Installation of a certain hardware takes a random amount of time with a standard deviation of 5 minutes. A computer technician installs this hardware on 64 different computers, with the average installation time of 42 minutes. Compute a 95% confidence interval for the mean installation time. Explain your interval in context.
Answer:
The 95% confidence interval for the mean installation time is between 40.775 minutes and 43.225 minutes. This means that for all instalations, in different computers, we are 95% sure that the mean time for installation will be in this interval.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96*\frac{5}{\sqrt{64}} = 1.225[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 42 - 1.225 = 40.775 minutes
The upper end of the interval is the sample mean added to M. So it is 42 + 1.225 = 43.225 minutes
The 95% confidence interval for the mean installation time is between 40.775 minutes and 43.225 minutes. This means that for all instalations, in different computers, we are 95% sure that the mean time for installation will be in this interval.
The 95% confidence interval for the mean installation time is (40.775, 43.225) and this can be determined by using the formula of margin of error.
Given :
Standard deviation is 5 minutes. Sample size is 64.Mean is 42 minutes.95% confidence interval.The following steps can be used in order to determine the 95% confidence interval for the mean installation time:
Step 1 - The formula of margin of error can be used in order to determine the 95% confidence interval.
[tex]M = z \times \dfrac{\sigma}{\sqrt{n} }[/tex]
where z is the z-score, [tex]\sigma[/tex] is the standard deviation, and the sample size is n.
Step 2 - Now, substitute the values of z, [tex]\sigma[/tex], and n in the above formula.
[tex]M = 1.96 \times \dfrac{5}{\sqrt{64} }[/tex]
[tex]M = 1.225[/tex]
Step 3 - So, the 95% confidence interval is given by (M - [tex]\mu[/tex], M + [tex]\mu[/tex]) that is (40.775, 43.225).
The 95% confidence interval for the mean installation time is (40.775, 43.225).
For more information, refer to the link given below:
https://brainly.com/question/6979326
Quadrilateral ABCD is a rhombus.
AD = 13 cm & BD = 24 cm,
find AC
Answer:
64
Step-by-step explanation:
WILL MARK BRAINLIEST! THANK YOUUUU
An equilateral triangle has a side length of 40.
Another side of the same triangle measures 3x + y.
The third side of the same triangle measures 4x - 2y.
What are the values of x and y that would keep the triangle equilateral?
Answer:
x=12, y=4
Step-by-step explanation:
All the sides are the same length.
3x+y = 40
4x-2y = 40
Eliminate y terms: divide second equation by 2 and add to first equation
2x-y = 20
3x+y = 40
---------------
5x = 60
x = 12
y = 40-3x = 4
Answer:
We know that all sides of the equilateral triangle is equal.
Given :---
An equilateral triangle has a side length of 40.
Another side of the same triangle measures
3x + y.
The third side of the same triangle measures
4x - 2y.
According to the above problem, the equation are
3x+y=40........(i) and 4x-2y=40.........(ii)
Divide the equation (ii) by 2, we get
2x-y=20..........(iii)
Now solving for x and y we get,
3x+y=40.......(i)
2x-y=20........(iii)
5x =60
x=60/5
x=12
Putting the value of x in equation in equation (iii) we get
24-y=20
y=24-20
y=4
The values of x and y that would keep the triangle equilateral are 12 and 4 respectively.
Hence, the value of x is 12 and y is 4.0p
2. Milk is on sale for 45 % off when it is normally $3.75 per gallon. How much will a gallon of milk cost?
O $1.69
$2.06
$2.05
$2.10
Answer:
A-$1.69
Step-by-step explanation:
45% of 3.75 is 1.6875
1.6875 needs to be rounded to the nearest hundredth
So it would make 1.68
Answer:
2.05
Step-by-step explanation:
x/3.75=45/100 cross multiply. x= about $1.7 but that's not the answer. to find the amount a gallon of milk costs, subtract 3.75 by 1.7, which gives you 2.05.
There are 7 girls and 10 boys taking lifeguard lessons. Write the ratio that compares the number of girls taking lifeguard lessons to the total number of students taking lifeguard lessons
Answer:
7 to 10 or 70%
Step-by-step explanation:
sarah spent a total of 10 on oranges and apples at the supet marke
t. if she spent 3 dollars less for oranges than she did on apples how much did sarah spend on oranges
42 % of what number is .21
Answer:
0.5
Step-by-step explanation:
0.21=42%
0.21/42=1%
0.005=1%
0.005 x 100 = 100%
0.5=100%
0.5
An online shopping club has 10,000 members when it charges $7 per month for membership. For each $1 monthly
increase in membership fee, the club loses approximately 400 of its existing members. Write and simplify a function
R to represent the monthly revenue received by the club when x represents the price increase.
Answer:
The function that can be used in the online shopping club about its monthly revenue is:
[tex]R = -400x^{2} +7200x+70000[/tex]
Step-by-step explanation:
First, we're gonna take into account the different values we have in the exercise:
10,000 members$7 per month for membershipLoses of 400 members by each $1 monthly increaseHow the variable [tex]x[/tex] represents the price increase, we can do the formula below:
[tex](10000 - 400x) * (7+x)[/tex]In this formula, we represent in the first part that by each 1 in the variable [tex]x[/tex], the total of members will be reduced in 400, in the second part, we mention that at the same time, the membership fee will be increased in the same value of [tex]x[/tex]. Now we must simplify this function:
[tex](10000 - 400x) * (7+x)[/tex]We operate the values:
[tex]70000+10000x-2800x-400x^{2}[/tex]Solve we can:
[tex]70000+7200x-400x^{2}[/tex]And organize:
[tex]-400x^{2} +7200x+70000[/tex]At the end, how [tex]R[/tex] represents the monthly revenue received by the club, we use that variable for our formula:
[tex]R=-400x^{2} +7200x+70000[/tex]Find the perimeter of a triangle with side lengths: (y + 5) ft, (3y + 5) ft, and (4y - 3) ft.
Answer:
8y + 7
Step-by-step explanation:
add them: y + 5 + 3y + 5 + 4y - 3 = 8y + 7
A club’s first meeting was attended by 72 people. Nine times as many people went to the first meeting than the second meeting. How many people attended the second meeting?
Answer:
8 people attended the second meeting.
Step-by-step explanation:
Given that:
Number of people who attended the first meeting = 72
Let,
x be the number of people who attended second meeting.
9 times people of second meeting = Number of people who attended first meeting
9x = 72
Dividing both sides by 9
[tex]\frac{9x}{9}=\frac{72}{9}\\x=8[/tex]
Hence,
8 people attended the second meeting.
After four rounds, 74 teams are eliminated from a robotics competition. There are 18 teams remaining. Write and solve an equation to find the number of teams t that started the competition.
#1
Ben and Irene shared an apple. Ben ate 3/4of the apple
and Irene ate 1/4
of the apple.
How much of the apple did Ben and Irene eat?
Answer:
all of it. because he ate 3/4 and she ate 1/4
Answer:4/4 of the apple
Step-by-step explanation: Ben ate 3/4 of the apple and Irene ate 1/4 parts of the apple what is 1 + 3 =4 and there are 4 part of the apple so 4 is how much they ate and 4 is how much there is to eat so it would be 4/4
(sorry if this does'nt help)
A triangle has sides measuring 2 inches and 7 inches. If x represents the
length in inches of the third side, which inequality gives the range of possible
values for x?
A. 25x37
B. 5 sxs 9
C. 2
D. 5< x < 9
Answer:
its d.
Step-by-step explanation:
the other guy is wrong
Using sides of a triangle rule, the inequality gives the range of possible values for x is 5 < x < 9.
What is sides of a triangle rule?
The sides of a triangle rule asserts that the sum of the lengths of any two sides of a triangle has to be greater than the length of the third side.
Given that two sides of triangle are 2 and 7 inches.
Let the third side be x inches.
x < 2+7 ⇒ x < 9
7 < 2 + x ⇒ x > 5
2 < 7 + x, which is true for any positive value of x.
Thus, 5 < x < 9.
Learn more about sides of a triangle rule here
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Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. 88 and -92
Answer:
The distance between them is 180 units
Step-by-step explanation:
Given
[tex]a = 88[/tex]
[tex]b = -92[/tex]
Required
Using absolute value, calculate the distance between them
The distance d is calculated as:
[tex]d = |b - a|[/tex]
Substitute values for a and b
[tex]d = |-92 - 88|[/tex]
[tex]d = |-180|[/tex]
[tex]d = 180[/tex]
It can also be calculated using:
[tex]d = |a - b|[/tex]
Substitute values for a and b
[tex]d = |88 - (-92)|[/tex]
Open bracket
[tex]d = |88 +92|[/tex]
[tex]d = |180|[/tex]
[tex]d = 180[/tex]
3. Mandy obtains a $155,000 20/6 balloon mortgage with a rate of 4.25%. What will her monthly payments be? (2 points)
O $959.81
O $1044.46
O $1110.47
$1225.74
Answer:
$279.98
Step-by-step explanation:
A 20/6 balloon payment means loan amortization is for 20 years and constant payments is for 6 years after which balloon payment is due.
The formula to calculate her constant payments based on a 15 year amortization plan is
A= P × r × r(1+r)^n/(1+r)^n-1
Where A = constant monthly payments for the 6 year period
r= interest rate
P= mortgage value loan
n= number of months =20×12=240 payments
Substitute values in the formula:
A= $155000× 0.0425×0.0425(1+0.0425)^240/(1+0.0425)^240-1
A= $279.98
To calculate what she would pay before balloon payment is due, we simply multiply her monthly payments $279.98 by number of payments 240
PLEASE ASAP 829283+749294(284+64304)-639562=
Answer:
use the calculator by doing this types of question
Answer:
48395590593
Step-by-step explanation:
calculator
find
the value of :
sin 0° + cos 0° + tan 45°
Answer:
this is easy
Step-by-step explanation:
sin 0 is 0
cos 0 is 1
tan 45 is 1
so ...
0+1+1 is 2
Need this turned in by tonight. Solving for x. My brain is fried, I have been doing math for the last 4 hour.Help!!!!!
Answer:
18. x = 24.519. x = 421. x = 10Step-by-step explanation:
Corresponding sides have same ratio
Q18
7/6 = x / (27- 6)6x = 7*21x = 147/6x = 24.5Q19
(x + 5)/15 = (5x + 1)/35(x + 5)/3 = (5x + 1)/77(x + 5) = 3(5x + 1)7x + 35 = 15x + 315x - 7x = 35 - 38x = 32x = 4Q21
(x + 6)/24 = (2x - 2)/27(x + 6)/8 = (2x - 2)/98(2x - 2) = 9(x + 6)16x - 16 = 9x + 5416x - 9x = 54 + 167x = 70x = 10What is the constant proportionally of the graph
Help me
Answer:
The constant proportionally of the graph is:
k = 8Step-by-step explanation:
We know that when 'y' varies directly with 'x', we get the equation
y ∝ x
y = kx
k = y/x
here 'k' is called the constant of proportionality.
From the graph, it is clear that:
at x = 0.5, the value of y = 4
so substituting x = 0.5 and y = 4 in the equation
k = y/x
k = 4/0.5
k = 8
at x = 1, the value of y = 8
so substituting x = 1 and y = 8 in the equation
k = y/x
k = 8/1
k = 8
Therefore, the constant proportionally of the graph is:
k = 8Ssssssssssssssssssssssssssssssssssssssssssssssssss
Which type of transformation is described by (x, y)
->
+ (x + 3, y — 2)?
Answer:
(x, y) → (x+3, y-2) means Translation 3 units left and 2 units down.
Step-by-step explanation:
Given the rule of transformation:
(x, y) → (x+3, y-2)
If we move horizontally 3 units to the right, 3 is added to the x-coordinate of any given point, and then 2 units down.
In other words,
(x, y) → (x+3, y-2) means Translation 3 units left and 2 units down.
For example,
Let say if we have the point A(4, 5)
Using the translation rule:
(x, y) → (x+3, y-2)
A(4, 5) → A'(4 + 3, 5 - 2) → A'(7, 3)
Therefore, the new position of A(4, 5) after translating 3 units left and 2 units down would be: A'(7, 3)
Solve
7W + 3 = 5W + 9
Answer:
W = 3
Step-by-step explanation:
7W + 3 = 5W + 9.
Get all the varibles onto one side, and get all the integers onto the other side, we get:
7W - 5W = 9 - 3.
Simplifing, we get:
2W = 6
W = 3.
Graphs that represent situations that may not have numerical values are Called?
Scottie is testing to see if people who go to a lot of movies do better than average on the Verbal SAT (which has a mean of 500 and a standard deviation of 100 and is normally distributed). She has a sample of six people. What kind of hypothesis testing do we use
Answer:
The kind of hypothesis testing we can use is z-test for means
Step-by-step explanation:
Given that;
sample mean x" = 500
standard deviation σ = 100
sample size n = 6
What kind of hypothesis testing do we use?
There are two cases where z-test can be use;
first, when we know the population standard deviation or variance
and secondly, when the population size is more than 30.
So from the question, the population standard deviation was given, which is 100.
Since we know the S.D, it meets the first condition.
Therefore, The kind of hypothesis testing we can use is z-test for means
3 ÷ 1/8 show your work on paper! :D
Answer:
24
Step-by-step explanation:
3 : 1/8 = 3/1 · 8/1 = 3 · 8/1 · 1 = 24/1 = 24
Hope this helped!
The sum of nineteen and four times a number equals 39. Suppose x represents the unknown number. Translate this problem into a mathematical statement.
Answer:
19 + 4x = 39
Step-by-step explanation:
Which of the following can a seismograph not show scientists?
help please i’ll try to give brainliest:)
9514 1404 393
Answer:
108
Step-by-step explanation:
The circumference of a circle is given by ...
C = 2πr
The circle shown has a radius of 9 in, so the circumference is ...
C = 2π(9 in) = 18π in
__
When the circle is dilated by a factor of 6, the circumference is multiplied by 6. It becomes ...
dilated C = 6(18π in) = 108π in
The multiplier of π inches is n = 108.
ACTIVITY 1
Directions: Find the unknown principal P, rate r, time t, and simple
interest Is by completing the table. Use separate sheet/s of paper for your
answer.
Principal (P)
Rate (T)
Time (t)
8%
15
2%
5
Simple Interest
(Is)
(1)
10,000
3,600
175,500
10,000
(2)
360,000
500,000
2
(3)
10.5%
Activity 2
Directions: Find the unknown principal P, maturity value, and
compound interest Ic by completing the table. Use separate sheet/s of paper
for your answer.
Maturity Value
Principal (P) Rate(r) Time(t)
Compound
Interest (Ic)
(1)
10,000
(3)
8%
2%
15
5
(2)
50,000
Answer:
500,000
2
(3)
10.5%
Activity 2
Directions: Find the unknown principal P, maturity
A line with a positive slope will go up and to the right on the graph. True false
Answer:
True
Step-by-step explanation:
Let's say the slope of an equation is 3/2. You move the point by moving it up by three and moving it to the right by two or moving it down by 3 and moving it to the left by two.
If the equation was - 3/2. You would move the point by moving it up by three and moving it to the left by two or moving it down by three and moving it the right by two.