1. Business is major
The sampling distribution of p
PROBLEM:
According to the National Center for Education Statistics, 20% of students who
recently earned bachelor's degrees were business majors. Imagine taking an SRS of
300 students who recently earned bachelor's degrees and calculating p = the
proportion of students in the sample who majored in business.
(a) Identify the mean of the sampling distribution of p.
(b) Calculate and interpret the standard deviation of the sampling distribution of p.
Verify that the 10% condition is met.
(c) Describe the shape of the sampling distribution of p. Justify your answer.
Answers
a) The mean of the sampling distribution of p is of 0.2.
b) The standard deviation of the sampling distribution of p is of: 0.0231, which is the amount that the sample proportions may differ from 0.2.
c) The shape of the sampling distribution of p is approximately normal.
How to define the sampling distribution of p?The sampling distribution of p is defined according to the Central Limit Theorem, which states that the sampling distribution of a proportion p in a sample of size n has:
Approximately normal shape.Mean equals to p.Standard deviation equals to [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex]The parameters for this problem are given as follows:
p = 0.2, n = 300.
The 10% condition is given as follows:
np = 300 x 0.2 = 60 > 10.n(1 - p) = 300 x 0.8 = 240 > 10.Then the standard error of the sampling distribution of p is calculated as follows:
[tex]s = \sqrt{\frac{0.2(0.8)}{300}} = 0.0231[/tex]
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Related Questions
What theorem would this one be?
Answers
Answer:
C. Yes, SAS
Step-by-step explanation:
You want to know the congruence theorem that lets you say ∆ACD≅∆CAB, given that AB=CD and AB║CD.
Congruent trianglesThe triangles are congruent if an angle or side can be shown congruent, in addition to at least one angle and at least one side.
Here, the sides AB and CD are shown congruent. The side AC is congruent to itself, so we only need the angle(s) between them to show the triangles are congruent.
The Alternate Interior Angles theorem tells you that transversal AC creates congruent angles CAB and ACD with respect to the parallel lines AB and CD.
Hence we can show triangle ACD and CAB are congruent by the SAS congruence theorem.
Yes, The triangle is congruent by Angle - Side - Angle congruence theorem.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
⇒ AB || CD
Now,
In figure,
⇒ AB || CD
So, In triangle ACD and triangle CAB;
⇒ AB || CD
So, By definition of alternate angles,
⇒ ∠ BAC = ∠ DCA
And, ∠ DAC = ∠ ACB
Here, Line AC is common in both tringle.
Hence, By Angle - Side - Angle congruence theorem,
⇒ Δ ACD ≅ Δ CAB
Thus, The triangle is congruent by Angle - Side - Angle congruence theorem.
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what is 2 divided by 238
Answers
Answer:
0.0084033613
Step-by-step explanation:
Right answer needed thank you!
Answers
The inequality - 2 · x + y > - 4 represents the figure on Cartesian plane.
How to derive the inequality shown in the image
In this problem we have a picture with a representation of a linear inequality of the form:
y > m · x + b
Where:
m - Slope of the line.b - Intercept of the line.By analytic geometry, a line can be generated from the knowledge of the location of two points on Cartesian plane. First, determine the equation of the line:
m · 0 + b = - 4
2 · m + b = 0
b = - 4
2 · m = - b
m = - b / 2
m = 2
Second, write the inequality:
y > 2 · x - 4
- 2 · x + y > - 4
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10. What was the snow level at 8 a.m., when x = 8?
Answers
The snow level at 8 a.m., when x = 8, was 30cm.
What is linear equation?The simplest equation for expressing and resolving an unknown number is a linear equation in one variable. It is usually a straight line and is easily pictorial portrayed. A simple way to convey a mathematical assertion is with a linear equation. Unknown numbers can be represented by any variable or symbol. There are several easy ways to solve a linear equation.
solutiony = 2x + 14.
Here, y is the amount of snow in inches, and x is the number of hours after midnight
To find the snow level at 8 a.m. we take the value of x = 8.
⇒ y = 2*8 + 14
⇒ y = 16 + 14
⇒ y = 30cm
So, The snow level at 8 a.m., when x = 8, was 30cm.
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this question is incomplete. The complete question is
the snow level is modeled by the function y = 2x + 14. Here, y is the amount of snow in inches, and x is the number of hours after midnight (x = 0). 10. What was the snow level at 8 a.m., when x = 8?
The quotient of y and 3 added to 9 equals 10
Answers
Answer:
Step-by-step explanation:
Are you after a solution for y?
quotient of y and 3 is a fancy word for division
y/3+9=10
To solve for y subtract 9 from both sides
y/3+9-9=10-9
y/3=1
To solve for y
multiply both sides by 3
3(y/3)=1*3
y=3
Frames-for-All sells framed pictures to hotels and other corporations across the country. Last year, the company sold a total of 720,460 pictures. This year, they sold 972,621 picyures. What is the percent of increase in yearly sales?
Answers
The percent of increase in yearly sales is 35%.
What is a percentage increase?A percentage increase means the eventual increase in the quantity in percent form. The percentage increase formula is use to compare growth in a quantity from the initial value to its final value over a period of time.
The formula for getting a percentage increase is "[(Final Value - Initial Value)/Initial Value] × 100"
Initial value = 720,460 pictures
Final value = 972,621 pictures.
The percentage increase:
= [(972,621 - 720,460] / 720,460} * 100
= 0.35 * 100
= 35%
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Nevach and Michael are helping their friend Nabhitha move. If Nevaeh can
move 6 boxes for every 24 boxes that Michael moves, then how many boxes
can Michael move for every box that Nevaeh moves?
Michael boxes
24
Answers
Answer:
For every 1 box Naveah moves, Michael moves 4 boxes
Given angle 1 is congruent to angle 3
prove angle 6 is congruent angle 4
Answers
Proof of angle 6 is congruent to angle 4 is given.
What is congruent?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
Angles of equal measure are said to have congruent angles.
Given,
∠1 ≅ ∠3
And we know from the vertical angles, property;
The angles opposite each other when two lines cross.
They are always equal.
And here we have two pairs of vertical angles,
So, ∠1 = ∠4
and ∠3 = ∠6
And ∠1 ≅ ∠3 is given.
So, ∠1 ≅ ∠4
and ∠3 ≅ ∠6
Comparing, we get
∠4 ≅ ∠6
Therefore, ∠4 ≅ ∠6 is proved.
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cantor showed that for any set a, we have |a| < |p(a)|. what does this statement mean? select the correct interpretation.
Answers
George Canter showed that, for any set a, we have |a|<|p(a)|. This is a well-known theorem of canter, known as the 'Canter's Theorem'.
Proving this theorem:
Proof: At the first instance, we need to show that, A bar ≤P(A) bar, we will define the injection by f:A→P(A) by: f(a)={a}. Let g be the contradiction.
We need to prove that there is no bijection g:A→P(A).
Now, Let: S={a∈A:a∉g(a)}⊆A.}
In the present condition, there are two possibilities, first, x∈S and second, x∉S.
Therefore,
1. If x∈S, then x∉g(x)=S, i.e., x∉S, a contradiction.
2. If x∉S, then x∈g(x)=S, i.e., x∈S, a contradiction.
Thus, such a bijection, is not possible.
This theorem, coined by Canter, basically implies that there is no largest cardinal number present. There are 'n' number of cardinal numbers present, i.e., there are infinite number of cardinal numbers.
Now, suppose that, A is a set of all sets, this was proved by the continuum hypothesis. But, the continuum hypothesis can't be proved. It can't be disproved also.
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10. A statue casts a shadow 30 feet long. At the same time, a person who is 5 feet tall casts a
shadow that is 6 ft long. How tall is the statue?
A. 30 ft
B. 25 ft
C. 18 ft
D.12.5 ft
Answers
Add -0.25+ 3 1/6+ 2 1/12. Write in simplest form
Answers
Answer: 5
Step-by-step explanation: because
A quarter of a year is 1/4 of a year. There are 12 months in a year. How many months are in a quarter of a year? Draw a diagram to illustrate the problem.
Answers
There are Three months in a quarter of a year.
To determine what is being asked, divide the total number by the denominator and get the portion using the numerator:
1 year = 4 quarters
1 quarter= [tex]\frac{1}{4}[/tex] year
1 year = 12 months
Thus,
1 quarter = (Total number of months in year) ÷ (Total number of quarters in a year)
1 quarter = [tex]\frac{12}{4}=3[/tex]
So, There are Three months in a quarter of a year.
One year typically refers to a period of 365 days or 12 months. It usually includes the entire calendar year from January 1st to December 31st. It can also refer to a fiscal year (a period of 12 consecutive months used for accounting purposes) or a school year (which may start in late summer).
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There are Three months in a quarter of a year.
To determine what is being asked, divide the total number by the denominator and get the portion using the numerator:
1 year = 4 quarters
1 quarter= [tex]\frac{1}{4}[/tex] year
1 year = 12 months
Thus,
1 quarter = (Total number of months in year) ÷ (Total number of quarters in a year)
1 quarter = [tex]\frac{12}{4} =3[/tex]
So, There are Three months in a quarter of a year.
One year typically refers to a period of 365 days or 12 months. It usually includes the entire calendar year from January 1st to December 31st. It can also refer to a fiscal year (a period of 12 consecutive months used for accounting purposes) or a school year (which may start in late summer).
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In FGH, h=840 inches. F=93° and G=49°. Find the length of g, to the nearest 10th of an inch.
Answers
The length of g 1029.8 in the given ΔFGH.
What is Trigonometric Functions?
Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
The Law of Sines (or Sine Rule) is very useful for solving triangles:
[tex]\frac{a}{sinA} = \frac{b}{sinB} + \frac{c}{sinC}[/tex]
840 / sin(38) = g /sin(49)
g = (840 / sin(38) ) *sin(49)
g= (840/0.615) *0.754 = 1029.8
Hence, the length of g 1029.8 in the given ΔFGH.
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10 grams is the same as how many ounces?
Answers
The value of the one-gram quantity in ounces will be 0,35274 ounces.
What is unit conversion?Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the quantity of some materials is measured in 10 grams. The quantity of the material in ounces will be calculated as,
1 grams = 0.035274
10 grams = 10 x 0.035274
10 grams = 0.35274 ounces
Therefore, the value of the one-gram quantity in ounces will be 0,35274 ounces.
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the manufacturer of cans of salmon that are supposed to have a net weight of 6 ounces tells you that the net weight is actually a normal random variable with a mean of 6.16 ounces and a standard deviation of 0.13 ounce. suppose that you draw a random sample of 38 cans. find the probability that the mean weight of the sample is less than 6.15 ounces.
Answers
The probability that the mean weight of the sample is less than 6.15 ounces as per the given data is 0.1806.
Mean, μ = 6.16 ounces
Standard Deviation, σ = 0.13 ounce
Sample size, n = 38
We are informed that the weight of the cans is distributed in a bell-shaped manner, which is a normal distribution.
Formula:
Z-score = ( x - ц) /standard deviation
Standard error due to sampling
=SD/√n
=0.13/ √(38)
=0.021
P(weight of the sample is less than 6.15 ounces)
P(X < 6.15) =P( Z< (6.15 - 6.16)/0.021 )
= P(Z> -0.476)
=0.1806 ( as per the Z- score table)
The probability that the sample's mean weight is less than 6.15 ounces is 0.1806.
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!HELP! The tennis tournament that Amanda is playing has 10 games and the tennis tournament that Jennifer is playing has 8 games. What is the minimum amount of tournaments they each need to play in order to have played the same number of games? How many games would this be? Write to explain your thinking.
Answers
The minimum amount of tournaments Amanda and Jennifer each need to play in order to have played the 40 number of games are 4 and 5 respectively.
What is the LCM?Least Common Multiple is the meaning of the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It may also be computed using two or more real numbers.
Given that Amanda is playing has 10 games and the tennis tournament that Jennifer is playing has 8 games.
Now we will find the minimum same number of games in tournaments,
for that we will find the LCM of the numbers.
LCM of Amanda games in tournament and Jennifer games in tournament.
LCM of 10 and 8 is 40.
Therefore, the minimum amount of tournaments Amanda and Jennifer each need to play in order to have played the 40 number of games are 4 and 5 respectively.
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Translate the phrase into an algebraic expression.
The sum 9 of C and.
WHAT IS THE ANSWER.
Answers
An expression does not include an equal sign and the way to put the equation would be by adding the two given variables.
If light can travel 31 times around the world in 4 seconds, find the number of times it can circle the world in 10 seconds.
Answers
Answer:
The answer is 77.5
Step-by-step explanation:
If light travels 31 times around the Earth in 4 seconds then in 8 seconds it would be 62 times and 15.5 is half of 31 and then we add 15.5 to 62 and we get 77.5. Hope this helps!
Answer:
In 4 seconds light can travel = 31 times
Then in 10 second it can travel=
31/4 ×10 =77.5times
Answer this question:
Your friend thinks that the triangles shown below are congruent by SAS. Is your friend correct? Explain.
Choose the correct answer below.
A.
Yes, the figure indicates that three corresponding sides are congruent.
B.
No, the congruent angles are not the included angles.
C.
Yes, the figure indicates that two corresponding sides and their included angle are all congruent.
D.
No, the congruent sides are not the included sides.
E.
Yes, the figure indicates that two corresponding angles and their included side are all congruent.
F.
No, the figure only indicates that two corresponding sides are congruent, not three as required by the SAS Postulate.
Answers
Answer:
B. No, the congruent angles are not the included angles.
Step-by-step explanation:
The SAS (Side-Angle-Side) Postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
In the given figure, we can see that two sides of the two triangles are congruent: side AB is congruent to side DE, and side AC is congruent to side DF. However, the included angles, which are the angles formed by these sides, are not congruent. Angle BAC is not congruent to angle EDF.
Since the included angles are not congruent, we cannot use the SAS Postulate to conclude that the two triangles are congruent. Therefore, the correct answer is B: No, the congruent angles are not the included angles.
Answer:
B. No, the congruent angles are not the included angles.
Step-by-step explanation:
You want to know if the triangles shown are congruent by SAS.
SASThe SAS congruence postulate tells you that two triangles are congruent if the angles between corresponding congruent sides are congruent. (The A=angle is between the S=side in SAS.)
In the diagrams, the marked angles are not between the marked sides. The SAS postulate cannot be used with these triangles.
In short, ...
No, the congruent angles are not the included angles
<95141404393>
Find the simple interest on $1975 for 4.5 years at rate of 9.1% per year
Answers
Answer:
$808.76
Step-by-step explanation:
You want the simple interest earned on $1975 at the rate of 9.1% per year for 4.5 years.
InterestThe amount of simple interest is given by the formula ...
I = Prt
where principal P is invested at rate r for t years.
ApplicationUsing the given values, the amount of interest earned is ...
I = $1975·0.091·4.5 = 808.7625 ≈ $808.76
The amount of simple interest is $808.76.
<95141404393>
the edge of a cube is growing at a rate of 6 inches per second at the instant when the edge of the cube has a length of 11 inches. what is the rate of change of the volume of the cube at that instant?
Answers
The edge of a cube is growing at a rate of 6 inches per second at the instant when the edge of the cube has a length of 11 inches. Hence, the rate of change of the volume of the cube at that instant will be 2178 [tex]inches^3[/tex] /s.
The volume of the cube V = [tex]a ^ 3[/tex]
where 'a' is the edge.
Rate of increase of volume = dV / dt = 3a^2 da/dt.
da/dt = 6 inches /s
dV / dt = 3 [tex]a^2[/tex] da/dt.
When a = 11 inches.
dV /dt = 3 x [tex]11 ^2[/tex] x 6
= 3 x 121 x 6
= 2178 [tex]inches^3[/tex] /s
Hence, the rate of change of the volume of the cube at that instant will be 2178 [tex]inches^3[/tex] /s.
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b) The perimeter of the shape is 25.71 cm
Calculate the value of the radius x.
Take – to be 3.142
Answers
Answer:
Questions and answers
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Question
The perimeter of a shape is 25.71 cm calculate the value of the radius X takes pie to be 3.142
Answer · 15 votes
Answer:5 cmStep-by-step explanation:Given a semicircle with perimeter 25.71 cm, we are required to find the radius of the circle.Circumference of a Semicircle=Length of the Circular part+Length of the diameter[tex]=\pi r+2r[/tex][tex]If \: \pi=3.142, C=25.71\Then:\25.71=3.142r+2r (3.142+2)=25.71\5.142r=25.71 =25.71 \div5.142 =5cm[/tex]
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Question
The perimeter of the semicircle is 25.71 cm. Calculate the value
find the equation of the line that contains the point p(4, 5) and is perpendicular to the graph of y = 5/4 x − 1.
Answers
Answer:
y = - [tex]\frac{4}{5}[/tex] x + [tex]\frac{41}{5}[/tex]
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{5}{4}[/tex] x - 1 ← is in slope- intercept form
with slope m = [tex]\frac{5}{4}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{5}{4} }[/tex] = - [tex]\frac{4}{5}[/tex] , then
y = - [tex]\frac{4}{5}[/tex] x + c ← is the partial equation of the perpendicular line
to find c substitute (4, 5 ) into the partial equation
5 = - [tex]\frac{16}{5}[/tex] + c ⇒ c = 5 + [tex]\frac{16}{5}[/tex] = [tex]\frac{25}{5}[/tex] + [tex]\frac{16}{5}[/tex] = [tex]\frac{41}{5}[/tex]
y = - [tex]\frac{4}{5}[/tex] x + [tex]\frac{41}{5}[/tex] ← equation of perpendicular line
find2% of the product of 19 and the average of 63,500, 65,000 and 66,500
Answers
By using percentage, it can be calculated that
2% of the product of 19 and the average of 63,500, 65,000 and 66,500 = 24700
What is percentage?
Suppose, there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.
For example, 7% means [tex]\frac{7}{100}[/tex]. Here, 7 is expressed as a percentage of 100.
This is a problem on percentage
The numbers are 63,500, 65,000 and 66,500
Average = [tex]\frac{63500 + 65000 + 66500}{3}[/tex] = 65000
Product of 19 and 65000 = 65000 [tex]\times[/tex] 19 = 1235000
2% of 1235000 = [tex]\frac{2}{100} \times 1235000[/tex] = 24700
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Solve using substitution.
Answers
Answer:
The answer is 2
Step-by-step explanation:
5x + 7y = -11
y = -3
Now, put the value of y in the given equation we get,
5x + 7y = -11
5x + 7(-3) = -11
5x - 21 = -11
5x - 21 + 21 = 21 - 11
5x = 10
5x/5 = 10/5
x = 2
Thus, The value of x is 2
a study was conducted at a university to analyze whether the preference for hamburgers or fried chicken is related to the gender of the student. the table below shows the results of the study: hamburgers fried chicken female: 15 23 male: 24 16 suppose we use this sample data and a .05 significance level to test the claim that the meal preference and the gender of the student are not related. what can we conclude?
Answers
To test the claim that meal preference and gender are not related, you can use a chi-squared test for independence.
The null hypothesis for this test is that there is no relationship between the variables, while the alternative hypothesis is that there is a relationship. To conduct the test, you will need to calculate the chi-squared statistic and compare it to the critical value from a chi-squared distribution with one degree of freedom. The degrees of freedom for this test are calculated as (number of rows - 1) * (number of columns - 1), which in this case is (2-1)*(2-1) = 1.
To calculate the chi-squared statistic, you will need to compare the observed frequencies in the table to the expected frequencies if the null hypothesis were true. The expected frequency for each cell is calculated as the row total * column total / sample size.
For example, the expected frequency for females who prefer hamburgers is (39 * 15)/59 = 12.71. The chi-squared statistic is then calculated as the sum of the squared differences between the observed and expected frequencies, divided by the expected frequencies. In this case, the chi-squared statistic would be:
((15-12.71)^2/12.71) + ((23-26.29)^2/26.29) + ((24-26.29)^2/26.29) + ((16-12.71)^2/12.71) = 7.39
To determine whether this result is statistically significant, you would compare the chi-squared statistic to the critical value from a chi-squared distribution with one degree of freedom. At a significance level of 0.05, the critical value is 3.84. Since the chi-squared statistic (7.39) is greater than the critical value (3.84), you can reject the null hypothesis and conclude that there is a relationship between meal preference and gender in this sample.
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What is the answer to this equation 12 1/4 - 5 2/3
Answers
Answer:
6 7/12
Step-by-step explanation:
"12 1/4 - 5 2/3" is an expression. It is not said to equal anything. The "=" sign makes it an equation. But we can evalute an expression by simplyfying it. Let's do the subtraction. We first need to convert one of the fractions so that it has the same denominator as the other.
12 1/4 - 5 2/3 can be written as (12 - 5)+(1/4 - 2/3)
(12 - 5)+(1/4 - 2/3)
(7)+(1/4 - 2/3) Let's convert both fractions to have denominators of 12 [since 4*3 = 12]
7 + 1/4 - 2/3
7 + (1/4)*(3/3) - (2/3)*(4/4) [Multiply the tqo fractions by (3/3) and (4/4), repectively. This is OK since both are the equivalent of multiply by 1. But it converts the denominators so that we can now add or subtract.
7 + (3/12) - (8/12)
7 - (5/12)
or 6 7/12
Which inequality represents all the values of x for y<(or equal to)-6(x-18)-2 when y=46
Answers
The value of x is x ≤ 9 for which y ≤ -5(x - 18) - 2 when y = 43.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
The given inequality is y ≤ -5(x - 18) - 2.
Now the values of x when y = 43 is,
43 ≤ - 5(x - 18) - 2.
43 ≤ - 5x + 90 - 2.
43 - 88 ≤ - 5x.
- 45 ≤ - 5x.
5x ≤ 45.
x ≤ 9.
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using the points 0,2 and -3,4 write an equation in slope intercept form
Answers
Answer: y=—2/3x+2
Step-by-step explanation:
the fundamental theorem of arithmetic: for each positive integer n> 1 there is a unique set of primes. whose product is n. which assumption would be a component of a proof by mathematical induction or strong mathematical induction of this theorem?
Answers
Fundamental theorem of arithmetic states that each positive integer n is greater than 1 represented by unique set of prime numbers.
Explanation:
Fundamental theorem of arithmetic states that all the positive integer n is greater than 1 represented by multiples of prime numbers or the number itself is a prime number.
For example :
Let us consider 56 be a integer greater than 1
56 = 2 × 2 × 2 × 7
2 and 7 both are prime numbers
another example :
29 = 29 × 1
29 itself is a prime number.
Factorization of the given numbers itself prove the fundamental theorem of arithmetic.
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