Allen owns 70% of Bull Corp. If the company has 721,250 shares,
3. How many shares does Allen own?
4. If he paid $21.45 per share what was his initial total investment?
5. If the shares are now worth $60.18, what are shares total value now?
6. What would be his capital gain if he sold his shares at the new value?

The amount of your tax refund is $1,414

To find the tax refund, we need to subtract the amount of federal taxes owed after deductions from the amount of federal taxes already paid.

Tax refund = Federal taxes paid - Federal taxes owed after deductions

Tax refund = $12,042 - $10,628

Tax refund = $1,414

Rounding to the nearest cent, the tax refund is $1,414.00.

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Miriana rolled the sequence of 3 and then 6 two more times than the theoretical probability would have predicted.

The theoretical probability of rolling a three-on-one number cube is 1/6, and the same is true for rolling a six. Since the two rolls are independent,

The probability of rolling a three and then a six in the sequence is the product of the probabilities: (1/6) x (1/6) = 1/36.

To find the expected number of times this sequence would occur in 180 experiments, we multiply the probability by the number of experiments: (1/36) x 180 = 5.

So, if Miriana had rolled the number of cubes according to the theoretical probability, we would have expected her to roll the sequence of 3 and then 6 five times in 180 experiments.

However, she actually rolled this sequence 7 times, so she rolled it 2 more times than the theoretical probability would have predicted.

Therefore, Miriana rolled the sequence of 3 and then 6 two more times than the theoretical probability would have predicted.

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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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The possible dimensions (length and width) of the field which is rectangle are (26m, 5m) or (5m, 26m) and (28m, 4m) or (4m, 28m)

Let's assume the length of the rectangle be L and the width be W.

We know that we have three sides of the rectangle to fence, so the total length of the fence will be L+2W = 36m.

Also, we know the area of the rectangle = L×W = 154 sq.m

Using the two equations above, we can solve for L and W as follows:

L = 36 - 2W (from the first equation)

Substituting this value of L in the second equation:

(36 - 2W)W = 154

2W² - 18W + 77 = 0

We get two possible values of width: W = 5 or W = 4

For W = 5, L = 26

For W = 4, L = 28

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No, the relation is not a function.

Given the relation in the question:

x: -2, -4, -1, -4, 5, 3

y: 1, -3, 2, 8, 0, -1

A function is simply a relationship that maps one input to one output.

To determine whether the relation is a function, we need to check whether each x-value in the relation is associated with a unique y-value.

Looking at the x-values, we see that there are repeated values of -4, which means that there are multiple y-values ( -3 and 8 ) associated with x = -4.

The mapping of x to y is not well-defined for all values of x, since one value of x is associated with multiple values of y, hence, it is not a function.

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12π inches is the circumference of the given circle with a diameter of 12 inches.

The circumference of a circle can be found using the formula C = π*d, where d is the diameter of the circle.

If the diameter of the circle is 12 inches, then the circumference is:

C = π* d

C = π * 12 inches

C = 12π inches

So, the circumference of the circle in terms of π is 12π inches.

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The three adverbs in the sentence are:

hard (modifying the verb "raining")

clearly (modifying the verb "see")

almost (modifying the verb "crashed")

1) "Hard" is an adverb of manner that describes how the rain was falling. It indicates that the rain was falling with intensity or force, which made it difficult for the driver to see.

2) "Clearly" is an adverb of manner that describes how the driver was seeing. It indicates that the driver was having difficulty seeing due to the heavy rain, which was affecting their vision.

3) "Almost" is an adverb of degree that modifies the verb "crashed." It indicates that the driver came very close to crashing their shiny new car, but managed to avoid a collision at the last moment.

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Answer:

C. 16√5

Step-by-step explanation:

Use the Pythagorean Theorem.

[tex]48^2 = 32^2 + x^2\\2304 = 1024 + x^2\\x^2 = 1280\\x = \sqrt{1280}\\[/tex]

[tex]\sqrt{1280}[/tex] is also equal to [tex]16\sqrt{5}[/tex].

The given data results in the following Frequency Distribution

Class Frequency

21-27 3

28-34 8

35-41 7

42-48 8

49-55 4

In statistics, frequency distribution is a way of organizing data into categories, or intervals, and counting how many observations fall into each category. It helps us understand the distribution of data and identify patterns within it.

To construct a frequency distribution using 5 classes, we need to first determine the range of the data:

Range = Maximum value - Minimum value

= 52 - 21

= 31

We can then calculate the width of each class:

Width = Range / Number of classes

= 31 / 5

= 6.2

Since we cannot have a fractional width, we round up to the nearest whole number. The class width is therefore 7.

Next, we need to determine the class intervals, or boundaries, which are the values that define each class. We start with the minimum value and add the class width successively:

Class 1: 21-27

Class 2: 28-34

Class 3: 35-41

Class 4: 42-48

Class 5: 49-55

We can now count how many observations fall into each class. The resulting frequency distribution is shown below:

Class Frequency

21-27 3

28-34 8

35-41 7

42-48 8

49-55 4

In this frequency distribution, we can see that the majority of the observations fall into the middle three classes, with fewer observations in the first and last classes. This suggests that the data is roughly symmetric and evenly distributed around the center.

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A) The total cost for 45khw of electricity is 27.50c.

B) The total cost for 60khw of electricity is 76.70c.

C) Total cost for 100khw of electricity is 76.70c.

To calculate the cost of electricity for different amounts of kWh, we need to use the sliding scale tariffs provided by the local municipality. Here are the calculations for the given scenarios:

A. For 45 kWh of electricity:

The first 50 kWh cost 0.55c per kWh, so the cost is 50 x 0.55 = 27.50c

There is no electricity used beyond the first 50 kWh, so the total cost is 27.50c.

B. For 60 kWh of electricity:

The first 50 kWh cost 0.55c per kWh, so the cost is 50 x 0.55 = 27.50c

The next 10 kWh cost 0.82c per kWh, so the cost is 10 x 0.82 = 8.20c

The total cost is 27.50c + 8.20c = 35.70c.

C. For 100 kWh of electricity:

The first 50 kWh cost 0.55c per kWh, so the cost is 50 x 0.55 = 27.50c

The next 60 kWh cost 0.82c per kWh, so the cost is 60 x 0.82 = 49.20c

The remaining 40 kWh are not covered by the sliding scale tariff and their cost is unknown.

The total cost is 27.50c + 49.20c = 76.70c.

In summary, the cost of electricity varies depending on the amount of kWh used, and we need to use the sliding scale tariffs to calculate it correctly.

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The first derivative of the function f(x) = x^4 + 3x^2 + 2 at x=2 using Richardson's method with h=0.01 is approximately 33.8933.

To calculate the first derivative of the function f(x) = x^4 + 3x^2 + 2 using Richardson's method, we need to first calculate the approximate values of the function at x=2 and x=2+h, where h=0.01.

So, we have:

f(2) = 2^4 + 3(2^2) + 2 = 24

f(2+h) = (2+h)^4 + 3(2+h)^2 + 2

= 16 + 32h + 24h^2 + 8h^3 + h^4 + 12 + 12h + 3h^2 + 2

= h^4 + 8h^3 + 24h^2 + 35h + 30

Now, we can use Richardson's extrapolation formula to calculate the first derivative of the function at x=2:

f'(2) ≈ (4f(2+h) - f(2)) / (3h)

Substituting in the values we have:

f'(2) ≈ (4(h^4 + 8h^3 + 24h^2 + 35h + 30) - 24) / (3h)

= (4h^4 + 32h^3 + 96h^2 + 140h + 96) / (3h)

= (4h^3 + 32h^2 + 96h + 140) / 3

Now, we can substitute h=0.01 to get the value of the first derivative at x=2:

f'(2) ≈ (4(0.01^3) + 32(0.01^2) + 96(0.01) + 140) / 3

≈ (4(0.000001) + 32(0.0001) + 0.96 + 140) / 3

≈ (0.000004 + 0.0032 + 0.96 + 140) / 3

≈ 140.9632 / 3

≈ 33.8933

Therefore, the first derivative of the function f(x) = x^4 + 3x^2 + 2 at x=2 using Richardson's method with h=0.01 is approximately 33.8933.

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The difference between the median math test score, as shown by the ox plots, is: 12.5.

The median of a data set is displayed in a box plot as the value that is at the vertical line that divides the rectangular box. This is also 50% mark of the data set.

Thus, the data set for afternoon, as shown in the box plot has a median that is 75, while the median of the data set for morning is 87.5.

Find the difference of their medians:

Difference of their medians = 87.5 - 75 = 12.5.

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When someone aged 20 sets up an IRA retirement account with an APR of 5% and deposits $65 at the end of each month, when he retires at age 65, the account will have a future value of $131,718.42.

b) Compared to the total deposit he made over time ($35,100.00), he generated a total compounded interest of $96,618.42.

The future value can be determined using an online finance calculator, which compounds the interest at 5% over a period of 540 months or 45 years.

Number of years = 45 years (65 - 20)

N (# of periods) = 540 months (45 years x 12)

I/Y (Interest per year) = 5%

PV (Present Value) = $0

PMT (Periodic Payment) = $65

Results:

Future Value (FV) = $131,718.42

Sum of all periodic payments = $35,100.00 ($65 x 540 months)

Total Interest = $96,618.42

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The exponential function that models the relationship between the two points is [tex]y = 41.62 (1.0824)^x.[/tex]

We have,

To write an exponential model given two points (6,85) and (7,92), we can use the general exponential function form:

y = a[tex]b^x[/tex]

where y is the dependent variable, x is the independent variable, a is the initial value (when x = 0), and b is the base of the exponential function.

To find the values of a and b, we can use the two given points as follows:

When x = 6, y = 85:

85 = a b^6

When x = 7, y = 92:

92 = a b^7

We now have a system of two equations with two unknowns (a and b).

We can solve for a by dividing the second equation by the first equation:

92/85 = (ab^7) / (ab^6)

1.0824 = b

Substitute this value of b into one of the equations to solve for a:

85 = a (1.0824)^6

a = 41.62

Therefore,

The exponential function that models the relationship between the two points is [tex]y = 41.62 (1.0824)^x.[/tex]

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1560 g.

To convert 1.56 kg to g, we can use the conversion factor 1 kg = 1000 g:

1.56 kg = 1.56 x 1000 g = 1560 g

Therefore, the answer is 1560 g.

The graph of the given inequalities is Attached below.

From the given inequalities:

As the first inequality is not strictly true, the graph of it is a straight solid line that passes through the points (0, 2) and (2/3, 0), with the shaded area being further from the origin ( as it fails the zero point test )

As the second inequality is not stringent, the graph of the inequality is a straight solid line that passes through the points (0,-4) and (8,0), with the shaded area pointing in the direction of the origin (since the inequality passes the zero point test)

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Complete question:

Which graph represents the system of inequalities?

y + 3x ≥ 2

y + 4 ≥ 1/2x

The value of the expression is $-56x² + 266x + 261

Algebraic expressions are simply described as mathematical expressions that consists of coefficients, certain variables, terms, constants and factors.

Algebraic expressions are also identified with arithmetic operations, such as;

From the information given, we have;

$49x^2+14x(19-7x)+(19-7x)^2

expand the bracket, we get;

49x² + 266x - 98x² + 361 - 7x²

Now, collect the like terms, we get;

49x² - 98x² - 7x² + 266x + 361

Add or subtract the values

$-56x² + 266x + 261

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Answer:  5km

Step-by-step explanation:

The formula for Surface area of a square pyramid

SA= [tex]L^{2} + 2Ls[/tex]         where L is the length on the bottom and s is the slant height

                                L=1 km              s=2 km

SA = [tex]1^{2} +[/tex] 2(1)(2)

=1+4

=5km

Answer:

x=144

Step-by-step explanation:

since they are similar their sides have a common ratio

24/x=42/7

7x=42*24

7x=1008

x=144

Answer:

Step-by-step explanation:

In mathematics, the expression "to the power of" pertains to the exponent, signifying how many times a key number is to be multiplied by itself.

Expressing this idea in English can be done well by using the term "to the power of." To show this, 2 raised to the third power can be interpreted as 2 multiplied by itself three times, resulting in 8.

Therefore, the possible reason behind using the word "power" is probably due to the fact that when the exponent rises, the outcome number is wide, either being greater or smaller, made on the base being above or below 1. This implies that the figure holds more significant value.

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Answer:  C

Step-by-step explanation:

Think about y=[tex]x^{3}[/tex]     This is an odd function because the highest exponent(degree) is odd

A.  is wrong. Symmetry is where you can fold it and it would be the same.  If i folded y=[tex]x^{3}[/tex] along the y- axis it would not be the same.  

B is wrong. Transformations are where has it moved, which has nothing to do with odd functions in general

C.  is correct.  It is folded along y=x and flipped.

D. is wrong.  If folded y=x it's in the same quadrant but it's not the same, its' reversed.

Answer:

A

Step-by-step explanation:

The four math sentences that have an answer of 2.4 are 1.2 + 1.2, 1.2 * 2, 3.6 - 1.2 and  4.8/2

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

An answer of 2.4

Using a different operation in each sentence., we have the following math sentences

1.2 + 1.2

1.2 * 2

3.6 - 1.2

4.8/2

The solution to each of the above sentences is 2.4

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The statements can be arranged correctly as follows:

1. Word Form shows a number written in words.

2. Standard form shows a number written using digits.

3.  Digit is one of the numerals from 0 to 9

4. Place value the position of a digit in a number, which determines its value.

5.  Period each three-digit part of a whole number, separated by commas

6. Expanded form shows a number written as an addition statement

We can determine the terms by first understanding the mathematical meanings. Word form is a term used in math to denote expressions written in word B.

Also, the standard form is a way of shortening large numerical values using digits. Digits are single numbers that run between 0 to 9 and they make up the higher values of numbers.

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Answer:

6x-50-7(3x+10)=0

Distribute the -7:

6x - 50 - 21x - 70 = 0

Combine like terms:

-15x - 120 = 0

Add 120 to both sides:

-15x = 120

Divide both sides by -15:

x = -8

Answer:

Rational

Step-by-step explanation:

Improper fractions are always rational.

A bag of daffodil bulbs costs $12 and a bag of windflower bulbs $8.

Let's use the letters "w" for the price of a bag of windflower bulbs and "d" for the price of a bag of daffodil bulbs.

We may construct the following system of equations based on the above information:

Perry's sales:

w + d = 20 (equation 1)

Darryl's sales:

7w + d = 68 (equation 2)

To solve for w and d, we can use the elimination method. Multiplying equation 1 by -1, we get:

-w - d = -20

Adding this to equation 2, we eliminate d and get:

6w = 48

Dividing both sides by 6, we get:

w = 8

Substituting this value of w into equation 1, we can solve for d:

8 + d = 20

d = 12

Therefore, a bag of windflower bulbs costs $8 and a bag of daffodil bulbs costs $12.

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