Use the formula z = x-μ/σ
and the given information to find the missing piece of information
1. Given x = 75, μ = 80, o = 5, find z.

From the data in the table, we can conclude that when x = 4, then the residual will equal -1.

To determine the residual, we can begin by obtaining the difference between the given and the predicted values of y.

So, Residual = Gven value - Predicted value.

When x = 4 in the table, Given value is 9 and predicted value is 10. So, 9 - 10 = -1. So, we can say that the residual value is -1.

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Answer:

The residual is the difference between the actual y-value and the predicted y-value on a regression line. Since no table or equation is provided, we cannot calculate the exact residual. However, I can explain the concept to you.

Step-by-step explanation:

In general, to calculate the residual, we would need a regression equation or a line of best fit. This equation allows us to predict the y-values for different x-values. Then, we can compare the predicted values to the actual values given in the table to find the residuals.

If you have the regression equation or the line of best fit, I can help you calculate the residual for a specific x-value.

The translation used to create the image is 3 units to the right, as each point of the original polygon was moved 3 units to the right to obtain the corresponding point of the image polygon.

What is Polygon?

Geometry defines a polygon as a closed shape composed of continuous line segments, or sides, that do not intersect.

Translation is a transformation in geometry that moves an object without changing its shape, size, or orientation. It involves sliding an object along a straight line in a certain direction and distance.

According to given information:

To determine the translation used to create the image, we can observe the original and transformed polygons and look for changes in their positions. The vertices of the original polygon ABCD are (1,5), (3,1), (7,1), and (5,5), while the transformed polygon A'B'C'D' has vertices (8,5), (10,1), (14,1), and (12,5).

Comparing the vertices of the two polygons, we notice that all of the points have been shifted 7 units to the right to obtain the transformed image. This means that every x-coordinate of the original polygon has been increased by 7, which can be written as a translation vector (7, 0).

Therefore, the translation used to create the image is 7 units to the right.

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Answer: What is the ratio of pulled-pork sandwiches to barbeque chicken sandwiches at the Greenfield Community Picnic?

Let's call the number of pulled-pork sandwiches "P" and the number of barbeque chicken sandwiches "C". According to the problem, the organizers are making 2 pulled-pork sandwiches for every 5 barbeque chicken sandwiches. This means that:

P/C = 2/5

To simplify this ratio, we can multiply both sides by a common factor that will make the denominators the same. In this case, the smallest common multiple of 2 and 5 is 10, so we can multiply both sides by 10:

10(P/C) = 10(2/5)

Simplifying this expression, we get:

2P = 4C

Dividing both sides by 2, we get:

P/C = 2/4

Simplifying this fraction, we get:

P/C = 1/2

Therefore, the ratio of pulled-pork sandwiches to barbeque chicken sandwiches at the Greenfield Community Picnic is 1:2.

Step-by-step explanation:

Answer: Let's start by calculating the probability that an 18-year-old driver is involved in an accident:

P(accident) = 124/2000 = 0.062

Let's assume that the insurance company pays the full cost of the accident, which is $15,000. Then the expected cost of covering one 18-year-old driver is:

Expected cost = P(accident) x Cost of accident = 0.062 x $15,000 = $930

If the insurance company wants to make a 20% profit on policies, they need to charge a premium that covers their expected cost plus their desired profit. The premium, denoted by P, can be calculated as follows:

P = (Expected cost + Desired profit) / (1 - Profit margin)

where Profit margin is the percentage of the premium that represents the profit. In this case, Profit margin is 20%, or 0.20.

Substituting the values we have calculated, we get:

P = ($930 + 0.20 x $930) / (1 - 0.20)

= $1,236.00

Therefore, the insurance company should charge 18-year-old drivers a premium of $1,236.00 to make a 20% profit on policies.

Step-by-step explanation:

Each side of Tavon's backyard is 7 meters long.This answer makes sense because a square has four equal sides, so if the perimeter of the square is 28 meters,

How to solve the problem?

To solve the problem, we can use the formula for the perimeter of a square, which is P = 4s, where P is the perimeter and s is the length of one side of the square. Since we know that the fence around Tavon's backyard is 28 meters, we can set this equal to the perimeter of the square and solve for s:

28 = 4s

Dividing both sides by 4, we get:

s = 7

Therefore, each side of Tavon's backyard is 7 meters long.

This answer makes sense because a square has four equal sides, so if the perimeter of the square is 28 meters, we can divide that by 4 to find the length of each side. In this case, we get 7 meters, which is a reasonable length for a side of a backyard. Additionally, since the problem tells us that the backyard is shaped like a square, we know that each side must be the same length, so it makes sense that we would find a single value for s that satisfies the equation P = 4s.

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Your Complete question is :-14. The fence around Tavon's backyard is

28 meters. The backyard is shaped likea square. How long is each side of the backyard?

The value of the test statistic is 6.04 (rounded to two decimal places).

A test statistic is a numerical value that is calculated from sample data and is used in hypothesis testing. It measures how many standard deviations a sample statistic (such as a sample mean or proportion) is away from the hypothesized population parameter.

To find the test statistic, we need to perform a hypothesis test using the given sample data and the claim about the population. We can use a one-sample proportion z-test for this purpose.

Null Hypothesis: p = 0.5 (claim that 50% of adults would erase their personal information online if they could)

Alternative Hypothesis: p > 0.5 (claim that more than 50% of adults would erase their personal information online if they could)

We can calculate the test statistic using the formula:

where:

sample proportion = 0.65

p = hypothesized proportion = 0.5

n = sample size = 415

Plugging in the values, we get:

z = (0.65 - 0.5) / sqrt(0.5 * 0.5 / 415)

z = 6.04

Therefore, the value of the test statistic is 6.04 (rounded to two decimal places).

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Answer:

Step-by-step explanation:

i believe it is nearly as hard as my usual amount of challenge

The value of Y is 54 degrees

A pentagon is described as any five-sided polygon or 5-gon that has a sum of the internal angles in a simple pentagon is 540°.

we know that every side of a regular pentagon is same.

So we have an isosceles triangle. The  correspond angle of y, must equal to y (degree) too.

we also have that every inner angle of a regular pentagon is 360/5=72.

So we can calculate angle y, by the equation y+y+72=180.

Therefore y=54

In conclusion,  the regular pentagon each interior angle measures 108°, and each exterior angle measures 72°

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Complete question is attached in image;

Answer:

Step-by-step explanation:

Circle

Solve for circumference

C≈977.04

Radius

155.5

Solution

C=2πr=2·π·155.5≈977.03532 = 977.03

Answer:

977.03

Step-by-step explanation:

C=2πr=2·π·155.5≈977.03532 = 977.03

The expression 10m‾‾√ is an expanded form of the mathematical term ln10.

Therefore, the bank can lend out $1,600 of Fiona's money.

Percent, denoted by the symbol "%", is a way of representing a fraction or proportion out of 100. It is used to express a part of a whole in terms of hundredths. For example, 50% is the same as 50 out of 100, which simplifies to 1/2 or 0.5 as a decimal. Percentages are commonly used in many areas such as finance, statistics, and everyday life to express changes, rates, or comparisons.

Here,

If Fiona deposits $2,000 and the bank has a reserve ratio of 20%, then the bank can lend out 80% of her deposit.

Reserve = 20% x $2,000

= $400

Amount available for lending = $2,000 - $400

= $1,600

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The missing data value in the project is 25.5.

Range is a statistical measure that represents the difference between the highest and lowest values in a dataset. It is calculated by subtracting the smallest value in the dataset from the largest value.

To find the missing data value, we need to use the given range and the known data values.

The range is the difference between the highest and lowest values in the data set. So, if we sort the given data values in increasing order, we have:

11, 15, 15, 22, 29, 31

The range is 33, which means that:

highest value - lowest value = 33

31 - 11 = 33

So, the missing data value must be between 22 and 29 (since those are the values that are next to each other in the sorted list). To find the exact value, we can take the average of 22 and 29:

(22 + 29) / 2 = 25.5

Therefore, the missing data value is 25.5.

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When the two sections are combined, the total number of circles would be ten, representing the value of 5 times 2, which is 10.

Number is a mathematical concept used to quantify or measure a quantity. It is a symbol or group of symbols that stands for a quantity, such as 2, 4, 5, 10, and so on. Numbers are used to express amounts, to count, and to measure. They are also used to represent relationships between quantities and to compare quantities.

A place value disk can be used to represent the value of 5 times 2, which is equal to 10. The disk would have two sections, one representing the number 5 and the other representing the number 2. The number 5 would be represented by five single circles in the “ones” section, and the number 2 would be represented by two single circles in the “ones” section. When the two sections are combined, the total number of circles would be ten, representing the value of 5 times 2, which is 10.

The place value disk is a useful visual tool to help students understand the concept of multiplication. It allows them to clearly see how the number of circles in each section are multiplied to get the final answer. This can help them better understand the concept of multiplication and how it works.

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Complete questions as follows-

The correct option is -  D. f(x) = 30[tex]e^{x}[/tex] is the exponential function which is shown by the given curve.

For modelling a connection where the dependent variable changes proportionally to a constant variation in the independent variable, the exponential function is utilised.

Often, the function is written as exp (x) It is extensively utilised in the fields of mathematics, physics, chemistry, engineering, physical science, and economics.

Assume that an is the starting point, x is the exponent function's power, and e is the growing factor.

Exponent is provided as

y = a(e)ˣ

According to the graph, the exponent function's value at x = 0 will be 30.

The purpose will then be

30 = a(e)⁰

30 = a

The exponent function is then provided as,

y = 30eˣ

As a result, the graph in the functions below will have a value of y = 30eˣ.

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Answer:

Step-by-step explanation:

Answer:  The question is asking us to find the derivative of the function f(x), but the function given is g(x). Therefore, we will assume that the question is asking us to find the derivative of g(x) and proceed accordingly.

To find the derivative of g(x), we need to apply the power rule and the sum rule of derivatives. The power rule states that if f(x) = x^n, then f'(x) = nx^(n-1), and the sum rule states that if f(x) = u(x) + v(x), then f'(x) = u'(x) + v'(x).

Using these rules, we can find the derivative of g(x) as follows:

g(x) = 3x² + 7x - 1

g'(x) = (3x²)' + (7x)' - (1)'

g'(x) = 6x + 7 - 0

g'(x) = 6x + 7

Therefore, the derivative of g(x) is g'(x) = 6x + 7.

Step-by-step explanation:

Answer:

The circumference of the circle is 119.32 ft.

Step-by-step explanation:

The circumference of a circle can be solved through the formula:

C = πd

where d is the diameter

Given: d = 38 ft

π = 3.14

Solve:

C = πd

C = 3.14 (38 ft)

C = 119.32 ft

The given exponents term can be written in the form of [tex](a^{4})^{12}[/tex] .

What about exponents?

Exponents are a mathematical operation that involves multiplying a base number by itself a certain number of times. Exponents are often referred to as powers, and the base number is raised to a power, which is usually represented by a superscript number. For example, 2^3 means 2 raised to the power of 3, which is 2 x 2 x 2 = 8.

Exponents are commonly used in many areas of mathematics, including algebra, calculus, and geometry. They are used to represent very large or very small numbers, to simplify calculations, and to express repeated multiplication in a more compact form. Exponents can also be negative or fractional, allowing for the representation of roots and other mathematical concepts.

According to the given information:

In the given question [tex](a^{48} )[/tex] can be written as,

[tex](a^{4})^{12}[/tex] = [tex](a^{4})^{12} = a^{48}[/tex]

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The diameter of the semicircle is with an area of 76.97 square yards is 14 yards.

Semicircle is half that of a circle, hence the area will be half that of a circle. Area of semi circle = 1/2 × πr²

Where r radius and π is constant pi.

Since we are given the area of the semicircle as 76.97 square yards, we can set up the following equation:

76.97 = 1/2 × (πr²)

Multiplying both sides by 2, we get:

153.94 = πr²

Dividing both sides by π, we get:

r² = 49

Taking the square root of both sides, we get:

r = 7

Therefore, the diameter of the semicircle is: d = 2r  = 2(7) = 14 yards

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The approximated area of the shaded region is 92.54 square units

From the question, we have the following parameters that can be used in our computation:

The area of the shaded region in the figure is calculated as

Shaded region = Circle - Isosceles right triangle 1 - Isosceles right triangles 2

Using the given dimensions, we have

Shaded region = 3.14 * 6^2 - 1/2 * 5^2 - 1/2 * 4^2

Evaluate

Shaded region = 92.54

Hence, the shaded region is 92.54 square units

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The correct statement is

Option (a) g(x) is the graph of f(x) translated 2 units to the right.

The general rule for translating a graph is as follows:

To translate the graph of y = f(x) horizontally by h units, we replace x with (x - h) in the equation of the function.

This implies the graph moving h units to the right if h is positive, or to the left if h is negative.

To translate the graph of y = f(x) vertically by k units, we add k to the equation of the function, resulting in y = f(x) + k.

This implies the graph is moving k units up if k is positive, or down if k is negative.

Here  we have

The graphs of f(x) = x and g(x) = f(x+2)

=> g(x) = x + 2

We observe that the graph g(x) is formed by adding 2 units to the x coordinate of f(x)

Therefore,

The correct statement is

Option (a) g(x) is the graph of f(x) translated 2 units to the right.

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In the equation 1 over 2 x + y=c, the constant proportionality is defined as c. It displays the line's y-intercept and slope.

If the ratio of one statistic to the other is constant, then there is a proportional relationship between the two variables.

The ratio of y to x is the constant of proportionality if x and y have a proportional connection. At times, we can also say that x is to y.

The proportionality constant, or c, in the equation 1 over 2 x + y = c serves as a gauge for how quickly two variables change. The proportionality constant's value doesn't change when the value of one of the variables does.

A linear equation with two variables, x and y, is 1 over 2x + y = c. In the x-y plane, it symbolises a straight line.

If x = 0

Then,

1/2(0) + y = c

y = c

The proportionality constant, c, can be seen in the equation

1 over 2 x + y = c.

This number, which is unrelated to the actual values of the variables, shows the relationship between the two variables x and y.

The slope of the line connecting the two variables is another name for the constant of proportionality.

Two variables, x and y, are included in the equation 1 over 2 x + y = c in addition to the proportionality constant. The two quantities that

are being compared are represented by these variables.

In the equation 1 over 2 x + y=c, the proportionality constant is defined as c. It displays the line's y-intercept and slope.

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The Complete questions as follows-

Explain what the constant of proportionality means in the equation 1 over 2 x + y = c

Answer: 3/2 or 1 1/2 or 1.5

Step-by-step explanation:

9/8 times 2 is 2.25 or 9/4

9/4-6/8= 3/2 or 1 1/2 or 1.5

The percentage of people between the ages of 21 and 34 who prefer football are: 25%

A random sample is a subset of a larger population that is chosen so that every person or thing has an equal chance of being chosen.

To find the percentage, we need to find the number of people between 21 and 34 who prefer football and divide by the total number of people in that age range:

Number of people between 21 and 34 who prefer football: 9

Total number of people between 21 and 34 are:  36

So the percentage of people between the ages of 21 and 34 who prefer football are:

⇒ (9 / 36) x 100%

⇒ 25%

Rounding to the nearest whole number, the answer is 25%

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Complete figure-

The value or measure of following are :-

x = 17.18°

∠JK = 143.78°

∠MJ = 116.48°

∠LMK = 47.17°

A segment of a circle called an arc is made up of two endpoints on the circle and the curve that connects them.

Since the two lines JL and MK intersect at the center of the circle at point N, the angles formed by them are inscribed angles of the circle. Moreover, the angles formed by an inscribed angle and its corresponding arc are equal. Therefore, we can write:

∠JNK = ½ arc JNK = ½(5x+23)° = 2.5x + 11.5°

∠KNL = ½ arc KNL = ½(17x-41)° = 8.5x - 20.5°

We are also given that arc MNJ and LNK are similar, so their corresponding angles are equal. Similarly, arc MNL and JNK are similar, so their corresponding angles are equal. Let's use these facts to find x:

∠MNJ = ∠LNK

The arc MNJ is equal to the sum of arcs MNL and LNK. Therefore, we have:

½(5x+23)° + ½(17x-41)° = ∠MNJ + ∠LNK

2.5x + 11.5° + 8.5x - 20.5° = 2∠MNJ

11x - 9° = 2∠MNJ

∠MNL = ∠JNK

The arc MNL is equal to the sum of arcs MNJ and JNK. Therefore, we have:

½(5x+23)° + ½(8.5x-20.5°) = ∠MNL + ∠JNK

2.75x + 1.5° = 2∠JNK

1.375x + 0.75° = ∠JNK

Since ∠MNJ = ∠LNK and ∠MNL = ∠JNK, we can write:

2∠MNJ + 2∠JNK = 360°

Substituting the expressions we found for ∠MNJ and ∠JNK, we get:

22x - 18° = 360°

22x = 378°

x = 17.18° (rounded to two decimal places)

Now that we know x, we can find the values of the other angles of arc-

∠JNK = 1.375x + 0.75° = 24.43°

∠KNL = 8.5x - 20.5° = 119.35°

∠MNJ = (11x - 9°)/2 = 92.05°

∠LNK = ∠MNJ = 92.05°

∠MNL = 360° - ∠MNJ - ∠JNK = 243.52°

∠JK = ∠JNK + ∠KNL = 143.78°

∠MJ = ∠MNJ + ∠JNK = 116.48°

∠LMK = 360° - ∠MNJ - ∠JNK - ∠KNL = 47.17°

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Answer:

[tex]\frac{64}{25}[/tex]

Step-by-step explanation:

[tex]\frac{4^{3} }{5^{2} }[/tex]

4³ = 64

5² = 25

[tex]\frac{64}{25}[/tex] is already in simplest form, so it is the answer.

Answer:

The final exam scores in a statistics class were normally distributed with a mean of and a standard deviation of . Find the probability that a randomly selected student scored more than on the exam. The target inside diameter is but records show that the diameters follows a normal distribution with mean and standard deviation .

Step-by-step explanation:

there are 3,360 ways in which the top 3 cars can finish the race.

How to Determine the number of ways?

To determine the number of ways in which the top 3 cars can finish the race, we can use the concept of permutations. A permutation is an arrangement of objects in a specific order. In this case, the order of the cars finishing the race matters.

The number of ways to determine the first place finisher is 16, as any of the 16 cars can finish in first place. Once the first place finisher has been determined, there are only 15 cars remaining, and any one of them can finish in second place. Therefore, there are 15 possible ways to determine the second place finisher.

Similarly, once the first and second place finishers have been determined, there are 14 cars remaining, and any one of them can finish in third place. Therefore, there are 14 possible ways to determine the third place finisher.

To find the total number of ways in which the top 3 cars can finish the race, we can multiply the number of possibilities for each place together:

16 x 15 x 14 = 3,360

Therefore, there are 3,360 ways in which the top 3 cars can finish the race.

It is important to note that this calculation assumes that each car is unique and that there are no ties for any of the top 3 positions. If there were ties, the calculation would become more complicated and would involve combinations as well as permutations.

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