(2x +3) ² - (2x -5)²

Result in (d) refutes the claim in (a), since it is less than the 5% level of significance. Actual proportion is lower than 0.4.

A recent article in a national newspaper claimed that 40% of all students in US colleges drink some alcoholic beverages at least once a week. A students association argued that actually fewer students drink alcohol. In support of its claim the student association has sampled at random 500 students and found that only 180 of them stated that they do drink at least once a week.

Calculate the Claimed Population Proportion

The claimed population proportion is p=0.4

Calculate the Parameters for the Normal Distribution of Sample Proportion

By the Central Limit Theorem, the distribution of the sample proportion p is the normal distribution with mean μj=p=0.4 and standard deviation σj=npq= √[(0.4)(0.6)/500]=0.047.

Calculate the Observed Sample Proportion

The observed sample proportion of those who said "Yes" (that they do drink at least once a week) is pˆ0=500/180=0.36.

Calculate the Probability to Observe Such, or Smaller, Sample Proportion if the Claim in (a) Were to be Correct

Using the CLT and the parameters in (b), the probability to observe such, or smaller, sample proportion if the claim in (a) were to be correct is Pr(p≤pˆ0)=0.056.

Conclusion

The result in (d) refutes the claim in (a), since it is less than the 5% level of significance. This means that we reject the null hypothesis that the proportion of students drinking at least once a week is 0.4, and instead conclude that the actual proportion is lower than 0.4.

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Hence, in response to the provided question, we can say that  As a result, the set of all positive real numbers is the range of this equation.

An algebraic equation is a method of connecting two quotes by using the equals symbol (=) to express equality. In algebra, an explanation is a definitive expression that verifies the equivalency of two formula. For example, the identical character divides the numbers 3x + 5 and 14. A linear equation might be used to recognize the connection that existing between the texts written on separate sides of a letter. The product and application both frequently the same. 2x - 4 equals 2, for example.

x = 2y is the provided equation.

y denotes the exponent of 2 in this equation. The exponent's base, 2, is a positive real number. As a result, y can be any real number. This equation's domain is all real numbers.

Because 2y is always positive, regardless of the value of y, the range of this equation is all positive real integers. Also, 2y can approach 0 as y approaches negative infinity, but it never does because 2y is always positive. As a result, the set of all positive real numbers is the range of this equation.

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Step-by-step explanation:

Slope is y2 - y1 / x2 - x1

X1 =2 y1 =4 x2 =-4 y2= 0

0 - 4/ - 4 - 2 = - 4/-6

Sslope =2/3 or 0.67

Round it up if you are asked to.

The side length x is given as follows:

[tex]x = \frac{7}{\sqrt{3}}[/tex]

The number that belongs in the green box is of 7.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For the side x, we have that:

Hence the tangent can be applied, as follows:

tan(30º) = x/7

x = 7 x tangent of 30 degrees

[tex]x = 7 \times \frac{1}{\sqrt{3}}[/tex]

[tex]x = \frac{7}{\sqrt{3}}[/tex]

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The measure of the length of x is equal to 7/√2 using the trigonometric ratio of tangent for angle 60°.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

recall that tan 60° = √2

tan 60° = 7/x {opposite/adjacent}

√2 = 7/x

by cross multiplication

x = 7/√2.

Therefore, the measure of the length of x is equal to 7/√2 using the trigonometric ratio of tangent for angle 60°.

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Answer:

X = 34

Step-by-step explanation:

360-108 = 252

252-88 = 164

5x-6

164+6 = 170

170/5 = 34

The value of t in the figure is calculated using the concept of similar triangles to be equal to

The value of t is solved using the concept of similar triangles. this involves taking the proportions of the sides which are equal to each order

The calculation is completed as follows

JK / JG = KI / GH

substituting the values of each side

1 / 2 = t / t + 27

cross multiplying

t + 27 = 2t

collecting like terms

27 = 2t - t

27 = t

We can therefore say that the value of t is equal to 24

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By inspecting the table, it can be seen that f(x) must be shifted left by 4 units in order to match g(x). Thus, Left by 4 units is the answer.

A quadratic function is a function of the form f(x) = ax² + bx + c, where a, b, and c are real numbers and a ≠ 0.

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. The solutions of the equation are the points at which the graph of the function intersects the x-axis.

The functions, that are quadratic, f(x) and g(x) are described in the table. From the table, it can be seen that f(x) and g(x) are not equal to each other, as the values for each x are different. To match f(x) and g(x), one of the functions must be shifted.

By inspecting the table, it can be seen that f(x) must be shifted left by 4 units in order to match g(x).

This can be calculated by subtracting the g(x) values from the f(x) values for each x.

For example, at x = -2, the difference between f(x) and g(x) is -32.

This difference is the same for all x values, meaning that f(x) must be shifted left by 4 units to match g(x). Thus, the correct answer is Left by 4 units.

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The correct answer to the given question is a)29, (b) 91cm is median waist measurement and (c)13cm is interquartile range

(a)From the graph, 11 men have a waist measurement of 85cm and below. Since the cumulative frequency is 40

Number of men who have a waist measurement of more than 85 cm

= 40 − 11

= 29

(b)Median

Given a dataset of size N = 40, the median can be calculated as:

Median = (N + 1) / 2

where N is the total number of items in the dataset.

Substituting the given value of N, we get:

Median = (40 + 1) / 2

Median = 20.5

Since the median has to be a whole number, we take the 20th item as the median. Tracing 20 from the y-axis to the x-axis, the median waist measurement is 91cm.

(c)Interquartile Range = Q3 - Q1

To find the first quartile, denoted as Q1, you need to determine the value that separates the lowest 25% of the dataset from the rest of the dataset.

The formula for the first quartile is: Q1 = (N + 1) / 4

where N is the total number of items in the dataset.

Substituting the given value of N, we get:

Q1 = (40 + 1) / 4

Q1 = 10.25

Since we need to find the 10th item, which corresponds to the 25th percentile of the dataset, we take the integer part of Q1, which is 10. Therefore, the first quartile, Q1, is the 10th item.

​From the graph, at y= 10, x= 84 cm

To find the third quartile, denoted as Q3, you need to determine the value that separates the highest 25% of the dataset from the rest of the dataset.

The formula for the third quartile is: Q3 = 3(N + 1) / 4

where N is the total number of items in the dataset.

Substituting the given value of N, we get:

Q3 = 3(40 + 1) / 4

Q3 = 30.75

Since we need to find the 30th item, which corresponds to the 75th percentile of the dataset, we take the integer part of Q3, which is 30. Therefore, the third quartile, Q3, is the 30th item.

From the graph, at y= 30, x =97 cm

Therefore: Interquartile Range = 97 - 84 = 13cm

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Complete Question

a) how many men have a waist measurement of more than 85 cm

b) what is the median waist measurement

c) what is the interquartile range of the waist measurements

The answer to your question is:

a) To find the object's velocity after 2 seconds, we need to take the derivative of the function s(t) = -0.8t^2 + 32t. The derivative of s(t) is s'(t) = -1.6t + 32. To find the velocity after 2 seconds, we plug in t = 2 into the derivative equation: s'(2) = -1.6(2) + 32 = 28.8 meters per second. Therefore, the object's velocity after 2 seconds is 28.8 meters per second.

b) To find the time it takes the object to reach its maximum height, we need to find the value of t that makes the derivative of s(t) equal to zero. This is because the derivative of s(t) represents the velocity of the object, and the velocity is zero at the maximum height. So we set s'(t) = 0 and solve for t:

0 = -1.6t + 32
1.6t = 32
t = 20 seconds

Therefore, it takes the object 20 seconds to reach its maximum height.

c) To find the object's maximum height, we plug in the value of t that we found in part b into the original equation for s(t):

s(20) = -0.8(20)^2 + 32(20) = 320 meters

Therefore, the object's maximum height is 320 meters.

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[tex]cos \beta = \frac{adjuscent}{hypotenuse} \\ cos15 = \frac{47}{x} \\ x = \frac{47}{cos15} \\ x = 48.7[/tex]

Answer:

To find out how many windows Kendall can wash in one hour, we can divide the number of windows washed by the time taken:

Number of windows washed per hour = (Number of windows washed) / (Time taken)

We can first convert the mixed number 10 1/2 to an improper fraction:

10 1/2 = (10 x 2 + 1) / 2 = 21/2

Substituting the given values:

Number of windows washed per hour = (21/2) / (3/4) hours

To divide by a fraction, we can multiply by its reciprocal:

Number of windows washed per hour = (21/2) x (4/3) = 28 windows/hour

Therefore, Kendall can wash 28 windows in one hour at this rate.

Answer:

14 windows

Step-by-step explanation:

All you have to do is a simple equation 10 1/2÷3 which equals 14

The length of the other  parallel side of the parallelogram (b2) is 8.3m with the area of the parallelogram 100m².

It is a four-sided shape that has two pairs of parallel lines with all sides equal in length.

The area of the parallelogram is 100m² and the height is 10m, so the base of the parallelogram is 13m. This forms a right triangle with one side of the parallelogram. To calculate the length of the other non-parallel side (b²), we can use the squaring method.

This can be expressed as:

a² + b² = c²

Where a and b are the two shorter sides of the triangle, and c is the longest side.

Substituting in the values given, we get:

x² + 10² = 13²

x²=13²-10²

x= √169-100

x = √69

x = 8.3m

Therefore, the length of the other non-parallel side of the parallelogram (b2) is 8.3m.

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After solving the equation using the elimination method, the value of x is 1 and y is 3.

The given system of equations are:

y = x + 2...............(1)

y = 5x - 2...............(2)

We solving equation by the elimination method.

The elimination method is a method of solving systems of linear equations. It involves performing operations on the equations, such as addition and multiplication, to transform the equations into simpler forms.

Subtract equation 1 and equation 2

x+2 - 5x + 2 = 0

-4x + 4 = 0

Subtract 4 on both side, we get

-4x = -4

Divide by -4 on both side, we get

x = 1

Now put the value of x in equation 1.

y = 1 + 2

y = 3

The solution set is {1, 3}.

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The complete question is:

Find the value of x and y.

y = x+2

y=5x-2

The value of the angle X is 99 degrees. Option E

To determine the value of the angle, we need to note that the sum of the interior angles of a given regular polygon is determined with the formula;

(n -2)180

Such that 'n' is the number of sides of the polygon

From the information given, we have that;

The value of n = 6

Then, the sum of interior angles = (6-2)180 = 4(180)

Multiply the values

= 720

Equate the angles

x + 108 + 146 + 101 + 113 + 153 = 720

Add the values

x = 720 - 621

subtract the values

x = 99 degrees

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Answer:

(1.5)x + 1.5 = 30

Step-by-step explanation:

Answer:

Uhm i think its ABD weeweee

Step-by-step explanation:

Because monkeys wooowooo not weewee so the commentary would be weeeweee

After answering the presented question, we can conclude that As a result, the equation that reflects the stock's value after two years in terms of x is: 0.7161x

An equation is a mathematical statement that proves the equality of two expressions connected by the equal symbol '='. 2x - 5 Equals 13, for example. Expressions include 2x-5 and 13. The character '=' joins the two expressions. A mathematical formula with two algebraic expressions on either side of an equal sign (=) is known as an equation. It demonstrates the relationship of equivalence between the left and right formulas. In every formula, LHS = RHS (left side = right side).

Because the stock's value fell by 7% after the first year, it is now worth:

x - 0.07x = 0.93x

The stock's value dropped by 23% after the second year, therefore it would be worth:

0.93x - 0.23(0.93x) = 0.93x - 0.2139x = 0.7161x

As a result, the expression that reflects the stock's value after two years in terms of x is:

0.7161x

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Answer:

[tex] \frac{1}{9} [/tex]

Step-by-step explanation:

Deal with negative and numerical exponents separately;

Negative exponent means reciprocal;

2 means sqared;

So:

[tex] {3}^{2} = 9 \\ {3}^{ - 2} = \frac{1}{9} [/tex]

Therefore , the solution of the given problem of triangle comes out to be EG  = 23.14.

A triangle is a hexagon because it has two or more extra polygon sections. Its form is a simple rectangular one. A and B are the only 2 different edges of a form that can set it apart from a regular triangular. When bounds are still not precisely collinear, Euclidean geometry produces a single section rather than a full cube. Three edges and three angles make up a triangle.

Here,

The length of EG can be determined as follows if EF = 24:

First, we calculate the length of FG using the Pythagorean theorem:

=> FG² = EF² - EG²

=> 10² = 24² - EG²

=> EG² = 24² - 10²

=> EG² = 536

=> EG = √536 ≈ 23.14

Consequently, EG 23.14 when FG = 10 and GH = 7 if E is the right angle apex of a right triangle EFG and EF = 24.

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The probability that during a 10-hour flight an airplane will fail to reach its intended destination or crash is

To solve this problem, we can use the binomial distribution, which gives the probability of k successes in n independent trials, each with the same probability of success p. In this case, a "success" is defined as the engine not failing, and a "failure" is defined as the engine failing.

Let X be the number of engines that fail during the flight. Since each engine can fail independently of the other engine, X follows a binomial distribution with n = 2 (the number of engines) and p = 0.21 (the probability of a single engine failing). The probability of X failures is:

P(X = 0) + P(X = 1) + P(X = 2)

where P(X = k) = (n choose k) * p^k * (1 - p)^(n - k), and (n choose k) is the binomial coefficient.

Using this formula, we can calculate the probability of each possible value of X and add them up:

P(X = 0) = (2 choose 0) * 0.21⁰* 0.79²= 0.6241

P(X = 1) = (2 choose 1) * 0.21¹* 0.79¹= 0.32994

P(X = 2) = (2 choose 2) * 0.21² * 0.79⁰ = 0.04689

Therefore, the probability of the plane failing to reach its intended destination or crashing is:

P(X >= 1) = P(X = 1) + P(X = 2) = 0.32994 + 0.04689 = 0.37683

So the probability of the plane not making it to its destination is about 37.7%.

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To the nearest tenth, the quantity of the amount after [tex]7[/tex] weeks is around [tex]1804.74[/tex].

Quantity simply refers to how much or how many of anything there are. A quantity can also be an amount, a number, or a measurement. It responds to the "how much?" query. Numbers may also be used to understand quantities, such as this book has 55 pages, this container has 'x' quantities of black pens, etc.

Numbers can be used to express quantities, such as 55 pages or reading. Entire numbers, fractions, fractions, percentages, or units of measurement like space, money, length, or weight can all be used to express these values. Quantities may also be stated using uncommon units.

[tex]A_{0} = 3600[/tex]

[tex]r = 0.01[/tex] (since the rate of decay is [tex]1[/tex]%)

[tex]t = 7[/tex] weeks [tex]= 56[/tex] days (since there are [tex]7[/tex] days in a week)

We can first find the value of [tex]e^{-rt}[/tex] as follows:

[tex]e^{-rt} = e^{-0.0187} = 0.5013[/tex]

Substituting into the formula, we have:

[tex]A = 3600 * 0.5013 ≈ 1804.74[/tex]

Therefore, the value of the quantity after [tex]7[/tex] weeks, to the nearest hundredth, is approximately [tex]1804.74[/tex].

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Each squad has to have an equal amount of men and women. The maximum number of teams that can participate is 8.

A location in mathematics where a function has its maximum value. The value is an absolute maximum if it exceeds or is equal to all other function values. It is a relative or local maximum if it is simply greater than any neighboring point.

Number of girls = 16.

Number of boys = 20.

In order to calculate the maximum number of teams that can enter, we must determine the most prevalent criteria for both boys and girls based on the information provided. As follows:

Factors of 18 [tex]= 1, 2, 4, 8[/tex]  and 16.

Factors of 24 = [tex]1, 2, 3, 4, 6, 8, 12[/tex] and 24.

Highest common factor = 8

Therefore, the greatest number will be 8.

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The probability P(z < 1.645) is the area under the standard normal curve to the left of 1.645.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain. Probability is used to assess the outcome of any random event, such as the roll of a die or the flip of a coin. It can also be used to measure the likelihood of future events, such as the stock market rising or falling.

This probability is calculated by using Table 3 in Appendix I. The probability is 0.9500, which means that 95% of the area under the normal curve is to the right of 1.645.

This phenomenon is occurring because the normal distribution is symmetrical. The area to the left and to the right of the mean are equal, and thus the probability of P(z < 1.645) is the same as the probability of P(z > 1.645). The normal distribution is also unimodal, meaning that there is a single peak and all other data points have lower probability than the peak. Since the peak of the normal distribution is at the mean (0 in this case), any value to the right of the mean will have a higher probability than any value to the left of the mean. Thus, the probability of P(z > 1.645) is greater than the probability of P(z < 1.645).

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The probability P(z < 1.645) is the area under the standard normal curve to the left of 1.645.

What is Probability?

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain.

This probability is calculated by using Table 3 in Appendix I. The probability is 0.9500, which means that 95% of the area under the normal curve is to the right of 1.645.

The symmetric nature of the normal distribution is what is causing this phenomena. Because the area to the left and right of the mean are equal, the likelihood that z will be less than or more than 1.645 is equally likely. Furthermore, the normal distribution is unimodal, which means that there is only one peak and that all other data points have a probability that is smaller than the peak. Since the mean (0 in this case) is where the normal distribution's peak occurs, any value to the right of the mean will be more likely to occur than any value to the left of the mean. As P(z > 1.645) is more likely than P(z 1.645), the former is true.

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Thus, the resulting function after an 8 unit right translation and a 5-unit vertical stretch is obtained as:  f(x) = 5* log1/7(x+8)

Any applied either a horizontal or vertical shift to an object is referred to as a translation in geometry. In geometry, a translation is a displacement that occurs either horizontally to the left but rather right or straight up or down. It may also consist of a mix of the two.

The simplest technique to modify a geometric object is to identify its main points and translate those. By "connecting the dots," you can then finish the object.

The stated function:

f(x) = log1/7x

translation 8 units right will give (x + 8)

Function : f(x) = log1/7(x+8)

Now, vertical stretch by a factor of 5.

Function : f(x) = 5* log1/7(x+8)

Thus, the resulting function after an 8 unit right translation and a 5-unit vertical stretch is obtained as:  f(x) = 5* log1/7(x+8)

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The correct question is-

f(x) = log1/7x ; translation 8 units right followed by a vertical stretch by a factor of 5. The resultant function will be?

Answer:

1

Step-by-step explanation:

we just find the middle of the 2 places

In quadrilateral ABCD abοve, AD || BC and CD =1/2AB. the measure οf angle is B 90°

A quadrilateral is a clοsed shape and a type οf pοlygοn that has fοur sides, fοur vertices and fοur angles. It is fοrmed by jοining fοur nοn-cοllinear pοints. The sum οf interiοr angles οf quadrilaterals is always equal tο 360 degrees.

Since AD is parallel tο BC, we have:

∠ABC + ∠BCD = 180° (interiοr angles οn the same side οf the transversal AD)We alsο knοw that CD = 1/2AB. Let's call the length οf AB "x". Then we have:

CD = 1/2AB

CD = 1/2x

Nοw, let's lοοk at triangle BCD. We knοw that the sum οf the angles in a triangle is 180°, sο we have:

∠BCD + ∠CBD + ∠BDC = 180°

We alsο knοw that ∠BCD = ∠ABC (because they are cοrrespοnding angles), sο we can substitute ∠ABC fοr ∠BCD:

∠ABC + ∠CBD + ∠BDC = 180°

Nοw, let's use the fact that CD = 1/2x tο find the length οf BD:

BD = AB - CD

BD = x - 1/2x

BD = 1/2x

Sο, BD is half the length οf AB. This means that triangle BCD is a 30-60-90 triangle, with ∠CBD = 60° and ∠BDC = 30°.

Substituting these values intο οur equatiοn abοve, we get:

∠ABC + 60° + 30° = 180°

Simplifying, we get:

∠ABC + 90° = 180°

Subtracting 90° frοm bοth sides, we get:

∠ABC = 90°

Therefοre, the measure οf angle B is 90°.

D) 90°.

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If two lines have the same slope, it means that they have the same steepness or inclination and will never intersect, no matter how far they are extended in either direction.

Parallel lines are two or more lines in a two-dimensional plane that never intersect, regardless of how far they are extended in either direction. In other words, they have the same direction or slope but different y-intercepts.

In the given Question,

To draw similar slope triangles on each line, we can choose any two points on the line and connect them with a straight line segment. Then, we can calculate the rise (change in y) and run (change in x) between the two points and use these values to determine the slope of the line using the formula:

slope = rise / run

If we draw similar slope triangles on both parallel lines r and s, we will find that the ratios of the rise to the run are equal for both lines. This means that the slopes of the two lines are equal, and we can express this mathematically as:

slope_r = slope_s

This relationship between the slopes of parallel lines is important in many applications of mathematics, including geometry, trigonometry, and calculus.

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Answer:

[tex]\boxed{f(x)=(3)(2)^x}[/tex]

Step-by-step explanation:

First, we need to substitute the coordinates of the two given points in the ecuation [tex]f(x)=ab^x[/tex]:

[tex]3=ab^{0} \qquad \textbf{ec.1}\\6=ab^{1} \qquad \textbf{ec.2}[/tex]

Remember that any number raised to the power 0 is equal to 1.  So:

[tex]3=a \qquad \textbf{ec.3}[/tex]

now, we can substitute in ec.2 and solve for b:

[tex]6=3b\\ b=2[/tex]

Finally:

[tex]f(x)=(3)(2)^x[/tex]

Therefore, we have found the solution to the exercise

[tex]\text{-B$\mathfrak{randon}$VN}[/tex]

modeling function the population of carp with respect to time is: P(t) = 100 * [tex]e^{0.707t}[/tex]

To model the population of carp with respect to time, we can use the following exponential growth formula:

P(t) = P(0) * [tex]e^{rt}[/tex]

where P(0) is the initial population, r is the annual growth rate, and t is the number of years from now.

We know that initially there are 100 carp in the lake, so P(0) = 100.

We also know that the population varies by 20 fish seasonally, so the annual growth rate is:

r = ln(625/100) / 5 = 0.707

Thus, the function modeling the population of carp with respect to time is:

P(t) = 100 * [tex]e^{0.707t}[/tex]

where t is the number of years from now.

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Zack wheeler had a war of 7. 8 in the 2021  season this means that He scored an average of 7.8 runs per game.

This means that Zack scored an average 7.8 runs per game.

An average is a single number represented as a list of numbers, usually the sum of the numbers divided by the number of numbers in the list (arithmetic mean). For example, the numbers 2, 3, 4, 7, and 9 (for a total of 25) have an average of 5. Depending on the context, the average can be another statistic, such as the median or the mode. Average personal income, for example, is often given as the median – a figure below 50% of personal income and above 50% of personal income – because the average would be higher if some personal income of billionaires were included. Therefore, it is recommended to avoid using the word "average" when referring to measures of central tendency.

Complete Question:

Zack Wheeler had a WAR of 7.8 in the 2021 season. What does this mean?

A. He scored an average of 7.8 runs per game.

B. His team won an average of 7.8 more games than other teams in MLB.

C. His team won around 7.8 more games than it would have with a replacement player.

 D. He scored around 7.8 more runs than a replacement player would have.

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