using angle A as the reference angle, what is the ratio of the opposite side to the adjacent side?
write the ratio as a fraction
Answers
Answer:
20/21
Step-by-step explanation:
Opposite / Adjacent = RT / AR
You have to find RT
Use the Pythagorean Theorem
AR^2 + TR^2 = AT^2
21^2 + TR^2 = 29^2
441 + TR^2 = 841 Subtract 441 from both sides
TR^2 = 841 - 441
TR^2 = 400
sqrt(TR^2) = sqrt(400)
TR = 20
Ratio: TR / AR = 20/29
Related Questions
I really need the answer with explanation
Answers
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
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.
Answers
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
10 points
question 5: a, b, and c.
Answers
Answer:
the First One By Adding Four
The Second One Add Five And Two
The Third Add Two And Substract Four
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.
Answers
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]
Solve for x:
1.1.1
x² - 6x=0
Answers
Answer:
zoom in
mark me as brainliest
Separate the solutions and the quadratic equations are:
X=6,X=0
What is the relationship of the 4’s in the following numbers: 54,987 32,465
Answers
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.
4 × 1 + 3 × 1/10 + 9 x 1/1,000 in word form
Plsss 15 points :)
Answers
Answer:
four multipled by one plus three multiplied by one tenth plus 9 multiple by one one thousandth
Solve for X and Y
20x 25x 7x 5y 20x
Answers
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)
if z=14 and x=83 , then what is the value of y?
Answers
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
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
Answers
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.
Tan x= sin x/cos X. Therefore tan (90-A) =
Answers
Answer:
tan (90° - A) = cot A
Step-by-step explanation:
tan (90° - A) = sin (90° - A) / cos (90° - A) = cos A / sin A = cot A
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
Answers
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.
Someone please help me answer this!! Show me all steps you used please!!!
Answers
Answer:
144
Step-by-step explanation:
20²-16²
pythagorean theorem
a²=b²-c²
Express 1/3 as a repeating decimal and round to the nearest hundredth.
Answers
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
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
Answers
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 are the factors of x2 - 12x + 36?
Answers
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)
What is the measure of m?
12
4
n
m
m
[?]
Enter
will give brainliest
Answers
Answer:
8 I think
Step-by-step explanation:
if I'm wrong don't get offended
EVERYBODY LOOK.
^^^^^^^^^^^^^^^^^^^
40 FREEPOINTS
Answers
Answer:
Oh ok add me abelthegoat8
Step-by-step explanation:
Answer:
I don't have sc, but thx for the points! :)
Step-by-step explanation:
have a good day!
which is most likely the next step in the series?
Answers
Answer: the correct answer is a
Step-by-step explanation:
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?
Answers
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.
Which of the following is equivalent to the expression below?
4x + 2(3-x)
6x + 6
3x+6
5x + 6
2x +6
Answers
Answer:
2x + 6
Step-by-step explanation:
you have to factorize the above equation first and you'll get the answer
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?
Answers
Answer:
$5
Step-by-step explanation:
If every candy bar is $0.50 and they sell 10 just do
0.50 x 10 = 5
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.
Answers
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 :(
The store sells 6 donuts for $15 Kim has $37.50 how many donuts can she buy?
Answers
Answer:
12 if the donuts are sold in boxes and not singular, 15 if you can buy a smaller sized box
Step-by-step explanation:
Hope this helps! have a great day!
6/15 = 2.50
37/2.50 = 15
(since 6 donuts are equal to 15 dollars you would need to divide 6 and 15 to get the original price ( which would be 2.50) and now that you have the original price you can divide the original price from the amount that she originally has to figure out how many donuts that she needs ( 37.50 / 2.50 = 15) which would leave kim to have 15 donuts
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.
Answers
Answer:
8h ≥ 154
Step-by-step explanation:
Mark me Brainllest
An item sells for $40. The sales tax on
the item is 8%. What is the sales tax and
total cost?
Answers
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
Find the length of the third side. If necessary, round to the nearest tenth.
Answers
Answer:
must be 14
Step-by-step explanation:
Please please help!!!!!!!!
Answers
Explication:
Multiply 3 with 8 to turn the 3 whole points into parts.
3 x 8 = 24
Add the 7 pieces you already have,
24 + 7 = 31
Put it over 8 then you have your answer.
Answer = 31/8
(Now you know how to do it!)
I need help I already failed the first attempt
Answers
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 :)
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
Answers
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.