The width of the interval will be reduced to 1.5 if the sample size is increased by a factor of 25.
To find how much the sample size n must be increased if the width of the confidence interval is to be halved, use the following formula:
W = (zα/2 x σ/√n)W/2 = (zα/2 x σ/√n')
Where W is the initial width of the confidence interval,
zα/2 is the critical value of the standard normal distribution that corresponds to the level of significance α and the appropriate two-tailed area,
σ is the population standard deviation,
n is the initial sample size, and
n' is the new sample size needed to halve the width of the interval.
Rearranging the second equation to solve for n', we get:
n' = n(4)
So the sample size needs to be increased by a factor of 4, or 300% if the width of the confidence interval is to be halved.
If the sample size is increased by a factor of 25, the effect it will have on the width of the interval can be found using the following formula:
W' = (zα/2*σ/√25n) = (zα/2*σ/5√n)
The width of the interval will be divided by 5, or reduced to one-fifth of its initial value.
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The following shows a graph of y = x^2+ 5
Can we use this graph to find the solutions of 0 = c^2 + 5? Why or why not?
we can, now if we look at 0 = x² + 5, that's when the parabola y-value is 0, that is, what's "x" when y = 0? well, if we look at the graph, the graph never touches the x-axis, so that means the graph never has any "real roots", only complex ones or imaginary ones. We can tell because the graph never touches the x-axis.
A party tent is used for an outdoor event. Ropes of equal length support each tent pole. The angle each rope makes with the ground is 52°.
What is the height of each tent pole?
Therefore, the height of each tent pole is approximately 8.07 meters.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the study of the relationships between the sides and angles of triangles. It is used to solve problems involving triangles, such as finding the length of a side or the measure of an angle. Trigonometry is based on the use of trigonometric functions, which are ratios of the sides of a right triangle.
Here,
We can use trigonometry to solve this problem. Let's call the height of the tent pole "h" and the length of the rope "r". Then, we can use the tangent function to find the height:
tan(52°) = h/r
Rearranging this equation, we get:
h = r * tan(52°)
We know that the length of each rope is equal, so we can choose any arbitrary length for r. For simplicity, let's assume that each rope is 10 meters long. Then, we can plug in the values into the equation:
h = 10 * tan(52°)
Using a calculator, we get:
h ≈ 8.07 meters
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True or False: Of the major economies in the world, Italy had the highest growth rate of real GDP per capita between 1982 and 2009
The given statement regarding the GDP of major economies of the world is False.
To determine the accuracy of this statement, we would need to gather data on the real GDP per capita growth rates of major economies between 1982 and 2009 and compare them. Without this data, we cannot definitively say whether the statement is true or false. However, based on historical trends and current economic data, it is unlikely that Italy had the highest growth rate of real GDP per capita during this time period.
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Sam works for his father for 2
; of the year and works for his mother = of the remainder year. What is the
ratio of the time Sam spends working for his mother to the time he spends working for his father per year?
6/1
1/2
2/1
1/6
1/9
The ratiο οf the time Sam spends wοrking fοr his mοther tο the time he spends wοrking fοr his father per year is 1/6 οr 1:6. Thus, οptiοn D is cοrrect.
What is the ratiο?The relative size οf twο quantities expressed as the quοtient οf οne divided by the οther; the ratiο οf a tο b is written as a:b οr a/b.
If Sam wοrks fοr his father fοr 2/5 οf the year, then he wοrks fοr his mοther fοr the remaining time, which is 1 - 2/5 = 3/5 οf the year.
Tο find the ratiο οf the time Sam spends wοrking fοr his mοther tο the time he spends wοrking fοr his father per year, we can write:
Sam wοrked fοr his father = 2/3 οf year
Remaining time = 1/3
Sam wοrked fοr his mοther = 1/3(remainder year)=(1/3)*(1/3)
=1/9
Ratiο οf time spent fοr mοther and father is
= (1/9):(2/3)
=(1/3):2
= 1:6
Sο, οptiοn d) 1/6 is cοrrect answer
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Complete question:
Sam works for his father for 2/3; of the year and works for his mother = of the remainder year. What is the
ratio of the time Sam spends working for his mother to the time he spends working for his father per year?
6/11/22/11/61/9Exercise 3-23A (Algo) Using ratio analysis to assess financial risk LO 3-5
The following information was drawn from the balance sheets of two companies. Company Assets = Liabilities + Equity
East 206,000 91,000 115,000
West 603,000 169,000 434,000
Required
a. Compute the debt-to-assets ratio to measure the level of financial risk of both companies. B. Compare the two ratios computed in requirement a to identify which company has the higher level of financial risk
The answer based on debt to assets ratio for east and west company are,
East company debt to assets ratio is equal to 0.44.
West company debt to assets ratio is equal to 0.28.
After comparing both the company debt to assets ratio East company is at higher level of financial risk.
Assets = Liabilities + Equity
For East company,
206,000 = 91,000 + 115,000
Assets = 206,000
liabilities = 91,000
Equity = 115,000
For West company,
603,000 = 169,000 + 434,000
Assets = 603,000
liabilities = 169,000
Equity = 434,000
Debt-to-assets ratio = Total liabilities divided by the total assets.
Debt-to-assets ratio for East
= 91,000 / 206,000
= 0.44
Debt-to-assets ratio for West
= 169,000 / 603,000
= 0.28
Comparing the two ratios,
0.44 > 0.28
This implies,
Company East has a higher debt-to-assets ratio is greater than the compared to Company West.
This represents that Company East has a higher level of financial risk.
As larger proportion of their assets are financed through debt.
This shows it is difficult to repay if the company experiences financial difficulties.
Company West has a lower level of financial risk as smaller proportion of their assets are financed through debt.
Therefore, the answer of the following questions are,
Debt to asset ratio of east company = 0.44
Debt to asset ratio of west company = 0.28
Company east has a higher financial risk level .
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John's parents deposited $1000 into a savings account as a collage fund when he was born. How much will john have in this account after 18 years at a yearly simple interest rate of 3. 25%?
John's parents deposited 1000 into a savings account as a college fund when he was born. We need to find out how much John will have in this account after 18 years at a yearly simple interest rate of 3.25%.
We can use the formula for simple interest to solve this problem.
The formula for simple interest is:
I = PRT
Where,I = interest
P = principal (the initial amount of money)
R = rate of interest (as a decimal)
T = time (in years)
We are given that John's parents deposited 1000 when he was born. So, P = 1000. The interest rate is 3.25% per year, which is 0.0325 as a decimal. And we are given that the time is 18 years, so T = 18 years.Using the formula for simple interest, we can find the amount of interest earned:
I = PRTI = (1000)(0.0325)(18)I = 585
We can then add the interest earned to the principal to find the total amount of money in the account after 18 years:
A = P + IA = 1000 + 585A = 1585
Therefore, John will have 1585 in this account after 18 years at a yearly simple interest rate of 3.25%.
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A veterinarian estimated the weight of a puppy to be 9kg. The actual weight of the puppy was 9.5kg Find the absolute error and the percent error of the veterinarian's estimate. If necessary, round your answers to the nearest tenth.
Answer:
The absolute error is the absolute value of the difference between the actual value and the estimated value:
Absolute error = |actual value - estimated value| = |9.5 kg - 9 kg| = 0.5 kg
The percent error is the absolute error expressed as a percentage of the actual value:
Percent error = (|actual value - estimated value| / actual value) x 100%
Plugging in the given values, we get:
Percent error = (0.5 kg / 9.5 kg) x 100% = 5.3%
Rounding to the nearest tenth, the absolute error is 0.5 kg and the percent error is 5.3%.
Please, I really want this pleaseeeeeeweeee
The value of ∠K is 78°
What is tangent of a circle?The tangent of a circle is a straight line that touches the circle at exactly one point, and it is perpendicular to the radius of the circle at that point.
Given that, a tangent JK is lying on the circle H whose radius are HJ and HM,
So, ∠HMJ = ∠HJM = 84°
and JK ⊥ HJ (JK is a tangent on radius HJ)
So, ∠HJK = 90°
∠HJM + ∠MJK = ∠HJK
84° + ∠MJK = 90°
∠MJK = 6°
Using exterior angle property;
∠MKJ + ∠MJK = ∠HJM
∠MKJ + 6° = 84°
∠MKJ = 84° - 6° = 78° (∠MKJ means ∠K)
Therefore, ∠K = 78°
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A bus company charges $2 per ticket but wants to raise the price. The daily revenue is modeled by R(x)=-30(x-6)^2+320, where x is the number of $0.15 price increases and R(x) is the revenue in dollars. What should the price of the tickets be for a maximum profit? Hint: don’t forget what price where you started.
The ticket price that maximizes profit is $2.90.
What is profit and how is it related to revenue and cost?
In business and economics, profit is the amount of money earned after all expenses and costs have been deducted from revenue. Profit is a key metric used to measure the financial success of a company or enterprise. It is calculated as follows:
Profit = Revenue - Cost
Revenue is the total income earned from the sale of goods or services, while cost is the total expense incurred to produce and sell those goods or services. Profit is an important measure of financial performance because it reflects how efficiently a company is using its resources to generate income.
Finding the price that maximizes profit:
We need to find the value of x that corresponds to the maximum value of the revenue function R(x). The price of the tickets can then be determined by adding the value of x to the initial price of $2.
Using the revenue function [tex]R(x)=-30(x-6)^2+320[/tex], we can find the value of x that maximizes the revenue as follows:
Take the derivative of R(x) with respect to x:
[tex]R'(x) = -60(x-6)[/tex]
Set the derivative equal to zero and solve for x:
[tex]R'(x) = 0[/tex]
[tex]-60(x-6) = 0[/tex]
[tex]x = 6[/tex]
Determine the second derivative of R(x) to check that x = 6 corresponds to a maximum:
[tex]R''(x) = -60[/tex]
Since R''(x) is negative, this confirms that x = 6 corresponds to a maximum.
Calculate the corresponding revenue at x = 6:
[tex]R(6) = -30(6-6)^2 + 320[/tex]
[tex]R(6) = 320[/tex]
Determine the ticket price by adding the value of x to the initial price of $2:
Ticket price = $2 + $0.15(x)
Ticket price = $2 + $0.15(6)
Ticket price = $2.90
Therefore, the ticket price that maximizes profit is $2.90.
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bacteria such as v. cholerae are known to follow an exponential growth curve rate, and will double their number every 15 minutes. fortunately, anti-bacterial hand wash can kill 99.9% of bacteria on a surface. if a colony of 500 v. cholerae cells are left alone for 2 hours, then anti-bacterial handwash is applied thoroughly, how many bacterial cells are left?
After using the antibacterial hand wash, there will be a remaining count of 203 bacterial cells.
The initial colony has 500 bacterial cells. We need to find the number of bacterial cells that will be left after 2 hours if an antibacterial hand wash is applied thoroughly. The antibacterial hand wash can kill 99.9% of the bacteria on a surface.
The doubling time of bacteria is given as 15 minutes. This means that every 15 minutes, the bacterial population doubles, which gives us an exponential growth rate. Therefore, the growth rate is given as follows:k = ln2 / Td where k is the growth rate, and Td is the doubling time.
Substituting the values we get:k = ln2 / 15min = 0.0462 min⁻¹We can find the number of bacteria present after a time t if the initial number of bacteria is N0 and the population growth rate is k using the following equation: Nt = N0 * e^(kt)where Nt is the number of bacteria after time t.As we know, the bacterial colony has 500 cells initially.
We can find the number of bacterial cells after 2 hours, which is 120 minutes, using the following equation: Nt = 500 * e^(0.0462 * 120min) = 202,599 bacteria. However, after applying an antibacterial hand wash, 99.9% of the bacteria will be killed.
This means that only 0.1% of the bacterial population will remain. We can find the number of bacteria that will be left using the following formula:N_final = N_initial * (1 - %killed)N_final = 202,599 * (1 - 0.999) = 203 bacteria
Therefore, there will be 203 bacterial cells left after applying the antibacterial hand wash.
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Colleen paid $13.70 to download 12 songs from an online music service. Some of the songs were on sale and cost $0.99 each. The rest were regularly priced at $1.25 per song. Let x represent the number of sale priced songs, and let y represent the number of regularly priced songs. This situation can be represented by the system x+y=12 and 0.99x+1.25y=13.7 . How many of each type of song did Colleen purchase?
Using equations, we can find that the number of sale-priced songs is 5 and the number of regularly priced songs is 7.
What exactly is an equation system?Equations are mathematical statements with the equals (=) symbol and two algebraic expressions on either side. This illustrates the equality of the relationship between the expressions printed on the left and right sides. The formula LHS = RHS (left hand side equals right hand side) is utilised in all mathematical equations. To determine the value of an unknown variable that represents an unknown quantity, you can solve equations. A statement is not regarded as an equation if it has no "equal to" symbol.
As per the question, equation given are:
x + y = 12
x = 12 - y
Now, substituting the value in:
0.99x+1.25y = 13.7
= 0.99(12-y) +1.25y = 13.7
= 11.88 - 0.99y + 1.25y = 13.7
= 0.26y = 13.7 - 11.88
0.26y = 1.82
y = 1.82/0.26
y = 7
Now, substitute this value,
x = 12 - 7
x = 5
As a result, there are 5 songs on sale and 7 songs that are regularly priced.
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Target is selling a speaker for $166.50. It is at Costco for $90. What percentage did
Target markup the speaker?
Answer:
45.6%
Step-by-step explanation:
166.50 minus 45.6% equals 90 dollars
21 x 8 ÷ 12 as a equivalent ratio?
Answer:
There are many options, like:
14/1 or 28/2...
Step-by-step explanation:
First write the system:
(21 x 8) / 12
Then simplify the brackets:
(168) / 12
= 14
Then you can put 14 over 1 as an example of proportionality:
14/1 : (21 x 8) / 12
Or multiply it by 2, 3 etc.:
42/3 : (21 x 8) / 12.
HELP 20 POINTS
NO WRONG ANSWERS OF LINKS THEY WILL GET REPORTED
Answer:
The second one, (x+1)(3x+2)
The answer is (x+1)(3x+2)
hope it helps
kendrick lamar is incredibly story teller but i dont like his music like when he raps fast thats unpelasent
An American rapper, is known for his poetic, and complex lyrical style.
How Kendrick Lamar becomes a story teller?Kendrick Lamar is a highly talented storyteller, however, some people may not like his music when he raps quickly as it can be unpleasant.What are the aspects of Kendrick Lamar's music?
An American rapper, is known for his highly poetic, socially conscious, and complex lyrical style.
However, his musical talent has been highly praised by critics and audiences alike.
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14. When finding the volume of prisms and pyramids, a unit cube can be used. Why is a unit sphere not a good unit of volume measurement for all spheres?
Therefore, for spheres of different sizes, we need to use different measuring units, unlike prisms and pyramids, where a unit cube can be used as a standard unit for all shapes with the same base and height.
What is volume?Volume is a measure of the amount of space occupied by a three-dimensional object. It is the measure of the total amount of space that an object takes up. The standard unit of volume is the cubic meter (m³) in the International System of Units (SI), but other units such as cubic centimeters (cm³) and cubic inches (in³) are also commonly used. The volume of an object can be calculated using different formulas depending on its shape and dimensions.
Here,
A unit sphere is not a good unit of volume measurement for all spheres because spheres come in various sizes and diameters. The unit sphere has a radius of 1, and while it can be used to measure the volume of spheres with radii equal to 1, it cannot be used to measure the volume of spheres with different radii.
For example, if we want to find the volume of a sphere with a radius of 2, we cannot use the unit sphere as a measuring unit. Instead, we would need to use a larger sphere with a radius of 2 as our measuring unit.
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The school cafeteria has 150 cups of strawberries and 450 cups of blackberries. How many total cups of berries does the school cafeteria have?
Total number of cups of berries does the school cafeteria have is 600
Addition is a basic mathematical operation that involves combining two or more numbers or quantities to find a total or sum. In other words, it is the process of finding the total amount when two or more numbers are added together.
To find the total number of cups of berries in the school cafeteria, you can add the number of cups of strawberries and blackberries.
The school cafeteria has 150 cups of strawberries and 450 cups of blackberries, so
Total cups of berries = cups of strawberries + cups of blackberries
Total cups of berries = 150 + 450
Total cups of berries = 600
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Classify the expression: 5x3 + 2x − 3
Answer:
12+2x
Step-by-step explanation:
5×3= 15
15+ 2x - 3
collect like terms
15-3+2x
12+2x
therefore 5×3+ 2x - 3 = 12 +2x
what is the difference of (4m^2-5) -(5m-20)
Answer:
4m^2+15-5m
Step-by-step explanation:
Remove parentheses.
4m^2-5-5m+20
Collect like terms.
4m^2+(-5+20)-5m
Simplify
4m^2+15-5m
Alia left to go on a camping trip at 12:55. She returned from the trip the following
day at the time shown on the following day at 10:40
How long was she away for?
Give your answer in hours and minutes.
Answer:
Step-by-step explanation: 12:55 she returned at 10:40 12:55 plus 5 minutes is 1:00 plus 9 hours and 40 minutes is 10:40 she was 9 hours and 45 minutes awayIf Pythagoras, the Greek mathematician, was born in 582 BCE and died on his birthday in 497 BCE, how old was he when he died?
Born: 582 BCE
Died: 497 BCE
582-497= 85
Answer: 85 years old
a business student is interested in estimating the 90% confidence interval for the proportion of students who bring laptops to campus. he wants a precise estimate and is willing to draw a large sample that will keep the sample proportion within nine percentage points of the population proportion. what is the minimum sample size required by this student, given that no prior estimate of the population proportion is available?
Answer:
n=106
Step-by-step explanation:
Given p = 0.5 and 1-p = q = 0.5Margin of error = 0.08 Confidence level = 90% Z score for 90% confidence level = 1.65As we know - Margin of error = z * Sqrt (pq/n)Substituting the given value, we get – 0.08 = 1.65 * Sqrt (0.5*0.5/n)Squaring both the sides and solving, we get n = 1.65^2*0.5^2/0.08^2n = 106.34 = 106
a daily mail is delivered to your house between 1:00 p.m. and 6:00 p.m. assume delivery times follow the continuous uniform distribution. determine the percentage of mail deliveries that are made after 5:00 p.m.
The percentage of mail deliveries that are made after 5:00 p.m is 33.3%.
The continuous uniform distribution is a probability distribution that is used when all outcomes are equally likely, and they are spread out over a given interval.
In this case, the interval is from 1:00 p.m. to 6:00 p.m.
To determine the percentage of mail deliveries that occur after 5:00 p.m., we need to calculate the probability that the delivery time falls after 5:00 p.m.
The probability of a delivery time falling after 5:00 p.m. can be found by subtracting the probability of it falling before 5:00 p.m. from 1.
The probability of a delivery time falling before 5:00 p.m. is found by calculating the area under the probability density curve between 1:00 p.m. and 5:00 p.m.
This can be found using the following formula:
P(x ≤ 5:00 p.m.) = (5:00 p.m. – 1:00 p.m.) / (6:00 p.m. – 1:00 p.m.)
This gives us a probability of 0.667.
Therefore, the probability of a delivery time falling after 5:00 p.m. is 1 – 0.667 = 0.333, or 33.3%.
This means that 33.3% of the daily mail deliveries are made after 5:00 p.m.
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Corresponding graph of the slope
emma buys a gift basket online for 30% off the list price. she has to pay $5.50 for shipping. the total charge is $45.20. what is the list price of the gift basket?
The list price of the gift basket is $65.20. This can be determined by taking the total charge of the gift basket ($45.20) and subtracting the shipping charge of $5.50. The remaining $39.70 is the discounted amount of the gift basket.
Since the gift basket was discounted by 30%, the original list price can be determined by dividing the discounted amount by 70%, which is 0.7. Then, the list price can be calculated by multiplying the discounted amount by 1.43 (the reciprocal of 0.7). Therefore, the list price of the gift basket is $65.20.
This method of calculating the list price of the gift basket is called reverse-discounting. The process of reverse-discounting involves subtracting the discounted amount from the total charge to get the original list price. This method is useful when the discount rate is known and the total charge is given. It allows for the original list price of the item to be determined quickly and accurately.
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if y varies directly as x, and y=7 when x=3, find when x=7
By definition, direct variation takes the following form:
y=kx
Where k is the proportionality constant.
You can find k given the information in the problem:
7=3k
k=3/7
You can now find y when x=7 as follows:
y=(7*3)
Values can be substituted. Then:
y=(7*7)/3
y=49/3
If y varies directly from x, then the value of y = 49/3 when x = 7.
If y varies directly from x, we can write its relationship in the form of the equation below :
y = m*x
Where m is the slope of the line on the graph.
From the given data:
y=7
x=3,
We can substitute these values in the above equation and find m :
7 = m*3
m = 7/3
So, the equation can also be written as follow:
y = 7/3 x
Finding y when x=7, then substituting the x value in the above equation we get:
y = (7/3)*(7)
y = 49/3
Therefore the value of the y = 49/3.
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the top of an l-shaped desk has the dimensions shown. what volume of wood is needed to make the top of the desk? complete the explanation of how you solved this problem.
The volume of wood needed to make the top of the l-shaped desk is 0.728 cubic feet
The top of an l-shaped desk has the dimensions shown in the diagram. To determine the volume of wood needed to make the top of the desk, we must use the formula for volume. The formula for volume is length times width times height, or V = lwh. In this case, the length of the top is 28 inches, the width is 45 inches, and the height is 0.75 inches.
Plugging these values into the volume formula gives us V = 28 x 45 x 0.75, which equals 1260 cubic inches. Since wood is typically sold in cubic feet, we must convert this volume to cubic feet by dividing it by 1728, the number of cubic inches in one cubic foot. 1260/1728 = 0.728, so the volume of wood needed to make the top of the desk is 0.728 cubic feet.
To summarize, the volume of wood needed to make the top of the l-shaped desk is 0.728 cubic feet. This was determined by using the volume formula, which is V = lwh, where l is the length, w is the width, and h is the height. The length, width, and height of the desk top were 28 inches, 45 inches, and 0.75 inches, respectively. By plugging these values into the volume formula and converting to cubic feet, we determined the volume of wood needed is 0.728 cubic feet.
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Please help with 14!! 30 points please give a correct answer
Answer:
r=8
Step-by-step explanation:
a. -3(6-r)=6
-18+3r=6
3r=6+18
3r=24
r=[tex]\frac{24}{3}[/tex]
r=8
b. 3r instead of -3r
in a causal study of the effect of shelf placement on sales of a brand of cereal, which is the dependent variable? group of answer choices where the cereal was placed on the shelf sales of the cereal concomitant variation of the cereal none of the above
A causal study is a study that seeks to determine whether one variable causes another variable.
The independent variable is the variable that is believed to cause the change in the dependent variable, while the dependent variable is the variable that is believed to be influenced by the independent variable.
In a causal study of the effect of shelf placement on sales of a brand of cereal, the independent variable is where the cereal was placed on the shelf. The dependent variable is sales of the cereal.
This is because the sales of the cereal are influenced by where it is placed on the shelf.The answer to the question is sales of the cereal.
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explain the difference between a population characteristic and a statistic. a population characteristic is a quantity that summarizes a ---select--- . a statistic is a quantity calculated from the values in a ---select--- .
Answer:
population, sample
Step-by-step explanation:
A population characteristic is a quantity that summarizes a
population
Correct: Your answer is correct.
. A statistic is a quantity calculated from the values in a
sample
