The mean annual salary of classroom teachers is approximately the normal with a mean of $ 45,969. Assume a standard deviation of $7600. Do the following for the variable "annual salary" of classroom teachers.
Determine the sampling distribution of the sample mean for samples of size 64.
The sample mean is μₓ
Answer:
$7,600
Step-by-step explanation:
What is the answer for this using substitution?
9514 1404 393
Answer:
(x, y) = (2, -2)
Step-by-step explanation:
We would normally choose to use substitution when x or y could be easily solved-for without having fractions involved. That is not the case here. However, we observe that the term 3y appears in both equations, so we can substitute for "3y" instead of "y".
From the second equation, ...
3y = 5x -16
Substituting into the first equation, ...
2x +(5x -16) = -2
7x = 14 . . . . . . . . . add 16
x = 2 . . . . . . . . . . divide by 7
Using our equation for y, we get ...
3y = 5(2) -16 = -6
y = -2 . . . . . . . . . divide by 3
The solution is (x, y) = (2, -2).
Find the average value of a function
Answer:
The average value of g is:
[tex]\displaystyle g_{ave}=\frac{1}{6}e^6-\frac{49}{6}\approx 59.071[/tex]
Step-by-step explanation:
The average value of a function is given by the formula:
[tex]\displaystyle f_{ave}=\frac{1}{b-a}\int_a^b f(x)\, dx[/tex]
We want to find the average value of the function:
[tex]g(x)=e^{3x-3}-4x[/tex]
On the interval [1, 3].
So, the average value will be given by:
[tex]g_{ave}=\displaystyle \frac{1}{3-1}\int_1^3 e^{3x-3}-4x\, dx[/tex]
Simplify. We will also split the integral:
[tex]\displaystyle g_{ave}=\frac{1}{2}\left(\int_1^3e^{3x-3}\, dx-\int _1^3 4x\, dx\right)[/tex]
We can use u-substitution for the first integral. Letting u = 3x - 3, we acquire:
[tex]\displaystyle u=3x-3\Rightarrow du = 3\, dx\Rightarrow \frac{1}{3} du=dx[/tex]
We will also change the limits of integration for our first integral. So:
[tex]u(1)=3(1)-3=0\text{ and } u(3)=3(3)-3=6[/tex]
Thus:
[tex]\displaystyle g_{ave}=\frac{1}{2}\left(\frac{1}{3}\int_0^6 e^{u}\, du-\int _1^3 4x\, dx\right)[/tex]
Integrate:
[tex]g_{ave}=\displaystyle \frac{1}{2}\left(\frac{1}{3}e^u\Big|_0^6-2x^2\Big|_1^3\right)[/tex]
Evaluate. So, the average value of g on the interval [1, 3] is:
[tex]\displaystyle g_{ave}=\frac{1}{2}\left(\frac{1}{3}\left[e^6-e^0\right]-\left[2(3)^2-2(1)^2\right]\right)[/tex]
Evaluate:
[tex]\displaystyle\begin{aligned} g_{ave}&=\frac{1}{2}\left(\frac{1}{3}(e^6-1)-16\right)\\&=\frac{1}{2}\left(\frac{1}{3}e^6-\frac{1}{3}-16\right)\\&=\frac{1}{6}e^6-\frac{49}{6}\approx59.071\end{aligned}[/tex]
Is it possible for a cross section of a cylinder to have a triangular shape?
It is not possible for a cross section of a cylinder to have a triangular shape
What is cross section?Cross section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher-dimensional spaces
What is Cylinder?A cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes
What is triangular shape?A triangle is a shape formed when three straight lines meet
Cross section of the cylinder is depends on how we cut .The cross-section of a cylinder may be either circle, rectangle, or oval
Hence, the cross section of of a cylinder can not be a triangular shape
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Solve the equation (216/739)^1/3
The plane was flying long so it's true!
60% of all violent felons in the prison system are repeat offenders. If 32 violent felons are randomly selected, find the following probabilities. Round your answers to 4 decimal places.
a. Exactly 20 of them are repeat offenders.
b. At most 19 of them are repeat offenders.
c. At least 20 of them are repeat offenders.
Target sells 12 bottles of water for 2$ and sells 24 bottles for 3$, what is the better price?
Answer:
The 24 bottles for 3$
Step-by-step explanation:
12 bottles for 2$ x 2
= 24 bottles for 4$
This means the 24 bottles for 3$ is the better price per bottle.
For questions 3 that’s all i need help please !!! For a test and please put your answers below !!!
Answer:
D - 1,078
Step-by-step explanation:
if you take 26.96 x 40, you will get 1,078
Find the equation of this line
Answer:
-6x+4
Step-by-step explanation:
y-intercept is at 4 which is b.
It goes down 6 units as it decreases from 4 to -2.
Since it decreases 6 is negative
therefore -6x+4
Need help quickly! Thanks
Answer:
y = [tex]-2^x[/tex]
Step-by-step explanation:
If the equation of a function is in the form of y = h(x)
When the graph of this function is reflected across x-axis,
Transformed function will be,
y = -h(x)
Further reflected across y-axis, then the transformed function will be,
y = -h(-x)
By this rule,
Given equation when reflected across x-axis,
y = [tex]-(\frac{1}{2})^{x}[/tex]
Further reflected across y-axis,
y = [tex]-(\frac{1}{2})^{-x}[/tex]
y = [tex]-(2^{-1})^x[/tex]
y = [tex]-2^x[/tex]
You have been commissioned to design a monument to Mr. Mullen. The monument consists of a pool 100 ft long where observers stand on one side of the pool and a giant statue of Mr. Mullen holding a cat stands on the other. If you want the angle of elevation from the ground to be 42 degrees, how tall must you make the statue?
a. 100 ft
b. 90 ft.
c. 111 ft
d. 67 ft
e. 74 ft
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Answer:
b. 90 ft
Step-by-step explanation:
The opposite and adjacent sides of the relevant triangle are given.
Tan = Opposite/Adjacent
tan(42°) = h/(100 ft)
h = (100 ft)tan(42°) ≈ 90.04 ft
The statue must be about 90 ft tall.
Answer:
a. 100 ft
b. 90 ft.
c. 111 ft
d. 67 ft
e. 74 ft
its b.90 ft.
from 2005 to 2015, a population of lions decreased by 2% annualy. there were 1500 of this population of likns in 2005. how many lions wew left by 2015
Answer:
30
Step-by-step explanation:
I think that's the answer but if I'm wrong tell me right away I'll try another method.
60
VW
The equation BSA = models the relationship between SSA
in square meters, the patient's weight W in kilograms, and the
patient's helght H in centimeters.
a. Solve the equation for H.
Answer:
yo bro idek bro, gimme brainliest
Step-by-step explanation:
Can you guys please help me zoom in if you can’t see I’ll mark you brainliest be genuine !
Answer:
Volume: 528 ft^3
Surface Area: 444.72
Step-by-step explanation:
For the surface area, I'm not quite sure, but the volume is correct.
Hope this helped! :)
( ﾟдﾟ)つ Bye
The time needed to complete a final examination in a particular college course is normally distributed with a mean of 79 minutes and a standard deviation of 8 minutes. Answer the following questions.
Answer:
A) 0.0088
B) 0.2997
C) 5
Step-by-step explanation:
Given: Mean: Ч = 79 minutes
Standard deviation : б = 8 minutes
The formula for z score:
z= x-ц/σ
a) For x=60 minutes
z= 60-79/8 = -2.375
The p-value = P(z< -2.375) = 0.0087745 ≈ 0.0088
b) For x= 75 minutes
z= 75-79/8 = -0.5
The p-value = P(60 < x < 75) = P (-2.375 < z < -0.5)
= P(-0.5)-P(-2.375)= 0.3085 -0.0088 =0.2997
c) For x=90 minutes
z= 90-79/8 = 1.375
The p-value = P (z > 1.375)= 1-P(z < 1.375)
= 1-0.9154342 = 0.0845658
If the number of students in the class=60.
Then, the number of students will be unable to complete the exam in the alotted time = 0.0845658 x 60 = 5.073948 ≈ 5
In the formula, l = a + (n - 1)d make d as the subject. Find d when l = 10, a = 2, n = 5.
I = a + (n - 1)d [Given formula]
To Find:-Find d when I = 10, a = 2, n = 5
Solution:-I = a + (n - 1)d [Given]
Putting the value of I = 10, a = 2, n = 5 we get,
10 = 2 + (5 - 1)d
10 = 2 + 4d
10 - 2 = 4d
8 = 4d
d = [tex] \frac{8}{4} [/tex]
d = 2
Value of d is 2. [Answer]An equation is shown.
3.8+y=14.2
What is the value for x that makes the equation true?
Answer:
y=10.4
Step-by-step explanation:
If you mean Y instead of x then the answer is 10.4
3.8+y=14.2
-3.8 -3.8
y=10.4
Answer:
y/x=10.4
Step-by-step explanation:
3.8+y=14.2 Subtract 3.8 from both sides
y=10.4
Consider an experiment of tossing a coin twice in a row.
The probability of occurrence of two heads in a row is
A) 0.25
B) 0.20
C) 0.50
Your goal is to create a college fund for your child. Suppose
you find a fund that offers an APR of 5% How much should
you deposit monthly to accumulate $170,000 in 15 years?
Answer:
the monthly payment is $636.02
Step-by-step explanation:
The calculation of the monthly amount deposited i.e. PMT is shown below:
GIven data
NPER = 15 × 12 months = 180
RATE = 5% ÷ 12 = 0.4167%
PV = $0
FV = $170,000
based on the above information
The formula is given below:
= PMT(RATE;NPER;PV;FV;TYPE)
After applying the given formula, the monthly payment is $636.02
3.14 Unit
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What is the slope of the line that passes through the points (3, 1) and (-2,5)?
-
-
Please help
Answer:
m = -4/5
Step-by-step explanation:
We need to find the slope of the line that passes through the points (3, 1) and (-2,5).
The slope of the line is given by :
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Put x₁ = 3, x₂ = -2, y₁ = 1 and y₂ = 5
Put all the values,
[tex]m=\dfrac{5-1}{-2-3}\\\\=\dfrac{4}{-5}\\\\=\dfrac{-4}{5}[/tex]
So, the correct option is (b).
Solve the equation for x, where x is restricted to the given interval.
y=8cot4x, for x in (0, pi/4)
HELP ME OUTT PLSS BXJXID
Answer:
d
Step-by-step explanation:
Answer: D
Step-by-step explanation:
The probability of picking a brown pencil greater than the probability as NOT picking a brown pencil because there more brown pencils than purple so there is a higher chance you will get a brown than NOT get a brown.
Convert 210° to radian measure in terms of pi
Answer:
[tex]210^\circ = \frac{7}{6}\pi[/tex]
Step-by-step explanation:
Given
[tex]\theta = 210^\circ[/tex]
Required
Convert to radians
To convert to radians, we make use of:
[tex]Radians = \theta * \frac{\pi}{180^\circ}[/tex]
Substitute: [tex]\theta = 210^\circ[/tex]
[tex]Radians = 210^\circ* \frac{\pi}{180^\circ}[/tex]
[tex]Radians = \frac{210^\circ* \pi}{180^\circ}[/tex]
Simplify fraction
[tex]Radians = \frac{7\pi}{6}[/tex]
[tex]Radians = \frac{7}{6}\pi[/tex]
Hence:
[tex]210^\circ = \frac{7}{6}\pi[/tex]
Suppose that you're paid $63.24 for 7 hours of work. What is your hourly pay rate?
Answer:
$9.03
Step-by-step explanation:
Using x for pay rate
63.24=7x Divide both sides by 7
x=9.03
Using the vertical line test. Is this a function?
Answer:
Can't get one(Read explanation)
Step-by-step explanation:
What you do to find out if its a function is see if any of the dots are in the same x value. If they are, its not a function. If they aren't it is a function.
MAFS.912. G-GMD. 1.3
A regular pyramid has a square base. The perimeter of the base is 36
inches and the height of the pyramid is 15 inches. What is the volume of
the pyramid in cubic inches?
A. 180
B. 405
C. 540
D. 1215
Answer:
b
Step-by-step explanation:
The volume of the square pyramid is 405 cubic inches.
The correct answer is option (B).
What is the volume of the square pyramid?V = 1/3 × base area × h,
where h is the height of the pyramid.
What is the perimeter of square?P = 4 × a
where, 'a' represents the side of the square
For given example,
Let 'a' be the side length of the square base.
We have been given the perimeter of the square base is 36.
⇒ P = 36
⇒ 4 × a = 36
⇒ a = 9
So, the length of the side of the square base is 9 in.
Using the formula of the volume of the pyramid,
⇒ V = (1/3) × base area × h
⇒ V = (1/3) × a² × h
⇒ V = (1/3) × (9)² × 15
⇒ V = 27 × 15
⇒ V = 405 cubic inches
Therefore, the volume of the square pyramid is 405 cubic inches.
The correct answer is option (B).
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the lengths of two sides of a triangle are 8in. and 13in. find the range of possible lengths for the third side
Answer:
5<x<21
Step-by-step explanation:
when any two sides are added together they have to be greater than either side... to find the range
add the two sides together to get the upper end of the range 8+13=21
and to get the lower end of the range subtract 13-8=5
so the range is 5<x<21
the third side CAN NOT be 5 or 21, must be between them
For large parties, a restaurant charges a reservation fee of $30, plus $20 per person. The total charge for a party of x people is f(x) = 20x + 30. How will the graph of this function change if the reservation fee is raised to $65 and the per-person charge is lowered to $12?
PLEASE HELP !! ILL GIVE BRAINLIEST !!
Answer:
top right one
Step-by-step explanation:
cuz verticle angles are across each other
Better not be a scam :)
-
A rectangular prism has how many flat surfaces?
Answer:
it has 6 faces
Step-by-step explanation:
A rectangular prism has 6 flat surfaces.
How to find a rectangular prism?A rectangular prism is a polyhedron with two congruent and parallel bases.
Another name for a rectangular prism is cuboid.
A rectangular prism has 6 faces, 8 vertices and 12 edges.
Flat surface are called plane.
We see that a rectangular prism has six sides and all of its sides are rectangles.
Therefore, all the sides of a rectangular prism are flat surfaces. Since a rectangular prism has six sides; it has six flat surfaces.
The diagram is a rectangular prism.
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