3. Describe how the results from Class 1, Class 2, and Class 3 differ.

Answer:

3. 504,875 shares

4. $10,829,568.75

5. $30,383,377.5

Step-by-step explanation:

1. For the first one, you just need to find 70% of 721,250, which we can do several ways:

If Allen owns 70% of Bull Corp, he owns 0.7 x 721,250 = 504,875 shares.

Therefore, Allen owns 504,875 shares of Bull Corp.

you can use cross-multiplication to solve this problem as well. Here's how:

Let X be the number of shares that Allen owns.

According to the problem, Allen owns 70% of the total number of shares, which is 721,250.
So we can write:

X/721,250 = 70/100

To solve for X, we can cross-multiply:

100X = 70 * 721,250

Simplifying the right-hand side:

100X = 50,487,500

Dividing both sides by 100:

X = 504,875

Therefore, Allen owns 504,875 shares of Bull Corp, which is the same answer we got earlier.

I added a picture below.

2. If Allen paid $21.45 PER share we just multiply that by he amount of shares, which is 504,875:

If Allen owns 504,875 shares of Bull Corp, and he paid $21.45 per share, his initial total investment would be:

Total investment = Number of shares * Price per share

Total investment = 504,875 * $21.45

Total investment = $10,829,568.75

Therefore, Allen's initial total investment was $10,830,093.75.
i added a picture for this too.

3. Just replace the 21.45 with 60.18:

If the shares are now worth $60.18, the total value of Allen's shares would be:

Total value = Number of shares * Current price per share

Total value = 504,875 * $60.18

Total value = $30,383,377.5

Therefore, the total value of Allen's shares now is $30,382,078.50.

Added a picture.

From the given figure, we have the following:

In Mathematics and Geometry, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

Based on the cartesian coordinate (grid) above, the coordinates points and quadrants should be identified as follows;

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Complete Question:

From the given figure, write

a) The coordinates of the points B and F. b) The point identified by the coordinates (1,1)

c) The abscissa of the points D and H.

d) The ordinates of the points A and C.

e) The quadrant in which points B and I lie.

f) The perpendicular distance of the point G from the x-axis.

g) The perpendicular distance of the point I from the y-axis.

h) The point whose perpendicular distance from y- axis is 2 units​

The record long jump is 8 inches short of 10 yards.

First, we need to convert 10 yards to inches. Since 1 yard = 3 feet and 1 foot = 12 inches, we have:

10 yards = 30 feet

= 30 x 12 inches

= 360 inches

To find how many inches short of 10 yards the long jump is, we can subtract the length of the long jump from 360 inches:

360 inches - 29 feet 4 inches

= 360 inches - (29 x 12 + 4) inches

= 360 inches - 352 inches

= 8 inches

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The equation of a circle with diameter endpoints of (13, -1) and (15, 9) will be x² + y² - 28x - 8y + 186 = 0.

Given that:

Endpoints of diameter, (13, -1) and (15, 9)

The equation of the circle when endpoints of diameter are given is written as,

(x - x₁)(x - x₂) + (y - y₁)(y - y₂) = 0

The equation of the circle is calculated as,

(x - 13)(x - 15) + (y + 1)(y - 9) = 0

x² - 28x + 195 + y² - 8y - 9 = 0

x² + y² - 28x - 8y + 186 = 0

The equation of a circle with diameter endpoints of (13, -1) and (15, 9) will be x² + y² - 28x - 8y + 186 = 0.

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0≤x≤6 best describes the domain of the function.

The domain of a function describes the set of all possible input values.

In this case, the input variable is x, which represents the time in hours.

Since the horse runs for 6 hours, it is not possible for x to be greater than 6.

Additionally, x cannot be negative or zero, since time cannot be negative or zero.

Therefore, the domain of the function is 0 ≤ x ≤ 6.

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The measure of the arc length AB is 16π/15 centimeters.

Since,

An arc length is simply the distance between two points along a section of a curve.

We know that;

The arc length is expressed as:

s = 2πr × (θ/360°)

Where s is the arc length, r is the radius, θ is the angle and π is constant pi.

Given that:

Radius r = 3cm

Angle θ = 64 degree

Arc length s = ?

Now, Plug the values into the above formula

s = 2πr × (θ/360°)

s = 2 × π × 3cm × ( 64°/360°)

s = 16π/15 cm

Therefore, the arc length is 16π/15 cm.

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Answer:

15456

Step-by-step explanation:

My work is attached to this answer

(a) Volume of the cylinder is 153 cm³

(b) Volume of the cone is 51 cm³

(c) Volume of the cone = 1/3 × Volume of the cylinder

From the question, we are to determine the volume of the cylinder and the volume of the cone

The volume of a cylinder can be calculated by using the formula,

V = πr²h

Where V is the volume

r is the radius

and h is the height

From the given information,

A = πr² = 17 cm²

A is the area of the base

h = 9 cm

Thus,

V = 17 cm² × 9 cm

V = 153 cm³

Therefore,

Volume of the cylinder is 153 cm³

(b)

For the volume of the cone

V = 1/3 πr²h

Substitute the given parameters

V = 1/3 × 17 cm² × 9 cm

V = 17 cm² × 3 cm

V = 51 cm³

Hence,

Volume of the cone is 51 cm³

(c)

Volume of the cone = 1/3 × Volume of the cylinder

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The expected number of education majors in the sample is 20.

Since 80 out of 200 freshmen are education majors, the probability of randomly selecting an education major from the population is:

P(edu major) = 80/200 = 0.4

To find the expected number of education majors in a sample of 50 freshmen, we can use the formula for the expected value of a discrete random variable:

E(X) = n x p

Substituting the given values, we get:

E(X) = 50 x 0.4 = 20

Therefore, the expected number of education majors in a sample of 50 freshmen is 20.

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The summation of the given expression is as follows:

17.) = 5

18.) = 1

19.) = 1/2

For question 17.)

The summation of 2k+3 when K= 1

= 2(1)+3

= 2+3

= 5

For question 18.)

The summation of (3/2)^k where k = 0 would be = 1

For question 19.)

The summation of 1/2^k+1 where k = 0

= 1/2^0+1

=1/2^1

=1/2

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Answer:

The silver will cost $1908.5125 to make one solid sphere

Step-by-step explanation:

The formula for the volume of a sphere is:

V = (4/3)πr^3

where r is the radius of the sphere.

Substituting the given value for the radius:

V = (4/3)π(4.5 cm)^3

= (4/3)(3.14)(91.125 cm^3)

= 381.7025 cm^3

The cost of the silver can be calculated by multiplying the volume by the cost per cm^3:

Cost = 381.7025 cm^3 × $5.00/cm^3

= $1908.5125

The  line integral of F around the perimeter of the rectangle with corners (3,0),(3,2),(-3,2),(-3,0) traversed in that order is -333.06456

The F can be rewritten as

F(x,y)  = [6(x+y) , 6sin(y)

The path C on which we are going to evaluate the integral is

The distance between Alberto and the base of the building is  93.4ft

We can view this as a right triangle, such that one cathetus (opposite to the known angle) measures:

40ft - 6ft = 34ft

And the known angle is 70°, we want to get the other leg of the right triangle, so we can use the tangent trigonometric relation which is:

tan(angle) = (opposite cathetus)/(adjacent cathetus)

Replacing the things that we know we get:

tan(70) = x/34ft

tan(70)*34ft = x = 93.4ft

That is the distance.

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Thermal energy and heat transfer principles guide the design of efficient systems, minimizing heat loss and maximizing performance.

It is crucial to take into account a number of aspects that may impact the functionality and efficiency of systems and objects that include thermal energy and heat transmission. You would need to take into account things like the kind and quantity of heat source, the materials utilized, the insulation, and the processes employed for heat transfer, for instance.

Additionally, you would have to think about ways to increase heat transmission effectiveness and reduce heat loss. High thermal conductivity materials may be used, or the system may be designed to have more heat-transfer surface area.

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Both lines will be solid lines and the intersection of the point will be at (1/3, 1).

Given that:

y ≥ −3x + 2

y ≥ 3x

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The region above the line y ≥ −3x + 2 is considered.

The region above the line y ≥ 3x is considered.

And both lines will be solid lines and the intersection of the point will be at (1/3, 1).

The graph is given below.

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The value of the number is 18. Option A

To determine the product of the expression, we need to consider that;

Algebraic expressions are described as those mathematical expressions that are composed of terms, their coefficients, the variables and the factors and constant values.

These expressions are also made up of mathematical operations. These operations are;

From the information given, we have that;

The product of six and a number is 108

Let the number be x, we have;

6x = 108

Divide sides by the coefficient

x = 18

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The graph is a function, the domain is (-∝, ∝), the range is (-∝, 4] and the graph is symmetrical with the y-axis

Given that we have the graph

As a general rule of the vertical line test

For a graph to represent a function, a line drawn from the x-axis must intersect with the graph at most once

Using the above as a guide, we have the following:

The graph would not intersect with a line from the x-axis more than once

Hence, the graph is a function

The domain is the set of input values

In this case, we have

Domain = (-∝, ∝) i.e. all set of real values

The range is the set of output values

In this case, we have

Range = (-∝, 4]

When the graph is rotated across the y-axis, the graph maintains it orientation

This means that the graph is symmetrical with the y-axis

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The equation 2 (p+ 7) = 4 - 8p has only one solution that is; -9.

We know that solution of an equation refers usually to the values of the variables involved in that equation that if substituted in place of that variable would give a true mathematical statement.

We need to determine the solutions does the equation 2 (p+ 7) = 4 - 8p have;

Now solving for p,

2 (p+ 7) = 4 - 8

Open the bracket,

2p+ 14 = 4 - 8

Combine the like terms,

2p = -4 - 14

2p = -18

p = -18/2 = -9

Therefore, the equation has only one solution which is -9.

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If he business checking account for a pottery store had a balance of $7349.44 before checks for $1349.67 and $344.12 were written, checkbook balance after checks and deposit are processed is $6613.25.

To find the checkbook balance, we need to add up the initial balance, subtract the amounts of the written checks, and add the deposit made by the store manager.

Starting with the initial balance of $7349.44, we subtract the amount of the first check for $1349.67, leaving a balance of $6000.77. Then we subtract the second check for $344.12, leaving a balance of $5656.65.

Finally, we add the deposit made by the store manager for $956.60, which gives us a final balance of $6613.25.

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The probability that the friend is between 10 and 30 minutes late is approximately 0.6667, or 66.67%.

Since the probability density function is uniform, the probability of the friend being between 10 and 30 minutes late is equal to the area of the rectangle that lies between x = 10 and x = 30, and below the curve of the probability density function.

The height of the rectangle is equal to the maximum value of the probability density function, which is 1/30 since the interval of possible values for x is [0, 30] minutes.

The width of the rectangle is equal to the difference between the upper and lower limits of the interval, which is 30 - 10 = 20 minutes.

Therefore, the probability of the friend being between 10 and 30 minutes late is:

P(10 < x < 30) = (height of rectangle) x (width of rectangle)

= (1/30) x 20

= 2/3

≈ 0.6667

So the probability that the friend is between 10 and 30 minutes late is approximately 0.6667, or 66.67%.

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The probability that a person will wait for more than 9 minutes is approximately 0.0912 or 9.12%. This means that out of 100 people, about 9 of them will wait for more than 9 minutes in the line.

We know that,

To solve this problem, we need to use the normal distribution and standardize the variable of interest. We know that the mean waiting time is 5 minutes and the standard deviation is 3 minutes, so we can write: Z = (X - μ) / σ

where X is the waiting time, μ is the mean waiting time (5 minutes), σ is the standard deviation (3 minutes), and Z is the standardized variable.

To find the probability that a person will wait for more than 9 minutes, we need to find the area under the normal curve to the right of 9. We can do this by standardizing 9 using the formula above: Z = (9 - 5) / 3 = 1.33 .

We can use a standard normal table or a calculator to find the probability that Z is greater than 1.33. Using a calculator, we find that this probability is approximately 0.0912.

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Answer:

The sample space describing all possible outcomes is:

{H1, H2, H3, H4, T1, T2, T3, T4}

The outcomes for the event that the coin toss is heads are:

{H1, H2, H3, H4}

Step-by-step explanation:

If it pertains to using the format H1 to mean that the coin toss is heads and the number chosen is 1.

The possible shapes of the fencing are a parallelogram and a rectangle.

Given that, a worker fences in a construction site using four pieces of fencing that have lengths of 20, yards 16, yards, 20 yards, and 16 yards.

We need to tell possible four-sided shapes that the worker can enclose with the fencing.

So, we can see that, the pair of sides are equal,

Which is condition in a parallelogram and a rectangle.

Hence, the possible shapes of the fencing are a parallelogram and a rectangle.

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Based on the percentage of blue paint to red paint, Bo's purple paint will be bluer.

The percentage refers to the quotient of one value (proportion of blue paints) compared to another (the sum of blue and red paints).

Percentages are ratios expressed over 100.

                           Blue     Red   Ratio (%) of Blue to Red

Bo's paints            3          4       3:4 = 43% (3/7 x 100)

Sum of ratios = 7

Latanya's paints   2          3       2:3 = 40% (2/5 x 100)

Sum of ratios = 5

Thus, based on the ratios or percentages of to red paints, Bo's purple paint will be bluer than Latanya's.

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The transformation that maps the pre-image (red) onto the image (blue) is reflection

Given that

the pre-image (red) and the image (blue)

From the figure, we can see that

Both triangles are mirrors of one another

As a general rule

When two shapes with the same orientation and properties mirror one another, then the transformation between the shapes is the reflection transformation

This means that the transformation of the two triangles is a reflection transformation

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A feasible solution to minimizing turbidity value is through the use of an iterative technique, entailing either gradient descent method or simulated annealing method.

The stopping criterion for this approach would be at 0.1 percent.  It involves sequentially determining water turbidity dependent on the coagulant dosages used in adjustment procedures based on preceding calculated values.

By further implementing this process until the specified percentage average is met, ease and accuracy in assessing turbidity levels are achievable.

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Answer:

Step-by-step explanation:

The pattern that the scatterplot would suggest, given that they have an exponential relationship is :

A function expressed as y = ab^x or y = a × e^(kx), where a, b, and k are constants represents an exponential relationship between two variables. Exponential functions demonstrate continuous increase or decrease throughout their entire domain; they do not alter direction.

In the event that the base 'b' is greater than 1, or if 'k' is positive, the function increases its output, otherwise, it will decrease when either or both conditions apply ('b' being between zero and one, or 'k' being negative). The concavity of a function is determined by the second derivative which takes on the form of an exponential function for all exponential functions, producing unchanged concavity throughout its entire domain.

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There are 560 cubes with edge lengths of 1/2 cm needed to fill the rectangular prism.

The volume of a rectangular prism is found by multiplying its length by its width by its height.

So, the volume of this rectangular prism is:

Volume = length x width x height

Volume = 7 cm x 4 cm x 2 1/2 cm

Volume = 70 cm³/2

Now, we need to find out how many cubes with edge lengths of 1/2 cm can fit into this volume.

The volume of each cube with an edge length of 1/2 cm is:

Volume of cube = edge length x edge length x edge length

Volume of cube = (1/2 cm)³

Volume of cube = 1/8 cm³

To find no. of cubes are needed, we need to divide the volume of the rectangular prism by the volume of each cube:

Number of cubes = (Volume of rectangular prism) / (Volume of each cube)

Number of cubes = (70 cm³/2) / (1/8 cm³)

Number of cubes = (70 cm³/2) x (8/1 cm³)

Number of cubes = 560 cubes

Therefore, 560 cubes with edge lengths of 1/2 cm are needed.

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The average rate of change of the height of the rocket is 11.25/(a - 1)

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

h(1) = 23 meters and h(a) = 34.25 meters.

The average rate of change of the height of the rocket is

Rate = Change in height /Time

So, we have

Rate = (34.25 - 23)/(a - 1)

Evaluate

Rate = 11.25/(a - 1)

Hence, the rate = 11.25/(a - 1)

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Complete question

Melissa launches a rocket from a 3-meter-tall platform. The height, h, of the rocket, in meters, can be modeled by the given graph.

Melissa knows that h(1) = 23 meters and h(a) = 34.25 meters.

What is a reasonable estimate of the average rate of change of the height of the rocket, in meters per second