Answer:
The 95% confidence interval [tex] 81.852 < \mu < 280.098 [/tex]
Step-by-step explanation:
From the question we are told that
The sample mean is [tex]\= x = 180.975[/tex]
The standard deviation is [tex]\sigma = 143.042[/tex]
The sample size is n = 8
Given that the confidence level is 95% then the level of significance is
[tex]\alpha =( 100- 95) \%[/tex]
=> [tex]\alpha =0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{ 143.042 }{\sqrt{8} }[/tex]
=> [tex]E = 99.123 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex]180.975 -99.123 < p < 180.975 +99.123[/tex]
=> [tex] 81.852 < \mu < 280.098 [/tex]
Using the t-distribution, it is found that the 95% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments, in millions of dollars, is (61.39, 300.56).
The information given is:
Sample mean of [tex]\overline{x} = 180.975[/tex].Sample standard deviation of [tex]s = 143.042[/tex]Sample size of [tex]n = 8[/tex].We have the standard deviation for the sample, hence, the t-distribution is used.
The interval is given by:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
The critical value for a two-tailed 95% confidence interval with 8 - 1 = 7 df is t = 2.3646.
Then:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 180.975 - 2.3646\frac{143.042}{\sqrt{8}} = 61.39[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 180.975 + 2.3646\frac{143.042}{\sqrt{8}} = 300.56[/tex]
The 95% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments, in millions of dollars, is (61.39, 300.56).
To learn more about the t-distribution, you can take a look at https://brainly.com/question/25077184
a person buys a washing machine in the condition that he shall pay sum of INR 5880 at the cash down payment and the same sum at the end of the first year and two years. what is the total interest paid by him in this scheme, if the rate of interest is 5% compounded yearly?
Answer: $827
Step-by-step explanation:
Given that :
Cash down payment = 5880
Payment at end of first year = 5880
Payment at end of second year = 5880
Interest rate = 5% = 0.05 compounded yearly
Let purchase amount = y
Amount left after cash down = amount on which interest is paid = y - 5880
Interest at end of first year :
(y - 5880) * 0.05 = 0.05y - 294
Amount to pay plus interest :
Amount left after cash down payment - amount paid at end of first year + interest
y - 5880 - 5880 + 0.05y - 294
y - 12054 + 0.05y
= 1.05y - 12054
2nd year interest :
(1.05y - 12054) * 0.05
= 0.0525y - 602.7
Amount left + interest = 2nd year payment
(1.05y - 12054) + (0.0525y - 602.7) = 5880
1.1025y - 12656.7 = 5880
1.1025y = 5880 + 12656.7
1.1025y = 18536.7
y = 18536.7 / 1.1025
y = 16813.33
Hence,
Sales price of washing machine = 16813.33
Total amount paid = (5880 + 5880 + 5880) = 17640
Interest paid = $(17640 - 16813.33) = $826.67
= $827
The total interest paid by him in this scheme, if the rate of interest is 5% compounded yearly is INR 826.67
Given:
Down payment = INR 5880
Payment at end of first year = INR 5880 (same as down payment)
Payment at end of second year = INR 5880 (same as down payment)
Interest rate = 5%
= 5/100
= 0.05 compounded yearly
Amount of purchase = x
Amount remaining after down payment
= x - 5880
Interest at end of first year :
(x - 5880) * 0.05(5,880)
= 0.05x - 294
Amount to pay plus interest = Amount remaining after down payment - amount paid at end of first year + interest
= x - 5880 - 5880 + 0.05x - 294
= x - 12,054 + 0.05x
= 1.05x - 12,054
2nd year interest :
(1.05x - 12054) * 0.05
= 0.0525x - 602.7
Amount left + interest = 2nd year payment
(1.05x - 12054) + (0.0525x - 602.7) = 5880
1.1025x - 12656.7 = 5880
1.1025x = 5880 + 12656.7
1.1025x = 18536.7
divide both sides by 1.1025
x = 18536.7 / 1.1025
x = 16,813.33
Therefore, The cost of washing machine b is INR 16,813.33
Total amount paid = (5880 + 5880 + 5880) = INR 17,640
Amount of Interest paid = (17640 - 16813.33)
= INR 826.67
Read More:
https://brainly.com/question/18456266
Bob the builder is making 540 kg of concrete mix.
Concrete is made by mixing cement, sand and gravel in the ratio 1:3:5
How much gravel does he need?
Answer:
300 kg
Step-by-step explanation:
Let Constant Ratio be x:
x+3x+5x = 540
9x = 540
x = 60 kg
So, weight of gravel (W) = 5x
5 x 60
W = 300 kg (ANS)
3.
Billy has 20 pencils. Melissa gives Billy some shells.
Billy has 20 pencils. Now Billy has 36 shells. How many shells did Melissa
give him?
melissa give him?
Answer:
36. Melissa did not give Billy any pencils.
Answer:
Step-by-step explanation:
Melissa gave Billy 36 shells
What is the Square root of 3664?
Answer:
60.5
Thanks!
Mark me brainliest!
~[tex]FieryAnswererGT[/tex]~
Six country music bands and 3 rock bands are signed up to perform at an all-day festival. How many different orders can the bands play in if each band type must play in a row
Answer:
hey do you still need the answer
Step-by-step explanation:
100 points please help me asap!!
Answer:
[tex](x+5)^2=4[/tex]
Step-by-step explanation:
We have:
[tex]x^2+10x+21=0[/tex]
First, subtract 21 from both sides:
[tex]x^2+10x=-21[/tex]
Now, we can complete the square. We will divide the coefficient of the b term and square it. So:
[tex](\frac{b}{2})^2\Rightarrow(\frac{10}{2})^2=(5)^2=25[/tex]
So, we will add 25 to both sides:
[tex](x^2+10+25)=-21+25[/tex]
The left is the perfect square trinomial pattern. Add on the right:
[tex]((x)^2+2(5)(x)+(5)^2)=4[/tex]
Final step:
[tex](x+5)^2=4[/tex]
Rashad has 24 almonds and 32 walnuts for making snack bags. He wants to make as many snack bags as possible and wants each bag to have the same amount of almonds and walnuts. What is the largest number of snack bags he could make?
Question 4 options:
3 bags
4 bags
8 bags
16 bags
Answer:
4 bags
Step-by-step explanation:
Answer:
3 bags
Step-by-step explanation:
each bag will have 8 almonds and 8 walnuts.
What number times 10 equals 30 tens
Answer:
30
Step-by-step explanation:
Because 30 tens = 300
30 x 10 = 300
The temperature in the morning was -15 degrees. By the afternoon it was 45 degrees. What was the change in temperature?
Answer:
60 degrees
Step-by-step explanation:
Answer:
The answer is 60
Step-by-step explanation:
45-60 = -15
Help math math ASAP pelsss
Answer:
y = 3x - 6
Step-by-step explanation:
What you do is you plug both points in for the equation 2 times and solve as a system of equations.
Equation of a line: y = mx + b
(x,y) = (3,3)
(x,y) = (6,12)
3 = 3m + b
12 = 6m + b
Subtract equations to get rid of b to solve for m.
12 - 3 = 6m - 3m + b - b
9 = 3m
m = 3
Plug m back into both equations get b.
3 = 3(3) + b
b = -6
12 = 6(3) + b
b = -6
y = 3x - 6
Answer:
[tex]\displaystyle y = 3x - 6[/tex]
Step-by-step explanation:
First, find the rate of change of the line:
[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-3 + 12}{-3 + 6} = m \hookrightarrow \frac{9}{3} = m \\ \\ \boxed{3 = m}[/tex]
_______________________________________________
Now plug all the information into the Slope-Intercept Formula. It does not matter which ordered pair is chosen:
[tex]\displaystyle 12 = 3[6] + b \hookrightarrow 12 = 18 + b; -6 = b \\ \\ \boxed{\boxed{y = 3x - 6}} \\ \\ OR \\ \\ 3 = 3[3] + b \hookrightarrow 3 = 9 + b; -6 = b \\ \\ \boxed{\boxed{y = 3x - 6}}[/tex]
I am joyous to assist you at any time.
5055 X 550 + 32 - 99 + 43333 X 5 =
first right gits branlist
Answer:
the answer is 2996848
Step-by-step explanation:
Please help me with this
Answer:
Step-by-step explanation:
Both angles added together = 180 degrees. They both have a straight line as their base.
So let <ABC = x
Then <CBD = 3x Add the two angles
x + 3x = 180 Combine
4x = 180 Divide by 4
4x/4 = 180/4
x = 45
So 3x = 3*45 = 135
Which lines or segments are parallel? Justify your answer.
Answer:
KR //MT
Since angle JKR and LMT are equal as they are corresponding angle.
Points A, B, and C are on line AC.
A horizontal line has points A, B, C. A line extends from point B up and to the left to point D. Angle D B C is 140 degrees.
Angle CBD has a measure of 140°. What is the measure of angle ABD?
40°
50°
60°
70°
Answer:
50° Because considering the total angles is still half a line segment 50° is
Answer:
40 degrees A for me on EDG 2022
Step-by-step explanation:
June 21st
Angles a and B are supplementary if the measure of the angle a is 81 what is the measure of angle b
Answer: 99
Step-by-step explanation:
Supplementary angles add to 180 degrees, 180-81=99
The perimeter of the figure below is 35. Find
the missing value.
Answer: 7 feet
Step 1: Add the values of the sides we know the length of.
9 + 9 + 10 = 28.
Step 2: Subtract the number 28 from 35.
35 - 28 = 7
The answer is 7. Hope this helps!
Answer:
35 - 28 = 7
Step-by-step explanation:
7
Thanks bro...
Graph f(x)=−0.25x+4.
Use the line tool and select two points to graph the line.
The file attached is the answer
Answer:
Step-by-step explanation:
Given function to be graphed is,
f(x) = -0.25x + 4
Table for the graph of the given function will be,
x -2 0 2 4 6 8
f(x) 4.5 4 3.5 3 2.5 0
Now we can plot these points on the graph to find a line.
Graph of the linear function will be as the graph attached.
Answer:
Step-by-step explanation:
I took the test
Help help math math math
Answer:
y=5x+7
Step-by-step explanation:
y-y₁=m(x-x₁) will be our starting equation
Now input (-2, -3) and 5 as our slope because a parallel line has the same slope.
y-(-3)=5(x-(-2)) Input
y+3=5(x+2) Simplify
y+3=5x+10 Distribute 5 into the parenthesis
y=5x+7 Subtract 3 from both sides
Answer:
y=5x+7
Step-by-step explanation:
y=1.5283e^0.011x when x = 2020
Answer:
This is the answer, and I'm not very sure of it
Please help!! I'm pretty sure it's A or D. I'm not sure which one though.
The perimeter of a rectangle is 14 inches. The equation that represents the perimeter of the rectangle is 2l+2w=14, where l represents the length of the rectangle and w represents the width of the rectangle. Which value is possible for the length of the rectangle?
6 inches
7 inches
8 inches
9 inches
Answer:
6 inches
Step-by-step explanation:
6 inches is the only feasible answer because if the length is 6 inches, you have 6 + 6 which equals 12. This leaves 2 more units for the perimeter so the width would be 1 unit. The other choices could not exist, because 7 x 2 is 14 (no units left for width, and the width of a rectangle cannot be 0), 8 x 2 is 16, and 9 x 2 is 18.
do the values in the table represent a proportional relationship?
x 2 3 4 5
y 5 6 7 8
Answer:
yes a 1:1 ratio
Step-by-step explanation:
Please answer right ....
Answer:
[tex]2\frac{13}{120}[/tex]
Step-by-step explanation:
**Fractions for addition and/or subtraction need equal denominators
Alike denominators in parentheses
[tex]4\frac{2}{5} -(1\frac{2}{3}+\frac{5}{8})\\4\frac{2}{5} -(1\frac{2}{3}(\frac{8}{8}) +\frac{5}{8}(\frac{3}{3} ))\\4\frac{2}{5}-(1\frac{16}{24}+\frac{15}{24})\\4\frac{3}{5} -(1\frac{31}{24} )\\4\frac{3}{5} -(2\frac{7}{24} )[/tex]
[tex]4\frac{2}{5}-2\frac{7}{24}[/tex]
Solve
[tex]4\frac{2}{5}-2\frac{7}{24} \\4\frac{2}{5}(\frac{24}{24}) -2\frac{7}{24}(\frac{5}{5})\\4\frac{48}{120}-2\frac{35}{120}\\2\frac{13}{120}[/tex]
solution for .05n + .10d = .75
Answer:
d=−0.5n+7.5, n=−2d+15
Step-by-step explanation:
Write the domain and range of the function using interval notation.
Answer:
D: -12
R:6
Step-by-step explanation:
I hope this right
Find the measure of one interior angle of a regular 23-gon.
A. 164.3
B. 160
C. 165.6
D. 161.1
question is attached thanks
Take two points
(0,0)(-2,-4)Slope:-
[tex]\\ \sf\longmapsto \dfrac{-4}{-2}=2[/tex]
Equation in point slope form
[tex]\\ \sf\longmapsto y-y_1=m(x-x_1)[/tex]
[tex]\\ \sf\longmapsto y=2x[/tex]
In slope intercept form
y=2x+0Answer:
Step-by-step explanation:
Line passes through origin (0, 0) so y-intercept is zero: b=0
At x=2, y=4 so slope is 4/2=2: m=2
Answer is y = 2x
Solve for x. Choose the best simplified radical answer where applicable. NO LINKS!!
Answer:
d. x = 10 (the correct answer is marked)
Step-by-step explanation:
The Pythagorean theorem tells you the sum of the squares of the sides of a right triangle is the square of the hypotenuse.
x² +4² = (2√29)²
x² +16 = 116 . . . compute the squares
x² = 100 . . . . subtract 16
x = 10 . . . . take the square root
Answer:
d) [tex]\sf x=10[/tex]
Step-by-step explanation:
Pythagoras' Theorem: [tex]\sf a^2+b^2=c^2[/tex]
(where [tex]\sf a[/tex] and [tex]\sf b[/tex] are the legs, and [tex]\sf c[/tex] is the hypotenuse, of a right triangle)
Given:
[tex]\sf a=4[/tex][tex]\sf b=x[/tex][tex]\sf c=2\sqrt{29}[/tex]Substituting these values into the equation and solving for [tex]\sf x[/tex]:
[tex]\sf \implies 4^2+x^2=(2\sqrt{29})^2[/tex]
[tex]\sf \implies 16+x^2=116[/tex]
[tex]\sf \implies x^2=116-16[/tex]
[tex]\sf \implies x^2=100[/tex]
[tex]\sf \implies x=\pm \sqrt{100}[/tex]
[tex]\sf \implies x=\pm10[/tex]
Since distance is positive, [tex]\sf x=10[/tex] only
Therefore, the answer is d) [tex]\sf x=10[/tex].
Carmen bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $200 less than the desktop. She pald for the computers
using two different financing plans. For the desktop the interest rate was 9% per year, and for the laptop it was 7% per year. The total finance charges for one
year were $306. How much did each computer cost before finance charges?
Lizzie runs every 8 days and Wilson runs every 12 days. If they both ran together today, in how many days will they run together again?
Answer:
We have to find the LCM(least common multiple) of the two numbers.
24 is the LCM, because;
Multiples of 8 are -
8 x 1 = 8
8 x 2 = 16
8 x 3 = 24
Multiples of 12 are -
1 x 12 = 12
2 x 12 = 24
24 is their least common multiple.