This year, the student council president has decided to raise funds for the school prom by selling Justin Bieber T-shirts. In the past, they’ve sold an average of 1500 shirts at about $12 each. This year, they plan to decrease the price of the shirts. Based on student feedback, for every $0.50 decrease in price, 20 more T-shirts will be sold.
a) Determine the demand (price) function in terms of x , the number of t-shirts sold
b) Determine the marginal revenue function. Then, determine the marginal revenue from the sales of 1800 T-shirts and interpret its meaning.

The transformation of the points and shapes after being transformed are calculated below

The coordinates of B in the figure is

B = (5, 1)

A translation of (x-4, y-3) means

B' = (5 - 4, 1 - 3)

B' = (1, -2)

Here, we have the following corresponding points

Pre = (2, 1)

Image = (-1, 2)

This represents

(x, y) = (-y, x)

This represents (d) 270° clockwise rotation

Given that the smaller figure is gotten from a bigger figure

Then the dilation is a reduction and the scale factor could be 1/2 or 1/4

We have

P = (3, -2) and S = (4, -5)

For the first transformation, we have

(x - 2, y)

P' = (1, -2) and S' = (2, -5)

For the second, we have

P'' = (1, 2) and S'' = (2, 5)

Here, we have

A = (-2, -5)

This means that the new ordered pair of point A is

A' = (-2, -5) * 1/2

A' = (-1, -2.5)

Hence, the new ordered pair of point A is (-1, -2.5)

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Answer:

Below

Step-by-step explanation:

12 000 * r = 9600

r = 9600  / 12000 = .8  

 So multiply each term by .8 to get the next term:

year 1     12 000

year 2    12 000 * .8

year 3    12 000 * .8  * .8

Year 4   12 000 * .8 * .8  * .8    = 12 000 * .8^3

.

.

year 7  12 000 * (.8)^6 = $ 3145.73

an = a1 r^(n-1)

an = 12 000 (.8)^n-1

The surface area of the cylindrical tube is approximately 240.21 square inches.

What formula do we use to find the surface area of a cylinder?

The surface area of a cylinder is the sum of the areas of all its surfaces, including the curved surface area and the area of its two circular bases. It is a measure of the total area that the cylinder covers.

To find the surface area of a cylinder, we use the formula

[tex]A = 2\pi rh + 2\pi r^2[/tex]

where r is the radius of the base, h is the height of the cylinder, and π is a constant equal to approximately 3.14.

Calculating the surface area of the cylindrical tube -

The base of the tube has a diameter of 3 inches, which means the radius is 1.5 inches. The length of the poster is given as 24 inches, so we will assume that the height of the cylindrical tube is also 24 inches.

Substituting the values we have into the formula, we get:

[tex]A = 2\pi (1.5)(24) + 2\pi (1.5)^2[/tex]

[tex]A = 2\pi (36) + 2\pi (2.25)[/tex]

[tex]A = 72\pi + 4.5\pi[/tex]

[tex]A = 76.5\pi[/tex]

Using the approximation of [tex]\pi = 3.14[/tex], we get:

[tex]A[/tex]≈[tex]240.21[/tex] square inches .

Therefore, the surface area of the cylindrical tube is approximately 240.21 square inches.

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This is due tο the fact that as x grοws, the quadratic cοmpοnent in g(x) and f(x), respectively, predοminates οver the cοnstant term and the linear term.

A functiοn is a mathematical fοrmula that relates every element in οne set, knοwn as the dοmain, tο a single element in anοther set, knοwn as the range. The relatiοnship between input and οutput, the relatiοnship between a variable and its rate οf change, and many οther real-wοrld phenοmena are all examples οf this basic mathematical idea. Algebraic expressiοns, graphs, tables, and even wοrds can be used tο describe functiοns. They are a crucial instrument in many disciplines, including cοmputer science, statistics, and calculus.

given:

Fοr rising values οf x, the fοllοwing functiοn exhibits the fastest grοwth:

h(x) = 6x² + 1.

This is due tο the fact that as x grοws, the quadratic cοmpοnent in g(x) and f(x), respectively, predοminates οver the cοnstant term and the linear term. As a result, οf the functiοns listed, h(x) grοws at the fastest pace.

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The equation of the line through the points (-3,7) and (2, 17) is y = 2x + 13.

To find the equation of the line through the points (-3,7) and (2, 17), we need to first find the slope of the line and then find the y-intercept.

Step 1: Find the slope of the line
The slope of a line is given by the formula:
m = (y2 - y1)/(x2 - x1)
Where (x1, y1) and (x2, y2) are the two points on the line.

Plugging in the given points, we get:
m = (17 - 7)/(2 - (-3))
m = 10/5
m = 2

Step 2: Find the y-intercept
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. We can plug in one of the given points and the slope we found to solve for b.

Using the point (-3,7), we get:
7 = 2(-3) + b
7 = -6 + b
b = 13

Step 3: Write the equation in slope-intercept form
Now that we have the slope and y-intercept, we can write the equation of the line in slope-intercept form:
y = 2x + 13

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Answer:

[tex]\dfrac{\text{d}y}{\text{d}x}=4x-1[/tex]

Step-by-step explanation:

Differentiating from First Principles is a technique to find an algebraic expression for the gradient at a particular point on the curve.

[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Differentiating from First Principles}\\\\\\$\text{f}\:'(x)=\displaystyle \lim_{h \to 0} \left[\dfrac{\text{f}(x+h)-\text{f}(x)}{(x+h)-x}\right]$\\\\\end{minipage}}[/tex]

The point (x + h, f(x + h)) is a small distance along the curve from (x, f(x)).

As h gets smaller, the distance between the two points gets smaller.

The closer the points, the closer the line joining them will be to the tangent line.

To differentiate y = 2x² - x + 3 using first principles, substitute f(x + h) and f(x) into the formula:

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{2(x+h)^2-(x+h)+3-(2x^2-x+3)}{(x+h)-x}\right][/tex]

Simplify the numerator:

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{2x^2+4xh+2h^2-x-h+3-2x^2+x-3)}{x+h-x}\right][/tex]

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{2x^2-2x^2+x-x+3-3+4xh+2h^2-h)}{h}\right][/tex]

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{4xh+2h^2-h)}{h}\right][/tex]

Separate into three fractions:

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{4xh}{h}+\dfrac{2h^2}{h}-\dfrac{h}{h}\right][/tex]

Cancel the common factor, h:

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[4x+2h-1\right][/tex]

As h → 0, the second term → 0:

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=4x-1[/tex]

A-1 = (A - 2I)-1(A2 + 2A + 4I)-1.

6. To show that T:R2→R2 defined by T([x y]) = [x y 0] is not a linear transformation, consider T(u+v) = T([u1 + v1, u2 + v2]) = [u1 + v1, u2 + v2, 0]. Since T(u+v) is not equal to T(u) + T(v), which is [u1, u2, 0] + [v1, v2, 0] = [u1 + v1, u2 + v2, 0], then T is not a linear transformation.

7. Assume A is a square matrix that satisfies A3 - 3A + 2I = 0. This equation can be written as (A - 2I)(A2 + 2A + 4I) = 0. Since A - 2I is non-zero and A2 + 2A + 4I is non-zero, then A - 2I and A2 + 2A + 4I are both invertible and therefore A is invertible. Since A is invertible, A-1 = (A - 2I)-1(A2 + 2A + 4I)-1.

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The given polynomial is P(x) = x^3 + 5x^2 - 6x + 6. The given c is 3. To use the Remainder Theorem, we must divide P(x) by (x - c). The result of this division will be a quotient and a remainder. The remainder is the value of the polynomial when x = c, so in this case when x = 3, the remainder is 45.

This is because when x = 3, P(x) = 45. Therefore, according to the Remainder Theorem, the remainder when we divide P(x) by (x - 3) is 45. This means that when we divide P(x) by (x - 3), the remainder is 45. Thus, the Remainder Theorem can be used to determine the remainder when we divide a polynomial P(x) by (x - c), where c is some given constant.

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The value in the red box would be 19√7.

An algebraic expression is a made up of terms both constants and variables. For example, we can write -

2x + 3y + z

5x + y

x + 8y

Given is a pyramid as shown in the image.

We can write -

b{4} = 2√7 - 4√7 = - 2√7

b{4} = - 2√7

- 4√7 + b{9} = 3√28

b{9} = 3√28 + 4√7

b{9} = 6√7 + 4√7

b{9} = 10√7

b{6} = 10√7 - √7

b{6} = 9√7

b{2} =  - 2√7 + 6√7

b{2} = 4√7

b{3} = 3√28 + 9√7

b{3} = 6√7 + 9√7

b{3} = 15√7

b{1} = 4√7 + 15√7

b{1} = 19√7

Therefore, the value in the red box would be 19√7.

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{QUESTION IN ENGLISH -

Look at the following pyramid, in which each box has a number that is formed by adding the two bottom boxes.

What is the number that occupies the red box?}

Answer:

3m-4

Step-by-step explanation:

marcie's age be x

her father age is four less than three times

the equation tht describes her father age is 3m-4=40

The exact value of Sin^-1 (cos π) can be found without using a calculator by using the properties of the unit circle and the trigonometric functions.

First, we need to find the value of cos π. On the unit circle, the point (1,0) corresponds to an angle of 0 radians or 0°. The point (-1,0) corresponds to an angle of π radians or 180°. Therefore, cos π = -1.

Next, we need to find the inverse sine of -1. The inverse sine function, Sin^-1, is the inverse of the sine function. This means that Sin^-1(sin x) = x. Therefore, we need to find an angle x such that sin x = -1.

On the unit circle, the point (0,-1) corresponds to an angle of 3π/2 radians or 270°. Therefore, sin 3π/2 = -1. This means that Sin^-1(-1) = 3π/2.

Therefore, the exact value of Sin^-1 (cos π) is 3π/2.

Answer: 3π/2.

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1- This is a rotation matrix because the determinant is 1 and the transpose is equal to the inverse. 2- The line passing through the origin and the point (1, 1, 1) is the axis of rotation. 3- 120° is the angle of rotation.

1. To show that this is a rotation matrix, we need to check that the matrix satisfies the following properties:
- The determinant of the matrix is 1.
- The transpose of the matrix is equal to its inverse.
The matrix that transforms a vector (x1, x2, x3) into (x2, x3, x1) is:
| 0  1  0 |
| 0  0  1 |
| 1  0  0 |
The determinant of this matrix is:
det = 0×0×0 + 1×1×1 + 0×0×0 - 0×0×1 - 1×0×0 - 0×1×0 = 1
The transpose of this matrix is:
| 0  0  1 |
| 1  0  0 |
| 0  1  0 |
The inverse of this matrix is:
| 0  0  1 |
| 1  0  0 |
| 0  1  0 |
Since the determinant is 1 and the transpose is equal to the inverse, this is a rotation matrix.

2. To find the axis of rotation, we need to find the eigenvector of the matrix corresponding to the eigenvalue of 1. The characteristic equation of the matrix is:
| -λ  1  0 |
| 0  -λ  1 |
| 1  0  -λ | = 0
Expanding the determinant, we get:
-λ × (-λ × (-λ)) - 1 × 1 x 1 = 0
λ = 1
The eigenvector corresponding to the eigenvalue of 1 is:
| -1  1  0 | | x1 | = | 0 |
| 0  -1  1 | | x2 |   | 0 |
| 1  0  -1 | | x3 |   | 0 |
Solving this system of equations, we get:
x1 = x2 = x3
So the eigenvector is:
| 1 |
| 1 |
| 1 |
This means that the axis of rotation is the line passing through the origin and the point (1, 1, 1).

3. To find the angle of rotation, we can use the formula:
cosθ = (trA - 1)/2
Where trA is the trace of the matrix A. The trace of the matrix is:
trA = 0 + 0 + 0 = 0
So the angle of rotation is:
cosθ = (0 - 1)/2 = -1/2
θ = 120°
Therefore, the angle of rotation is 120°.

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Answer:

1.4

Step-by-step explanation:

If 6/p =15/3.5

You can cross multiply the equation

6x3.5 =15P

21=15P

Divide both sides by 15

21/15 = P

1.4 =P

From the system of equations one apple pie costs $6 and one lemon meringue pie costs $7.

A group of equations that need to be solved concurrently is referred to as a system of equations. The values of the variables that satisfy each and every one of the system's equations are the solutions to the corresponding equations. Systems of equations can be solved using a variety of techniques, such as substitution, elimination, and graphing. Systems of equations can be used to simulate situations in business, science, and engineering when there are several variables at play. Systems of differential equations, linear equations, and quadratic equations are a few examples of systems of equations.

Let us suppose the cost of the apple pie = x.

Let us suppose the cost of the meringue pie = y.

Given that, Dan sold 14 apple pies and 9 lemon meringue pies for a total of $147.

14x + 9y = 147

For Jenny:

8x + 12y = 132

Using the elimination method we have:

Multiplying Dan's equation by 4 gives:

56x + 36y = 588

Multiplying Jenny's equation by 3 gives:

24x + 36y = 396

Subtracting the second equation from the first:

32x = 192

x = 6

Substitute the value of x in equation:

14(6) + 9y = 147

84 + 9y = 147

9y = 63

y = 7

Hence, from the system of equations one apple pie costs $6 and one lemon meringue pie costs $7.

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Answer:

24

Step-by-step explanation:

The sum of the three angles in a triangle is always 180 degrees.

Let x be the measure of the third angle.

Then we have:

102 + 54 + x = 180

Simplifying the left side:

156 + x = 180

Subtracting 156 from both sides:

x = 180 - 156

x = 24

Therefore, the measure of the third angle is 24 degrees.

Answer: you can see herhere

Step-by-step explanation:

try times like x=1 and find the answer true

Given,

f(x) = -2x + 4

g(x) = -6x - 7

To find,

The value of f(x) - g(x)

Solution,

The value of f(x) - g(x) is 4x + 11.

We can simply solve the given mathematical problem by the following process.

We know that,

f(x) = -2x + 4

g(x) = -6x - 7

Now,

f(x) - g(x) = (-2x+4) - (-6x-7)

             = -2x - 4 + 6x + 7

             = 4x + 11

Thus, the value of f(x) - g(x) is 4x+11.

Step-by-step explanation:

in the part a take the f(x) as the normal equation but in the place of x put the equation of g , its as g is now x .

in part b its the exact same only that instead of the x in equation of g(x) the gave you a number to plug into the x

The equivalent equations are given as follows:

Equivalent equations are equations that have the same result when they are solved.

The first equation is solved as follows:

2 + x = 5

x = 5 - 2

x = 3.

The second equation is solved as follows:

x + 1 = 4

x = 4 - 1

x = 3.

Hence it is equivalent to the first, as both have the same result of x = 3.

The third equation is solved as follows:

9 + x = 6

x = 6 - 9

x = -3.

The fourth equation is solved as follows:

x - 4 = 7

x = 7 + 4

x = 11.

The fifth equation is solved as follows:

-5 + x = -2

x = -2 + 5

x = 3.

Which is equivalent to the first and to the second equation.

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Answer:

Let x be the number of additional miles Tammy needs to run this week to reach her goal of at least 10 miles per week.

To determine the inequality, we can start with the given information and use the inequality symbol for "greater than or equal to" (≥):

4.5 + x ≥ 10

This inequality states that the sum of the distance Tammy has already run this week (4.5 miles) and the additional distance she still needs to run (x miles) must be greater than or equal to 10 miles in total for her to reach her goal.

To solve for x, we can start by subtracting 4.5 from both sides of the inequality:

x ≥ 10 - 4.5

Simplifying, we get:

x ≥ 5.5

Therefore, Tammy must run at least 5.5 more miles this week to reach her goal of at least 10 miles per week.

Step-by-step explanation:

wag na mag delete pls lng ang bob0 nyo namn pag na delete nyo toh mga admin

Elevation = 0 - 1050 × Time or Elevation = -1050t, where Elevation is in feet and Time is in hours, is the expression that describes the connection between the submarine's elevation and time.

Seconds, mins max, minutes, days, periods, months, and years are the fundamental elements of time. To determine the time of day, we use secs, minutes, as well as hours; to determine the date, we use times, months, and years. The lesser measures of time are seconds, minutes, and hours, while the larger ones are days, months, and years.

Assuming that the submarine is descending at a constant rate, we can use the equation:

Elevation = Initial Elevation - Rate × Time

where Initial Elevation is the starting elevation (in this case, the surface), Rate is the rate of descent, Time is the time elapsed, and Elevation is the current elevation.

In this case, the Initial Elevation is 0 feet (the surface), the Rate is -1050 feet per hour (since the submarine is descending at a rate of 1050 feet per hour), and Time is the elapsed time in hours.

Therefore, the equation that represents the relationship between the submarine's elevation and time is:

Elevation = 0 - 1050 × Time

or

Elevation = -1050t

where Elevation is in feet and Time is in hours.

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2x^2 + 7x + 3 factors into (2x + 1)(x + 3).

What is factoring?

The factoring approach can be used if the quadratic polynomial can be divided into two linear factors:

Look for two numbers that add up to b and multiply to c.

With these numbers, rewrite the quadratic polynomial as the sum of two terms.

Choose the term that has the most in common with each group of terms.

Remove the common binomial factor between the two groups.

Take the quadratic polynomial 2x2 + 7x + 3, for instance. We must choose two values that sum up to seven and multiply by three in order to factor this polynomial. These are the numbers 3 and 1. The quadratic can then be rewritten as follows:

2x² + 3x + 4x + 3

Then, for each collection of terms, we factor out the term with the highest common factor:

x(2x + 3) + 1(4x + 3)

Lastly, we remove the common binomial factor between the two groups:

(2x + 1)(x + 3)

As a result, 2x2 + 7x + 3 equals (2x + 1)(x + 3).

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The amount that Beth borrowed at the annual interets of 30% is found to be  £4880.

We can use the relation to find the original borrowed which is,

original amount x (1 + interest rate)² = total amount to be paid

The interest in annual so the value of interest of the loan that Beth took is 30% and the amount to be paid is £8112. Let x be the borrowed amount,

Now, putting all the values in the relation above-mentioned,

Based on the given conditions, formulate:

x+(1+30%)² = 8112

x(1.3)² = 8112

Divide both sides of the equation by the coefficient of variable,

x = 8112/(1.30)²

Calculated value of x = 4800

The original amount that Beth borrowed is £4880.

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The point estimate for p(cap) and q(cap) as per defined condition of mainstream media is equal to 0.700 and 0.300 respectively.

Total number of adults in the country = 4393

Number of adults think mainstream media is more interested in making money = 3074

The point estimate for p, denoted as p(cap),

p(cap) represents proportion of individuals in the sample.

Individual who think mainstream media is more interested in making money than in telling the truth.

This implies,

p(cap)

= 3074/4393

≈ 0.700

The point estimate for q, denoted as q(cap), is the proportion of individuals in the sample.

Individuals who do not think mainstream media is more interested in making money than in telling the truth.

This implies,

q(cap)

= 1 - p(cap)

= 1 - 0.700

≈ 0.300

Therefore, the point estimate for p(cap) is approximately 0.700 and the point estimate for q(cap) is approximately 0.300.

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The above question is incomplete, the complete question is:

Let p be the population proportion for the following condition. Find the point estimates for p and q.

A study of 4393 adults from country A, 3074 think mainstream media is more interested in making money than in telling the truth.

The point estimate for p, p(cap), is (Round to three decimal places as needed.)

The point estimate for q, q(cap), is (Round to three decimal places as needed.)

P therefοre has a value οf 45/2 and x = -0.4.

A mathematical assertiοn that twο expressiοns are equivalent is knοwn as an equatiοn. It frequently includes οne οr mοre variables, which are unknοwable things with a wide range οf pοssible values. Finding the value οr values οf the variable that make the equatiοn true is the aim οf equatiοn sοlving. Mοst equatiοns take the fοrm: expressiοn is alsο expressiοn. Fοr instance, the fοrmula x + 2 = 5 states that the prοduct οf x and 2 is 5.

given

If the answer tο the equatiοn px² + 16x + 4 = 0 is x=-2/3, we can be cοnfident that we will οbtain an equivalence if we replace x = -2/3 in the fοrmula.

Adding x=-2/3 tο the sοlutiοn results in:

p(-2/3)² + 16(-2/3) + 4 = 0

Simplifying the phrase:

(4/9)p - (32/3) + 4 = 0

(4/9)p = (32/3) - 4

(4/9)p = (20/3)

By adding (9/4) tο bοth ends, we get:

p = (20/3) * (9/4)

p = 15

P therefοre has a value οf 45/2.

For x,

15x² + 16x + 4 = 0

3x(5x + 2) + 2(5x + 2)

(3x + 2)(5x + 2)

x = -2/3 and x = -0.4

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The minimum payment would be $23.70 if we only used the 15% rule.

Minimum payment refers to the smallest amount of money that a borrower or a credit card holder must pay towards their outstanding balance each billing cycle in order to avoid late fees. This minimum payment is usually a percentage of the total balance due or a fixed dollar amount whichever is greater.

The minimum payment is either 15% of the new balance or $25, whichever is greater.

If the new balance is $158, we can first find 15% of the new balance:

15% of $158 = 0.15 * $158 = $23.70

So, the minimum payment would be $23.70 if we only used the 15% rule.

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(a) For a line, the ratio of the change in y to the change in x is called the slope of the line.
(b) The point-slope form of the equation of a line with slope m passing through (x1, y1) is y - y1 = m(x - x1).

The slope of a line is a measure of its steepness and is calculated by finding the ratio of the change in y (the rise) to the change in x (the run) between two points on the line.

The point-slope form of the equation of a line is a way to write the equation of a line when you know its slope and one point on the line. It is written as y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is the point on the line.

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Answer:

a) The data would be discrete because it can only take on a finite number of values.

The teacher used a scale of integers from 0 to 10, which means that the data can only take on one of those 11 values. Continuous data, on the other hand, can take on an infinite number of values within a given range.

b) The data would be ordinal data because it can be ordered or ranked.

The scale of integers from 0 to 10 represents a ranking of how much homework was completed, with 0 being the lowest and 10 being the highest. Nominal data, on the other hand, cannot be ordered or ranked and is used to classify or categorize things.

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The answer of the question based on the probability  that The spinner shows has 4 equal sized sections. Jackson spins the spinner 32 times the answer is 8 times.

A event is any outcome or the set of outcomes of experiment or random process.

An event can be as like as a single outcome or as complex as a combination of the outcomes. For example, flipping a coin and getting heads is an event, as is rolling a die and getting a 6.

The spinner has 4 equal sized sections, then each section has a probability of 1/4 or 25% of being landed on when the spinner is spun.

If Jackson spins the spinner 32 times, we can find the expected number of times each section will be landed on by multiplying the probability of landing on each section by the total number of spins:

Expected number of times to land on each section = (Probability of landing on section) x (Total number of spins)

Expected number of times to land on each section = (1/4) x (32)

Expected number of times to land on each section = 8

Therefore, we can expect each section to be landed on approximately 8 times out of the 32 spins.

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The first experiment is not a binomial experiment because it does not meet the criteria of a binomial experiment. The criteria of a binomial experiment are:

1. The experiment consists of a fixed number of trials, n.
2. Each trial has only two possible outcomes: success or failure.
3. The trials are independent of each other.
4. The probability of success, p, remains constant for each trial.

In the first experiment, the trials are not independent of each other because the marbles are selected without replacement. This means that the probability of success changes with each trial. Therefore, it is not a binomial experiment.

The second experiment is a binomial experiment because it meets the criteria. There are a fixed number of trials (100), each trial has only two possible outcomes (steel penny or not steel penny), the trials are independent of each other (one penny is selected and then replaced), and the probability of success remains constant (1% for each trial). Therefore, p = 0.01 and n = 100.

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