If the array includes just the positive integers [tex]{\displaystyle 1,2,...,n^{2}}{\displaystyle 1,2,...,n^{2}}[/tex], the magic square is said to be normal. Some authors take magic square to mean normal magic square.
A magic square is a square grid of numbers that has the same sum for every row, column, and diagonal. It is a mathematical puzzle that has been known and studied for thousands of years. Magic squares can be of different sizes, but the most common are those with odd numbers of rows and columns.
The concept of magic squares dates back to ancient China, where they were believed to have mystical properties. In India, they were used for divination and as part of religious rituals. In Europe, magic squares were popularized in the 16th century, where they were used as a form of mathematical entertainment. Magic squares are not only interesting mathematical puzzles but also have practical applications.
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Complete Question: -
Fill the given squre with numbers from 0 to 8 ( using each of them exactly once) in such a way that the sum of the numbers in the first second and third rows are third rows are in the ratio 1 : 2 : 3. At the same time the sum of the numbers in the first second and third columns also have to be in the same ratio.
The matrix 1 −1 ]5
0 0 ]0 is in reduced row-echelon form. Determine the solution of the corresponding system of linear equations. Write the solution as an ordered pair. For parametric solutions use either x = t or y = t as the parameter. (If an answer does not exist, enter DNE.)
The solution to the system of linear equations associated with the reduced row-echelon form matrix is (0, 0). This indicates that both variables, x and y, have a value of zero.
The reduced row-echelon form of a matrix is the simplest way to represent the solution to a system of linear equations. In the case of a matrix with two rows and two columns, a solution is produced when the matrix is in its reduced row-echelon form. Specifically, for the given matrix, 0 0, the solution to the corresponding system of linear equations is (0, 0). This indicates that both variables, x and y, have a value of zero. This is because the reduced row-echelon form is the simplest way to represent the solution to a system of linear equations. In this form, all the leading entries are ones and all the other entries are zero. Since the matrix is 0 0, this indicates that the solution is (0, 0). This solution can be seen as an ordered pair, where the first value represents the solution for the x variable, and the second value represents the solution for the y variable. In this case, both values are zero, which means that the solution to the system of linear equations is (0, 0).
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The complete question is
The matrix 1 −1 ]5 0 0 ]0 is in reduced row-echelon form. Determine the solution of the corresponding system of linear equations. Write the solution as an ordered pair. For parametric solutions use either x = t or y = t as the parameter form matrix(0,0).
You consume 14 pounds of turkey annually. At a discount store, the price of turkey is $0.99 less per pound than at a supermarket. How much would you save annually, in dollars, if you bought all of your turkey at the discount store?
The required we can save $13.86 annually by buying all your turkey at the discount store.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Let's call the price of turkey per pound at the supermarket "x". Then the price of turkey per pound at the discount store would be x - $0.99.
Since we consume 14 pounds of turkey annually, the cost of the turkey at the supermarket would be 14 × x dollars.
And the cost of the turkey at the discount store would be 14 × (x - $0.99) dollars.
Therefore, the amount you would save annually by buying all your turkey at the discount store is,
= 14 × x - 14 × (x - $0.99) = 14 × $0.99
= $13.86
So, we would save $13.86 annually by buying all your turkey at the discount store.
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In Carlsbab, NM, 8 bats ate 40 grams of insects in one night. At this rate, how many grams of insects could 48 bats eat in 1 night?
Answer: 240 Grams.
Step-by-step explanation: First I need to find how many grams each bat eats, then multiply the 48 bats by each gram the bats eat. And you would get 240!
graph the inequalities
2y+8x<4
5x+20 is greater than or equal to -10y
The graph to the inequality is added as an attachment
How to determine the graph to the inequalityFrom the question, we have the following parameters that can be used in our computation:
2y+8x<4
5x+20 is greater than or equal to -10y
Express properly
2y+8x<4
5x+20 > -10y
Next, we make a plot of the system to determine the solution
The shaded area in the plot represent the solution to the inequality
In this case, the shaded area has a coordinate of (1.143, -2.571)
Hence, the solution is (1.143, -2.571)
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How you would solve a problem with variables on both sides of the equation?
Answer:
im him
Step-by-step explanation:
12. Trystan and Kendall have decided to buy a new home that costs $300,000. They want to make a 20% down payment and
finance the rest. Their bank has offered an opportunity to buy down the quoted interest rate of 4.75% by 0.125% per point
purchased. Each point will cost 1% of the amount borrowed. Trystan and Kendall were hoping the interest rate was no more than
4.5% What will it cost to buy down the quoted interest rate to 4.5%?
To buy down the quoted interest rate from 4.75% to 4.5% will cost Trystan and Kendall $4,800 after the down payment.
What is the down payment?The down payment refers to the initial cash payment for the purchase of an item on mortgage.
The down payment is required by the financier to evaluate the buyer's financial readiness.
The cost of the new home = $300,000
Down payment = 20% or $60,000 ($300,000 x 20%)
Mortgage loan required = $240,000 ($300,000 - $60,000)
Bank quoted interest rate = 4.75%
Desired interest rate = 4.5%
Difference in interest rate = 0.25% (4.75% - 4.5%)
Rate of buy down of the quoted interest per point = 0.125%
The number of points to buy down the interest rate = 2 (0.25/0.125)
The cost of each point = 1% of $240,000 = $2,400
The total cost of 2 points = $4,800 ($2,400 x 2)
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7. MP Reason Abstractly The number of customers in a store on the first
day is represented by (6x-3). The number of customers on the second
day is represented by (x - 1). Write an expression to find how many more
customers visited the store on the first day. Then evaluate the expression
if x is equal to 50. (Example 6)
Answer:
6x-3 - (x-1) is the expression.
You want to make sure to bring the - over both the "x" and the "-1". You end up with the expression 5x-2. I need more info to "evaluate the expression", it is not possible to evaluate it currently because of limited information on what the expression would equal.
1. What must the values of a and b be for PQRS to be a parallelogram?
2. The diagonals of parallelogram ABCD intersect at P. Select all the statements that must be true.
The value of a and b are; a = 2, b = 4
What is a parallelogram?That quadrilateral in which opposite sides are parallel is called a parallelogram.
Given that the diagonals of parallelogram ABCD intersect at P.
4a + b = 2a + 8
4a - 2a + b = 8
2a + b = 8 -----------------(I)
b = 8 - 2a
11b - 10a = 6b
11b - 6b -10a = 0
5b - 10a = 0 ---------(II)
Substitute b = 8 - 2a in equation (II)
5(8-2a) - 10a = 0
40 - 10a - 10a = 0
40 - 20a = 0
-20a = - 40
a = -40/-20
a = 2
Plugin a = 2 in equation (I)
b = 8 -4
b = 4
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What is y=2x?
what is 12 x 12 in like righting
Answer:
Step-by-step explanation:
y = 2x:
This is an equation for a straight line in which "y" is proportional to "x" with a coefficient of 2. If you plot this line on a coordinate plane, it will have a slope of 2 and y-intercept of 0.
12 x 12:
This is a mathematical expression for finding the product of 12 and 12. The result is 144. In mathematical writing, it's usually written as "12 * 12 = 144".
which number can each term of the equation be multiplied by to eliminate the decimals before solving?
The number that can each terms of the equation be multiplied by to eliminate the decimals before solving is 100
The equation is
5.6j + 0.12 = 4 + 1.1j
The equation is defined as the mathematical expression that shows the relationship between one expression and another expression with equal sign. The equation consist of mathematical operator like addition, subtraction, division and multiplication
The equation is
5.6j + 0.12 = 4 + 1.1j
Here three term has fractional part.
In 0.12 there are two digits after the decimal point to eliminate the decimal number we have to multiply the number with 100 .
Then the equation will become
560j + 12 = 400 + 110j
Therefore, the number is 100
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The given question is incomplete, the complete question is
Which number can each term of the equation be multiplied by to eliminate the decimals before solving?
5.6j + 0.12 = 4 + 1.1j
Use the law of sines to find each missing side or angle
15
12
128
X
The missing angle is approximately 108.5 degrees.
What is the law of sines?Law of sines is a trigonometric formula that relates the sides and angles of any triangle. Specifically, the law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in the triangle.
Using the law of sines:
sin(128°)/15 = sin(x)/12
Multiplying both sides by 12:
sin(x) = 12sin(128°)/15
Taking the inverse sine of both sides:
x = sin^-1(12sin(128°)/15)
x ≈ 108.5°
Therefore, the missing angle is approximately 108.5 degrees.
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Factor 80+60. Write your answer in the form a(b+c) where a is the GCF of 80 and 60.
Answer:
20(4+3)
Step-by-step explanation:
GCF of 80 and 60 = 20
20*4=80
20*3=60
20(4+3)
hope this helps! :)
A bride-to-be had already finished assembling 15 wedding favors when the maid of honor came into the room to help. The bride assembles at a rate of 2 favors per minute. In contrast, the maid of honor works at a speed of 5 favors per minute. Eventually, they will both have assembled the same number of favors. How many favors will each have made? How long will that take?
The bride-to-be and her maid of honor will each have made __ favors in __ minutes.
Using an equation, the bride-to-be and her maid of honor will each have made 25 favors in 5 minutes.
What is an equation?An equation is a mathematical statement showing that two or more mathematical expressions are equal or equivalent.
Equations are depicted using the equal symbol (=), while mathematical expressions, which combine variables, constants, and values only use mathematical operands.
The total number of wedding favors assembled by the bride-to-be = 15
The bride's assembling rate per minute = 2 favors
The maid of honor's assembling rate per minute = 5 favors
Let x = the number of minutes used
Let the number of favors assembled by the bride = 15 + 2x
Let the total number of favors assembled by the maid of honor = 5x
For the two to assemble the same number of favors, 15 + 2x = 5x
15 = 3x
5 = x
Thus, in 5 minutes the bride-to-be and her maid of honor will have assembled 25 favors each.
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sole the system of equations y=9x+14 and y=6x+35 x= and y=
The solution of the system of linear equations y = 9x + 14 and y = 6x + 35 will be (7, 77).
What is the solution to the equation?An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.
The system of linear equations is given below.
y = 9x + 14 ....1
y = 6x + 35 ....2
From equations 1 and 2, then we have
9x + 14 = 6x + 35
3x = 21
x = 7
The value of 'y' is given as,
y = 6 (7) + 35
y = 42 + 35
y = 77
The solution of the system of linear equations y = 9x + 14 and y = 6x + 35 will be (7, 77).
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What is meant by the present value of money?
A. The sum of the deposit and the simple interest
B. The amount borrowed or deposited
C. The difference between the future value and
D. The maximum amount of money that can be deposited
Answer: The amount borrowed or deposited
Step-by-step explanation:
there isn't really an explanation, I just know the answer because I took a test with the exact same question and answer
Option C is correct, The difference between the future value and the amount of interest earned is the present value of money
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
The present value of money refers to the value of a future amount of money in today's dollars, based on a certain interest rate or discount rate.
It is the amount of money that would need to be invested today, at a given rate, to equal the future amount.
To calculate the present value of a future amount of money, we need to discount the future amount based on the interest rate or discount rate, which accounts for the time value of money
The difference between the future value and the amount of interest earned.
Hence, option C is correct, the difference between the future value and the amount of interest earned is the present value of money
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Use the appropriate formula to determine the periodic deposit.
How much of the financial goal comes from deposits and how much comes from interest?
a) Periodic Deposit = (A - P×(1 + r/n)ⁿᵗ) × (n / ((1 + r/n)ⁿᵗ - 1))
b) The amount of the financial goal that comes from deposits is $60305.24 and the amount that comes from interest is = $149694.76.
What is compound interest?Compound interest is a method of calculating interest on a principal amount that includes not only the initial principal but also the accumulated interest from previous periods.
a. The formula for periodic deposits, assuming a fixed interest rate and the same amount of deposit made at the end of each period, is:
Periodic Deposit = (A - P×(1 + r/n)ⁿᵗ) × (n / ((1 + r/n)ⁿᵗ - 1))
Where:
A = Financial goal
P = Initial deposit (assumed to be 0 in this case)
r = Annual interest rate (as a decimal)
n = Number of compounding periods per year
t = Time (in years)
Substituting the given values, we have:
Periodic Deposit = (210000 - 0*(1 + 0.035/12[tex])^{(12\times 13)}[/tex] * (12 / ((1 + 0.035/12[tex])^{(12\times 13)}[/tex] - 1))
= $543.15 (rounded to the nearest cent)
Therefore, the periodic deposit needed to reach the financial goal of $210000, with a 3.5% annual interest rate compounded monthly over 13 years, is $543.15 at the end of each month.
b. To determine how much of the financial goal comes from deposits and how much comes from interest, we can use the following formula for the future value of an annuity:
FV = P * ((1 + r/n)ⁿᵗ - 1) / (r/n) + A * (1 + r/n)ⁿᵗ
Where:
FV = Future value of the annuity (i.e., the financial goal)
P = Initial deposit
A = Periodic deposit
r, n, t = Same as before
Substituting the given values and solving for P, we have:
P = (210000 - 543.15 * (1 + 0.035/12[tex])^{(12\times 13)}[/tex] ) * (0.035/12) / ((1 + 0.035/12[tex])^{(12\times 13)}[/tex] - 1)
= $60305.24 (rounded to the nearest cent)
Therefore, the amount of the financial goal that comes from deposits is $60305.24, and the amount that comes from interest is $210000 - $60305.24 = $149694.76.
Hence,
a) Periodic Deposit = (A - P*(1 + r/n)ⁿᵗ) * (n / ((1 + r/n)ⁿᵗ - 1))
b) The amount of the financial goal that comes from deposits is $60305.24 and the amount that comes from interest is = $149694.76.
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AB and BC form a right angle at point B. If A= (-3,-1) and B=(4,4), what is the equation of BC
Answer: AB and BC form a right angle at point B, so BC is perpendicular to AB. To find the equation of BC, we can use the slope-point formula, which is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.
The slope of a line perpendicular to AB can be found by finding the negative reciprocal of the slope of AB. To find the slope of AB, we need to find the difference in the y-coordinates and divide it by the difference in the x-coordinates:
m_AB = (y2 - y1) / (x2 - x1)
= (4 - (-1)) / (4 - (-3))
= 5 / 7
The slope of a line perpendicular to AB is the negative reciprocal of m_AB:
m_BC = -1 / m_AB = -1 / (5/7) = -7/5
Now that we have the slope of BC, we can use the slope-point formula to find the equation of BC. We'll use the point B = (4, 4) as (x1, y1):
y - 4 = -7/5 (x - 4)
y = -7/5 x + 4(7/5) + 4
y = -7/5 x + 36/5
So the equation of BC is y = -7/5 x + 36/5.
Step-by-step explanation:
Find the size of angle x.
Give your answer in degrees (°).
41°
77°
x
Watch video
36°
Not drawn accurately
According to the information, the value of the missing angle would be 206°, in a quadrilateral.
How to calculate the value of the missing angle?To calculate the value of the missing angle we must take into account that the angles of a quadrilateral must add up to 360°. On the other hand, the angles of a triangle must sum to 180°.
According to the previous information, if it is a triangle, then we must add the angles that we know and then subtract it from 180°.
41° + 77° = 118°118° - 180° = 62°On the other hand, if it is a quadrilateral we must add the angles and subtract them from 360°.
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what is the cubed root of -343
Answer:
-7
Step-by-step explanation:
Answer: -7
Step-by-step explanation: I hope this helped you out!!!! Please mark me as brainiest.
Mary wants to hang a mirror in her room. The mirror and frame must have an area of 7 square feet. The mirror is 2 feet wide and 3 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?
x2 + 14x - 2 = 0
2x2 + 10x - 7 = 0
3x2 + 12x - 7 = 0
4x2 + 10x - 1 = 0
The correct quadratic equation that can be used to determine the thickness of the frame, x, is: 2x² + 10x - 7 = 0, Therefore Option B is the right answer
Here's how we can get this equation:
We are given that the mirror and frame together have an area of 7 square feet. The mirror itself has an area of 2 x 3 = 6 square feet. So, the area of the frame is 7 - 6 = 1 square foot.
Let's assume that the width of the frame is x feet. Then the overall width of the mirror and frame becomes 2 + 2x, and the overall length becomes 3 + 2x. The area of the mirror and frame can be expressed as:
(2 + 2x)(3 + 2x) = 6 + x(10 + 4x)
We know that this expression equals 7, so we can set it equal to 7 and obtain the quadratic equation:
2x² + 10x - 7 = 0
Therefore, the correct quadratic equation is 2x² + 10x - 7 = 0.
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hal is asked to write an exponential function to represent the value of a $10,000 investment decreasing at 2% annually. what multiplicative rate of change should hal use in his function?0.020.981.021.98
If he want to write an exponential function to represent the value of a $10,000 investment decreasing at 2% annually, then the multiplicative rate will be 0.98
The initial investment = $10000
decreasing percentage = 2%
Therefore, the second term will be the 98% of the first term
The first term = 10000
The second term = 10000 × 98/100
= 10000 × 0.98
= 9800
The common ratio is the ratio of the second term to the first term
The common ratio = second term / first term
= 9800 / 10000
= 0.98
Therefore, the multiplicative rate of change should Hal use in his function is 0.98
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Is y= -5 a function?
Answer:
It is a function. You can identify when something is a function by finding whether plugging in any x value will result in one y value.
Find the values of x, y, and z
The values of x, y and z are given as follows:
x = 6.25.y = 6.67.z = 5.What are similar polygons?Similar polygons are polygons that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.There are two similar trapezoids for this problem, hence the proportional relationship for the side lengths is given as follows:
x/15 = 10/24 = y/16 = z/12.
Applying cross multiplication, the value of x is given as follows:
24x = 15 x 10
x = 15 x 10/24
x = 6.25.
The value of y is given as follows:
y = 16 x 10/24
y = 6.67.
The value of z is given as follows:
z = 12 x 10/24
z = 5.
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Sidney made root beer floats for her friends when they came over. The table shows the ratio of cups of ice cream to cups of soda used to make the floats. Ice Cream (cups) Soda (cups) 3.5 10.5 8 24 12.5 37.5 17 ? At this rate, how much soda will Sidney use for 17 cups of ice cream? 42 cups 51 cups 54 cups 62 cups
Answer: the correct answer is 51
Step-by-step explanation: i solved this on my quiz
i hope this helps!
Sidney will use 54 cups of soda for 17 cups of ice cream, So the answer is 54 cups.
What is the ratio?
A ratio is a relationship between two things when it is expressed in numbers or amounts. For example, if there are ten boys and thirty girls in a room, the ratio of boys to girls is 1:3, or one to three.
We can start by noticing that the ratio of cups of ice cream to cups of soda used to make the floats is always 1:3.
To find out how much soda Sidney will use for 17 cups of ice cream, we can set up a proportion:
3.5/10.5 = 8/24 = 12.5/37.5 = 17/x
Solving for x, we can cross-multiply:
3.5x = 10.5 * 17
x = 54
Therefore, Sidney will use 54 cups of soda for 17 cups of ice cream, So the answer is 54 cups.
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How is [tex]\frac{22}{7}[/tex] a rational number
Answer:
Step-by-step explanation: 22/7 is a rational number because it can be expressed as a ratio or fraction of two integers. The numerator (22) and denominator (7) are both integers, and the denominator is not equal to zero, so 22/7 is a well-defined fraction. Since every fraction represents a rational number, 22/7 is also a rational number
which expression is equivalent to 4(x-4)
Answer:
4x * -16
Step-by-step explanation:
You use the distributive property and multiply 4 by everything in the parentheses. The 16 is negative because you keep the minus sign with the number behind it.
Question 12Miple Choice Worth 4 pores)
(08.02 MC)
The expression 4x+13 represents the time it takes a commuter to travel in the morning to work. The expression 10x-2 represents the time it takes a commuter to
havel in the evening from work What is the total travel time?
Otx+18
Ox+11
06+21
Ox+15
If the functions be f(x) = 4x + 13 and g(x) = 10x − 2 then the expression (f + g)(x) be 4x + 11.
What is meant by functions?A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y. The set X is known as the function's domain, while the set Y is known as the function's codomain. Initially, functions were just an idealized representation of the relationship between two changing quantities.
Given f(x) = 4x + 13 and g(x) = 10x − 2
We must add both functions to reflect the amount of time it takes to travel east and west in order to calculate the round-trip time.
Let the equation be (f + g)(x) = f(x) + g(x)
substitute the values in the above equation, we get
= (4x + 13) + (10x − 2)
simplifying the above equation, we get
= 4x + 13 + 10x − 2
= 4x + 10x − 2 + 13
= 4x + 11
Therefore, the expression (f + g)(x) be 4x + 11.
The completed question is:
The function f(x) represents the time it takes an airplane to travel east. The function g(x) represents the time it takes an airplane to travel west. Given f(x) = 4x + 13 and g(x) = 10x − 2, solve for (f + g)(x) to determine the total roundtrip time.
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Which parallelogram has the greatest area?
Area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.
To find the area of a parallelogram, we use this equation:
Base × height = areaNow that we have this equation, we can apply it to each parallelogram.
3 × 5 = 155 × 3 = 154 × 4 = 164 × 3 = 12Now, we can figure out which has the greatest area.
Therefore, the parallelogram that has the greatest area is 3, or III.
Answer:
III
Step-by-step explanation:
the area (A) of a parallelogram is calculated as
A = bh ( b is the base and h the perpendicular height )
I
A = 3 × 5 = 15 units²
II
A = 5 × 3 = 15 units²
III
A = 4 × 4 = 16 units²
IV
A = 4 × 3 = 12 units²
parallelogram III has the greatest area
what is the standard error? group of answer choices the standard error is the standard deviation of the sampling distribution the standard error is a measure of how representative a sample statistic is likely to be of the population parameter. the standard error is calculated using the standard deviation of the sample all of the options describe the standard error.
The correct option is "the standard error is the standard deviation of the sampling distribution." Correct option is A.
The standard error is a measure of the variability of a sampling distribution, which is the distribution of sample statistics (e.g., mean, proportion) that would be obtained from multiple random samples of the same size from the same population.
The standard error represents the standard deviation of the sampling distribution, and it provides a measure of the precision of the sample statistic in estimating the population parameter.
The standard error is not the same as the standard deviation of the sample, which is a measure of the variability of the individual observations in the sample.
The standard deviation of the sample is typically used to estimate the standard deviation of the population, while the standard error is used to estimate the variability of the sample statistic and to construct confidence intervals or perform hypothesis tests.
While the other options are related to the concept of the standard error, they are not equivalent or fully accurate descriptions of what the standard error represents.
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Complete question is:
What is the standard error?
group of answer choices
A. the standard error is the standard deviation of the sampling distribution
B. the standard error is a measure of how representative a sample statistic is likely to be of the population parameter.
C. the standard error is calculated using the standard deviation of the sample all of the options describe the standard error.
Robert plans to make a box-and-whisker plot of the following set of data.
27, 14, 46, 38, 32, 18, 21
Which of the following should Robert's box-and-whisker plot look like?
Robert's box-and-whisker plot should look like the following: C. box-and-whisker plot C.
What is a box-and-whisker plot?In Mathematics, a box plot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Next, we would sort the observations (data set) from the least to greatest as follows:
14, 18, 21, 27, 32, 38, 46}.
Based on the information provided above, the five-number summary for the given data set include the following:
Minimum = 14
First quartile = 18.
Median = 27.
Third quartile = 38.
Maximum = 46.
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