com/question/30499691
#SPJ1
Four friends shared 7 chocolate bars. Each of them was given an equal share of the chocolate bars. How many chocolate bars did each person get?
A: 4/7
B : 6/8
C: 1 1/4
D: 1 3/4
We are given:
There were 7 chocolate bars, evenly shared between 4 friends
Number of Bars one person will get:
Number of bars one person will get = Number of Bars / Number of Friends
Number of Bars = 7 / 4
but since this number does NOT match any of the given options, we will convert it to a mixed fraction
The number of bars one person will get will be \(1\frac{3}{4}\), written as a mixed fraction.
Therefore, the correct answer is option D
Answer:
4 friends =7 chocolate
1 friend =7/4 chocolate =1 3/4 part of chocolate.
HELP ASPAPP The general form of an equation is x2+y2−25x+3y+1=0.
What is the equation of the circle in standard form?
Answer:
the first (top) answer option. ... = 129/100
Step-by-step explanation:
the for me qualifying or disqualifying term is the constant term as the product and sum of all the constant parts.
the general form has the constant parts
... + 1 = 0
so, all the constant terms from the squares on the left side minus the constant term on the right side must be 1.
let's start from the bottom : the 4th answer option.
the constant parts are
... + (-1/5)² + ... + (3/2)² = 121/100
... + 1/25 + ... + 9/4 = 121/100
... + 0.04 + ... + 2.25 = 1.21
... + 2.29 - 1.21 = ... + 1.08
and NOT 1. so, this is wrong.
the 3rd answer option.
... + (-1/3)² + ... + (-3/2)² = 221/100
... + 1/9 + ... + 9/4 = 221/100
... + 0.111111... + ... + 2.25 = 2.21
... + 0.111111... + ... + 2.25 - 2.21 = 0
... + 0.111111... + ... + 0.04 = 0
... + 0.111111 + 0.04 = 0.15111111...
and NOT 1. so, this is wrong.
the 2nd answer option.
... + (-1/5)² + ... + (3/2)² = 229/100
... + 1/25 + ... + 9/4 = 229/100
... + 0.04 + ... + 2.25 = 2.29
... + 2.29 - 2.28 = ... + 0
and NOT 1. so, this is wrong.
the first answer option.
... + (-1/5)² + ... + (3/2)² = 129/100
... + 1/25 + ... + 9/4 = 129/100
... + 0.04 + ... + 2.25 = 1.29
... + 2.29 - 1.29 = ... + 1
this IS 1. so, this is correct.
this corresponds now to the original
... + 1 = 0
Answer: Choice A (May vary from test to test)
Step-by-step explanation:
(x-1/5)^2 + (y+3/2)^2 = 129/100
Just an FYI:
I can't stress this enough... Add equation symbols when applicable, for example: √,^,/, etc. You can't expect to have someone give the correct answer when you literally typed the equation out incorrectly.An inlet pipe on a swimming pool can be used to fill the pool in 26 hours. The drain pipe can be used to empty the pool in 27 hours. If the pool is 2/3 filled and then the inlet pipe and drain pipe are opened, how many more hours would it take to fill the pool? Round your answer to two decimal places, if needed.
Let's start by finding the rates at which the inlet and drain pipes can fill and empty the pool, respectively.
The rate of the inlet pipe is:
1 pool / 26 hours
The rate of the drain pipe is:
-1 pool / 27 hours (note the negative sign, indicating that it is emptying the pool)
When both pipes are open, the net rate of filling the pool is the sum of their rates:
1/26 - 1/27 = 1/702
This means that when both pipes are open, the pool is being filled at a rate of 1/702 of the pool per hour.
If the pool is 2/3 filled, then it still needs to be filled by 1/3 of its volume. Let's assume that the volume of the pool is V, so the amount of water that needs to be added to the 2/3 filled pool is:
(1/3)V
The time it takes to fill this amount of water is:
[(1/3)V] / [(1/702) pool/hour]
Simplifying this expression, we get:
(1/3)V x (702/1) hours/pool
234 hoursV / pool
Rounding this answer to two decimal places, we get:
234.57 hours (rounded to 2 decimal places)
Therefore, it would take approximately 234.57 more hours to fill the pool when both the inlet and drain pipes are open.
Answered By Unish ©
Verified Answer ✅
Please Mark As Brainliests for more help
Convert each measurement
18 meters = ??? centimeters
Answer:
18 meters = 1800 milimeters
Step-by-step explanation:
Hope this helps! :3
plz mark as brainliest!
Answer:
Just search it up. The answer is 1800
Step-by-step explanation:
Type.
Or there's another way.... you multiply if you want to convert a unit that is greater to smaller, and you divide if you want to convert a smaller unit to a larger one.
For example hours to minutes:
You cross out the word that matches. Here it's hour.
3.15 hours X 60 min/1 hour=189 min
189min X 60 sec/1min=11340 sec
and if it's from smaller to greater you divide, get it?
Solve for q if 5q-21/14=1
Answer:
q=0.5 or 1/2
Step-by-step explanation:
5q-21/14=1
add 21/14 to both sides
5q=2.5
divide both sides by 5
q=0.5 or 1/2
How many different pairs of faces are congruent in a rectangular prism that is not a cube
Answer:
2
Step-by-step explanation:
every rectangular prism has 6 faces, 2 will be congruent together and thw other 4 will be congruent to each other
Which expression represents the distance between 1.8 and 9.4 on the number line?
Answer:
the distance between 1.8 & 9.4=9.2
2. LN bisects LL. Calculate NM. 2 8 in. 5 in. K M 4 in. N
KN/NM = KL/LM
4/NM = 8/5
\(\frac{4}{NM}=\frac{8}{5}\)cross-multiply
\(8NM\text{ = 4}\times5\)\(8NM=20\)Divide both-side of the equation by 8
\(NM=\frac{20}{8}\)\(NM=2.5\)HELP ALGEBRA IF YOU KNOW THIS PLS HELPPP
Answer:
I think its third answer..24=w*+5w
In some racing events, downhill skiers receive the average of their times for three trials. Would you prefer the average time to be the mean or the median if you had… one very good time and two average times?
Answer:
Median
Step-by-step explanation:
i think median would be better than mean. This is because with mean, your adding it together then dividing it(by 3 in this case), making the end number higher. tou dont want a higher number in this case.
ex: your numbers are 50, 55,and 90
median = 55 (as it's the middle number)
mean = 65 ( 90+ 55+ 50 / 3)
so median is the lower number, meaning it would be better in this** case.
Write a polynomial that represents the area of the shaded region
The polynomial that represents the area of the shaded region is given as follows:
x² - 3x + 36.
How to obtain the area of a rectangle?The area of a rectangle is given by the multiplication of the width and the length of the triangle, as follows:
A = lw.
For the entire region, the area is given as follows:
A = (x + 1)(x + 1)
A = x² + 2x + 1.
The area of the white region is given as follows:
Aw = 5(x - 7)
Aw = 5x - 35.
Then the area of the shaded region is given as follows:
As = A - Aw
A = x² + 2x + 1 - (5x - 35)
A = x² + 2x + 1 - 5x + 35
A = x² - 3x + 36.
More can be learned about area at https://brainly.com/question/15673093
#SPJ1
(Rewriting Rational Numbers MC)
Three lakes lost water during a drought. Lake Jensen lost 1/9 of its water, Lake Parlow lost 10% of its water, and Lake
Stockton lost of its water. Which lake lost the least amount of water?
21
200
O Lake Jensen
O Lake Parlow
O Lake Stockton
O All three lakes lost the same amount of water
Using the equivalent decimals, the lake that lost least amount of water is Lake Partlow
Lake Jensen lost 1/9 of its water
We have to convert the simple fraction to decimal form
1/9 = 0.11
Lake Partlow lost 10% of its water
The percentage is a number or ratio that can be represented as a fraction of 100.
10% = 10/100
= 0.1
Lake Stockton lost 21/200 of its water
Convert the simple fraction to decimal form
21/200 = 0.105
Lake Partlow lost 10% of its water. that is the least amount of water.
Hence, Using the equivalent decimals, the lake that lost least amount of water is Lake Partlow
Learn more about equivalent decimals here
brainly.com/question/28517838
#SPJ1
Owen has a credit card with an APR of 12.5% and a balance of $1,892.32. The interest is compounded monthly. What is the monthly periodic rate?
0.104
0.0125
0.0104
0.125
Answer:
0.125%
Step-by-step explanation:
To find the percentage, just move the decimal place two places.
Answer:
Answer is c or 0.0104.
Step-by-step explanation:
12.5/12= 1.04...
1.04/100= 0.0104
How would you explain the proper use of distributive property ?
2) In reply to an inquiry about the animals on his farm, the farmer says: "I
only ever keep sheep, goats, and horses. In fact, at the moment they are
all sheep bar three, all goats bar four, and all horses bar five." How many
does he have of each animal?
The number of horse is 1, goat is 2 and sheep is 3 a man has.
The problem we are dealing with is related to the linear equation which is referred to as the algebraic condition where each term has an exponent of 1 and when this condition is graphed, it continuously comes about in a straight line.
Now w consider x to be the number of sheep, y to be the number of goats, and z to be the number of horses the man owns.
the actual equation for the total number of animals he owns is :
x+ y+ z
according to the first condition:
that all sheep bar three, means
y+ z=3
similarly, for the other condition, it will be
x+ z=4 and x+ y=5
Now we adding the three equations:
y + z +x +z +x +y=5+4 +3
2(x+y+z)=12
x+y+z=6........equation(1)
As x + y = 5
Put this in equation in (1), we get
x+y+z = 6
5 + z = 6
z = 1
x + z = 4
x + y + z = 6
y + 4 = 6
y = 2
Now we know
x + y + z = 6
x + 1 + 1 = 6
x = 4
So simplifying the other equation we get, that the number of horse is 1, goat is 2, and sheep is 4.
To know more about linear equations refer to the link:
https://brainly.com/question/2030026
#SPJ9
Question 10 of 10
Which of the following is not a characteristic of both observational studies
and experiments?
A. Results are not used to prove cause and effect.
B. Data are collected about a population.
O C. The researcher exercises direct control over at least one variable.
D. The subjects are observed, and their behavior is recorded.
Answer:
B. Data are collected about a population.
Step-by-step explanation:
Data collected isn't experimenting. Experimenting is when you modify certain things in the population, not just take data from it. Hence, option b is just observation, not experimenting.
suppose the equation z^2+4z+20+iz(A+1)=0 where A is constant has complex conjugate root if one of the root of this quadratic is z=B+2i where B is real constant find possible value of A ? please help me I need your help
If one of the roots is \(w=B+2i\), then the other root is its conjugate \(\bar w=B-2i\). So we can factorize the quadratic to
\(z^2 + 4z + 20 + iz (A+1) = (z-(B+2i)) (z-(B-2i))\)
Expand the right side and collect all the coefficients.
\(z^2 + (4+(A+1)i) z + 20 = z^2 - 2B z + B^2+4\)
From the \(z\) and constant terms, we have
\(\begin{cases}4 + (A+1)i = -2B \\ 20 = B^2 + 4 \end{cases}\)
From the second equation we get
\(B^2 = 16 \implies B = \pm4\)
Then
\(4+(A+1)i = \pm8\)
\((A+1)i = 4 \text{ or } (A+1)i = -12\)
Since \(\frac1i=-i\), we have
\(-\dfrac{A+1}i = 4 \text{ or } -\dfrac{A+1}i = -12\)
\(A+1 = -4i \text{ or } A+1 = 12i\)
\(\boxed{A = -1 - 4i \text{ or } A = -1 + 12i}\)
suppose that prices of a gallon of milk at various stores in one town have a mean of $3.55 with a standard deviation of $0.14 . using chebyshev's theorem, what is the minimum percentage of stores that sell a gallon of milk for between $3.27 and $3.83 ? round your answer to one decimal place.
Therefore, the minimum percentage of stores that sell a gallon of milk for between $3.27 and $3.83 is 75%, rounded to one decimal place.
What is standard deviation?Standard deviation is a measure of the amount of variation or dispersion in a set of data values. It measures how spread out the data is from the mean or average value. A low standard deviation indicates that the data is closely clustered around the mean, while a high standard deviation indicates that the data is more spread out. It is calculated as the square root of the variance, which is the average of the squared differences from the mean.
Here,
Chebyshev's theorem states that for any dataset, regardless of its distribution, at least 1 - 1/k² of the data will fall within k standard deviations of the mean, where k is any positive number greater than 1. To find the minimum percentage of stores that sell a gallon of milk for between $3.27 and $3.83, we can first find how many standard deviations away from the mean these prices are:
$3.27 is (3.27 - 3.55)/0.14 = -2 standard deviations from the mean
$3.83 is (3.83 - 3.55)/0.14 = 2 standard deviations from the mean
Thus, the distance between $3.27 and $3.83 is 4 standard deviations (2 in each direction).
Using Chebyshev's theorem with k = 2 (since we want to know the minimum percentage within 2 standard deviations), we have:
=1 - 1/2²
= 1 - 1/4
= 0.75
This means that at least 75% of stores sell a gallon of milk for between $3.27 and $3.83.
To know more about standard deviation,
https://brainly.com/question/23907081
#SPJ1
When an object is weighed on a scale, the number displayed may vary from the object’s actual weight by at most 0.4 pounds. The scale says the object weighs 125.8 pounds. Part A: Write an absolute value inequality that describes the range of the actual weight of the object. Use the variable w to represent the actual weight of the object. Part B: Solve the absolute value inequality for w. Express your answer as a compound inequality.
The compound inequality that represents the range of the actual weight of the object is 125.4 ≤ w ≤ 126.2.
Part A: The absolute value inequality that describes the range of the actual weight of the object is:
|w - 125.8| ≤ 0.4
Part B: To solve the absolute value inequality, we can break it down into two separate inequalities:
w - 125.8 ≤ 0.4 and - (w - 125.8) ≤ 0.4
Solving the first inequality:
w - 125.8 ≤ 0.4
Add 125.8 to both sides:
w ≤ 126.2
Solving the second inequality:
-(w - 125.8) ≤ 0.4
Multiply by -1 and distribute the negative sign:
-w + 125.8 ≤ 0.4
Subtract 125.8 from both sides:
-w ≤ -125.4
Divide by -1 (note that the inequality direction flips):
w ≥ 125.4
Combining the solutions, we have:
125.4 ≤ w ≤ 126.2
The object is 125.4 ≤ w ≤ 126.2.
for more questions on compound
https://brainly.com/question/3989769
#SPJ8
many solutions or no solutions -2(x-2)-4x=3(x-1)-9x
∑ Hey, claudiavg2000 ⊃
Answer:
No solutions.
Step-by-step explanation:
Given:
-2(x-2)-4x=3(x-1)-9x
Solve:
-2 ( x - 2 ) - 4x : -6x + 4
3(x - 1) - 9x : -6x - 3
Now we have;
-6x + 4 = -6x - 3
Subtract 4 from both sides:
-6x + 4 - 4 = -6x - 3 - 4
-6x = -6x -7
Add 6x to both sides:
-6x + 6x = -6x - 7 + 6x
Simplifying:
0 = -7
As you can see the sides are not equal.
Hence, This problem has no solution.
xcookiex12
8/18/2022
9. Find the length of TR if TL = 24 and TR:RV:VL is 3:4:5
Answer:
length TR = 6
Step-by-step explanation:
Length TL = 24
scale ratio = 3:4:5
T-------R--------V----------L
find: TR
24 / (3+4+5) = 2
length TR at 3 x 2 = 6
length RV at 4 x 2 = 8
length VL at 5 x 2 = 10
a total of 6 + 8 + 10 = 24
therefore,
length TR = 6
Points A(9, 2), B(5,6), and C(-3,-2)
are given. The distance between
point C and the perpendicular
bisector of AB is:
The distance between point C and the perpendicular bisector of AB is 2√3.
Given points A(9, 2), B(5,6), and C(-3,-2).
We need to find the distance between point C and the perpendicular bisector of AB.
We first need to find the midpoint of line segment AB using the midpoint formula:
Midpoint of AB
= [(x1 + x2)/2, (y1 + y2)/2]
= [(9+5)/2, (2+6)/2]
= [(14/2), (8/2)]
= (7, 4)
Now, we need to find the slope of the line AB:
Slope of AB= (y2 - y1) / (x2 - x1)
= (6-2) / (5-9)
= 4/-4
= -1
So, the slope of the perpendicular bisector to AB is 1 (negative reciprocal of -1).
Now we need to find the equation of the perpendicular bisector of AB, which passes through (7, 4) with a slope of 1.
Using point-slope form of the line: y - y1 = m(x - x1)y - 4
= 1(x - 7)y - 4
= x - 7y
= x - 3
Now we have the equation of the perpendicular bisector of AB.
Now we can find the distance between C and the line by finding the length of the perpendicular from C to the line.
To do this, we need to find the equation of the line that is perpendicular to the line we found, which passes through point C, and then find the point where the two lines intersect.
This new line has a slope of -1, since it is perpendicular to the line with slope 1.
Using point-slope form of the line:
y - y1 = m(x - x1)y - (-2)
= -1(x - (-3))y + 2
= -x - 3y
= -x - 5
Now we have the equation of the new line.
Now we can find the point of intersection of the two lines:
y = x - 3y
= -x - 5
Adding the two equations:
2y = -8y
= -4
The point of intersection is (-4, -4).
Now we can find the distance between C and (-4, -4) using the distance formula:
Distance between C and (-4, -4) = √(x2 - x1)2 + (y2 - y1)2
= √((-3 - (-4))2 + (-2 - (-4))2)
= √(12)
= 2√3
For more related questions on perpendicular bisector:
https://brainly.com/question/29132624
#SPJ8
A baseball team has 4 pitchers, who only pitch, and 12 other players, all of whom can play any position other then pitcher. For Saturday’s game, the coach has not yet determined which 9 players to use nor what the batting order will be, except that the pitcher will bat last. How many different batting orders at occur?
Answer::2,075,673,600 batting orders may occur.
Step-by-step explanation: A baseball team has 4 pitchers, who only pitch, and 12 other players, all of whom can play any position other then pitcher.
The temperature in a hotel is 21 °C.
The temperature in the hotel is 26,7°C warmer than at the top of the mountain.
The temperature at the top of the mountain is 3.2°C colder than at the bottom of the mountain.
Work out the temperature at the bottom of the mountain.
The temperature at the bottom of the mountain is 50.9 °C.
Let's work through the given information step by step to find the temperature at the bottom of the mountain.
The temperature in the hotel is 21 °C.
The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.
Let's denote the temperature at the top of the mountain as T_top.
So, the temperature in the hotel can be expressed as T_top + 26.7 °C.
The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.
Let's denote the temperature at the bottom of the mountain as T_bottom.
So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.
Now, let's combine the information we have:
T_top + 26.7 °C = T_bottom - 3.2 °C
To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:
T_bottom = T_top + 26.7 °C + 3.2 °C
T_bottom = T_top + 29.9 °C
Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:
T_bottom = 21 °C + 29.9 °C
T_bottom = 50.9 °C
Therefore, the temperature at the bottom of the mountain is 50.9 °C.
for such more question on temperature
https://brainly.com/question/14820864
#SPJ8
A student researcher compares the ages of cars owned by students and cars owned by faculty at a local state college. A sample of 263 cars owned by students had an average age of 7.25 years. A sample of 291 cars owned by faculty had an average age of 7.12 years. Assume that the population standard deviation for cars owned by students is 3.77 years, while the population standard deviation for cars owned by faculty is 2.99 years. Determine the 90% confidence interval for the difference between the true mean ages for cars owned by students and faculty. Step 1 of 3: Find the point estimate for the true difference between the population means.
Answer:
The point estimate for the true difference between the population means is 0.13.
The 90% confidence interval for the difference between the true mean ages for cars owned by students and faculty is between -0.35 years and 0.61 years.
Step-by-step explanation:
To solve this question, before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When we subtract two normal variables, the mean is the subtraction of the means while the standard deviation is the square root of the sum of the variances.
A sample of 263 cars owned by students had an average age of 7.25 years. The population standard deviation for cars owned by students is 3.77 years.
This means that:
\(\mu_s = 7.25, \sigma_s = 3.77, n = 263, s_s = \frac{3.77}{\sqrt{263}} = 0.2325\)
A sample of 291 cars owned by faculty had an average age of 7.12 years. The population standard deviation for cars owned by faculty is 2.99 years.
This means that:
\(\mu_f = 7.12, \sigma_f = 2.99, n = 291, s_f = \frac{2.99}{\sqrt{291}} = 0.1753\)
Difference between the true mean ages for cars owned by students and faculty.
Distribution s - f. So
\(\mu = \mu_s - \mu_f = 7.25 - 7.12 = 0.13\)
This is also the point estimate for the true difference between the population means.
\(s = \sqrt{s_s^2+s_f^2} = \sqrt{0.2325^2+0.1753^2} = 0.2912\)
90% confidence interval for the difference:
We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:
\(\alpha = \frac{1 - 0.9}{2} = 0.05\)
Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).
That is z with a pvalue of \(1 - 0.05 = 0.95\), so Z = 1.645.
Now, find the margin of error M as such
\(M = zs = 1.645*0.2912 = 0.48\)
The lower end of the interval is the sample mean subtracted by M. So it is 0.13 - 0.48 = -0.35 years
The upper end of the interval is the sample mean added to M. So it is 0.13 + 0.48 = 0.61 years.
The 90% confidence interval for the difference between the true mean ages for cars owned by students and faculty is between -0.35 years and 0.61 years.