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]
Ellis makes some biscuits. For every 200g of flour he uses, he needs 75g of butter
a. Write a ratio for the amount of flour to the amount of butter.
b. Write a formula forf, the amount of flour, in terms of the amount of butter, b.
c. Ellis makes 24 biscuits using 300g of flour.
How many biscuits can he make with 375g of butter?
Answer:
a) 8:3, b) no formula is there, c) 30
Step-by-step explanation:
because 200/75=8:3
because there formula being obtained
because 300/24=12.5
375/12.5=30
Which of the following is the minimum value of the equation y = 2x2 + 5?
5
0
−5
2
Students are given 3 minutes to complete each multiple-choice question on a test and 8 minutes for each free-response question. There are 15 questions on the test and the students have been given 55 minutes to complete it. A Table titled Test Time, showing Number of Questions, Time per Item in minutes, and Total Time in minutes. The first row shows Multiple Choice, with m, 3, and 3 m. The second row shows Free Response, with 15 minus m, 8, and x. The third row shows Total, with 15, blank, and 55. Which value could replace x in the table? Which value could replace x in the table?
Answer:
c
Step-by-step explanation:
Answer:
c is the correct answer
The area of a circle is 3.142cm square.find the radius and diameter of the circle
Answer:
50.24 or 50.272
Step-by-step explanation:
Square radius and then times by 3.14 or 3.142
4^2*3.14 = 50.24
4^2*3.142 = 50.272
A chemical engineer must report the average volume of a certain pollutant produced by the plants under her supervision. Here are the data she has been given by each plant:plantvolume of pollutantPittCross CreekSusquehannaWhat average volume should the chemical engineer report
Answer:
Please find the complete question in the attached file.
Step-by-step explanation:
Total quantities of plant-produced pollutants:
[tex]=(10.88+15.82+0.92) \ L\\\\=27.62\ L[/tex]
We are three medicinal plants here, Pinecrest, Macon, and Ogala. The average number of contaminants produced by plants would be
[tex]\to 27.62\div 3 \\\\\to \frac{27.62}{3} \\\\ \to 9.206 \ L[/tex]
A hotel manager believes that 23% of the hotel rooms are booked. If the manager is right, what is the probability that the proportion of rooms booked in a sample of 610 rooms would differ from the population proportion by less than 3%
Answer:
0.9216 = 92.16% probability that the proportion of rooms booked in a sample of 610 rooms would differ from the population proportion by less than 3%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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.
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]
A hotel manager believes that 23% of the hotel rooms are booked.
This means that [tex]p = 0.23[/tex]
Sample of 610 rooms
This means that [tex]n = 610[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.23[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.23*0.77}{610}} = 0.017[/tex]
What is the probability that the proportion of rooms booked in a sample of 610 rooms would differ from the population proportion by less than 3%?
p-value of Z when X = 0.23 + 0.03 = 0.26 subtracted by the p-value of Z when X = 0.23 - 0.03 = 0.2. So
X = 0.26
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.26 - 0.23}{0.017}[/tex]
[tex]Z = 1.76[/tex]
[tex]Z = 1.76[/tex] has a p-value of 0.9608
X = 0.2
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.2 - 0.23}{0.017}[/tex]
[tex]Z = -1.76[/tex]
[tex]Z = -1.76[/tex] has a p-value of 0.0392
0.9608 - 0.0392 = 0.9216
0.9216 = 92.16% probability that the proportion of rooms booked in a sample of 610 rooms would differ from the population proportion by less than 3%
A display case of disposable tablecloths are marked 5 for $3. If Peter has $21, how many plastic tablecloths can Peter get?
Answer:
35
Step-by-step explanation:
3x7=35
There are 60 students and 13 teachers on a bus .what is the ratio of students to teachers.
The figure shown represents a roof truss
design. Based on the markings on the figure,
which of the triangles can you prove are
congruent?
OPTION C is the correct answer.
The ΔAFE ≅ ΔBHG by the angle, side and angle theorem are congruent. Option (A) is correct.
What is the triangle?Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.
The figure shows models of a roof truss. Based on the markings, there is enough information to prove that
ΔAFE ≅ ΔBHG
∠EFA=∠GHB (90 degrees )
EF = GH (equal side)
EAF = GBH (the side opposite to the angle is equal)
ΔAFE ≅ ΔBHG (ASA )
Thus, ΔAFE ≅ ΔBHG by the angle, side and angle theorem are congruent.
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2.What is the value of x if x/4 + 12 = 4 ?
Answer:
Step-by-step explanation:
Answer:
hope it will help u
19. In a random sample of 250 students, we found that 75 work out 4 or more times a week. Find the 95% confidence interval for the proportion of students who work out 4 or more times a week.
Answer:
The 95% confidence interval for the proportion of students who work out 4 or more times a week is (0.2432, 0.3568).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
In a random sample of 250 students, we found that 75 work out 4 or more times a week.
This means that [tex]n = 250, \pi = \frac{75}{250} = 0.3[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3 - 1.96\sqrt{\frac{0.3*0.7}{250}} = 0.2432[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3 + 1.96\sqrt{\frac{0.3*0.7}{250}} = 0.3568[/tex]
The 95% confidence interval for the proportion of students who work out 4 or more times a week is (0.2432, 0.3568).
Using the Fenske equation, calculate the number of theoretical plates for a fractional distillation set up used to separate Ethyl acetate (the more volatile component) from hexane (less volatile component) in a mixture with the following experimental data:
n=log(X/Xb) -log(Y a/Yb)/ log α Fenske Equation
Experimental data: l
The following are the data optained from injection of a 1-microliter sample of the equimolar stock solution used in the distillation experiment into a GČ. The percent of the area under the appropriate peak is idicated.
a = 1.6
GC results of the stock mixture used in the experiment
Component Rt (retention time) Percent Area
Ethyl acetate 1.09 53 82
Hexane 1.58 47 18
GC results of a 1-microliter sample after 3 mL had been collected:
Component Rt (retention time) Percent Area
Ethyl acetate 1.09 82
Hexane 1.58 18
a. 3.9
b. 7.2
c. 7.0
d. 3.0
Next anyone help it always helps haha 20 points
Answer:
Distance between Amber and Claire's house = 17.63 blocks
Step-by-step explanation:
In this graph three points are showing the locations of Amber's, Betsey's and Claire's houses.
Each unit on the graph represents 1 block.
Amber walks from her house to Claire's house, then on to Betsey's house.
We have to calculate the distance covered by Amber.
Since Distance from Claire's house to Betsey's house = 7 blocks = 7 units
and distance between Amber and Betsey's house = 8 blocks = 8 units
Now we will calculate the distance between Amber and Claire's house by Pythagoras theorem.
Distance² = 7² + 8² = 49 + 64 = 113
Distance = √113 units = 10.63 units
Therefore, total distance walked by Amber = 10.63 + 7 = 17.63 units = 17.63 blocks
Answer:
the answer might be 17. 63 because there are 7 blocks in between them so try that sorry if its wrong
Althea has $100. She divides it evenly among her 4 children. Her oldest child, Raul, spends $15 of the amount he receives. How much money does Raul have left after he spends $15?
Which statements about this word problem are true? Check all that apply.
This is an example of a part-whole problem.
This is an example of a comparison problem.
Addition then multiplication can be used to solve the problem.
Division then subtraction can be used to solve the problem.
Division then multiplication can be used to solve the problem.
Step-by-step explanation:
she gives each of her children $25 each,if Raul spends $15 then he would have $10 left.
Division then subtraction can be used to solve the problem.
What is mathematical expressions?An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases.
Given
she gives each of her children $25 each,if Raul spends $15 then he would have $10 left.
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What piece of information is needed to prove the triangles are congruent through AAS?
Answer:
C. <C is congruent to <Y
Step-by-step explanation:
to be AAS the angles need to be next to each other
Can someone please help me??
Answer:
The maximum value of the function = 11, at x = 3 and y = 5
The minimum value of the function = -21, at x = 3 and y = -3
Step-by-step explanation:
Given;
F = 4y - 3x
The function is subject to y ≤ 2x - 1,
y ≥ -2x + 3,
x ≤ 3
y ≤ 2x - 1
- ( y ≥ -2x + 3)
-------------------
0 ≤ 4x - 4
4 ≤ 4x
1 ≤ x
thus, 1 ≤ x ≤ 3
When x = 3
y ≤ 2x - 1 ⇒ y ≤ 2(3) - 1, ⇒ y ≤ 5
y ≥ -2x + 3, ⇒ y ≥ -2(3) + 3, ⇒ y ≥ - 3
thus, -3 ≤ y ≤ 5
When x = 1
y ≤ 2x - 1 ⇒ y ≤ 2(1) - 1, ⇒ y ≤ 1
y ≥ -2x + 3, ⇒ y ≥ -2(1) + 3, ⇒ y ≥ 1
when x = 1 and y = 1
F = 4(1) - 3(1)
F = 1
when y = -3, and x = 3
F = 4(-3) - 3(3)
F = -12 - 9
F = - 21
When y = 5 and x = 3
F = 4(5) - 3(3)
F = 20 - 9
F = 11
Therefore, the maximum value of the function = 11, at x = 3 and y = 5
The minimum value of the function = -21, at x = 3 and y = -3
Whole numbers are closed under addition because the sum of two whole numbers is always a whole number. Explain how the process of checking polynomial division supports the fact that polynomials are closed under multiplication and addition.
Answer:
Sample Answer: If there is no remainder, then the dividend is equal to the quotient times the divisor.
The quotient and divisor are both polynomials, and their product, the dividend, is a polynomial.
If there is a remainder, then it gets added on to the product of the quotient and the divisor.
The sum of the remainder and the product of the quotient and divisor is the dividend, which is a polynomial.
Step-by-step explanation:
for sure enjoy!
Answer:
If there is no remainder, then the dividend is equal to the quotient times the divisor.
The quotient and divisor are both polynomials, and their product, the dividend, is a polynomial.
If there is a remainder, then it gets added on to the product of the quotient and the divisor.
The sum of the remainder and the product of the quotient and divisor is the dividend, which is a polynomial.
a car travels 10 km southeast and 15 km in a direction 60 degrees north of east. find the magnitude and direction
Answer:
the car travels 10km then 15km 60* north of east
Step-by-step explanation:
Given the function
Calculate the following values:
Answer:
f(-1) = 1
f(0) = 20
f(2) = 38
Step-by-step explanation:
f(-1) = 9×-1 + 10 = -9 + 10 = 1
f(0) = 9×0 + 20 = 0 + 20 = 20
f(2) = 9×2 + 20 = 18 + 20 = 38
we needed to use the second definition for f(0), because that is the same as saying x=0.
and that is in the domain of the second function definition ( x>=0).
What is the value of y in the solution to the system of equations?
1 2 3x + 2 y = 1
2x – 3y=-30
Answer:
y=1
Step-by-step explanation:
Answer:
SEESH thanks for the points
Step-by-step explanation:
3.6 subtract by 1.487 is egual to ______.Pls write in step by step.
Answer:
2.113
Step-by-step explanation:
[tex]3.600\\1.487 \ -\\\overline{2.113}[/tex]
Zach read a book for 10 minutes every weekend in the first month, 20 minutes in the second month, 40 minutes in the third month, and 80 minutes in the fourth month.
Victoria read a book for 35 minutes every weekend in the first month, 50 minutes in the second month, 65 minutes in the third month, and 80 minutes in the fourth month.
Which statement best describes the methods used by Zach and Victoria to increase the time they spent reading a book? (1 point)
Select one:
a. Zach's method is linear because the number of minutes increased by an equal factor every month.
b. Victoria's method is linear because the number of minutes increased by an equal number every month.
c. Both Victoria's and Zach's methods are exponential because the number of minutes increased by an equal factor every month.
d. Both Victoria's and Zach's methods are exponential because the number of minutes increased by an equal number every month.
9514 1404 393
Answer:
b. Victoria's method is linear because the number of minutes increased by an equal number every month
Step-by-step explanation:
Zach's reading doubled each month, a characteristic of an exponential function.
Victoria's reading increased by 15 minutes each month, characteristic of a linear function.
The only reasonable description among those offered is the one shown above: choice B.
PLEASE I NEED HELP!!
Answer:
it is (4,120)
hope this helps you
Solve the equation x^2+6x+1=0
Hello!
x² + 6x + 1 = 0 <=>
<=> x = -6±√6²-4×1×1/2×1 <=>
<=> x = -6±√36-4/2 <=>
<=> x = -6±√32/2 <=>
<=> x = -6±2²√2/2 <=>
<=> x = -6±4√2/2 <=>
<=> x = -6+4√2/2 <=>
and
<=> x = -6-4√2/2 <=>
<=> x = -3+2√2 <=>
and
<=> x = -3-2√2 <=>
x1 = -3-2√2 and x2 = -3+2√2
Good luck! :)
The mean monthly car payment for 121 residents of the local apartment complex is $372. What is the best point estimate for the mean monthly car payment for all residents of the local apartment complex
Answer:
Needed point estimate is $372
Step-by-step explanation:
Given:
Number of houses in resident area = 121
Monthly mean car payment = $372
Find:
Best point estimate for the mean monthly car payment
Explanation:
The "best point estimate" for such average monthly automobile payment for all inhabitants of the nearby apartment complex is used as the "sample mean." In this example, a $372 sample was obtained on 121 residents.
As a result, the needed point estimate is $372.
Which of the following best describes the relationship between angle a and angle bin the image below?
find the value of the following 425×167+233×425 step by step explanation
Answer:
so first we start from the left
425*167=70975
but instead of adding this to 233 we use pemdas so instead we do
233*425=99025
now we add them together
70975+99025=170000
Hope This Helps!!!
Answer:
170,000
Step-by-step explanation:
425 × 167 + 233 × 425
= (425 × 167) + (233 × 425)
= 70,975 + 99,025
= 170,000
solve 5x^2-2=-12 by taking the square root
Answer:
x = ±i√2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality
Algebra II
Imaginary root i
i = √-1Step-by-step explanation:
Step 1: Define
Identify
5x² - 2 = -12
Step 2: Solve for x
[Addition Property of Equality] Add 2 on both sides: 5x² = -10[Division Property of Equality] Divide 5 on both sides: x² = -2[Equality Property] Square root both sides: x = ±√-2Rewrite: x = ±√-1 · √2Simplify: x = ±i√2x - 3y +3=0
a) The length of the perpendicular drawn from the point (a, 3) on the line
3x + 4y + 5 = 0 is 4. Find the value of a.
Answer:
We know that for a line:
y = a*x + b
where a is the slope and b is the y-intercept.
Any line with a slope equal to -(1/a) will be perpendicular to the one above.
So here we start with the line:
3x + 4y + 5 = 0
let's rewrite this as:
4y = -3x - 5
y = -(3/4)*x - (5/4)
So a line perpendicular to this one, has a slope equal to:
- (-4/3) = (4/3)
So the perpendicular line will be something like:
y = (4/3)*x + c
We know that this line passes through the point (a, 3)
this means that, when x = a, y must be equal to 3.
Replacing these in the above line equation, we get:
3 = (4/3)*a + c
c = 3 - (4/3)*a
Then the equation for our line is:
y = (4/3)*x + 3 - (4/3)*a
We can rewrite this as:
y = (4/3)*(x -a) + 3
now we need to find the point where this line ( y = -(3/4)*x - (5/4)) and the original line intersect.
We can find this by solving:
(4/3)*(x -a) + 3 = y = -(3/4)*x - (5/4)
(4/3)*(x -a) + 3 = -(3/4)*x - (5/4)
(4/3)*x - (3/4)*x = -(4/3)*a - 3 - (5/4)
(16/12)*x - (9/12)*x = -(4/3)*a - 12/4 - 5/4
(7/12)*x = -(4/13)*a - 17/4
x = (-(4/13)*a - 17/4)*(12/7) = - (48/91)*a - 51/7
And the y-value is given by inputin this in any of the two lines, for example with the first one we get:
y = -(3/4)*(- (48/91)*a - 51/7) - (5/4)
= (36/91)*a + (153/28) - 5/4
Then the intersection point is:
( - (48/91)*a - 51/7, (36/91)*a + (153/28) - 5/4)
And we want that the distance between this point, and our original point (3, a) to be equal to 4.
Remember that the distance between two points (a, b) and (c, d) is:
distance = √( (a - c)^2 + (b - d)^2)
So here, the distance between (a, 3) and ( - (48/91)*a - 51/7, (36/91)*a + (153/28) - 5/4) is 4
4 = √( (a + (48/91)*a + 51/7)^2 + (3 - (36/91)*a + (153/28) - 5/4 )^2)
If we square both sides, we get:
4^2 = 16 = (a + (48/91)*a + 51/7)^2 + (3 - (36/91)*a - (153/28) + 5/4 )^2)
Now we need to solve this for a.
16 = (a*(1 + 48/91) + 51/7)^2 + ( -(36/91)*a + 3 - 5/4 + (153/28) )^2
16 = ( a*(139/91) + 51/7)^2 + ( -(36/91)*a - (43/28) )^2
16 = a^2*(139/91)^2 + 2*a*(139/91)*51/7 + (51/7)^2 + a^2*(36/91)^2 + 2*(36/91)*a*(43/28) + (43/28)^2
16 = a^2*( (139/91)^2 + (36/91)^2) + a*( 2*(139/91)*51/7 + 2*(36/91)*(43/28)) + (51/7)^2 + (43/28)^2
At this point we can see that this is really messy, so let's start solving these fractions.
16 = (2.49)*a^2 + a*(23.47) + 55.44
0 = (2.49)*a^2 + a*(23.47) + 55.44 - 16
0 = (2.49)*a^2 + a*(23.47) + 39.44
Now we can use the Bhaskara's formula for quadratic equations, the two solutions will be:
[tex]a = \frac{-23.47 \pm \sqrt{23.47^2 - 4*2.49*39.4} }{2*2.49} \\\\a = \frac{-23.47 \pm 12.57 }{4.98}[/tex]
Then the two possible values of a are:
a = (-23.47 + 12.57)/4.98 = -2.19
a = (-23.47 - 12.57)/4.98 = -7.23
How many flowers spaced every 4 inches are needed to surround a circular garden with a 15-foot radius? Round all circumference and area calculations to the nearest whole number.
Answer:
283 flowers
Step-by-step explanation:
c=2pi*r
c = 1130.973 =1131
1131/4
282.75 = 283
Monique made several batches of soup.
Each batch required 3/4 of a pound of potatoes. She used a total of 6 1/2 pounds. How many batches did she make?
Answer:
8 batches
in workings show whats left over but not counted.
As a batch its a whole number as the multiplier will usually be the fraction
and fraction / fraction should always show fraction but the whole number given with a remainder can be shown if not a whole number.
Step-by-step explanation:
6 1/2 = 6.5
and ;
3/4 of a pound = 0.75 of 1 pound
6.5 / 0.75 = 8.7 or in full workings write = 8.6666.....7
8.7/ 1 = 8 batches with 0.7 or 0.66667 left over
Answer In fraction for exam question given in fraction 8.7 = 8 batches
with 7/10 left over.