Answer:
The probability that the sample mean would differ from the true mean by less than 36 dollars is 0.7549.
Step-by-step explanation:
According to the Central Limit Theorem if an unknown population is selected with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from this population with replacement, then the distribution of the sample means will be approximately normally.
Then, the mean of the sample means is given by,
[tex]\mu_{\bar x}=\mu[/tex]
And the standard deviation of the sample means is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
The information provided is:
[tex]\mu=21604\\\sigma=727\\n=193[/tex]
As the sample size is large, i.e. n = 193 > 30 the central limit theorem can be used to approximate the sampling distribution of sample mean per capita income.
Compute the probability that the sample mean would differ from the true mean by less than 36 dollars as follows:
[tex]P(\bar X-\mu<36)=P(\frac{\bar X-\mu}{\sigma_{\bar x}}<\frac{36}{727/\sqrt{193}})\\\\=P(Z<0.69)\\\\=0.7549[/tex]
Thus, the probability that the sample mean would differ from the true mean by less than 36 dollars is 0.7549.
Which function is a quadratic function?
f(x) = 2x2
g(x) = 5x3
k(x) = –x
b(x) = –9x4
Answer:
A. f(x) = 2x2
Step-by-step explanation:
if f (x) = 3x2 V8 + x2, what is f'(1)
Answer:
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Step-by-step explanation:
find the height of the giraffe in the diagram. Show your work below.
The distance from the person to the mirror is 5 ft. The distance from the mirror to the giraffe is 15 ft.
15/5 = 3
Multiply the height of the person by 3:
5 ft = 60 inches 60+3 = 63 inches
63 x 3 = 189 inches
189/12 = 15.75 ft = 15 feet 9 inches
The giraffe is 15 ft 9 inches tall
PLEASE HELP Look at each statement. Does the statement describe a transformation of the graph of f(x) = x that would result in the graph of g(x) = x + 2? Select Yes or No for each statement.
The parent function is reflected across the y-axis.
A Yes B No
The parent function is translated 2 units up.
A Yes B No
The parent function is translated 2 units down.
A Yes B No
Answer:
B,A,B
Step-by-step explanation:
2. In AGHK, GH = 11, HK = 21, and GK = 15. To the nearest tenth, what is m
Answer:
ok here is the answer
Step-by-step explanation:
how about you stop cheating and do it by your self
A rabbit can run 35 mph a fox can run. 21 mph which animal is faster and by how much
How much sales tax will Justin pay on a Computer priced at $1,723.42 if the sales tax rate is 9.25%?
Answer:
$1882.84
Step-by-step explanation:
Total cost = 109.25% = 109.25% x $1723.42 = $1882.84 (2dp)
Topic: Percentage
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A ball is thrown straight up into the air from the top of a building standing at 50 feet with an initial velocity of 65 feet per second the height of the ball in feet can be modeled by the following function: h(t)=-16t^2++16t+96 When does the ball reach its maximum height?
Answer:
0.5 seconds (at 100 feet in the air).
Step-by-step explanation:
So, the height of the ball can be modeled by the function:
[tex]h(t)=-16t^2+16t+96[/tex]
Where h(t) represents the height in feet after t seconds.
And we want to find its maximum height.
Notice that our function is a quadratic.
Therefore, the maximum height will occur at the vertex of our function.
The vertex of a quadratic function in standard form is given by the formula:
[tex](-\frac{b}{2a}, f(-\frac{b}{2a}))[/tex]
In our function, a=-16; b=16; and c=96.
Find the x-coordinate of the vertex:
[tex]x=-\frac{(16)}{2(-16)}=1/2[/tex]
So, the ball reaches its maximum height after 0.5 seconds of its projection.
Notes:
To find it’s maximum height, we can substitute 1/2 for our function and evaluate. So:
[tex]h(1/2)=-16(1/2)^2+16(1/2)+96[/tex]
Evaluate:
[tex]h(1/2)=-4+8+96=100[/tex]
So, the ball reaches its maximum height of 100 feet 0.5 seconds after its projection.
13
Luke is painting the ceiling. He needs to lay down drop cloths so he does not get paint
on the floor. Each drop cloth is 8 feet by 6 feet. The room is 14 feet by 16 feet. How
many drop cloths will he need to cover the floor?
Type your answer
SUBMIT
Answer:
5 Drop Cloths
Step-by-step explanation:1 - Find the areas of both the room and the drop cloth
Drop Cloth:
A = L x W
A = 8 x 16
A = 48
Room:
A = L x W
A = 14 x 16
A = 224
2 - Divide the area of the room by the area of 1 drop cloth
This is to see how many times the area of the drop cloth will go into the area of the room
Room Area/Drop Cloth Area =
224/48 = 4.66666666... = 5 drop cloths
Hope this helps :)
Find the horizontal asymptote, if any, of the graph of the rational function. f(x)=16x5x2+7
Why was 56 and 36 points selected?
Alice is saving to buy a house and currently has $2,000 in her savings account. She's planning to contribute $150 to the account each month. Identify the function that describes the relationship between the number of months that pass (n) and the balance of her savings account, f(n).
Answer:
f(n)= 2,000+150n
Step-by-step explanation:
hope this helps.
Answer:
f(n) = 2,000 + 150(n − 1)
Step-by-step explanation:I took the test
Write a quadratic function h whose zeros are 9 and 1
Answer:(x^2)-10x+9
Step-by-step explanation:
Zeroes would be 9 and 1, so the equation would be (x-9)(x-1), and multiplying with FOIL gives us xsquared -10x+9
If the given zeroes of the equation are 9 and 1 the quadratic equation will be x²-10x+9.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
Any function of the form
[tex]\rm f(x) =ax^2+bx+c[/tex]
where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic function.
It is given that the zeroes of the equations are,9 and 1,
The equation with zeroes is represented as,
(x-a)(x-b) =0
Substitute the given values,
(x-9)(x-1) = 0
Open the bracket and perform the arithmetic operations,
(x(x-1) -9(x-1) = 0
x²-x-9x+9=0
x²-10x+9
Thus, if the given zeroes of the equation are 9 and 1 the quadratic equation will be x²-10x+9.
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Gina is a server at a restaurant. A table spends $34 on food and leaves Gina a 18% tip. What is Gina's tip?
A. $6.12
B. $40.12
C. $26
D. $8.24
Answer:
A.
tip: $6.12
total amount: $40.12
Answer:
A
Step-by-step explanation:
34.00 x .18 = 6.12
Take 18 and put a decimal in front of it and multiply it by the cost (34.00)
example if it were 20.00 and the tip was 5%
20.00 x .05
6. Challenge Problem: One owl hoots every 3 hours, a second owl hoots every 8 hours, and
a third owl hoots every 12 hours. If they all hoot together at the start, how many times
during the next 80 hours will just two of the owls hoot together?
Answer:
9 times
Step-by-step explanation:
The least common multiple (henceforth written as LCM) of 3 and 8 is 24. Therefore, these 2 owls hoot 72/24 = 3 times. The LCM of 3 and 12 is 12. These 2 owls hoot 72/12 = 6 times. The LCM of 8 and 12 is 24. These 2 owls hoot 72/24 = 3 times. Altogether, these owls hoot the LCM of 3, 8, AND 12, or 72/24 = 3 times. 3+3+6-3 = 9 times.
If they all hoot together at the start, 9 times during the next 80 hours will just two of the owls hoot together.
What is number theory?Number theory is the study of integers and functions of arithmetic.
One owl hoots every 3 hours.
Second owl hoots every 8 hours.
Third owl hoots every 12 hours.
If they all hoot together at the start, how many times during the next 80 hours will just two of the owls hoot together
Number theory indicates that the multiples of the periods of hooting are;
The multiples of 3 are; 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72,75, 78, 81, 82
The multiples of 8 are; 8, 16, 24, 32, 40, 48, 56, 64, 72, 80
The multiples of 12 are; 12, 24, 36, 48, 60, 72,
The least common multiple of 3 and 8 is 24, these 2 owls hoot 72/24 = 3 times.
The LCM of 3 and 12 is 12, these 2 owls hoot 72/12 = 6 times.
The LCM of 8 and 12 is 24, these 2 owls hoot 72/24 = 3 times.
Altogether, these owls hoot the LCM of 3, 8, AND 12, or 72/24 = 3 times. 3+3+6-3 = 9 times.
Therefore, 9 times during the next 80 hours will just two of the owls hoot together.
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A market research analyst claims that 32% of the people who visit the mall actually make a purchase. You think that less than 32% buy something and decide to test the claim. You stand by the exit door of the mall starting at noon and ask 82 people as they are leaving whether they bought anything. You find that only 20 people made a purchase.
Required:
a. State the null and alternative hypotheses to test that less than 32% of man visitors make a purchase.
b. Find the value of the test statistics z.
c. The p-value of the test is about:______
Answer:
p=32 p<32
Step-by-step explanation:
A rectangular prism is 10 inches long, 5 inches wide, and 6 1/2 inches tall. What is the volume in cubic inches of the prism?
Answer:
325 cubic inches
Step-by-step explanation:
10*5=50
50*6.5=325
Hope that helped! Please don't hate me if I did something wrong!
There are 230 calories in 4 ounces. How many calories are in 6 ounces
Answer:
345 calories
Step-by-step explanation:
Divide 230 by 4
57.5
Multiply 57.5 by 6 ounces
The answer is 345 calories
Hope this helped :)
Answer:
345 calories
Step-by-step explanation:
Since you know there are 230 calories in 4 ounces you can divide the 230 calories by 4 to find out how many calories are in each ounce.
230/4= 57.5
Since there are 57.5 calories in each ounce, you can multiply this by 6 ounces to find how many calories are in 6 ounces
57.5 x 6 = 345
Devon found that for every 4 miles he walks, he needs one bottle of water. He plotted his water usage on a graph but left out some possible points. On a coordinate plane, the points (4, 1) and (12, 3) are plotted.
Answer:
(8, 2)
Step-by-step explanation:
(4, 1)+(4, 1)+(4, 1)=(12, 3)
(4, 1)+(4, 1)=(8, 2)
Answer:
C
Step-by-step explanation:
(8.2)
What is the constant of proportionality in the equation y=25X?
Answer:
Step-by-step explanation:
y = kx
If y = 25x , then k = 25
Steph bought a used bicycle ,restored it and then marked it up by 1/4 of the price she paid. later, she sold it for the marked up price to $80 how much in dollars did steph pay for the bicycle?
Answer:
$ 64
Step-by-step explanation:
Let Steph paid $x to buy the used bicycle.
After restoring, she marked it up by 1/4 of the price she paid.
So, the marked price [tex]= x +\frac 1 4 x = \frac {5x}{4}[/tex]
As she sold the bicycle for the marked up price to $80.
So, [tex]\frac {5x}{4} = 80[/tex]
[tex]\Rightarrow x = \frac {80\times 4}{5}\\\\\Rightarrow x = 64.[/tex]
Hence, she paid $ 64 for the bicycle.
what is the number three and eight tenths as a decimal.
Answer:
3.8
Step-by-step explanation:
3 8/10 can be written as 3.xx because all we have to do is 8 divided by 10 which equals .8 so 3+.8=3.8
a company lost $5,676 over a year. How much money did they lose each month if it was slit evenly
Answer:
I think the answer is 2,838
A and B equal what?? Helpppp??
A is 155
B is 65
For a:
180-25 = 155
For b:
90-25 = 65
Answer:
a=155
b=65
Step-by-step explanation:
a
180-25
= 155
b
360-25-25-90-155
=65
How are x and y intercepts alike and different?
Answer:
x and y intercepts are alike because they both cross each other, they are different because the Y axis is vertical while the X axis is horizontal.
The similarities between [x] - intercept and [y] - intercept is discussed below.
What is the general equation of a Straight line?
The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line can be also written as -
Ax + By + C = 0
By = - Ax - C
y = (- A/B)x - (C/A)
We have [x] and [y] intercepts of a straight line.
The [y] - intercept is the line where the line cuts the [y] - axis whereas [x] - intercept is the line where the line cuts the [x] - axis.[y] - intercept has coordinates (0, y) and [x] - intercept has coordinates (x, 0).We can calculate the slope of the line using the [y] - intercept and the [x] - intercept as -m = (0 - y)/(x - 0)
m = - y/x
Therefore, the similarities between [x] - intercept and [y] - intercept is discussed above.
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I will be posting some questions whoever gets them right gets brainliest
3x+10=31. What is the value of 2x
Answer:
x = -7 is the answer
Step-by-step explanation:
answer is above
Solve for x. 4 In (4x) = 16
Answer:
x= 4
Step-by-step explanation:
4 x 4= 16
Answer:
Step-by-step explanation:
In 4x=26
4x=e^26
x= e^26/4
x=4.89×10^10
7. 21 is what percentage of 30? *
Answer:
70
Step-by-step explanation:
21/70 is .7 move to the right 2 times so 70%
Answer: 70
:D.............
A sphere has a radius of 11 Inches. A horizontal plane passes through the center of the sphere.
Part 1 out of 2
Describe the cross section formed by the plane and the sphere.
It is a (square, circle, or oval) with a radius of in.
Answer:
part 1
circle, 11
part 2
decrease
Step-by-step explanation:
How to simply a fraction
Answer:
In order to simplify a fraction there must be:
1. A number that will divide evenly into both the numerator and denominator so it can be reduced, or.
2. The numerator must be greater than the denominator, (an improper fraction), so it can be converted to a mixed number.
Answer:
To simply a fraction, you need to find the largest number that can go in to both the numerator and denominator. For example, 12/16, the largest number that can go into both it 4. Then divide the numerator and denominator by the large number which would be 3/4