We can use the formula: is/of = %/100.
% = 60
of = 160
[tex]\frac{x}{160}=\frac{60}{100}[/tex]
100x = 9600
x = 96
96 students participated in the fundraiser.
which is most likely the next step in the series?
Answer: the correct answer is a
Step-by-step explanation:
The average annual cost (including tuition, room, board, books and fees) to attend a public college takes nearly a third of the annual income of a typical family with college-age children (Money, April 2012). At private colleges, the average annual cost is equal to about 60% of the typical family's income. The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars.
Private Colleges
52.8 30.6 43.2 45.8 33.3
33.3 50.5 44.0 42.0 37.8
Public Colleges
20.3 22.8 28.2 18.5 15.6 25.6
24.1 14.4 28.5 21.8 22.0 25.8
Required:
a. Compute the sample mean and sample standard deviation for private and public colleges.
b. What is the point estimate of the difference between the two population means?
c. Develop a 95% confidence interval of the difference between the annual cost of attending private and pubic colleges.
Answer:
(a)
[tex]\bar x_1 =41.33[/tex] [tex]\sigma_1 = 7.48[/tex]
[tex]\bar x_2 =22.3[/tex] [tex]\sigma_2 = 4.53[/tex]
(b)
[tex]d = 19.03[/tex]
(c)
[tex]CI = 16.33[/tex] to [tex]21.73[/tex]
Step-by-step explanation:
Given
[tex]n_1 = 10\\ n_2 = 12[/tex]
And the accompanying data for private (1) and public (2) colleges
Solving (a): The sample mean and sample standard deviations
Private College
Calculating sample mean
This is calculated as:
[tex]\bar x_i = \frac{\sum x_i}{n_i}[/tex]
[tex]\bar x_1 =\frac{52.8+30.6+43.2 +45.8 +33.3+33.3 +50.5 +44.0 +42.0 +37.8}{10}[/tex]
[tex]\bar x_1 =\frac{413.3}{10}[/tex]
[tex]\bar x_1 =41.33[/tex]
Calculating sample standard deviation
This is calculated as:
[tex]\sigma_i = \sqrt\frac{\sum(x_i - \bar x_i)}{n_i-1}[/tex]
[tex]\sigma_1 = \sqrt\frac{(52.8-41.33)^2+(30.6-41.33)^2+.........+(37.8-41.33)^2}{10-1}[/tex]
[tex]\sigma_1 = \sqrt\frac{503.261}{9}[/tex]
[tex]\sigma_1 = \sqrt{55.9178888889[/tex]
[tex]\sigma_1 = 7.4778264816[/tex]
[tex]\sigma_1 = 7.48[/tex] -- approximated
Public College
Calculating sample mean
[tex]\bar x_2 =\frac{20.3 +22.8 +28.2 +18.5 +15.6 +25.6+ 24.1 +14.4 +28.5 +21.8 +22.0 +25.8}{12}[/tex]
[tex]\bar x_2 =\frac{267.6}{12}[/tex]
[tex]\bar x_2 =22.3[/tex]
Calculating sample standard deviation
[tex]\sigma_2 = \sqrt\frac{(20.3 -22.3)^2+(22.8 -22.3)^2+(28.2 -22.3)^2+(18.5 -22.3)^2+(15.6 -22.3)^2+................+(25.8-22.3)^2}{12-1}[/tex][tex]\sigma_2 = \sqrt\frac{225.96}{11}[/tex]
[tex]\sigma_2 = \sqrt{20.5418181818[/tex]
[tex]\sigma_2 = 4.532308262[/tex]
[tex]\sigma_2 = 4.53[/tex] -- approximated
Solving (b): Point estimate of the difference between the two population means
This is calculated as:
[tex]d = \bar x_1 - \bar x_2[/tex]
[tex]d = 41.33 - 22.3[/tex]
[tex]d = 19.03[/tex]
Solving (c): 95% confidence interval
First, calculate the degrees of freedom:
[tex]df = \frac{(\sigma_1^2/n_1 + \sigma_2^2/n_2)^2}{\frac{(\sigma_1^2/n_1)^2}{n_1 - 1} + \frac{(\sigma_2^2/n_2)^2}{n_2 - 1}}[/tex]
[tex]df = \frac{(7.48^2/10 + 4.53^2/12)^2}{\frac{(7.48^2/10)^2}{10 - 1} + \frac{(4.53^2/12)^2}{12 - 1}}[/tex]
[tex]df = \frac{53.3647}{31.3045/9 + 2.9244/11}[/tex]
[tex]df = \frac{53.3647}{3.7441}[/tex]
[tex]df = 14.2530[/tex]
[tex]df = 14[/tex]
Calculate the critical value (t)
At 95% confidence interval and df = 14;
[tex]df = 14[/tex]
The confidence interval is then calculated as:
[tex]CI = (\bar x_1 - \bar x_2) \± \sqrt{\sigma_1^2/n_1 + \sigma_2^2/n_2}[/tex]
[tex]CI = (41.33 - 22.3) \± \sqrt{7.48^2/10 + 4.53^2/12}[/tex]
[tex]CI = 19.03 \± \sqrt{7.305115[/tex]
[tex]CI = 19.03 \± 2.70[/tex]
Split
[tex]CI = 19.03 - 2.70[/tex] to [tex]19.03 + 2.70[/tex]
[tex]CI = 16.33[/tex] to [tex]21.73[/tex]
This implies that:
Private colleges have population mean annual cost of $16.33 to $21.73 more expensive than public colleges
What are the factors of x2 - 12x + 36?
Answer:
(x-6) (x-6) or (x-6)^2
Step-by-step explanation:
1.) Find factors of 36 that add up to 12
2.) 6 which makes this a perfect square
3.) you know to subtract because the middle term is negative and the third term is positive (two negatives make a positive)
i need help fast, thank you!!!
Answer:
D
Step-by-step explanation:
30 multiplied by 1.34 is 40.2
Samantha makes $8.00 an hour babysitting. With the money Samantha earns babysitting, she plans to buy herself a MP3 player that costs $154.00.
Which inequality represents the number of hours Samantha would have to babysit in order to have enough money to buy the MP3 player?
A youth group takes a bus to the movie theater. The cost of a drink is $2.25, the cost of popcorn is $3.45, and the cost of a ticket is $7.00. Each student gets a ticket, a drink, and popcorn. The bus rental costs $100.
If the total cost of the trip is $252.40, how many people went?
Sandra surveyed 15 of her friends to find the number of badges and stickers they owned.
Based on the distribution of data, which observation is correct?
The mean number of stickers is about 1.3 times the mean number of badges.
The mean number of stickers is about 1.3 times the mean number of badges.
The mean number of stickers is about 0.78 times the mean number of badges.
The mean number of stickers is about 0.78 times the mean number of badges.
The mean number of badges is greater than the mean number of stickers because the tallest column is farther right.
The mean number of badges is greater than the mean number of stickers because the tallest column is farther right.
The median number of badges is greater than the median number of stickers because the tallest column is farther right.
The median number of badges is greater than the median number of stickers because the tallest column is farther right.
Answer:
8h ≥ 154
Step-by-step explanation:
Mark me Brainllest
Find the length of the third side. If necessary, round to the nearest tenth.
Answer:
must be 14
Step-by-step explanation:
What is the relationship of the 4’s in the following numbers: 54,987 32,465
Answer:
The 4 in the number "32465" is 10 times less as the 4 in "54987"
Step-by-step explanation:
Write it out in expanded form 32465: "30000+2000+400+60+5" and 54987: "50000+4000+900+80+7" and 4000 in 54987 is 10 times greater than 400 in 32465.
I need help I already failed the first attempt
Step-by-step explanation:
Hi,
y - 1 = 2 - x has a negative slope.
x + y = 0 has a negative slope.
y = 4x - 3 has a positive slope.
y = 1 has a 0 slope.
x = 10 has an undefined slope.
I hope this helps :)
Someone please help me answer this!! Show me all steps you used please!!!
Answer:
144
Step-by-step explanation:
20²-16²
pythagorean theorem
a²=b²-c²
if z=14 and x=83 , then what is the value of y?
Answer:
y = 152
Step-by-step explanation:
The chord- chord angle x is half the sum of the arcs intercepted by the angle and its vertical angle, that is
[tex]\frac{1}{2}[/tex] (y + z) = 83 ( multiply both sides by 2 to clear the fraction )
y + z = 166
y + 14 = 166 ( subtract 14 from both sides )
y = 152
4. Which one of the following pairs of numbers contains like fractions?
A. 5/4 and 4/5
B.4/8 and 12/16
c. 6/7and 60/70
D.1/2 and 3/2
Answer:
6/7 and 60/70
Step-by-step explanation:
6 times 10 is 60
7 times 10 =70
[tex]\huge\red{\boxed{\tt{\colorbox{pink}{ANSWER:}}}}[/tex]
C. 6/7 and 60/706 × 10 = 60
7 × 10 = 70
꧁✰_______❀Edilyn❀_______✰꧂#CarryOnLearning
#NoToCopyPaste
For brainly user:Just please, idols ,if we are going to answer questions here on brainly, don't do the ones from the internet, then just copy and paste
You can search on the internet but make your own sentence okay? Thank you
What is the measure of m?
12
4
n
m
m
[?]
Enter
will give brainliest
Answer:
8 I think
Step-by-step explanation:
if I'm wrong don't get offended
4 × 1 + 3 × 1/10 + 9 x 1/1,000 in word form
Plsss 15 points :)
Answer:
four multipled by one plus three multiplied by one tenth plus 9 multiple by one one thousandth
I need help I will give you brainless
Answer:
what are u trying to find, what they each are?
Step-by-step explanation:
Answer:
circle =4
triangle = 2
square = 3
Step-by-step explanation:
circle= c
triangle = t
square = s
2c+t+s =13
t+s = 5
nultiply the second by -1 and add both
2c +t +s = 13
-t-s = -5
2c= 8
c= 4 CIRCLE = 4
3t +4 = 10
3t = 6
t= 2 TRIANGLE = 2
s+2=5
s=3 SQUARE = 3
Which expression is the simplest form of 2(4x + y) + 3(x - 6y) + x2?
O A. x2 + 11x-17y
B. x2 + 11x – 4y
C. x2 + 9x- 17y
O D. x2 + 11x-16y
Answer:
x² + 11x-16y
Step-by-step explanation:
The given equation is :
[tex]2(4x + y) + 3(x - 6y) + x^2[/tex]
It can be simplified as follows :
[tex]2(4x + y) + 3(x - 6y) + x^2\\\\=2(4x)+2y+3x-3(6y)+x^2\\\\=8x+2y+3x-18y+x^2\\\\=11x-16y+x^2[/tex]
So, the correct option is (d) i.e. x² + 11x-16y.
Which is the best example of an explicit statement from Thoughts and Sentiments that shows Cugoano's beliefs about slavery?
A. “However, notwithstanding all that has been done and written against it, that brutish barbarity, and unparalelled injustice, is still carried on to a very great extent in the colonies, and with an avidity as insidious, cruel and oppressive as ever.”
B. “However, it cannot but be very discouraging to a man of my complexion in such an attempt as this, to meet with the evil aspersions of some men, who say, ‘That an African is not entitled to any competent degree of knowledge, or capable of imbibing any sentiments of probity; and that nature designed him for some inferior link in the chain, fitted only to be a slave.’”
C. “By some of such complexion, as whether black or white it matters not, I was early snatched away from my native country, with about eighteen or twenty more boys and girls, as we were playing in a field.”
D. “But the supporters and favourers of slavery make other things a pretence and an excuse in their own defence; such as, that they find that it was admitted under the Divine institution by Moses, as well as the long continued practice of different nations for ages; and that the Africans are peculiarly marked out by some signal prediction in nature and complexion for that purpose.”
Answer:
A. “However, notwithstanding all that has been done and written against it, that brutish barbarity, and unparalelled injustice, is still carried on to a very great extent in the colonies, and with an avidity as insidious, cruel and oppressive as ever.”
Explanation:
Ottobah Cugoano's "Thoughts and Sentiments on the Evil of Slavery" provides a personal take on the issue of slavery and how evil of a practice it is for African Americans. At the same time, he also asserted that slaves had the right to rebel against their masters for the treatment they were put under.
One explicit statement that reveals the author's beliefs about the slavery system is "However, notwithstanding all that has been done and written against it, that brutish barbarity, and unparalelled injustice, is still carried on to a very great extent in the colonies, and with an avidity as insidious, cruel and oppressive as ever." Through these lines, Cugoano labels slavery as "brutish barbarity, and an unparallelled injustice ... insidious, cruel and oppressive..."
Thus, the correct answer is option A.
An item sells for $40. The sales tax on
the item is 8%. What is the sales tax and
total cost?
Answer:
$43.20 total
$3.20 sales tax
Explication:
40*1.08=43.2
Answer:
sales tax = $3.20
total cost = $43.20
Step-by-step explanation:
To calculate the sales tax on an item, multiply the price of the item by the tax percent in decimal form. To convert a percent to decimal form, divide the percent by (100).
Sales tax percent: 8%
In decimal form: 0.08
Multiply the sales tax in decimal form by the price of the item to find out the sales tax amount,
(item_price) * (sales_tax)
= (40) * (0.08)
= 3.2
Sales tax amount: $3.20
To find the total cost of the product, add the sales tax amount to the item price,
(item_price) + (sales_tax_amount)
= 40 + 3.20
= 43.20
A mirror has a parabolic surface defined by the equation y =StartFraction 1 Over 24 EndFraction x2 with the vertex (0, 0) at the center of the mirror. When the width of the mirror is 8 inches, what is the depth, y, of the mirror?
1/36 in.
1/6 in.
2/3 in.
2 2/3 in.
ITS C: 2/3 in.
Answer:
Step-by-step explanation:
Edge 2022
Answer:
c
Step-by-step explanation:
2/3 in
Professor Adeyemi is examining well-being after retirement in a city, and it is important to have excellent external validity. Professor Adeyemi selects two random numbers, 4 and 6, and gets a list of all of the retired people in the city. If Professor Adeyemi obtains the sample by starting with the 4th person on the list and selecting every 6th person, which of the following sampling techniques is most likely being used?
a. systematic sampling
b. stratified random sampling
c. quota sampling
d. cluster sampling
Answer:
A: systematic sampling
Step-by-step explanation:
The correct answer is systematic Sampling.
This is because, Systematic sampling is a method of sampling whereby the researchers choose members of a population at regular intervals e.g., when we select every 10th person on a particular list in the population.
And in this question, the professor starts with the 4th person on the list and selecting every 6th person. Thus, the answer is systematic Sampling.
richard can mow 2 of his neighbors lawns in 1.6 hours. He expresses this information as the ratio 2 lawns/1.6 hours. To find the number of lawns he mows each our, Richard can-
A-divide 2 by 1.6, resulting in 1.25
B- Multiply 1.6 by 2, resulting in 3.2
C- divide 1.6 by 2, resulting in 0.8
D- add 2 to 1.6, resulting in 3.6
Answer:
I think it's C.
1/6th of an hour would be 1:10 minutes. Also known as 70 minutes, so 70 divided by 2 equals 35.
The International Coffee Association has reported the mean daily coffee consumption for U.S. residents as 1.65 cups. Assume that a sample of 38 people from a North Carolina city consumed a mean of 1.84 cups of coffee per day, with a standard deviation of 0.85 cups. In a two-tail test at the 0.05 level, could the residents of this city be said to be significantly different from their counterparts across the nation?
Answer:
The calculated value t = 1.3788 < 2.0262 at 0.05 level of significance
the null hypothesis is accepted
There is no significant difference between their counterparts across the nation
Step-by-step explanation:
Step(i):-
Given that the mean of the U.S residents = 1.65
Given that the size of the sample 'n' = 38
Mean of the sample = 1.84
Given that the standard deviation of the sample (S) = 0.85
Step(ii):-
Null hypothesis:H₀:
There is no significant difference between their counterparts across the nation
Alternative Hypothesis:-H₁:
There is a significant difference between their counterparts across the nation
Test statistic
[tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{1.84-1.65}{\frac{0.85}{\sqrt{38} } }[/tex]
t = 1.3788
Degrees of freedom
ν = n-1 = 38-1 = 37
t₀.₀₅ ,₃₇ = 2.0262
The calculated value t = 1.3788 < 2.0262 at 0.05 level of significance
Null hypothesis is accepted
Final answer:-
There is no significant difference between their counterparts across the nation.
Hailey made the following statement: "It is impossible t o build a rectangular prism with a volume of 40 units 3 if one side measures 5 units." Key represents 1 cubic unit Select the two figures below that prove Hailey's statement is false.
Answer:
D
Step-by-step explanation:
Answer: B and C / the second one and the third one
Sorry if you already had to submit or answer this :(
Exercise 12.1.1: Coin flips and events. About A coin is flipped four times. For each of the events described below, express the event as a set in roster notation. Each outcome is written as a string of length 4 from {H, T}, such as HHTH. Assuming the coin is a fair coin, give the probability of each event. (a) The first and last flips come up heads. (b) There are at least two consecutive flips that come up heads. (c) The first flip comes up tails and there are at least two consecutive flips that come up heads.
Answer:
a [tex]Pr = 0.25[/tex]
b [tex]Pr = 0.50[/tex]
c [tex]Pr = 0.1875[/tex]
Step-by-step explanation:
Given
[tex]n = 4[/tex] --- number of times
[tex]r = 2[/tex] --- faces of a coin
First, is to determine the sample size.
This is calculated as:
[tex]Size =r^n[/tex]
[tex]Size =2^4[/tex]
[tex]Size =16[/tex]
Solving (a): First and last slip is head
This event is represented as:
[tex]E=\{HHHH, HHTH, HTHH, HTTH\}[/tex]
The probability is calculated as:
[tex]Pr = \frac{n(E)}{Size}[/tex]
[tex]Pr = \frac{4}{16}[/tex]
[tex]Pr = 0.25[/tex]
b) At least 2 consecutive flips that is heads.
This event is represented as:
[tex]E=\{HHHH,HHHT,HHTH,HHTT,THHH,THHT,HTHH,TTHH\}[/tex]
The probability is calculated as:
[tex]Pr = \frac{n(E)}{Size}[/tex]
[tex]Pr = \frac{8}{16}[/tex]
[tex]Pr = 0.50[/tex]
c) First is tail and at least 2 consecutive flips is head.
This event is represented as:
[tex]E=\{THHH,THHT,TTHH\}[/tex]
The probability is calculated as:
[tex]Pr = \frac{n(E)}{Size}[/tex]
[tex]Pr = \frac{3}{16}[/tex]
[tex]Pr = 0.1875[/tex]
I really need the answer with explanation
Answer:
A = 22 and B = 35
Step-by-step explanation:
The proportional value of x and y is simply
x times 3 1/2 = y
4250cm ........... m?
Answer:42.5
Step-by-step explanation:
4250cm = 42,5m
The answer is: 42,5
Please please help!!!!!!!!
Solve for X and Y
20x 25x 7x 5y 20x
9514 1404 393
Answer:
(x, y) = (5, 9)
Step-by-step explanation:
We must find the value of x before we can find the value of y. Fortunately, simply adding the arcs around the circle will give an equation for x.
25x +20x +7x +20x = 360 . . . . angles in degrees
72x = 360 . . . simplify
x = 5 . . . . . . divide by 72
__
The value of the external angle at J is half the difference of arcs GL and HK. That is, ...
5y = (25x -7x)/2 = 9x = 9(5) . . . . simplify, fill in for x
y = 9 . . . . . . divide by 5
__
(x, y) = (5, 9)
Which of the following is equivalent to the expression below?
4x + 2(3-x)
6x + 6
3x+6
5x + 6
2x +6
Answer:
2x + 6
Step-by-step explanation:
you have to factorize the above equation first and you'll get the answer
Express 1/3 as a repeating decimal and round to the nearest hundredth.
Answer:
1/3 is .333... so you can write .33.... or .33 with a line on top of the 3's
Step-by-step explanation:
.3 is in the tenths and .33 is in the hundredths place
During a fundraiser, students in Math Club make a $0.50 profit for every candy bar they sell. Let n represent the number of candy bars the club sells. Let t represent the total profit earned, in dollars. What is the total profit earned for selling 10 candy bars?
Answer:
$5
Step-by-step explanation:
If every candy bar is $0.50 and they sell 10 just do
0.50 x 10 = 5