Answer:
For the Broadway actors acting in their first role on Broadway, mean: 0.184, Standard Deviation: 0.063.
For the proportion of smokers, mean = 0.167, standard deviation = 0.068
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Suppose we took a survey of 38 Broadway actors and found that 18.4% of the actors we surveyed were first-timers.
This means that [tex]p = 0.184, n = 38[/tex]
What are the mean and standard deviation for the sampling distribution of p^?
Mean:
[tex]\mu = p = 0.184[/tex]
Standard deviation:
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.184*0.816}{38}} = 0.063[/tex]
Suppose you take a random sample of 30 smokers and find that the proportion of them who are current smokers is 16.7%.
This means that [tex]n = 30, p = 0.167[/tex]
What is the mean and the standard deviation of the sampling distribution of p^ ?
Mean:
[tex]\mu = p = 0.167[/tex]
Standard deviation:
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.167*0.833}{30}} = 0.068[/tex]
A duck has 1,100 feathers. It went for a swim in a pond and lost 2/100 of its feathers. How many feathers did it lose?
Answer:
It lost 22 feathers.
Step-by-step explanation:
To complete this problem, this expression will be used: 2x/100.
2(1100)/100 {Multiply 2 by 1100}
2200/100 {Simplify by cancelling out 100}
22/1 {Divide}
22 feathers were lost.
Find the sum end difference between the numbers 473 and the number obtained by reversing the digits
Answer:
Step-by-step explanation:
The given number is 473
The reverse number is 374
The sum is (473 + 274) = 847
The difference is (473 - 274) = 99
Canada has a population of 33 million while Russia has 144 million inhabitants. Indonesia population is 50% greater then that of Russia while it is only 72% of the population of the United States. How many million people must be added to the United States so that the population of that country becomes 10 times of Canada?
Answer: 30 million people must be added.
Step-by-step explanation: 50% of 144 million is 72 million. You add these to find Indonesia’s population. 144 million + 72 million= 216 million. If 216 million is only 72% of the US population, then divide 216 million by 72 to find 1%. 216 million/72=3 million. Multiply this by 100 to find the US population. 3 million times 100= 300 million. Now, multiply Canada’s population by 10. 33 million times 10= 330 million. Finally, subtract 300 million from 330 million to find the amount needed to make the US population 10 times that of Canada’s. 330 million-300 million=30 million. So , you need 30 million people in order to make the US population 10 times that of Canada’s.
If p is a given sample proposition n is the sample size, and a is the number of standard deviations at a confidence level, what is the standard error of the proportion?
Answer:
The standard error of a proportion p in a sample of size n is given by: [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
The standard error of a proportion p in a sample of size n is given by: [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Estimating Mean SAT Math Score
Type numbers in the boxes.
aby Part 1: 5 points
The SAT is the most widely used college admission exam. (Most community
aby Part 2: 5 points
colleges do not require students to take this exam.) The mean SAT math score
varies by state and by year, so the value of u depends on the state and the year. 10 points
But let's assume that the shape and spread of the distribution of individual SAT math scores in each
state is the same each year. More specifically, assume that individual SAT math scores consistently
have a normal distribution with a standard deviation of 100. An educational researcher wants to
estimate the mean SAT math score (u) for his state this year. The researcher chooses a random
sample of 661 exams in his state. The sample mean for the test is 494.
Find the 99% confidence interval to estimate the mean SAT math score in this state for this year.
(Note: The critical z-value to use, zc, is: 2.576.)
Your answer should be rounded to 3 decimal places.
Answer:
(483.981 ; 504.019)
Step-by-step explanation:
Given :
σ = 100
Sample size, n = 661
xbar = 494
We use the Z distribution since we are working with the population standard deviation ;
C.I = xbar ± (Zcritical * σ/√n)
Zcritical at 99% = 2.576
C.I = 494 ± (2.576 * 100/√661)
C.I = 494 ± 10.019
Lower boundary = (494−10.019) = 483.981
Upper boundary = (494+10.019) = 504.019
C.I = (483.981 ; 504.019)
Find the remainder when f(x)= 8x^3+ 4x^2
13x + 3 is divided by 2x + 5.
Answer:
-129
Step-by-step explanation:
2x+5=0
x=-5/2 [By the remainder theorem]
f(-5/2)=8(-5/2)^3+4(-5/2)^2+13(-5/2)+3
=-125+25-65/2+3
=-129.
I really need the help please and thank you
BBBBB BBBBBBBBBBBBBBBBBBBBBBBBBBBB
Determine whether (a) x = -1 or (b) x = 2 is a solution to this equation
Answer:
x = 2 is the solution to x + 1.5 = 3.5
Step-by-step explanation:
x + 1.5 = 3.5
-1.5 -1.5
--------------------
x = 2
Determine whether the ordered pair is a solution of the equation. Show your work to receive credit.
9. Is (-1,3) a solution to the equation y = -3x + 10?
10. Is (7,-2) a solution to the equation x – 4y = 15?
Please show work to help me understand.
Answer:
3=3 + 10
3 = 13(NO)
x-4y=15
7--8=15
15=15(YES)
I’m sorry, I suck at math, can someone please help me with this?
Answer:
w¹×w¹×w¹=w¹+¹+¹= w³
formula is a^m×a^n=a^m+n
What type of number can be written as a fraction
Answer:
a rational number is a number that can be written as a fraction
I hope this helps
The table below shows the number of pets kept by the students in a class.
-----------------------------------------------------------
No. of pets | No. of students
-----------------------------------------------------------
0 | 9
1 | k
2 | 2
3 | 1
4 | 2
-----------------------------------------------------------
If the median number of pets is 1, what is the smallest value of k ?
Answer:
The answer for this question is 5
Select the correct answer.
As part of a class project, a university student surveyed the students in the cafeteria lunch line to look for a relationship between eye color and hair color among students. The table below contains the results of the survey.
Answer: Choice B) 0.27
=========================================================
Explanation:
There are a lot of data values here, and it's possible to easily get lost in them. However, we're asked only about students with blond hair. So we only focus on the first row. Ignore everything else.
We see that there are 78 of these students total. Of this total, 21 have green eyes.
Therefore, the relative frequency of blonds with green eyes is 21/78 = 0.2692 which rounds to 0.27; so that's why the answer is choice B.
find the equation of the line which is parallel to the line 5 x + 4y = 18 and makes an intercept of 2 units on the x-axis
Answer:
[tex]{ \underline{ \sf{equation \: is : \: y = - \frac{5}{4} x + 2 }}}[/tex]
Step-by-step explanation:
[tex]y = mx + c \\ 4y = - 5x + 18 \\ y = - \frac{5}{4} x + \frac{9}{2} [/tex]
since it is parallel, the gradients are the same; m = -5/4
[tex]y = - \frac{5}{4} x + 2[/tex]
Answer:
y=-5x+2
Step-by-step explanation:
x intercept=2
points will be (2,0)
slope of given line:
4y=-5x+18
y=mx+c
comparing equation:
m=-5
lines are parallel so given slope is equal to required slope.
using point slope form:
y-0=-5(x-2)
y=-5x+2
A garden table and a bench cost $717 combined. The garden table costs $67 more than the bench. What is the cost of the bench?
Subtract the difference form the total:
717 - 67 = 650
Divide the remaining amount by 2:
650/2 = 375
The bench cost$375
In a certain country people own a total of about 352 million fish, cats, and dogs as pets. The number of fish owned is 14 million more than the total number of cats
and dogs owned, and 11 million more cats are owned than dogs. How many of each type of pet do people in this country own?
Answer:
dogs = 79
dats = 90
fish = 183
Step-by-step explanation:
let the total number of dogs owned be x
no. of cats owned = x+11
no. of fish owned = x+11+x+14= 2x+25
hence,
2x+25+x+11+x=352
4x=316
x=316/4= 79mil
no. of cats owned = 79 + 11 = 90
no. of fish owned = 2(79)+25=183
PLEASEEEE HELP I WILL GIVE BRAINLIEST
choose the equation for the graph.
Answer:
c
Step-by-step explanation:
plz gimme brainliest
i promise u its c
Answer:
c
Step-by-step explanation:
by solving a pair of linear equation X + Y is equal to 20 and x-y=10 the value of 'x' and 'y' are
Answer:
x=15, y=5
Step-by-step explanation:
x+y=20
x-y=10
Adding both equations;
(x+x) + (y-y) = 20+10
2x = 30
x = 30/2 = 15
Substitute x=15 into x+y=20
y= 20-x = 20-15= 5
6 times the sum of 5 and K
Answer:
6(5+k)
Step-by-step explanation:
The sum of 5 and k
5+k
6 times the sum
6(5+k)
What are all the factors of 618?
Answer:
1, 2, 3, 6, 103, 206, 309, 618
The polynomial p(x) = x3 – 7x - 6 has a known factor of (x + 1).
Rewrite p(x) as a product of linear factors.
p(x)
Hi there!
[tex]\large\boxed{(x -3)(x + 2)(x + 1)}[/tex]
We can use long division to find the other roots of p(x).
We know that x + 1 is a factor, so:
Set up:
Find how many times that the first term in the divisor goes into the first of the dividend. Subtract from like terms.
x² - x - 6
x + 1 | x³ + 0x² - 7x - 6
x³ + x²
0 - x² - 7x
- x² - x
0 - 6x - 6
-6x - 6
0 0
Therefore, x² - x - 6 is another factor. We can factor this further:
Find two numbers that add up to -1 and multiply into -6. We get:
-3, 2
(x - 3)(x + 2)
The entire polynomial factored is:
(x -3)(x + 2)(x + 1)
Cheyenne's bi-weekly gross pay is $529.81. She sees that $18.54 was deducted for Medicare tax. What percent of Cheyenne's gross pay has been withheld for Medicare tax? Round to the nearest tenth. (2 points)
0.35%
2.2%
3.5%
Answer:
I got 3.5%
Step-by-step explanation:
Hope this helps
A firm has a beta of 1.3 and a debt-to-equity ratio of .4. The market rate of return is 11.6
percent, the tax rate is 32 percent, and the risk-free rate is 3.3 percent. The pretax cost of debt
is 7.2 percent. What is the firm's WACC?
The WACC of the firm is 17.05%
The first step is to write out the parameters given in the question;
Beta= 1.3
Debt to equity ratio= 0.4
Market rate of return= 11.6%
= 11.6/100
= 0.116
Tax rate= 32%
= 32/100
= 0.32
Risk free rate= 3.3%
= 3.3/100
= 0.033
Pretax cost of debt= 7.2%
= 7.2/100
= 0.072
The firm's WACC can be calculated as follows
RS= 0.033+1.3(0.116-0.033)
= 0.033+1.3(0.083)
= 0.033+0.1079
= 0.1409
WACC= (1/1.4)(0.1409)+(2/1.4) (0.072)(1-0.32)
= (0.7142)(0.1409) + (1.4285)(0.072)(0.68)
= 0.1006+0.0699
= 0.1705(100)
= 17.05%
Hence the firm's WACC is 17.05%
Learn more via the link below
https://brainly.com/question/23926595?referrer=searchResults
Shahril bought a CD, 2 T-shirts and a pair of jeans for $133. Each
T-shirt cost $13 more than the CD. The pair of jeans cost $30 more
than each T-shirt. Find the cost of the CD.
Step-by-step explanation:
Let the price of CD, tshirt and jeans be x,y and z respectively.
given:
x+2y+2z=133......(i)
y=x+13.......(ii)
2z=y+30....(iii)
in eqn (iii) ,
2z=y+30
or, 2z=x+13+30
or, z=(x+43)/2....(iv)
now in eqn (i),
x+2y+2z=133
or, x+2(x+13)+2((x+43)/2) =133
or, x+2x+26+x+43=133
or, 4x=133-69
or, x= 64/4
•°• x=$16
(a) A body of mass 2kg is placed on a rough plane inclined at an angle of 30° to the
horizontal. The coefficient of friction between the body and the plane is 0.25. Find the
least force needed to prevent the body from slipping down the plane if this force acts
upwards at an angle of 30° to the line of greatest slope.
Answer:
8.6 N
Step-by-step explanation:
Let T be the unknown force
Let θ be the slope of the inclined plane to horizontal
Let φ be the angle of the force to the plane
Let μ be the coefficient of static friction
Let m be the mass
Let N be the Normal force of plane on mass
Let Ff be the friction force which will have a maximum at μN
Let g be gravity
Forces acting parallel to the plane. Upslope is positive
For minimum force T, friction will be max and acting upslope.
F = ma
Tcosφ - mgsinθ + Ff = m(0)
Tcosφ - mgsinθ + μN = 0
Tcosφ - mgsinθ + μ(mgcosθ - Tsin(θ + φ)) = 0
T(cosφ - μsin(θ + φ)) + μmgcosθ - mgsinθ = 0
T = mg(sinθ - μcosθ) / (cosφ - μsin(θ + φ))
T = 2(9.8)(sin30 - 0.25cos30) / (cos30 - 0.25sin(30 + 30))
T = 8.5547537...
I need you guy’s help answer thanks so much
Answer:
B. 7i
Step-by-step explanation:
first we need to find the root of the expression
[tex]\sqrt{-49} = \sqrt{49} *\sqrt{-1} \\ \\ \sqrt{49} = 7\\\\and\\\\ \sqrt{-1} = i[/tex]
so the answer is B. 7i
which is more 1 ton or 2,884 pounds?
If 2/3 of the girls in class have brown eyes and 1/4 of the girls have blue eyes what fraction of the girls in class have neither blue or brown
find the LCM of 220,440,660 by common division method
Answer: LCM = 1320
Step-by-step explanation:
2 | 220, 440, 660
2 | 110, 220, 330
2 | 55, 110, 165
3 | 55, 55,165
5 | 55, 55 , 55
11 | 11, 11, 11
| 1, 1, 1
= 2 × 2 × 2 × 3 × 5 × 11
= 1320
Therefore the LCM is 1320
Must click thanks and mark brainliest
Supervisor: "I need you to increase the number of customers you talk to daily by
20%."
Employee: "I talk to an average of 8 customers per hour during an 8 hour shift so
now I'll need to talk to customers per day."
68
77
85
97
160
NEXT
Answer:
77
Step-by-step explanation:
Currently:
Talk to 8 customers per hour, work 8 hours, so:
Talk to 8*8 = 64 customers.
With the increase:
Has to increase by 20%, so 64 is multiplied by 1 + 0.2 = 1.2. Then
64*1.2 = 76.8
Rounding up, 77 is the answer.
