Answer:
Approximately 256,140 recent college graduates have accumulated a student loan of more than $30,000.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Average cumulative debt of recent college graduates is about $22,500, standard deviation of $7,000.
This means that [tex]\mu = 22500, \sigma = 7000[/tex]
Proportion more than 30000.
1 subtracted by the pvalue of Z when X = 30000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30000 - 22500}{7000}[/tex]
[tex]Z = 1.07[/tex]
[tex]Z = 1.07[/tex] has a pvalue of 0.8577
1 - 0.8577 = 0.1423
Approximately how many recent college graduates have accumulated a student loan of more than $30,000?
0.1423 out of 1.8 million.
0.1423*1.8 = 0.25614 million = 256,140
Approximately 256,140 recent college graduates have accumulated a student loan of more than $30,000.
What is the x-value of the solution to this system of equations?
Y=2/7x-1
2x + 7y = -49
Answer:
x = -21/2
Step-by-step explanation:
y= 2/7 x-1
or, 7y= 2x -7
or, 2x -7y =7
2x + 7y = -49
4x = -42
x= -21/2
y= 2/7 × -21/2 -1
= -4
How many degrees does it take a capterpillar to turn upright
it is at least 180 degrees
A desk drawer is shaped like a rectangular prism. The height of the drawer is 7 inches. The bottom of the drawer has an area of 210 square inches.
What is the volume of the desk drawer?
pls help Ill give you brainiest and pic for your profile
Answer:
1470
Step-by-step explanation:
are Equilateral triangles always acute triangles.
Answer:
Yes, they can only have acute angles (all measure 60°)
Step-by-step explanation:
Help me with this please
Answer:
x = 37.5
Step-by-step explanation:
The easiest way to solve this is to realize that the bottom triangle is a an Isosceles triangle, with the upper angle being equal to 180 - 75 degrees. That gives us the number 105°
Because it's an Isosceles triangle, we can simply say that the bottom angles, including the one we want to calculate are equal and both add up 105 (again, because the angles in a triangle add up to 180, and we know the top one is 105).
That gives us:
(180 / 105) / 2
= 75 / 2
= 37.5
The base of the pyramid is a right triangle
The volume is ____ cubic cm.
Answer:
37 cubic cm should be the answer sorry if I am wrong
Slick Slack is a downloadable app that can be used to automatically generate excuses for being late to work based on the weather, traffic conditions, and the employer's line of business. One week after its release, 6,040 copies of Slick Slack were downloaded. After 5 weeks, 13,090 copies had been downloaded. Let x represent the number of weeks since Slick Slack was released, and y represent the number of copies that had been downloaded. Use the marginal change and the fact that 1 week after its release 5840 copies of Slick Slack were downloaded to determine the y intercept in the equation y = a + bx.
a) (x,y) =____.
b) write the equation in the form y = a + bx for the number of copies downloaded x weeks after its release.
Answer:
[tex](x_1,y_1) = (1,5840)[/tex]
[tex](x_2,y_2) = (2,13090)[/tex]
[tex]y = 1812.5x + 4027.5[/tex]
[tex]y_0 = 4027.5[/tex] --- y intercept
Step-by-step explanation:
Given:
x = weeks; y = copies
The right parameters are:
After 1 week, 5840 copies were downloaded
After 5 weeks, 13090 copies were downloaded
So, the (x,y) forms are:
[tex](x_1,y_1) = (1,5840)[/tex]
[tex](x_2,y_2) = (5,13090)[/tex]
Next, we calculate the slope (m) using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{13090 - 5840}{5 - 1}[/tex]
[tex]m = \frac{7250}{4}[/tex]
[tex]m = 1812.5[/tex]
The equation is then calculated using:
[tex]y = m(x - x_1) + y_1[/tex]
[tex]y = 1812.5(x - 1) + 5840[/tex]
[tex]y = 1812.5x - 1812.5 + 5840[/tex]
[tex]y = 1812.5x + 4027.5[/tex]
To calculate the y intercept, substitute 0 for x
[tex]y_0 = 1812.5*0 + 4027.5[/tex]
[tex]y_0 = 0 + 4027.5[/tex]
[tex]y_0 = 4027.5[/tex]
The thickness of the backfat in pigs is used in evaluating the quality of their flesh for consumption. To compare the backfat thickness of pigs raised on two different diets, an animal researcher randomly sampled a group of pigs raised on Diet 1 and another group raised on Diet 2:
Sample Mean Sample SD Sample Size
Diet 1 3.63 cm 0.29 cm 18
Diet 2 3.37 cm 0.25 cm 18
POOLED SE 0.09
A) After confirming all relevant assumptions, you want to test if the mean backfat thicknesses of the pigs raised on these two diets differs. What is the absolute value of the test statistic?
B) If the critical value for this test is 2.032 (confirm that it is), what would be an appropriate conclusion for this test?
A. An conclusion is not warranted for this test
B. This data provides evidence that mean backfat thickness of pigs on Diet 1 is different from pigs on Diet 2 (p<.05)
C. This data provides no evidence that mean backfat thickness of pigs on Diet 1 is different from pigs on Diet 2 (p<.05)
D. This data provides evidence that diet is independent of backfat thickness (p<.05)
E. There is no evidence that diet is independent of backfat thickness (p>.05)
Answer:
A) The test statistic is approximately 7.5056
B) E. There is no evidence that diet is independent of backfat thickness
Step-by-step explanation:
The given data are;
The sample mean for pigs raised on Diet 1, [tex]\overline x_1[/tex] = 3.63 cm
The sample SD for pigs raised on Diet 1, s₁ = 0.29 cm
The number of pigs in the sample for pigs raised on Diet 1, n₁ = 18
The sample mean for pigs raised on Diet 2, [tex]\overline x_2[/tex] = 3.37 m
The sample SD for pigs raised on Diet 2, s₂ = 0.25 cm
The number of pigs in the sample for pigs raised on Diet 2, n₂ = 18
The pooled SE = 0.09
A) The test statistic is given by the following formula;
[tex]t=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{\dfrac{s_{1}^{2} }{n_{1}}-\dfrac{s _{2}^{2}}{n_{2}}}}[/tex]
Therefore, we have;
[tex]t=\dfrac{(3.63-3.37)}{\sqrt{\dfrac{0.29^{2} }{18}-\dfrac{0.25^{2}}{18}}} \approx 7.5056[/tex]
The test statistic, t ≈ 7.5056
B) The degrees of freedom, df = n₁ - 1 = 18 - 1 = 17
At a confidence level of 95%, the critical value is 2.11
Given that the value of the test statistics tic if larger than the critical value, the null hypothesis is rejected and there is a difference in the backfat of the pigs on different diet
Therefore, there is no evidence that diet is independent of backfat thickness
PLEASE HELP ITS DUE IN AN HOUR!!!!!!
Answer:
3 units to the right of -5
Step-by-step explanation:
Solve | 2x | = | x + 3 | by graphing
Answer:the answer is 3 and -1
Step-by-step explanation:
X=3
And
X=-1
Question 11
2 pts
If the temperature at 10:00 am is -23° F and two
hours later at 12.00 pm the temperature rose 6
degrees Fahrenheit, what is the
temperature at
12:00 pm in degrees?
Help plzzzzzzxhshshxyxush
Answer:
a.
Step-by-step explanation:
because "six hundered one" is 601 and "five hundredths" is .05 so the only number with both those 2 is a so the awnser is a.
Please help trigonometry and special right trianglez
Answer:
Step-by-step explanation:
Triangles & Trigonometry
Answer:
Answer: x = y = 2√7
Step-by-step explanation:
x = (2√14)cos45
x = (2√14)½√2
x = √14(√2) = √28 = 2√7
y = (2√14)sin45
y = (2√14)½√2
y = √14(√2) = √28 = 2√7
Is 3times4 the same as 4 times 3
Answer:
Yes, 3x4=12 and 4x3=12
Step-by-step explanation:
Answer:
Yes
Step-by-step explanation:
3 × 4 = 12
4 × 3 = 12
x-3=14 use the opposite operation found in the equation.
Step-by-step explanation:
x-3=14
x=14+3
x=17
verification
x(17)-3=14
17-3=14
14=14
45,678 in expanded form
Answer:
40,000 + 5000 + 600 + 70 + 8
Step-by-step explanation:
take the numbers all off and break them down by their value.
WILL GIVE BRAINLIEST TO ANSWER
its x4 got it thanks give me brainliest
Jean worked 47 hours last week and was paid $527. How much was she paid per hour?
Answer:
11.2127659574
Step-by-step explanation:
Answer:
$11.21 per hour.
Step-by-step explanation:
Divide the pay by the hours worked and round to the nearest tenth.
527/ 47 = 11.21276596 then round to 11.21
PLEASE I NEED HELP CLICK ON THIS IMAGE
Answer:
D, 261
Step-by-step explanation:
Divide all of the answer choices by 9. The answer is the one with the whole number. 261/9=29 29=whole number so D is the answer.
Hope this helps! If it did, please give brainliest! It would help a lot! :D
Answer:
261
Step-by-step explanation:
If the farmer used 9 boxes and each had the same number, we need to find the number that's divisible by 9.
There's a great fact - a number is divisible by 9 if its sum of digits is divisible by 9.
Let's use that fact on the answers first:
281 -> 2 + 8 + 1 -> 11 -> 1 + 1 -> 2; not divisible by 9
273 -> 2 + 7 + 3 -> 12 -> 1 + 2 -> 3; not divisible by 9
261 -> 2 + 6 + 1 -> 9; divisible by 9
Please note that we could just say that 11 is not divisible by 9, but I wanted to show that we can do it again - nothing stops us and it still works.
To know why this method works, note that a number ABC is equal to:
100 * A + 10 * B + C = 99 * A + 9 * B + (A + B + C) = 9*(11*A + B) + (A + B + C)
And we know that 9*(11*A + B) is divisible by 9 because it's literally 9 times something. So A+B+C is equal to ABC minus something divisible by 9, and that proves what we needed.
Pls helpp It is due today
Answer:
$13.75
Step-by-step explanation:
d= 9.75
43 - 3(9.75) = 13.75
If the measure of angle CBD is 5(7x + 15) degrees, then what is the value of x. (Angle CDB is 180)
x =
Answer:
[tex]\huge\boxed{\sf x = 3 }[/tex]
Step-by-step explanation:
If the measure of :
∠CBD = 5 ( 7x + 15 )
Also,
∠CBD = 180°
Then,
5 (7x + 15) = 180
35x + 75 = 180
Subtract 75 to both sides
35x = 180 - 75
35x = 105
Divide both sides by 35
x = 105 / 35
x = 3
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Someone please explain how you got the answer please and thank you
Answer:
3 texts by madelyn, there were 2 texts from aubrey
Step-by-step explanation:
the ratio of maddie to aubrey was 18:12 which is 3:2
so 3 by maddie = 2 by aubrey
i used maddie because its shorter
Answer:
6 + 6 is 12 and 12 + 6 is 18 so i think its for every 6 text sent and then 6 again (6 in both boxes)
Step-by-step explanation:
adore your sasha pfp
WILL GIVE BRAINLIEST
Answer:
B. 12
Step-by-step explanation:
First, we need the degrees for A. So, cosx = 5/13 = 67.4
Now it will be easy to solve a. tan67.4° = a/5 = 12.011728511....
we round it to the nearest tenth and we get 12.
Step-by-step explanation:
By pythagoras theoram
[tex]c = \sqrt{a2 + b2} [/tex]
13=a²+5²a²=13²--5²a²=169--25a²=144I think this is a helpful for youplease i will give you brainly -1,8÷9 I need step by step
Answer:
-0.2
I couldn't get step by step but hope this answer helps out a little...
(Do you need it for ur assignment?)
Step-by-step explanation:
-18/9 = 2, 9 goes into 18, 2 times, but a negative divided by a positive always = a negative number so the answer would come out to be -2.
-18/9 = 2, 9 goes into 18, 2 times, but a negative divided by a positive always = a negative number so the answer would come out to be -2.
however is you were typing -1.8 / 9 then it would be -0.2. Multiplying -0.2 * 9 would give you -1.8. Same rule applies as to why it's negative
I wasn't sure if the comma was a typo in your question but I Hope this helps :)
A rectangle has a perimeter of 103.6 inches and a base of 39 inches. What is the height?
Answer:
12.8 IN.
Step-by-step explanation:
So, what exactly is perimeter?
Perimeter= 2L+ 2W
In this question we were given the length.ie.Base and the perimeter itself.
●Length is 39 In.
●Perimeter is 103.6 In.
●We don't know the width.
But, as per given the question, we know that;
1 length = 39 In.
2 lengths= 78 In.
Now that we know the total length we can find the total width.
See as follows,
103.6 - 78= 25.6
2 widths= 25.6
1 width= 25.6÷2
=12.8 In
find the circumference of the circle. PLEASE HELP I HAVE 5 MINUTES LEFT :(
Answer:
18.84
Step-by-step explanation:
Is it right ????????
Answer:
yeah
Step-by-step explanation:
5^-2 + 7^0
PLSSS HELP MEEE IM IN SCHOOL RIGHT NOW
TRY THIS
Step-by-step explanation:
Step-by-step explanation:
Given
[tex] {5}^{ - 2} + {7}^{0} \\ = \frac{1}{ {5}^{2} } + 1 \\ = \frac{1}{25} + 1 \\ = \frac{1 + 25}{25} \\ = \frac{26}{25} [/tex]
Hope it will help :)❤
The area of a sector of a circle of radius 5
cm, formed by an arc of length 3.5 cm is
(a) 8 cm?
(b) 8.75 cm?
(c) 9.5 cm?
(d) 7.9 cm?
Answer:
A = 8.75 cm²
Step-by-step explanation:
Given that,
Radius, r = 5 cm
The arc length, l = 3.5 cm
We need to find the area of a sector. Let [tex]\theta[/tex] be the angle. So,
[tex]\theta=\dfrac{l}{r}\\\\\theta=\dfrac{3.5}{5}\\\\\theta=0.7\ rad[/tex]
The formula for the area of sector when [tex]\theta[/tex] is in radian is given by :
[tex]A=\dfrac{1}{2}\times \theta r^2\\\\A=\dfrac{1}{2}\times 0.7\times 5^2\\\\A=8.75\ cm^2[/tex]
So, the area of the sector is 8.75 cm².
Answer: (b)
Step-by-step explanation:
Given
the radius of circle r=5 cm
arc length [tex]l=3.5\ cm[/tex]
Arc length is also given by
[tex]l=\dfrac{\theta }{360^{\circ}}\times 2\pi r[/tex]
[tex]\Rightarrow 3.5=\dfrac{\theta }{360^{\circ}}\times 2\pi \times 5\\\\\Rightarrow \theta =40.10^{\circ}[/tex]
Area of the sector is given by
[tex]\Rightarrow A=\dfrac{\theta }{360^{\circ}}\times \pi r^2\\\\\Rightarrow A=\dfrac{40.101^{\circ}}{360^{\circ}}\times 3.142\times 5^2\\\\\Rightarrow A=8.749\approx 8.75\ cm^2[/tex]