Answer: 3
Step-by-step explanation:
2 1/4 cups of brown sugar + ¾ cup of white sugar.=the total amount of sugar in this recipe
2 1/4 + 3/4 =3
or
2 1/4=2.25 and 3/4=.75
2.25+.75=3
A researcher found that for the years 2010 to 2018, the equation, y=-0.2(x-5)²+35, models the average gas mileage of new vehicles sold in Switzerland, where x is the number of years since 2010 and y is the average gas mileage, in miles per gallon (mpg).
During what year was the average gas mileage for new vehicles sold in Switzerland the greatest?
Please help me, I need help I didn't understand this!!!
The average gas mileage for new vehicles sold in Switzerland was the greatest in the year 2013.
How did we arrive at the answer?The equation models the average gas mileage of new vehicles sold in Switzerland as a parabolic function, y=-0.2(x-5)²+35.
To find the year in which the average gas mileage was the greatest, we need to find the vertex of this parabolic function.
The x-coordinate of the vertex is given by x = 5 + (-b/2a) = 5 - (-0.2/2(-0.2)) = 5 - (0.2/0.4) = 5 - 0.5 = 4.5 years since 2010, or the year 2013. The y-coordinate of the vertex can be found by substituting x = 4.5 years into the equation, y = -0.2(4.5-5)² + 35 = -0.2(0.5)² + 35 = 0.2 * 0.25 + 35 = 0.05 + 35 = 35.05 mpg.
So the average gas mileage for new vehicles sold in Switzerland was greatest in the year 2013, with a value of 35.05 mpg.
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If the denominator is a friendly number, you can Up or down, or use a
If the denominator is a friendly number, you can easily multiply it with another integer.
What is a Friendly Number in math?In number theory, friendly numbers are two or more natural numbers with a common abundancy index, the ratio between the sum of divisors of a number and the number itself.
Friendly numbers are numbers that are easy to work with. For example, multiples of 10 are “friendly” because they are easy to work with when we add or subtract.
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use markov's inequali5y 5o get an upper bound on the tail probability p(x>-t) nonegative random variable
The maximum value of P(X > -t) is 1 and the upper bound of P(X > -t) is -E[X]/t.
Markov's inequality states that if X is a non-negative random variable and c is a positive constant, then P(X > c) ≤ E[X]/c.
For example, let X be a non-negative random variable and let c = -t. Then the tail probability P(X > -t) can be upper bounded by Markov’s Inequality as: P(X > -t) ≤ E[X]/(-t).
To calculate P(X > -t) in terms of E[X], we can solve for P(X > -t) in the inequality. Therefore, P(X > -t) ≤ E[X]/(-t) can be rewritten as P(X > -t) ≤ -E[X]/t.
Since the left side of the inequality is a probability, it must be between 0 and 1. Therefore, the maximum value of P(X > -t) is 1 and the upper bound of P(X > -t) is -E[X]/t.
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there are 22 cherry trees in vince's orchard, and he wants to plant more. it takes him an hour to plant each tree. let h represent the number of hours vince spent planting and c represent the total number of cherry trees he will have. find the value of c when h
When h = 4, Vince will have 26 cherry trees in his orchard.
A linear equation is an algebraic equation with simply a constant and a first-order (linear) component of the form y=mx+b, where m is the slope and b is the y-intercept. The above is sometimes referred to as a "linear equation with two variables," where y and x are the variables.
If it takes Vince an hour to plant each tree, and h represents the number of hours Vince spent planting, then the total number of cherry trees he will have is given by the equation:
c = 22 + h
So when h = 4, the value of c can be found by substituting h = 4 into the equation:
c = 22 + 4 = 26.
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What’s the difference between slope-intercept form and and point slope formula
Point slope form and slope intercept form of a line are y - y₁ = m (x - x₁) and y = mx + c respectively.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
The point slope form of a line is given by,
y - y₁ = m (x - x₁),
where (x₁, y₁) is a point on the line, m is the slope and (x, y) be any point.
The slope intercept form of a line is given by,
y = mx + c
where m is the slope and c is the y intercept.
y intercept is the point where the line touches the Y axis. x coordinate will be 0 at that point.
The slope intercept form of a line can be found from the point slope by substituting (x₁, y₁) = (0, c)
y - c = m (x - 0)
y - c = mx
y = mx + c
Hence the slope intercept form of a line is y = mx + c and the point slope form is y - y₁ = m (x - x₁).
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Cynthia Besch wants to buy a rug for a room that is 25ft wide and 34ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 360 square feet of carpeting. What dimensions should the rug have?
The dimensions of the rug are: width is 15 feet length is 21 feet.
Let's call the width of the strip of floor around the rug "x". Then the width of the rug would be 25 - 2x, and the length of the rug would be 34 - 2x.
The total area of the rug should not exceed 360 square feet, so we can set up an equation to represent this:
(25 - 2x)(34 - 2x) = 360
Expanding and simplifying the left-hand side:
25 × 34 - 2 × 25 × x - 2 × 34 × x + 4 × x² = 360
850 - 118x + 4x² = 360
4x² - 118x+ 490 =0
Now we have a quadratic equation that we can solve using the quadratic formula or by factoring. Either way, we find that x = 24.5 or x = 5. Since x represents the width of the strip of flooring, x must be positive. Therefore, x = 5 is the solution.
So the width of the strip of flooring is 5 feet, and the dimensions of the rug are:
width: 25 - 2 × 5 = 15 feet
length: 34 - 2 × 5 = 21 feet
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x=2y in evryday words mean
In everyday words x = 2y means that twice of y makes x
What is multiplication by two?The general rule for solving all multiplication by two problems is to multiply the integer by two by adding the number to itself.
The order of your numbers doesn't matter while solving multiplication issues.
In the problem, x = 2y represents that twice of y is x
the inverse of this is half of x is y
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||
2. Complete the steps for factoring 2x3 - 36x² + 162x by writing words, numbers,
or expressions in the blanks.
2x336x2 + 162x=
(x2-18x+81)
_2x [x²-2(____)x+ (__________)²]
=
11
(x-.
_)(x-____
_2=(x-_9_) ²
Factor out
Rewrite the trinomial.
Use the
pattern.
Simplify.
The complete factorization of the given expression is 2x³ - 36x² + 162x = 2x (x - 9)².
What is factorization?An algebraic expression is factorised when it is written as the product of its factors. These variables, factors, or algebraic expressions could be present. The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics.
The steps to factorize the given expression is:
2x³ - 36x² + 162x
= 2x (x² - 18x + 81) Factor out 2x.
= 2x (x² - 2(9)(x) + (9)²) Rewrite the trinomial.
= 2x (x - 9) (x - 9) Use the whole square formula.
= 2x (x - 9)² simplify.
Hence, the complete factorization of 2x³ - 36x² + 162x = 2x (x - 9)².
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what is the sum that I'm supposed to do?
Answer:
a: 1/8 and 1/4. b: 1/2 1/4. c: 1/1 and 5/12. d: 1 1/2 and 3/4
Step-by-step explanation:
You had to find 2 fractions that add up to a number between the two numbers listed.
Find the next three terms
1.5, 4.5, 13.5, 40.5
Answer:
121.5, 364.5, 1093.5
Step-by-step explanation:
Divide 4.5 and 1.5 to find out how we get our next terms:
4.5 / 1.5 = 3
Every number is multiplied by 3 to become the next term, thus:
40.5 * 3
[121.5]
121.5 * 3
[364.5]
364.5 * 3
[1093.5]
Answer:
121.5, 364.5, 1093.5
Step-by-step explanation:
In this problem, we are asked to find the next three terms of the given geometric sequence.
To solve this simply, we can first identify the change, or difference, between the sequence's terms.
1.5, 4.5, 13.5, 40.5, ...
From 1.5 to 4.5, the difference is 3.
From 4.5 to 13.5, the difference is 9.
From 13.5 to 40.5, the difference is 27.
We can see that the difference between each term is one more power of three each time. So, we can continue the pattern.
For the next three terms, the difference from the previous term will be be 3 times the previous difference.
So, the differences will be: 81, 243, and 729.
We can add these numbers in a recursive sequence to get the next three terms of the sequence:
40.5 + 81 = 121.5
121.5 + 243 = 364.5
364.5 + 729 = 1093.5
you buy a bond with a fixed coupon rate of 5%. a year later, similar bonds that are issued have a coupon rate of 3%. which of the following is true?O The price of Juan’s bond will increase
O The interest rate of Juan’s bond will increase to reflect the current market
O The price of Juan’s bond will decrease
The correct option is : The price of Juan’s bond will decrease. Because similar bonds are offered a year later with a 3% coupon rate.
Explain about the coupon rate?A fixed-income security's nominal yield is expressed as a coupon rate.The coupon holder would yield less than the current market conditions when the market improves, as the bond won't pay more because its value was predetermined at issuance.When a bond is bought just on secondary market, the yield to maturity is the difference between the bond's interest costs, that could be higher or less than the coupon rate at the time the bond was issued.For the stated question:
You invest in a bond with a 5% fixed coupon rate. Similar bonds are offered a year later with a 3% coupon rate.Then, the price of Juan’s bond will decrease.
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consider the following table. age group frequency 18-29 9831 30-39 7845 40-49 6869 50-59 6323 60-69 5410 70 and over 5279 if you created the probability distribution for these data, what would be the probability of 30-39?
The probability of 30-39 age group is 18.83%. The probability of a given age group is the frequency of that group divided by the total frequency.
To find the probability of the age group 30-39, divide the frequency of this group (7845) by the total frequency (9831 + 7845 + 6869 + 6323 + 5410 + 5279 = 41,478). So the probability of 30-39 is 7845/41478 = 0.19.
In probability distributions, probabilities are calculated as the ratio of the number of occurrences of an event to the total number of possible events. To find the probability of an event in a specific age group, we need to calculate the ratio of the frequency of that age group to the total frequency of all age groups.
In this case, the frequency of the age group 30-39 is 7845. The total frequency of all age groups is 9831 + 7845 + 6869 + 6323 + 5410 + 5279 = 41,657.
So, the probability of the age group 30-39 is 7845/41657 = 0.1883 or 18.83%.
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I need help with this problem plsss
thanks! :)
Answer:
9.5
Step-by-step explanation:
[tex]1. \ \frac{AB}{PQ} =\frac{BM}{QN} ; = >[/tex]
[tex]2. \ \ \frac{11}{4.4} =\frac{BM}{3.8} ; \ = > \ BM=\frac{11*3.8}{4.4} =9.5.[/tex]
What is the probability of getting 4 kings when 5 cards are drawn from a standard deck of cards?
The probability of drawing four kings from a standard deck of cards in a single draw is 0.000001515, or 0.001515%.
The probability of drawing four kings from a standard deck of cards is extremely unlikely, as there are only four kings in a standard deck. This means that the probability of drawing four kings in a single draw of five cards is expressed mathematically as:
P(4 kings) = (4C4)*(48C1)/(52C5)
In this equation, 4C4 is the number of ways to select four kings from four kings, 48C1 is the number of ways to select one card of any other rank, and 52C5 is the total number of ways to select five cards from the deck.
Plugging in the numbers, we get the following equation:
P(4 kings) = (4!)*(48C1)/(52C5)
= (24)*(48C1)/(2598960)
= 0.000001515
Therefore, the probability of drawing four kings from a standard deck of cards in a single draw is 0.000001515, or 0.001515%.
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5x (2x + 6) in its equivelant form
Answer:
[tex]10x {}^{2} + 30x[/tex]
10) The temperature is below 80 degrees.
Answer:
ok so I don't get what you're trying to say but ok
Write the ratio 12 :30 in the form 1: n
Answer: 1:2.5
Step-by-step explanation:
Step by step explanation:
12:30
÷ by 12
= 1:2.5
The two bars are made of polystyrene, which has the stress-strain diagram shown. If the cross sectional area of bar AB is 2.3in^2 and BC is 4in^2, determine the largest force P that can be supported before any member ruptures. Assume that buckling does not occur. ???Does anybody know how to solve the problem completely or show an example with different numbers on how to get the answer?
The largest force that can be supported before any member ruptures is 8, the maximum force that bar BC can support.
To solve this problem, we need to find the maximum force (stress) that each bar can withstand before rupturing.
This can be found using the stress-strain diagram.
For bar AB with a cross sectional area of 2.3 in^2, the maximum stress that it can withstand is given by the maximum slope of the stress-strain diagram, which is approximately 1.
For bar BC with a cross sectional area of 4 in^2, the maximum stress that it can withstand is given by the maximum slope of the stress-strain diagram, which is approximately 2.
Since the force (stress) is equal to the stress times the cross sectional area, the largest force that bar AB can support is given by 1 * 2.3 = 2.3 and the largest force that bar BC can support is given by 2 * 4 = 8.
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(co 3) consider the following table: age group frequency 18-29 983 30-39 784 40-49 686 50-59 632 60-69 541 70 and over 527 if you created the probability distribution for these data, what would be the probability of 30-39?
The probability of 18-29 is 0.2213 or 22.13%, the probability of 30-39 is 0.1765 or 17.65%.
The probability of 30-39 can be calculated using the following formula:
P(30-39) = Frequency of 30-39 / Total Frequency
P(30-39) = 784 / 4443
P(30-39) = 0.1765
Therefore, the probability of 30-39 is 0.1765 or 17.65%.
To calculate the probability of any age group, the formula is the same. The probability is determined by dividing the frequency of the age group by the total frequency. To calculate the probability of any age group, you must first calculate the total frequency by adding up the frequencies of all the age groups. Then you can use the formula to calculate the probability of any age group.
For instance, to calculate the probability of 18-29, the formula would be:
P(18-29) = Frequency of 18-29 / Total Frequency
P(18-29) = 983 / 4443
P(18-29) = 0.2213
Therefore, the probability of 18-29 is 0.2213 or 22.13%.
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Z-scores are useful with regard to inferential statistics primarily because they offer a tool by which to determine whether _____. a. a sample is noticeably different from a population. b. a distribution of scores is standardized. c. a distribution of scores is symmetrically shaped. d. an individual is different from a sample.
Z-scores are useful with regard to inferential statistics primarily because they offer a tool by which to determine whether a sample is noticeably different from a population. The answer is A.
Inferential statistics is a branch of statistics that deals with making predictions, generalizations, or inferences about a population based on a sample of data collected from that population.
Z-scores are a measure of the number of standard deviations away from the mean that a particular score lies. By standardizing a distribution of scores, Z-scores allow us to compare scores from different distributions or from different populations. By determining the Z-score of a particular sample, we can determine whether it is noticeably different from a population based on its distance from the population mean.
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training the eccentric phase of plyometric movements with a new client will help them improve which of the following?
The eccentric phase of plyometric movements can help a new client improve power, agility, speed, balance, coordination, and stability.
The eccentric phase of plyometric movements can be an effective way to help a new client improve their overall performance. When training the eccentric phase, the client will be performing exercises that involve quickly stretching and contracting their muscles. This helps to increase power, agility, speed, balance, coordination, and stability. It also helps to reduce the risk of injury by strengthening the muscles and tendons around the joints. By training the eccentric phase of plyometric movements, the client will be able to improve muscular strength and endurance as well. Proper instruction and form should be explained and emphasized to ensure the client is performing the exercises safely and correctly. The client should also be encouraged to progress gradually as they become more comfortable with the exercises. With proper technique, consistent training, and progression, a new client can benefit greatly from training the eccentric phase of plyometric movements.
The complete question: Training the eccentric phase of plyometric movements with a new client will help them improve which of the following?
Select one:
a. Core stability
b. Power development
c. Landing mechanics
d. Force production
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The diameter of a cone's circular base measures 10 inches, and the slant height of the cone is 8 inches.
What is the approximate surface area of the cone?
Responses
146.3 in²
204.1 in²
314.2 in²
565.2 in²
The surface area of Cone is 204.1 inch².
What is Surface area of Cone?The surface area of a cone is equal to the curved surface area plus the area of the base: π r² + πlr
where r is the radius and l is the slant height
Given:
Radius= 5 inches
Slant height= 8 inches
So, the Surface area of Cone
= πr (l +r)
= 3.14 x 5 ( 8 + 5)
= 15.7 x 3
= 204.1 inch²
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on a circle of radius 9 feet, give the degree measure of the angle that would subtend an arc of length 6 feet. round your answer to the nearest hundredth, or two decimal places.
The circumference of the circle is 2 * pi * 9 = 56.5 feet. So, the degree measure is (6/56.5) x 360 = 51.1 degrees. Rounded to two decimal places, the degree measure is 51.1 degrees.
To find the degree measure of an angle that subtends an arc of length 6 feet on a circle of radius 9 feet, use the formula: degree measure = (arc length / circumference) x 360 degrees.
The degree measure of the angle that would subtend an arc of length 6 feet on a circle of radius 9 feet can be found by using the formula:
degree measure = (arc length / circumference) * 360
The circumference of the circle is 2 * pi * 9 = 18 * pi
So, degree measure = (6 / (18 * pi)) * 360 = (6 / 18) * (360 / pi) = 60 / pi
To convert this to degrees, we can use an approximation of pi as 3.14, so
degree measure = 60 / 3.14 = 19.11
Rounding to two decimal places, the degree measure is 19.11, which can be rounded to 19.11 degrees.
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A race car driver won a 300 mile race with a speed of
170.9 miles per hour. Find the driver's time.
Answer:
2.59hours
Step-by-step explanation:
Answer:2.59 hours.
Step-by-step explanation:
Speed = Distance/Time
Speed here is 115.7 mph
Distance here is 300 miles
Time here is unknown (t)
Plug the values into the equation
115.7 miles per hour = 300 miles/ t
Multiply both sides by t
115.7(t) = 300 miles
Divide both sides by 115.7 to get t alone
t = 300 miles/115.7mph
The miles here cancel out, so you'll be left with hours only. Hours is a time unit, so that's good1
t = 2.59 hours
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A country’s population in 1993 was 127 million
The population in 2008 is approximately 138 million.
To solve it, we will use the exponential growth formula:
P(t) = P0 *[tex]e^(rt)[/tex]
where
P(t) = population at time t
P0 = initial population (127 million)
e = natural logarithm base (approximately 2.71828)
r = rate of growth
t = number of years
To find the rate of growth, we can use the population in 2000 as a reference point.
P(7) = 132 million = P0 * [tex]e^(7r)[/tex]
Divide both sides by P0:
132 million / 127 million = [tex]e^(7r)[/tex]
Take the natural logarithm of both sides:
ln (132 million / 127 million) = 7r
Solve for r:
r = ln (132 million / 127 million) / 7
Now that we have the rate of growth, we can use it to estimate the population in 2008:
P(15) = 127 million * [tex]e^(15r)[/tex]
Plug in the value of r:
P(15) = 127 million * [tex]e^(15 * ln (132 million / 127 million) / 7)[/tex]
Using a calculator, the population in 2008 is approximately 138 million.
Round to the nearest million: 138 million.
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The correct question is:
A country's population in 1993 was 127 million. In 2000 it was 132 million. Estimate the population in 2008 using the exponential growth formula. Round your answer to the nearest million.
g decide whether or not the following are propositions. please also determine the truth value of all the propositions (if any):
1. "I am tired." Proposition: Yes, Truth Value: True
2. "7 + 8" Proposition: No, Truth Value: N/A
A proposition is a statement that is either true or false. In order to determine whether or not something is a proposition, we need to consider if the statement can be evaluated as true or false. For example, in the first statement, "I am tired," this is a proposition because it can be evaluated as true or false. It is true because the speaker is likely tired. In this case, the truth value of the proposition is true. In the second statement, "7 + 8," this is not a proposition because it cannot be evaluated as true or false. It is simply an arithmetic expression. Therefore, in this case, the truth value of the proposition is N/A.
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Learn before you teach Select an adult at random. Define events A: person
has earned a college degree, and T: person has chosen teaching as his or her
career. Rank the following probabilities from smallest to largest. Explain your
reasoning.
P(A) P(T) P(AT) P(TA)
The order of the probabilities from smallest to largest is P(T) < P(T|A) < P(A) < P(A|T).
A represents the event "Person earned a college degree"
T represents the event "Person's career is teaching"
P(A) represents the probability of event A (Person earned a college degree)
P(T) represents the probability of event T (Person's career is teaching)
P(T|A) represents the conditional probability of event T given event A (Probability of a degree holder being a professional teacher)
P(A|T) represents the conditional probability of event A given event T (Probability of a teaching career being held by a degree holder)
It is a universal fact that all teachers have a college degree, so:
P(A|T) > P(A) as having a college degree is a necessary condition for being a teacher
P(T|A) < P(A) as not all degree holders choose to become teachers
P(T|A) > P(T) as a smaller number of degree holders become teachers compared to the total number of teachers
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Melanie invests a total of $35,500 in two accounts. The first account earned a rate of return of 12%
(after a year). However, the second account suffered a 4% loss in the same time period. At the end
of one year, the total amount of money gained was $1,300.00. How much was invested into each
account?
$15,500 was invested in the first account
$20,000 was invested in the second account.
Solution
Let's call the amount invested in the first account "x". The amount invested in the second account would be $35,500 - x.
At the end of one year, the first account would have x * 1.12 = x + 0.12x = 1.12x dollars.
And the second account would have (35,500 - x) * 0.96 = 34,320 - 0.96x dollars.
The total amount of money gained at the end of one year would be 1.12x + 34,320 - 0.96x = 35,500 + $1,300 = $36,800.
We can set up an equation to solve for x:
1.12x + 34,320 - 0.96x = $36,800
0.16x = $2,480
x = $15,500
So, $15,500 was invested in the first account, and $35,500 - $15,500 = $20,000 was invested in the second account.
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how many kilometers is 2528.5 cm? calculate and type your answer with correct significant numbers (show your work for full credit).
2528.5 centimeters is approximately 0.0253 kilometers.
To convert centimeters to kilometers, we first need to convert centimeters to meters, then meters to kilometers.
1 kilometer = 1000 meters
1 meter = 100 centimeters
So, to convert 2528.5 centimeters to meters, we divide by 100:
2528.5 cm / 100 = 25.285 meters
And to convert meters to kilometers, we divide by 1000:
25.285 m / 1000 = 0.025285 km
Therefore, 2528.5 centimeters is approximately 0.0253 kilometers.
The answer can be rounded to 4 significant figures, which is the number of significant figures in the original measurement of 2528.5 centimeters:
0.0253 km (rounded to 4 significant figures)
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How do you find the sample standard deviation when given the population standard deviation? What formula do you use? If you can make up an example that would be great.
The estimate of the population standard deviation will be the estimated sample standard deviation
You must use sample data when you don't have access to population data. Consider the following hypothetical research question: What is the standard deviation of student heights in Azerbaijan? All of the residents are Azerbaijani students. To gather data on every student in Azerbaijan might be impossible or expensive.
As a result, you measure the heights of 100 pupils who were chosen at random. You next figure out the sample standard deviation. Keep in mind that the lack of population statistics prevents you from calculating the population standard deviation.
In this case, your best estimate of the population standard deviation will be the estimated sample standard deviation.
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