Answer:
a) 0.0749 = 7.49% probability that the student makes more than $15,000.
b) 0.227 = 22.7% probability that the student makes between $13,000 and $14,000.
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.
Full-time Ph.D. students receive an average of $12,837 per year.
This means that [tex]\mu = 12837[/tex]
Standard deviation of $1500
This means that [tex]\sigma = 1500[/tex]
a. The student makes more than $15,000.
This is 1 subtracted by the p-value of Z when X = 15000.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{15000 - 12837}{1500}[/tex]
[tex]Z = 1.44[/tex]
[tex]Z = 1.44[/tex] has a p-value of 0.9251.
1 - 0.9251 = 0.0749
0.0749 = 7.49% probability that the student makes more than $15,000.
b. The student makes between $13,000 and $14,000.
This is the p-value of Z when X = 14000 subtracted by the p-value of Z when X = 13000.
X = 14000
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{14000 - 12837}{1500}[/tex]
[tex]Z = 0.775[/tex]
[tex]Z = 0.775[/tex] has a p-value of 0.7708.
X = 13000
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{13000 - 12837}{1500}[/tex]
[tex]Z = 0.11[/tex]
[tex]Z = 0.11[/tex] has a p-value of 0.5438.
0.7708 - 0.5438 = 0.227
0.227 = 22.7% probability that the student makes between $13,000 and $14,000.
7.49% of the student makes more than $15,000, while 23.85% of the student makes between $13,000 and $14,000
What is z score?
Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
z = (raw score - mean) / standard deviation
Given that:
Mean = $12837, standard deviation = $1500
a) For >15000:
z = (15000 - 12837)/1500 = 1.44
P(z > 1.44) = 1 - P(z < 1.44) = 1 - 0.9251 = 0.0749
b) For >13000:
z = (13000 - 12837)/1500 = 0.11
For <14000:
z = (14000 - 12837)/1500 = 0.78
P(0.11 < z < 0.78) = P(z < 0.78) - P(z < 0.11) = 0.7823 - 0.5438 = 0.2385
7.49% of the student makes more than $15,000, while 23.85% of the student makes between $13,000 and $14,000
Find out more on z score at: https://brainly.com/question/25638875
F(x)=x+8;g(x)=x+2. Find f=g
Answer:
f(x) can not be equal to g(x)
Step-by-step explanation:
If the result is possible:
f(x) = g(x)
x + 8 = x + 2
x + 8 - (x + 2) = x + 2 - (x + 2)
6 = 0
Because 6 can't be equal to 0, so do f(x) can't be equal to g(x)
A capark has 34 rows and each row can acommodate 40 cars. If there are 976 cars parked, how many cars can still be parked?
Answer:
384 cars
Step-by-step explanation:
To find the total number of spaces in the carpark, we must multiply the number of rows by how many cars they can accommodate:
34 ⋅ 40 = 1360
As you can see, we have 1360 total spaces. Since there are 976 cars parked, and we want to find out how many spaces are left, we have to subtract the amount of cars parked from the total spaces.
1360 - 976 = 384
Therefore, our answer is 384, specifically, 384 cars.
Answer:
384 cars.
Step-by-step explanation:
40 * 34 - 976
= 1360 - 976
= 384.
The amount of money invested in a retirement fund is an example of which of the following?
a.
investment asset
b.
liquid asset
c.
long term asset
d.
use asset
Please select the best answer from the choices provided
Answer:
the answer is A
okay that it have a nice day
Answer:
the answer above me is correct!
Step-by-step explanation:
Edge 2021
Three Nissans, two Fords, and four Chevrolets can be rented for $106 per day. At the same rates two Nissans, four Fords, and three Chevrolets cost $107 per day, whereas four Nissans, three Fords, and two Chevrolets cost $102 per day. Find the rental rate for the Fords.
Answer:
The rental rate for the Fords is of $12 per day.
Step-by-step explanation:
This question is solved using a system of equations.
I am going to say that:
x is the cost of a Nissan.
y is the cost of a Ford.
z is the cost of a Chevrolet.
Three Nissans, two Fords, and four Chevrolets can be rented for $106 per day.
This means that:
[tex]3x + 2y + 4z = 106[/tex]
Two Nissans, four Fords, and three Chevrolets cost $107 per day
This means that:
[tex]2x + 4y + 3z = 107[/tex]
Four Nissans, three Fords, and two Chevrolets cost $102 per day.
This means that:
[tex]4x + 3y + 2z = 102[/tex]
From the first equation:
[tex]4z = 106 - 3x - 2y[/tex]
[tex]2z = 53 - 1.5x - y[/tex]
[tex]z = 26.5 - 0.75x - 0.5y[/tex]
Replacing into the third equation:
[tex]4x + 3y + 53 - 1.5x - y = 102[/tex]
[tex]2.5x + 2y = 49[/tex]
From the second equation:
[tex]2x + 4y + 3z = 107[/tex]
[tex]2x = 107 - 4y - 3z[/tex]
[tex]x = 53.5 - 2y - 1.5z[/tex]
[tex]x = 53.5 - 2y - 1.5(26.5 - 0.75x - 0.5y)[/tex]
[tex]x - 1.125x = 53.5 - 2y - 39.75 + 0.75y[/tex]
[tex]-0.125x = 13.75 - 1.25y[/tex]
[tex]0.125x = 1.25y - 13.75[/tex]
[tex]x = \frac{1.25y - 13.75}{0.125}[/tex]
[tex]x = 10y - 110[/tex]
Find the rental rate for the Fords.
We have to find y, so:
[tex]2.5x + 2y = 49[/tex]
[tex]2.5(10y - 110) + 2y = 49[/tex]
[tex]25y - 275 + 2y = 49[/tex]
[tex]27y = 324[/tex]
[tex]y = \frac{324}{27}[/tex]
[tex]y = 12[/tex]
The rental rate for the Fords is of $12 per day.
2 hundreds equal how many tens?
Lets see if ya'll know the answer cause i do
Answer:
200 is equal to 20 tens I guess lol
Answer:
20 tens
Step-by-step explanation:
200÷10=20 groups of ten
Select the correct expressions and value.
Identify the expressions and the value that are equivalent to 6 times 5 squared.
5x 6²
6 x 5
192
6 x 5 x 5
6x5x2
150
6 + 5 x 5
Reset
Next
Answer:
✔️6 × 5²
✔️6 × 5 × 5
✔️150
Step-by-step explanation:
6 times 5 squared is written as 6 × 5²
Thus:
6 × 25 = 150
Evaluate each of the expressions given to determine whether they are equivalent to 150 or not
✔️5 × 6² = 5 × 36 = 180 (NOT EQUIVALENT)
✔️6 × 5² = 6 × 25 = 150 (EQUIVALENT)
✔️192 ≠ 150 (NOT EQUIVALENT)
✔️6 × 5 × 5 = 6 × 25 = 150 (EQUIVALENT)
✔️6 × 5 × 2 = 6 × 10 = 60 (NOT EQUIVALENT)
✔️150 = 150 (EQUIVALENT)
✔️6 + 5 × 5 = 6 + 25 = 31 (NOT EQUIVALENT)
90units needed 8 units per case what's the #of cases & # of additional units
Answer:
# of cases: 11
Additional units: 2
Step-by-step explanation:
If each case can hold 8 units, and we want to find the total # number of cases, we have to divide the # of units (8) for one case by the total # units (90).
As you can see, after dividing by 8, we have a total of 11 cases and a remainder of 2 units. The remainder will be the # of additional units because we cannot have another case filled with 8 units.
HELP PLEASE HELP HELP
Answer:
The first one is the only one that makes sense.
Step-by-step explanation:
hope it helps!
Consider a political discussion group consisting of 6 Democrats, 6 Republicans, and 4 Independents. Suppose that two group members are randomly selected, in succession, to attend a political convention. Find the probability of selecting an Independent and then a Republican.
___.
(Type an integer or a simplified fraction.)
Answer:
10/16=5/8
6+6+4=16
The probability is 5/8
What is 4 × 1/7 on a numberline
Answer:
4/7
Step-by-step explanation:
When you multiply by fractions you multiply the numerators and denominators
4/1 x 1/7
Anything that doesnt have anything under it always has a 1 as its denominator
The lines shown below are parallel. If the green line has a slope of -2, what is
the slope of the red line?
Answer:
Hi! There's no picture, but we don't need that to find the answer. Parallel lines always have the same slope. I suppose you're saying that the green and red line are parallel -- so, the red line's slope is also -2.
-2 <--
Hope this helps!! Have a nice day & please mark brainliest if you don't mind!
It is known that the variance of a population equals 1,936. A random sample of 121 has been selected from the population. There is a .95 probability that the sample mean will provide a margin of error of _____. Group of answer choices 31.36 or less 1,936 or less 344.96 or less 7.84 or less
Answer:
Option d (7.84 or less) is the right alternative.
Step-by-step explanation:
Given:
[tex]\sigma^2=1936[/tex]
[tex]\sigma = \sqrt{1936}[/tex]
[tex]=44[/tex]
Random sample,
[tex]n = 121[/tex]
The level of significance,
= 0.95
or,
[tex](1-\alpha) = 0.95[/tex]
[tex]\alpha = 1-0.95[/tex]
[tex]Z_{\frac{\alpha}{2} } = 1.96[/tex]
hence,
The margin of error will be:
⇒ [tex]E = Z_{\frac{\alpha}{2} }(\frac{\sigma}{\sqrt{n} } )[/tex]
By putting the values, we get
[tex]=1.96(\frac{44}{\sqrt{121} } )[/tex]
[tex]=1.96(\frac{44}{11} )[/tex]
[tex]=1.96\times 4[/tex]
[tex]=7.84[/tex]
What is the five-number summary for this data set? 22, 29, 33, 38, 44, 47, 51, 56, 64, 69 Assume the numbers in each answer choice are listed in this order: min, Q1, median, Q3, max.
A. 22, 33, 45.5, 56, 69
B. 22, 38, 45.5, 51, 69
C. 22, 38, 41, 51, 69
D. 22, 33, 41, 56, 69
Answer: A: 22, 33, 45.5, 56, 59
Step-by-step explanation:
The minimum is the lowest number in the data, in this case, it was 22.
Q1 is the median of the lower quartile range, anything below the median of the overall data.
Median, the middle number in the overall data. You first need to put them from lowest to highest (numerical order). After that, I find it a lot easier to cross one from each side until I'm either left with one or two. If I'm left with one, then that is my median for the overall data set. If I'm left with two, then I simply need to add both the numbers together and divide it by 2. Typically if it is a whole number, and the numbers are 1 number value away from each other, it is usually just 0.5 more of the lower value of the two. (For example, the two numbers I come down to is 10 and 11. The median would be 10.5).
Q3 is the exact same principle as Q1 just on the upper quartile range. Just repeat what you did in Q1 but for the numbers above the overall median of the data set.
Maximum is the highest number in the data set, in this case, it was 69.
Hope this helps!
The absolute value inequality equation |2x – 1| > 3 will have what type of solution set?
Given:
The inequality is:
[tex]|2x-1|>3[/tex]
To find:
The solution set for the given inequality.
Solution:
We know that, if [tex]|x|>a[/tex], then [tex]x<-a[/tex] and [tex]x>a[/tex].
We have,
[tex]|2x-1|>3[/tex]
It can be written as:
[tex]2x-1<-3[/tex] or [tex]2x-1>3[/tex]
Case I:
[tex]2x-1<-3[/tex]
[tex]2x<-3+1[/tex]
[tex]2x<-2[/tex]
[tex]x<\dfrac{-2}{2}[/tex]
[tex]x<-1[/tex]
Case II:
[tex]2x-1>3[/tex]
[tex]2x>3+1[/tex]
[tex]2x>4[/tex]
[tex]x>\dfrac{4}{2}[/tex]
[tex]x>2[/tex]
The required solution for the given inequality is [tex]x<-1[/tex] or [tex]x>2[/tex]. The solution set in the interval notation is [tex](-\infty,-1)\cup (2,\infty)[/tex].
Therefore, the required solution set is [tex](-\infty,-1)\cup (2,\infty)[/tex].
Questions
1) Identify the missing features of this map ?
2) Write north , south , east or west to complete each sentence?
a) The rowboats are _____ of the campfire .
b) The camping trailers are _______ of the tent .
c) The cabins are ______ of the tents
d) The campfire is ______ of the camping trailers
e) The island is _____ of the cabins .
Do answer
Answer:
it is missing a scale because it should be at the bottom of the map
Please help me with this!
9514 1404 393
Answer:
7x -5 = 9x = 2Step-by-step explanation:
A) If we let x represent "a number", then "seven times a number" is 7x. When 5 is subtracted from that, we have ...
7x -5 . . . . . 5 subtracted from 7 times a number
This is said to be 9, so ...
7x -5 = 9 . . . . . . . 5 from 7 times a number is 9. Your equation.
__
B) To solve this, we can add 5 to both sides. This eliminates the constant term we don't want on the left.
7x = 14
Now, we can divide by 7, the coefficient of x that we don't want.
x = 14/7
x = 2
Pippa had 35 stickers.
She gave an equal number of stickers to 8 friends.
She gave each friend as many stickers as possible and kept the rest for herself.
How many stickers did Pippa keep for herself?
Answer: 3 stickers
Step-by-step explanation:
From the question, we know that Pippa's 8 friends have an equal amount of stickers, meaning that the number of stickers that Pippa gave out is a multiple of 8.
Also, we are able to know that Pippa gave as much as she can, meaning that she gave out the stickers until the number is the maximum multiple of 8.
First Five Multiple of 8 = 8, 16, 24, 32, 40
As we can see from the list, 8, 16, and 24 are all multiples of 8, but they are not the maximum number that could fit under 35 stickers. Similarly, 40 exceeds the number of stickers Pippa has. Thus, we are left with 32.
This means, Pippa gave out 32 stickers in total, and each friend got 4 stickers.
32 / 8 = 4 stickersAlso, this means Pippa would keep 3 stickers for herself.
35 - 32 = 3 stickersHope this helps!! :)
Please let me know if you have any questions
Find f′ in terms of g′
f(x)=x2g(x)
Select one:
f′(x)=2xf′(x)+2xg′(x)
f′(x)=2xg′(x)
f′(x)=2x+g′(x)
f′(x)=x2g(x)+2x2g′(x)
f′(x)=2xg(x)+x2g′(x)
f(x)g(x) if you find the derivative of two products, you get f(x)g’(x)+f’(x)g(x). Let’s say x^2 = f(x).
(x^2)(g’(x))+2x(g(x)) so it would be your last option, 2x(g(x))+x^2(g’(x))
Find the probability that z lies between 0 and 1.56.
Answer:
P(0 < z < 1.56)=0.4406
Step-by-step explanation:
William sold tooth pick for €2 a pack.On Selling 60% of his ware he still had 200 left.How much money did he collect from his entire sales?
Answer:
.......................
Write the expression as a trinomial (3a+4)(8-a).
Answer:
-3a² + 20a + 32
Step-by-step explanation:
(3a+4)(8-a)
24a - 3a² + 32 - 4a
-3a² + 24a - 4a + 32
-3a² + 20a + 32
I need answering ASAP please
Answer:
The choose (D) 1/3
I hope I helped you^_^
What is the solution to log (9x)-log, 3 - 3?
O X
col 00
8
X =
3
O x=3
OX=9
Answer:
x = 8/3
Step-by-step explanation:
Log₂(9x) – Log₂3 = 3
The value of x can be obtained as follow:
Log₂(9x) – Log₂3 = 3
Recall
Log M – Log N = Log (M/N)
Thus,
Log₂(9x) – Log₂3 = 3
Log₂(9x/3) = 3
Log₂3x = 3
3x = 2³
3x = 8
Divide both side by 3
x = 8/3
The least-squares regression equation
y = 968 – 3.34x can be used to predict the amount of monthly interest paid on a loan after x months. Suppose the amount of monthly interest after 30 months was $865.93.
What is the residual for the amount of monthly interest paid on a loan after 30 months?
–202.27
–1.87
1.87
202.27
Answer:
-1.87 (B)
865.93 - [968-3.34(30)] = -1.87
ED2021
If the price of a stapler increase from Rs 50 to Rs 54, find the percentage increase?
Solve for X: A=2B/x+3
the answer is 2B divided by A minus 3
Use the graphing calculator to graph the function f(x) = Vx. Which table of values contains points that lie on the
graph of the function?
9514 1404 393
Answer:
see below
Step-by-step explanation:
Assuming your Vx means √x, the values in the f(x) column will be the square root of the values in the x column. That is the case for the first table shown (also attached).
in how many ways can be arranged 2 different words in necklace?
Answer:
3
Step-by-step explanation:
chain by chain
parllel
series
Select all the terms that can be combined with 5.
4b
14a
100
3a’2
LET R equal the rental fee for one locker write an equation that represents the situation
Answer:
R x 1= price of 1 locker
Step-by-step explanation:
it would continue the same way. Just multiply R and the number of lockers.
Is there a certain situation it was asking about?
