The simplest form of (4y^2)^3(3y^2) is 192 y⁸.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
Given expression is (4y²)³(3y²).
The law of exponent formula are:
(a^m)^n = a^(mn)
(a^m)(a^n) = a^(m+n).
Now applying the formula (a^m)^n = a^(mn) in (4y²)³
(4y²)³ = 4³× y²ˣ³ = 64y⁶
Putting (4y²)³ = 64y⁶ in (4y²)³(3y²):
(4y²)³(3y²) = 64y⁶ × (3y²)
Now applying the formula (a^m)(a^n) = a^(m+n):
(4y²)³(3y²) = (64× 3) y⁶⁺²
(4y²)³(3y²) = 192 y⁸
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Suppose the life time (in hours) of a battery brand is normally distributed. A random sample of 16 batteries results in a sample variance of
3.25
hours
2
. We want to test if there is significant/sufficient evidence in the sample data to claim that the variance of the battery life population is different than 4 hours
2
at significance level of
0.05
. Which of the following is INCORRECT? A.
H 0
:σ 2
=4 vs H 1
:σ 2
=4
B. The test statistic is found to be
12.1875
C. We should reject the null hypothesis and there is sufficient evidence to claim that the variance of battery life is different than 4 hours
2
at significance level of
0.05
. D. None of the above.
there is not sufficient evidence to claim that the variance of the battery life population is different than 4 hours2 at a significance level of 0.05.
answer is D. None of the above.
To test if there is significant evidence to claim that the variance of the battery life population is different than 4 hours2, we can use a chi-square test.This is how the test statistic is computed:
X2 = (n-1)*(s2/σ2)
where n is the sample size, s2 is the sample variance and σ2 is the population variance.
In this case, n = 16, s2 = 3.25 and σ2 = 4
X2 = (16-1)*(3.25/4) = 12.1875
The critical value of X2 with 15 degrees of freedom and α = 0.05 is 24.996. Therefore, since 12.1875 < 24.996, we fail to reject the null hypothesis, and there is not sufficient evidence to claim that the variance of the battery life population is different than 4 hours2 at a significance level of 0.05.
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1.4 inches and the width is 4.1 inches. The company making the cell phone wants to make a new version whose length will be 1.75 inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone?
The side lengths of the new phone are proportional to the old phone, then the width of the new phone is 5.125 inches.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the given information in the question,
The dimensions of the older phones are,
Length, L(1) = 1.4 inches
Width, W(1) = 4.1 inches
The dimensions of the new phone are,
Length, L(2) = 1.75 inches
Width, W(2) = ?
Then the width of the new phone is,
1.4 × W(2) = 4.1 × 1.75
W(2) = (4.1 × 1.75)/1.4
W(2) = 5.125 inches.
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a parameter of the exponential smoothing model that provides the weight given to the most recent time series value in the calculation of the forecast value is known as the group of answer choices
The smoothing constant is the correct option.
What is exponential smoothing?
The exponential window function is a general method for smoothing time series data known as exponential smoothing. Exponential functions are used to assign weights that decrease exponentially over time, as opposed to the simple moving average, which weights previous observations equally.
Forecasts using exponential smoothing are precise.
This method generates reliable and accurate forecasts that anticipate the following period.
Demand projections and actual demand are shown in the forecast. This makes it possible to effectively plan for demand, which leads to accurate inventory levels.
In exponential smoothing, the higher the smoothing constant, the greater is the weight assigned to the values from the most recent period.
Hence, the smoothing constant is the correct option.
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A political action committee sends out a questionnaire to randomly-selected mailing addresses, asking people to rate the importance of a variety of economic and social issues facing the country. At the end of the questionnaire is an (optional) invitation to donate money to the organization. Which of the following statements about this survey is true?
A) The survey results are invalid because it’s impossible to word questions about politics without creating bias.
B) The survey results are invalid because only surveys conducted by phone are free from bias.
C) The survey results will underestimate support for this political action committee in the entire population because people who respond are less likely to support an organization that asks for money.
D) The survey results will overestimate support for this political action committee in the entire population because people more likely to respond if they are prepared to donate money.
E) Since the survey was sent to randomly-selected households, it should be free of bias.
Option c; The survey results will underestimate support for this political action committee in the entire population because people who respond are less likely to support an organization that asks for money. This is the correct statement about the survey.
What is politics?
Politics is a category of activities that are related to group decision-making or other types of power dynamics between people, such as the allocation of resources or status. Political science is the name of the area of social science that focuses on politics and governance.
Given,
A political action committee sends out a questionnaire to randomly-selected mailing addresses, asking people to rate the importance of a variety of economic and social issues facing the country. at the end of the questionnaire is an (optional) invitation to donate money to the political action committee.
We have to find the correct statement about the survey from the given options;
Because respondents are less inclined to support a group that solicits donations, the survey results will understate public support for this political action committee.
The correct statement about the survey is option c;
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Q. Which triangle congruence theorem can be used to prove the triangles are congruent?
SAS
SSA
ASA
AAS
SAS triangle congruence theorem can be used to prove the triangle are congruent.
What is triangle?A triangle is a simple polygon with three sides and three interior angles. It is one of the basic forms of geometry in which three vertices are connected, and is represented by the symbol △. There are different types of triangles, classified based on their sides and angles. Two triangles are congruent if all three corresponding sides are equal and all three corresponding angles are equal. These triangles can be moved, rotated, flipped, and flipped to look identical. When rearranged they match each other. The congruence symbol is "≅".
Angle is the space between two intersecting lines or surface at or close to the point where they meet.
The SAS Postulate says that is the triangles are congruent if any pair of the corresponding sides and I their included angles are be congruent.
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Based on the 2010 US census, the population of Milwaukee, Wisconsin, was about 96% of the population of Baltimore, Maryland. In 2010, if Milwaukee's population was about 595,000, which of the following is the best
approximation of Baltimore's population?
A 620,000
B 570,000
C 300,000
D 95,000
Answer: A
Step-by-step explanation:
Because Milwaukee's population is smaller than that of Baltimore, the only correct answer would be one that has the population of Baltimore higher than that of Milwaukee, which is only A
which option proves the following statement by contradiction? for all real numbers r and s, if r is rational and s is irrational, then r 2s is irrational. proof (by contradiction): suppose not. that is, suppose there are real numbers r and s such that r is rational and s is irrational and r 2s is rational. [we must show that this supposition leads logically to a contradiction.] by definition of rational,
Any whole number, fraction, or decimal that terminates or repeats is a rational number. Any number that cannot be divided into a fraction and hence does not meet the concept of a rational number is said to be irrational.
When it comes to rationality, we have
r + 2s = c/d and r = a/b.
The result of the substitution is a/b + 2s = c/d
2s= c/d-a/b=(bc-ad)/bd
s = (bc-ad)/2bd
Now that both (bc - ad) and (bd) are integers, bd is not equal to 0
As a result, the integer s is a quotient of the two integers (bc - ad) where bd is not equal to 0. So, s is rational according to the definition. This disproves the idea that s is irrational.
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Question 7 of 9
A
B
Answer here
D
Given that ZBCD and ZBCA form a straight angle, if ZBAC measures 20
degrees and ZABC measures 45 degrees, then the measure of ZBCD is
degrees.
What is the equidistant Theorem?
The Equidistant Theorem states that the distance between two points on a line is equal to the sum of the distances from each point to a third point. This theorem is often used to prove the existence of certain geometric shapes, such as triangles and circles.
What is the equidistant Theorem?The Equidistant Theorem is a useful tool for proving the existence of certain geometric shapes. By measuring the distance between two points and then measuring the distance from each point to a third point, the distance between the two points will be equal to the sum of the distances of the two points to the third point.
This theorem is helpful for constructing triangles and circles, as it allows us to quickly and accurately identify the necessary distances between the points. This theorem is also useful for finding the center of a circle, as the center of the circle is always equidistant from its circumference. As a result, the Equidistant Theorem is a fundamental theorem in geometry that is used to prove the existence of certain geometric shapes.
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you can paint a room in 8 hours. working together, you and your friend can paint the room in just 5 hours. How long does it take your friend to paint a room by himself?
It takes about 13.33 hours for the friend to paint a room by himself.
If two persons are working on the same project together, their work rates add up and they can finish the project faster. If x is the time taken by person 1 to complete a task, then the work rate is 1/x. If y is the time taken by person 2 to complete a task, then the work rate is 1/y. Then, the formula to calculate the work-rate problem is [tex]\frac{1}{x}+\frac{1}{y}=\frac{1}{t}[/tex].
Here, the rate of work done by person 1 is 1/8. Together, the rate is 1/5. Then,
[tex]\begin{aligned}\frac{1}{8}+\frac{1}{y}&=\frac{1}{5}\\\frac{y+8}{8y}&=\frac{1}{5}\\5y+40&=8y\\3y&=40\\y&=\frac{40}{3}\\&=13.33\end{aligned}[/tex]
Therefore, the answer is 13.33 hours.
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what is twice the area of the surface formed by points (1,0,0),(0,2,0),(0,0,3)?
The area of the triangle formed by points (1, 0, 0), (0, 2, 0) and (0, 0, 3) has an area of 3.5 square units, where a triangle with an area of 7 square units is twice the original one.
What is the twice of a surface formed by three coplanar points?
Three points are coplanar when they are contained by a plane. In addition, triangles can be constructed by means of three distinct points. The area of the triangle can be found by means of Heron's formula:
A = √[s · (s - a) · (s - b) · (s - c)]
s = 0.5 · (a + b + c)
Where:
A - Area of the triangle.a, b, c - Lengths of the sides of the triangle. s - Semiperimeter of the triangle.The length of each side can be found by the following Pythagorean formula:
l = √[(Δx)² + (Δy)² + (Δz)²]
Where:
Δx - Cambio en las coordenadas de x.Δy - Cambio en las coordenadas de y.Δz - Cambio en las coordenadas de z.First, calculate the side lengths:
a = √(1² + 2² + 0²)
a = √5
b = √(0² + 2² + 3²)
b = √13
c = √(1² + 0² + 3²)
c = √10
Second, calculate the semiperimeter of the triangle:
s = 0.5 · (√5 + √13 + √10)
s ≈ 4.502
Third, determine the area of the triangle:
A = √[4.502 · (4.502 - √5) · (4.502 - √13) · (4.502 - √10)]
A ≈ 3.5
A triangle with an area of 7 square units is twice the area of the original triangle.
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help me ples this is kinda hard ngl
will give brainliest if correct
To beat the school long jump record, John must jump an additional 5 1/4 inches
Calculating the additional distance to beat a long jump recordFrom the given question, we are to determine how farther John must jump in order to break the record
From the given information,
"A high school track team's long jump record is 23 ft 1 3/4 in"
and
"John's best long jump is 22 ft 8 1/2 in"
First, we will convert the distances to inches
NOTE: 1 ft = 12 inches
23 ft 1 3/4 in = 276 + 1 3/4 in = 277 3/4 in
22 ft 8 1/2 in = 264 + 8 1/2 in = 272 1/2 in
Now, to determine how farther John must jump, we will subtract the distances
277 3/4 in - 272 1/2 in = 5 1/4 in
Hence, he must jump 5 1/4 in farther
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Suppose you can afford to pay $ 325 a month for 9 years towards a new car with no down payment. If the current interest rates are 4.25%, how expensive a car can you afford?
The expensive a car that you can afford is $42666.42.
What is interest rates?
The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal, or the loaned amount. Typically, a loan's interest rate is expressed as an annual percentage rate, or APR (APR).
Given that you can deposit $325 each month. The interest rates is 4.25%.
Future Value of an Ordinary Annuity
[tex]S = R[\frac{(1+i)^n-1}{i}][/tex]
where
S is the future value;
R is the periodic payment;
i is the interest rate per period;
n is the number of periods.
The value of R is $325, i = 0.0425/12 = 0.00354
n = (12 × 9) =108
The future value is
[tex]S = 325[\frac{(1+0.00354)^{108}-1}{0.00354}][/tex]
S = 42666.42
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Cos(75) using cos(a+b)
Answer:
[tex]\sqrt{6}[/tex]/4 – [tex]\sqrt{2}[/tex]/4
Step-by-step explanation:
cos(a + b) = cos (a) cos(b) – sin (a) sin (b)
cos(75) =
cos(45 + 30) = ==> break it down into more solvable angles
cos (45) cos(30) – sin (45) sin (30) =
[tex]\sqrt{2}[/tex]/2 * [tex]\sqrt{3}[/tex]/2 – [tex]\sqrt{2}[/tex]/2 * 1/2 = ==> simplify
([tex]\sqrt{2}[/tex]*[tex]\sqrt{3}[/tex])/(2*2) – ([tex]\sqrt{2}[/tex]*1)/(2*2) =[[tex]\sqrt{6}[/tex]/4 – [tex]\sqrt{2}[/tex]/4]
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True or False: The range of sine is...
True
False
It is false that the range of the sine function is 0 ≤ ∅ ≤ π
How to determine the true statement?From the question, we have the following parameters that can be used in our computation:
Function: sine function
Also from the question, we have
Range: 0 ≤ ∅ ≤ π
As a general rule, we have:
The minimum value of a sine function is -1The maximum value of a sine function is 1This means that the range of the sine function is from [-1, 1].
This can also be represented as -1 ≤ ∅ ≤ 1
Hence. the given statement about the sine function is false
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Answer:
The answer is false.
Step-by-step explanation:
The range of the sine function is NOT 0 ≤ ∅ ≤ π
if y=-2x what would x equal when y=60?
which relationship shows an inverse variation
An example of inverse variation is y = 3/x .
What is Inverse Variation ?
Unlike the direct variation, where one quantity varies directly as per changes in another quantity, in the case of inverse variation, the first quantity varies inversely as per another quantity. Hence, the first quantity is inversely proportional to the other.
Let us say, x and y are two variables, then as per inverse variation:
y = k/x
or
xy = k
For example :
If x and y are in an inverse variation and k/3 = 2, and k/x = 3, then find the value of x when y = 2.
Given, k/3 = 2
then, k = 3 x 2 = 6
k/x = 3
So, x = k/3 = 6/3 = 2
Hence, if y = 2, then ;
x = k/y = 6/2 = 3
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Mackenzie is working two summer jobs, washing cars and landscaping. She must
work at least 17 hours altogether between both jobs in a given week. Write an
inequality that would represent the possible values for the number of hours washing
cars, w, and the number of hours landscaping, 1, that Mackenzie can work in a given
week.
please helpp!!!!
The inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours landscaping, is
w + l ≥ 17.
What is inequality?
In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.
Given:
Mackenzie is working two summer jobs, washing cars and landscaping. She must work at least 17 hours altogether between both jobs in a given week.
Total number of hours is w + l and it should be at least 17 hours, (equal to 17 or greater).
We can set inequality as:
w + l ≥ 17
Hence, the inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours landscaping, is w + l ≥ 17.
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(1 point) determine whether the line integral of each vector field (in blue) along the oriented path (in red) is positive, negative, or zero.
Through the graph we will determine if the line integral of each vector field is positive, negative, or zero. The answer to this question is:
-Positive
-Negative
-Zero
-Negative
-Zero
-Zero
What is the Line integral?
A line integral, also known as the route integral, curve integral, or curvilinear integral, is used to find the surface's area in three dimensions. In this integral, the function is evaluated along a curve. There are several applications of line integrals, such as in the field of electromagnetics, to find the force applied on a charged particle moving along a curve in a force field created by a vector field.
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Round 231469.335329 to the nearest thousand.
The value which is round off to the nearest thousand for 231469.335329 is 232000.
What is rounding off?
When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done. The important figures are preserved when numbers are rounded off.
The given value in the question is 231469.335329
The rules for rounding off says,
If the last digit of the given number is above 5 or equal to 5 then 1 is added to pre digit of last number and last digit is replaced by 0.
So, the given value,
231469.335329 the digit after the point is less than 5 so we eliminate the value without adding 1.
It becomes, 231469.00
In above value, if 231469 we add one to the before the last digit, it becomes 231470
As a next step, add the number in the 2 digit by adding 1 to before the 2nd digit, it becomes 231500.
Now Finally, the process of adding one to the 4 digit depends on the values of 3rd digit takes place and it becomes 232000.
Hence, the number is 232000.
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A quadrilateral with one pair of parallel side is a
A) Parallelogram
B) Square
C) Rectangle
D) Trapezium
A quadrilateral with one pair of parallel side is a D) Trapezium
Given :
A quadrilateral with one pair of parallel side is.
we know that ,
Trapezium :
A trapezium is a convex quadrilateral with exactly one pair of opposite sides parallel to each other.
The trapezium is a two - dimensional shape that appears as a table when drawn on a sheet of paper.
In Euclidean Geometry, a quadrilateral is defined as a polygon with four sides and four vertices.
so a trapezium also has four sides, four angles and four vertices.
Area of trapezium = 1/2 * ( a+ b ) h
where a and b are bases
and h is height of altitude.
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create a fraction model that represents 3 × 3/5
_______________________________________________________
1. Convert element to fraction: [tex]3=\frac{3}{1}[/tex]
[tex]\frac{3}{1} * \frac{3}{5}[/tex]
2. Apply the fraction rule: [tex]\frac{a}{b}* \frac{c}{d}=\frac{a*c}{b*d}[/tex]
[tex]\frac{3*3}{1*5}[/tex]
3. Multiply the numbers: [tex]3 * 3=9[/tex]
[tex]\frac{9}{1*5}[/tex]
4. Multiply the numbers: [tex]1*5=5[/tex]
[tex]\frac{9}{5}[/tex]
^Hence, our solution.
_________________________________
Hope this helps!
Sofia and her children went into a grocery store that sells bananas for $0.80 each and mangos for $2 each. Sofia has $20 to spend and must buy a minimum of 12 bananas and mangos altogether. If xx represents the number of bananas purchased and yy represents the number of mangos purchased, write and solve a system of inequalities graphically and determine one possible solution.
Using graphical method to solve the system of inequality, the number of banana is 2 and mango is 10
System of Linear InequalityA system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.
In this question, we can set the unknown variables as;
x = Number of bananay = Number of Mango0.2x + 2y = 20 ...eq(i)
x + y ≥ 12 ..eq(i)
Solving x and y
This can be done graphically;
The number of banana and mango is approximately 2 and 10 respectively
Kindly find the attached graph below
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The formula for finding the volume of a cube is V = s3, where s is the length of the side of the cube. Terrance has a cube that measures 3 inches long along each side. What is the volume of the cube? _______________inches3 ( just write the number)
The volume of the cube with a side edge of 3 inches will be 27 cubic inches.
What is a volume of a cube?Suppose that: The side length of the considered cube is L units. Then, we get:
Volume of that cube = L³ cubic units.
Terrance has a shape that actions 3 inches long along each side.
The edge length of the cube is 3 inches. Then the volume of the cube will be given as,
V = (3)³
V = 27 cubic inches
The volume of the cube with a side edge of 3 inches will be 27 cubic inches.
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The probability of Kaia scoring an A on her
math test (event A) is 0.82, and the probability of
Kaia scoring an A on her history test (event B) is
0.85. The probability of her scoring an A on both
tests is 0.697. Given this information, are events
A and B dependent or independent?
Answer:
dependent
Step-by-step explanation:
the probability of 0.697 is dependent upon Kaia scoring an 82, followed by an 85 on the other test
Check: multiply 0.82 by 0.85 and your will get 0.697
How do I solve this diagram map? Diagram shows the following:
1 - 3
2 - 5
3 - .....?
?..... - 17
10 - ......?
100 - ......?
The complete diagram map is given as,
1 - 3
2 - 5,
3 - 7,
8 - 17,
10 - 21
100 - 201
Given that,
To complete the map diagram,
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
The given map diagram follows the general term as nth term = 2n + 1
So for n = 3
= 2 [3] + 1
= 7
Similarly,
10th = 21
100th = 2001
For the value 17
17 = 2n + 1
n = 8
So the 8th term is 17 in the map diagram,
Thus, The complete diagram map has been shown.
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Which set of points includes all of the solutions for y = negative four fifths times x plus two?line going through 0 comma 2 and 5 comma negative 2 a (15, 10), (0, 2), and (−10, 10) b (−10, 10), (−5, 6), (0, 2), (5, −2), (10, −6) c (x, y) for all real numbers d (x, negative four fifths times x plus two) for all real numbers
The set of points includes all of the solutions is (x, - 4/5 x + 2).
What is the solution of an equation?
An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.
Given equation is
y = - 4/5 x + 2
The value of x can be any real number.
The value of y is - 4/5 x + 2.
The solution of the equation is (x, - 4/5 x + 2).
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Russell Slater bought 700 shares of Disney stock at $106.50 per share. Assume a commission of 4% of the purchase price. What is the total cost to Russell?
77532 is the total cost to Russell
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
Russell Slater bought 700 shares of Disney stock at $106.50 per share
The amount for 700 shares is 700×106.5
74550
commission of 4% of the purchase price.
We have to convert 4% to decimal value by dividing 4 by 100
0.04
Now multiply 0.04 with 74550 to get the commission
0.04×74550
2982
Now add this commission amount with 74550 to find total cost,
2982+74550
77532
Hence, 77532 is the total cost to Russell
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The heights of people in a certain population are normally distributed with a mean of 67 inches and a standard deviation of 3.8 inches. Determine the sampling distribution (shape, center, spread) of the mean for samples of size 45 .
The shape of the sampling distribution of the mean for samples of size 45 will be normal.
This is because the sampling distribution of the mean approaches normality as the sample size increases. The center of the sampling distribution will be 67 inches, which is the mean height of the population. The spread of the sampling distribution will be determined by the standard deviation of the population and the sample size. Specifically, the standard deviation of the sampling distribution will be equal to the standard deviation of the population divided by the square root of the sample size. In this case, the standard deviation of the sampling distribution will be 3.8 inches / sqrt(45) = 0.55 inches.
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In addition to the strength and direction of an association between two numerical variables, correlation analyses allow us to predict one variable's value based on the other variable. True False
The given statement is FALSE.
Given info,
In addition to the strength and direction of an association between two numerical variables, correlation analyses allow us to predict one variable's value based on the other variable.
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Finding the degree and direction of the link between two numerical variables is made easier with the use of correlation analysis.
The value of one variable can be predicted based on the value of another using regression analysis.
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