1. What is the diameter of the circle above?
2.
What is the radius of the circle above?

Answer:

226.865 square inches.

Step-by-step explanation:

The equation for the area of a circle is [tex]\pi r^2[/tex]. Let's use 3.14 for pi. The radius can be found by dividing 17/2 = 8.5. 8.5 squared is 72.25. Finally, multiply by pi to get 226.865.

Answer:

Give me time to figure this out hold on

Step-by-step explanation:

12

Answer:

Step-by-step explanation:

a. 100 divided by 75 = 1.3333333333333333333333333333333

1.3333333333333333333333333333333 times 43 = 57.333333333333333333333333333332

round it to the nearest whole number: ≅ 57%

The probability that their two sons will both have hemophilia is 0%.

Hemophilia is a sex-linked recessive disorder, which means that it is passed from mother to son. Since the woman does not have the disorder, she does not carry the gene for it and therefore her sons would not be affected by the disorder.

However, her daughters could be carriers of the disorder and could pass it on to their sons.

In order for a son to be affected by hemophilia, his mother must carry the gene for the disorder and the father must also have the gene. If the father does not have the gene, then the son will not have hemophilia.

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The doubling time of the culture is approximately 42.91 minutes.

The growth rate constant is a mathematical concept that is used to model the growth of a population. It represents the rate at which the population is increasing at any given moment. The doubling time is a measure of how long it takes for a population to double in size, and it can be calculated using the formula mentioned above.

The doubling time of a culture can be calculated using the formula: Doubling time = ln(2) / growth rate constant

Using the given growth rate constant of 0.01615468 min^-1, we can calculate the doubling time as:

Doubling time = ln(2) / 0.01615468 [tex]min^{-1}[/tex]

Doubling time ≈ 42.91 minutes

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The value of x in the given linear equation of 4x = 28 is determined as 7.

To find the value of x in the linear equation 4x = 28, we need to isolate x on one side of the equation.

We can do this by dividing both sides of the equation by 4:

4x/4 = 28/4

Simplifying:

x = 7

Thus, identify the equation and the variable: In this case, the equation is 4x = 28, and the variable we want to solve for is x. Also simplify the linear equation by dividing both sides by 4, we get x = 7, which is the solution.

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The complete question is below:

4x = 28

find the value of x

For the given analogous polygons, in exercise 37 x = 32, y = 18, and in exercise 38, x = 5, y = 166 °.

A polygon is an unrestricted polygonal chain made up of line parts that are connected to produce an area plane figure in figure. The borders or sides of an unrestricted polygonal chain are the individual pieces. The polygon's vertices or corners are the places where two lines meet. A solid polygon's body is its Centre. A polygon is a geometric object with two confines and a limited number of sides. A polygon's sides are made up of pieces of straight lines that are joined end to end. As a result, a polygon's line pieces are appertained to as its sides or edges. Vertex or angles relate to the crossroad of two-line parts, where an angle is created. Having three edges makes a triangle apolygon.What's a commen surable relationship? Proportional connections are connections between two variables where their rates are original. Another way to suppose about them is that, in a commensurable relationship, one variable is always a constant value times the other. That constant is known as the" constant of proportionality".

In the given question.

for exercise 37,[tex]39/(x-6)=27/y=24/1839/(x-6) =24/18=3/2[/tex]

on solving,[tex]3x-18= 78x=3227/y=3/23x=54y=18[/tex]

For exercise 38on comparing,[tex]x=5y-73=360-(61+116+90)y-73=93y=166degree[/tex]

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Answer:

multiply the length of the rectangle by the width of the rectangle.

Step-by-step explanation:

I'm tired for this

Answer:

They are congruent by AA- because the only thing they have in common is the 65 degree angles but the sides are all different

Step-by-step explanation:

The surface area of the rectangular solid with length 5 inches, width 2 inches, and height 4 inches is 76 sq inch. The answer is D.

What is surface area of rectangular solid ?

The surface area of a rectangular solid (also known as a rectangular prism) is the total area of all its faces. It can be calculated using the formula:

SA = 2lw + 2lh + 2wh

where l is the length of the rectangular solid, w is its width, and h is its height.

The rectangular solid has six faces: a top face, a bottom face, a front face, a back face, a left side face, and a right side face. The formula above accounts for the area of each of these faces.

According to the question:
The formula for the surface area of a rectangular solid is:

SA = 2lw + 2lh + 2wh

We are given that the length (l) of the solid is 5 inches, the width (w) is 2 inches, and the height (h) is 4 inches. Substituting these values into the formula, we get:

SA = 2(5)(2) + 2(5)(4) + 2(2)(4)

= 20 + 40 + 16

= 76 square inches

Therefore, the surface area of the rectangular solid with length 5 inches, width 2 inches, and height 4 inches is 76 square inches. The answer is D.

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Answer:

Assuming that g(x) represents the transformed function, the rule for g can be obtained by applying the translation and reflection operations in the correct order.

To translate the graph of f(x) down by 2 units, we need to subtract 2 from the function. This gives us:

h(x) = f(x) - 2 = 5^x - 2

Next, we need to reflect the graph of h(x) in the y-axis. To do this, we replace x with -x in the function. This gives us:

g(x) = h(-x) = 5^(-x) - 2

Therefore, the rule for g(x) that represents a translation 2 units down, followed by a reflection in the y-axis of the graph of

f(x) = 5^x is:g(x) = 5^(-x) - 2

The expected adult height for a toddler who is 34 inches tall at the 30-month checkup is around 5 feet 7 inches.

To determine the expected adult height, one must multiply the current height by 1.08. Since 34 inches x 1.08 is equal to 36.72 inches, the expected adult height is 5 feet 7 inches.

The calculation for adult height is an approximation. Factors such as nutrition, genetics, and gender play a role in final height.

It is important to note that this calculation is just a guide and the actual adult height may differ from the predicted adult height.

To get a more accurate estimation of the expected adult height, it is recommended to have multiple height checks throughout childhood and take into account growth patterns.

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Answer:

The three correct ways to describe an angle with a measure of 13° are:

Thirteen degrees

An acute angle with a measure of 13°

An angle that is less than a right angle and has a measure of 13°

Answer: His car was $415.18 in total

Step-by-step explanation: The calculation of the present value of a cash flow or other income stream that produces $1 in income over so many periods of time.

Amount borrowed = $12,500

Annual interest rate = 12.00%

Monthly interest rate = 1.00%

Period = 36 months

Let monthly payment be x

12,500 = x/1.01 + x/1.01^2 + x/1.01^3  … + x/1.01^35 + x/1.01^36

12,500 = x * (1 - (1/1.01)^36) / 0.01

12,500 = x * 30.107505

x = 12,500/30.107505  

x = 415.18

So, the monthly payment is $415.18

The analysis of the data to obtain the best fit line equations that model the data, indicates;

5. a. Quadratic

b. y = -0.1179·x² + 2.1124·x + 4.215

c. Please find the completed chart showing the predicted values and the  in the residuals in the following section.

6. a. A linear model may not be appropriate for the data in the residual plot

b. 4

c. 5

4. a. The exponential model of the function is; y = 100·e^(-0.124·t)

b. The weight after 8 weeks is about 37.1 grams

c. The sample will be 4 grams in about 26 weeks

5. a. The equation is; y = 22.703·x + 2.5733

b. The predicted y-value at x = 10 is; y = 229.60

c. The first time is about x ≈ 3.54

The best fit line is a line that is drawn through a set of data points in such a way that it minimizes the sum of squared errors of the data.

5. The best fit model can be obtained by plotting a scatter plot of the graph, which indicates that the best fit line resembles the shape of a parabola.

Therefore;

a. The best fit equation is; Quadratic

b. The best fit equation, obtained using technology is; y = -0.1179·x² + 2.1124·x + 4.215

The square of the correlation coefficient is; R² = 0.9584

The chart can be filled with the best fit equation as follows;

[tex]\begin{tabular}{ | c | c | c | c | c | }\cline{1-4}Distance (foot) & Height (foot) & Predicted Value &Residual \\ \cline{1-4}0 & 4 & 4.215 & -0.215 \\\cline{1-4}2 & 8.4 & 8.16588 & 0.23412 \\\cline{1-4}6 & 12.1 & 13.23804 & -1.13804 \\\cline{1-4}9 & 14.2 & 14.56626 & -0.36626\\\cline{1-4}12 & 13.2 & 13.77228 & -0.57228 \\\cline{1-4}13 & 10.5 & 13.03602 & -2.53602 \\\cline{1-4}15 & 9.8 & 10.8561 & -1.0561 \\\cline{1-4}\end{tabular}[/tex]

The predicted value are obtained by plugging in the x-value into the best fit equation and the residuals is the difference between the actual value and the predicted value.

6. a. A residual plot can be used to as assessment with regards to meeting the assumptions of a linear regression model.

A residual plot that is randomly scattered about zero indicates that a linear model is appropriate for the data.

The data points in the residual plot are not expressed as being randomly scattered around zero.

The pattern that exists in the residual plot indicates that the values are positive for x-values that are either low or high, and the middle x-values have a negative residuals. Therefr;

b. The number of positive residuals = 4

c. The number of negative residuals = 5

4. The general form of the exponential model of a function, y = A × e^(-k·t)  can be used to find the function for the data as follows;

A = The initial amount = The value at 0 = 100

y = The amount of radioactive material at a given time t

e = Euler's number = 2.71828

The datapoints in the table indicates;

88.3 = 100 × e^(-k × 1)

k = -㏑(0.883) ≈ 0.124

The exponential model is therefore; y = 100 × e^(-0.124·t)

b. The weight of the sample after 8 weeks can be obtained by plugging in t = 8 in the exponential function for the weight of the radioactive substance as follows;

y = 100 × e^(-0.124 × 8) ≈ 37.1

The weight of the sample after 8 weeks is about 37.1 grams

c. When the sample is 4 grams we get;

y = 4

4 = 100 × e^(-0.124 × t)

e^(-0.124 × t)  = 4/100 = 1/25

-0.124 × t = ln(1/25) = -ln(25)

t = ln(25)/0.124 ≈ 26

t ≈ 26 weeks

Therefore; The weight will be 4 grams after approximately 26 weeks

5. A linear regression can be performed using MS Excel to obtain the equation that models the data as follows;

y = 22.703·x + 2.5733

The square of the regression coefficient is; R² = 0.9995

a. The most appropriate equation to model the data in the table is; y = 22.703·x + 2.5733

b. The y-value when x = 10 can be predicted by plugging in x = 10 into the  model equation for the data as follows;

y = 22.703 * 10 + 2.5733 ≈ 229.60

Therefore;

c. The first time the y-value is 83, can be found by setting y = 83 in the equation and solve for x as follows;

83 = 22.703·x + 2.5733

22.703·x = (83 - 2.5733)

x = (83 - 2.5733)/22.703 ≈ 3.54

Therefore, the first time the y-value is 83 is when x is approximately 3.54

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Answer:

To calculate a percentage decrease, first, work out the difference (decrease) between the two numbers you are comparing. Next, divide the decrease by the original number and multiply the answer by 100. The result expresses the change as a percentage—i.e., the percentage change.

The best approximation of the volume of a cylinder with a radius of 10 mm, and a height of 5 mm using 3.14 for pi is 1,570 cubic millimeters.

The formula for calculating the volume of a cylinder is as follows:

V = πr²h

Where V is the volume, r is the radius of the cylinder, and h is the height of the cylinder.

Substituting the values given in the formula, we have :

V = πr²hV = 3.14 × (10 mm)² × (5 mm)V = 3.14 × 100 mm² × 5 mm

V = 1,570 cubic millimeters.

Therefore, the best approximation of the volume of a cylinder with a radius of 10 mm, and a height of 5 mm using 3.14 for pi is 1,570 cubic millimeters.

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we can estimate that about 440 patients in the medical office are in the age range 13-21.  The experimental probability of finding a patient in the age range 13-21 is 40%, which means that for every 10 patients in the medical office, 4 are in the age range 13-21.

To estimate how many patients are in the age range 13-21, we can use the proportion of the sample in the age range 13-21 and apply it to the entire population. In this case, we can use the proportion of patients in the age range 13-21 in the sample to estimate the number of patients in the age range 13-21 in the population.

The sample size is not given in the problem, but we are told that there are 1,100 patients in the medical office. Let's assume that the sample size is large enough to make a reasonable estimate.

So, if 40% of the sample is in the age range 13-21, then we can estimate that about 40% of the total population of 1,100 patients are also in the age range 13-21.

To calculate this, we can use the following formula:

estimated number of patients in the age range 13-21 = proportion in sample x total population

= 0.40 x 1,100

= 440

Therefore, we can estimate that about 440 patients in the medical office are in the age range 13-21.

It's important to note that this is just an estimate based on the experimental probability from the sample. The actual number of patients in the age range 13-21 may vary from this estimate due to sampling error or other factors. However, this estimate can still provide a useful approximation for planning and decision-making purposes.

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The amount of work (in foot-pounds) done in stretching a spring from its natural length to 0.8 feet beyond its natural length is 24.

so we have W=6lbs*(0.8ft-0.6ft)

=6lbs*0.2ft

=24ft-lbs.

Work is the measure of the amount of energy required to move an object over a certain distance, so to stretch the spring 0.8 feet beyond its natural length, 24 foot-pounds of work is done.

This can also be understood as the product of the force (6lbs) and the displacement (0.2ft). Work is a scalar quantity, meaning it only has magnitude and not direction.

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In circle , arc length is  18.84 ft and sector area = 75.36 ft .

What is arc?

In mathematics, an arc is referred to as a section of a circle's or curve's perimeter. The term "open curve" can also be used to describe it. The circumference, also known as the perimeter, is the measurement around a circle that defines its edge.

Length of an arc = Angle/360 * pi * diameter

                      =  135/360 * 3.14 * 16

                      = 18.84 ft

sector area = Angle/360 * π * r²

                    = 135/360 * 3.14 * 8 * 8

                   = 75.36 ft

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The evaluations of the composite functions expressions and operations are presented as follows;

1. (f + g)(x) = 2·x² + 7·x + 3

(f - g)(x) = 7·x + 21

(f · g)(x) = x⁴ + 7·x³ + 3·x² - 63·x - 108

(f/g)(x) = f(x)/g(x) = (x² + 7·x + 12)/(x² - 9)

2. (f + x)(x) = 3·x - 2

(f - g)(x) = x + 4

(f · g)(x) = f(x) × g(x) = (2·x + 1) × (x - 3) = x⁴ + 7·x³ + 3·x² - 63·x - 108

(f/g)(x) = (2·x + 1)/(x - 3)

3. f[h(-9)] = 25

4. h[f(4)] = 20

5. g[h(-2)] = 10

6. The composite function that converts inches into miles is; n/63360

Composite function is a function that is applied to the result of another function.

Part 1: Operations of Functions

1. f(x) = x² + 7·x + 12 and g(x) = x² - 9, therefore;

(f + g)(x) = f(x) + g(x) = (x² + 7·x + 12) + (x² - 9) = 2·x² + 7·x + 3

(f - g)(x) = f(x) - g(x) = (x² + 7·x + 12) - (x² - 9) = 7·x + 21

(f · g)(x) = f(x) × g(x) = (x² + 7·x + 12) × (x² - 9) = x⁴ + 7·x³ + 3·x² - 63·x - 108

(f/g)(x) = f(x)/(g(x)) = (x² + 7·x + 12)/(x² - 9)

2. f(x) = 2·x + 1 and g(x) = x - 3

(f + g)(x) = f(x) + g(x) = 2·x + 1 + (x - 3) = 3·x - 2

(f - g)(x) = f(x) - g(x) = 2·x + 1 - (x - 3) = x + 4

(f · g)(x) = f(x) × g(x) = (2·x + 1)·(x - 3) = 2·x² - x - 3

(f/g)(x) = f(x)/(g(x)) = (2·x + 1)/(x - 3)

Part 2; 3. f(x) = x², g(x) = 5·x, and h(x) = x + 4

f[h(-9)] = (h(-9))² = (-9 + 4)² = 25

4. f(x) = x², g(x) = 5·x, and h(x) = x + 4

h[f(4)] = (f(4) + 4) = (16 + 4) = 20

5. f(x) = x², g(x) = 5·x, and h(x) = x + 4

g[h(-2)] = (h(-2) × 5) = (-2 + 4) × 5 = 10

6. The formula F = n/12 converts n inches into feet f, and m = f/5280 converts feet to miles m.

Let F(N) represent the function that converts inches to feet and let G(F) represent the function that converts feet to miles. Then the composition function that converts inches to miles is G(F(N))

G(F(N)) = G(n/12) = (n/12)×(1/5280) = n/63360

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As the two triangles are congruent by AAS congruence rule, the segments AB is equivalent to FG.

If two triangles are the same size and shape, they are said to be congruent.

To establish that two triangles are congruent, not all six matching elements of either triangle must be located.There are five requirements for two triangles to be congruent, according to studies and trials.

The congruence properties are SSS, SAS, ASA, AAS, and RHS.

Now in the given figure,

D is the midpoint, so CE = BG.

∠ABC ≅ ∠FGE

That gives us, AB ≈ FG as sides corresponding to equivalent sides are also equivalent to each other.

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The values of the expression when using the completing the square method is given below

To complete the square for x²-16x+c, we need to add and subtract the square of half the coefficient of x, which is (-16/2)² = 64. So:

x² - 16x + c = (x - 8)² - 64 + c

To complete the square, we added (-16/2)² = 64, but we subtracted it again to keep the expression equivalent. Therefore, c - 64 is the value that completes the square.

Similarly, for x² + 7x + c, we add and subtract (7/2)² = 49/4:

x² + 7x + c = (x + 7/2)² - 49/4 + c

So c - 49/4 completes the square.

For x²- 9x, we add and subtract (9/2)² = 81/4:

x² - 9x = (x - 9/2)² - 81/4

Therefore, c - 81/4 completes the square.

To factor x²- 14x, we can factor out x:

x² - 14x = x(x - 14)

To factor x² + 30x, we can factor out x:

x² + 30x = x(x + 30)

To factor x²- 9x, we can factor out x:

x² - 9x = x(x - 9)

To solve x² + 10x = 16 by completing the square, we first add and subtract (10/2)² = 25:

x² + 10x + 25 - 25 = 16

(x + 5)² = 41

x + 5 = ±√41

x = -5 ±√41

To solve x² - 3x = 7 by completing the square, we first add and subtract (3/2)² = 9/4:

x² - 3x + 9/4 - 9/4 = 7

(x - 3/2)² = 37/4

x - 3/2 = ±√(37/4)

x = 3/2 ±√(37/4)

To solve x² + 15x = 12 by completing the square, we first add and subtract (15/2)² = 225/4:

x² + 15x + 225/4 - 225/4 = 12

(x + 15/2)² = 129/4

x + 15/2 = ±√(129/4)

x = -15/2 ±√(129/4)

a. Let L be the length of the wading pool. Then its width is L - 12. The height is 1 foot, so the volume is:

V = L(L - 12)(1) = L² - 12L

b. To complete the square for the expression L² - 12L, we add and subtract (12/2)² = 36:

L² - 12L + 36 - 36 = (L - 6)² - 36

So the volume can be written as:

V = (L - 6)² - 36

To find the dimensions of the wading pool that give a volume of 108 cubic feet, we set V = 108 and solve for L:

(L - 6)² - 36

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Answer:

We know that 1 yard is equal to 3 feet. Therefore, 7 yards is equal to:

7 yards = 7 × 3 feet = 21 feet

So, 7 yards is greater than 20 feet.

To complete the table to model the answer, we can write:

Quantity Value

20 feet 20 ft

7 yards 21 ft

Comparing the values, we can see that 7 yards is greater than 20 feet.

An effective visual representation of a function or a mapping between two sets is a mapping diagram. It consists of two vertical columns, one of which represents the domain set items and the other of which represents the range set elements. The items in the range set that match to those in the domain set are listed in the right column, and vice versa.

I assume you are given a mapping rule that relates elements in a set to other elements in another set, and you are asked to complete a mapping diagram based on this rule.

If the mapping rule is not specified, we cannot determine the values of a and b. However, assuming that the mapping rule is such that each element (x, y) in the set R is mapped to [tex](x + a, y + b)[/tex], we can complete the mapping diagram as follows:

The given set R is:

R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)}

If we apply the mapping rule to each element in R, we get:

(-3, -2) → (-3 + a, -2 + b)

(-3, 0) → (-3 + a, 0 + b)

(-1, 2) → (-1 + a, 2 + b)

(1, 2) → (1 + a, 2 + b)

To complete the mapping diagram, we need to find the values of a and b such that each mapped element is in the set R. That is, we need to find a and b such that:

(-3 + a, -2 + b) ∈ R

(-3 + a, 0 + b) ∈ R

(-1 + a, 2 + b) ∈ R

(1 + a, 2 + b) ∈ R

Substituting the values of R into each of these equations, we get:

(-3 + a, -2 + b) = (-3, -2), which gives a = 0 and b = 0

(-3 + a, 0 + b) = (-3, 0), which gives a = 0 and b = 0

(-1 + a, 2 + b) = (-1, 2), which gives a = 0 and b = 0

(1 + a, 2 + b) = (1, 2), which gives a = 0 and b = 0

Therefore, the values of a and b that complete the mapping diagram are a = 0 and b = 0.

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Answer:

True

False

72

72

96

30

See below.

Step-by-step explanation:

First statement: True

A unit cube is a cube with an edge length of 1 unit.

Its volume is (1 unit)³ = 1 unit³

Second Statement: False

A unit cube cannot be used to measure the volume of "other 2D shapes" since a 2D shape has no volume. Only a 3D shape can have a volume. The word "other" is also used incorrectly.

Problems:

9 × 2 × 4 = 72; 72 cubic units

6 × 3 × 4 = 72; 72 cubic units

Length = 4; Width = 4; Height = 6

4 × 4 × 6 = 96; 96 cubic units

Length = 3; Width = 5; Height = 2

3 × 5 × 2 = 30; 30 cubic units

Promotion 50√2 (or about 70.7) coupons need to be sent in order to get 100 customers to make a purchase.

The given problem states that around 80% of customers who receive a promotion coupon will visit the store. But only 20% of those in the store will make a purchase.

The problem asks us to determine how many promotion coupons have to be sent in order to get 100 customers to make a purchase.

Therefore, let the number of coupons to be sent be x.

Then, 80% of x people will visit the store. Therefore, the number of people who will visit the store is

(80/100)x or (4/5)x people.

However, only 20% of those in the store will make a purchase.

Therefore, the number of customers who make a purchase is (20/100) x (4/5)x = (1/25)x² customers.

We need to find x such that (1/25)x² = 100.

Therefore, x² = 25 × 100. Hence, x = √2500 or x = 50√2.

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Odd coefficients of the polynomial are obtained by multiplying both odd integers.

Even coefficients of the polynomial are obtained by multiplying both even integers.

Even and odd coefficients of the polynomial are obtained by multiplying both odd integers.

Lets take two integer m and n,

If both 'm' and 'n' are odd integers, then the coefficients of the polynomial obtained by multiplying out will be odd.

If both 'm' and 'n' are even integers, then the coefficients of the polynomial obtained by multiplying out will be even.

If one of 'm' and 'n' is even and the other is odd, then the coefficients of the polynomial obtained by multiplying out will be even and odd.

There are no other cases.

The general form of the polynomial obtained by multiplying out a binomial is:

[tex](a+b)^n = nC_0a^n + nC_1a^{(n-1)}b + nC_2a^{(n-2)}b^2 + .....+ nC_n-1ab^{(n-1)} + nC_nb^n[/tex]

where [tex]nC_k[/tex] is a binomial coefficient.

In general, for a polynomial [tex](a+b)^n[/tex], the coefficient of the term of degree k is [tex]nC_k[/tex].

The binomial coefficients are defined as:  [tex]nC_k = n! / (k!\times(n-k)!)[/tex]

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Answer:

slope of 3/4 = line C

undefined slope = line A

Step-by-step explanation:

remember that slope is [tex]\frac{rise}{run}[/tex]. Pick any two points on the graph and count up and over to find the rise/run.

OR

use the slope formula [tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex] to plug the two points into and find the slope.

- vertical lines are always undefined.

- horizontal lines have a slope of 0

Yes, we can say the shape of the sampling distribution for the sample mean if we know the population distribution.

However, if we do not know the population distribution, we cannot determine the exact shape of the sampling distribution for the sample mean. In this case, we can make use of the Central Limit Theorem (CLT) to make some assumptions about the shape of the sampling distribution. According to CLT, as the sample size increases, the sampling distribution of the sample mean becomes approximately normal, regardless of the shape of the population distribution, provided that the sample size is sufficiently large. Therefore, if the sample size is 19 and the population distribution is unknown, we can assume that the sampling distribution of the sample mean is approximately normal if the sample data is not heavily skewed or contains extreme outliers.

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