In 2021, Madison Square Garden employed 8,900 people. For a basketball game at the garden, there are seats for 19,812 fans. What is the number of fans per employee during a basketball game? Round to the nearest tenth.

The equation given is A(t) = 10,250(1 + r 0.04/12)^120. To solve for the value of the account, we need to calculate the right side of the equation. First, we need to calculate the exponent of 1+r 0.04/12. This is equal to 120, so the exponent is 120. Next, we need to multiply 10,250 by the exponent of 1+r 0.04/12. This will give us the value of the account. The answer is 1,895,167.50.

The volume of the triangular pyramid is 26 2/3 yd³

The formula for calculating the volume of a triangular pyramid is expressed with the equation

A = 1/3bh

Such that the parameters in the equation are;

The base area of the pyramid is;

Area = 1/2 × 4 × 5

Multiply the values

Base area =20/2

Base area = 10 yd

Substitute the value

Volume = 1/3 × 10 × 8

Multiply the values

Volume = 80/3

Divide the values

Volume = 26 2/3 yd³

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Answer:

93 million

Step-by-step explanation:

93 Million

the fraction of the class that are boys is 4/9. And the fraction of the class that are girls is 5/9.

What is ratio?

A ratio is a comparison of two or more quantities that are related in some way. It expresses the relationship between these quantities in terms of the number of times one quantity contains another. Ratios are usually expressed as a fraction, where the numerator represents the first quantity and the denominator represents the second quantity. For example, the ratio of boys to girls in a class of 40 students may be expressed as 2:3 or 2/3, meaning there are 2 boys for every 3 girls. Ratios can also be expressed in other forms, such as percentages or decimals. Ratios are commonly used in mathematics, science, engineering, and everyday life to compare quantities and make predictions or decisions.

A fraction is a number that represents a part of a whole or a ratio of two quantities. It consists of two numbers, a numerator and a denominator, separated by a line. The numerator represents the number of parts being considered, while the denominator represents the total number of parts in the whole or in the comparison. Fractions are used in many areas, such as mathematics, science, engineering, cooking, and everyday life. They can be added, subtracted, multiplied, and divided, and can be converted to decimals or percentages.

a) The total ratio of boys to girls in the class is 4+5 = 9. Therefore, the fraction of the class that are boys is 4/9.

b) The question is unclear as it seems to be asking for the same answer as in part (a). If you meant to ask for the fraction of the class that are girls, you can use the same approach: the fraction of the class that are girls is 5/9.

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f(x) = [tex]x^{2}[/tex] -> f(x) = [tex]x^2[/tex] - 18 (translation) -> f(x) = [tex](x-3)^2[/tex] - 18 (horizontal translation) -> f(x) = -6[tex](x-3)^2[/tex] + 18 - 6x (vertical stretching)

To transform the function f(x) =[tex]x^{2}[/tex] into f(x) = [tex]x^{2}[/tex] - 6x + 18, we need to apply a series of transformations. Here are the steps:

Translation: We need to shift the graph of f(x) = [tex]x^{2}[/tex] down by 18 units to obtain f(x) = [tex]x^{2}[/tex] - 18. This can be done by subtracting 18 from the function, which results in f(x) = [tex]x^2[/tex]- 18.

Horizontal translation: Next, we need to shift the graph of f(x) = [tex]x^{2}[/tex] - 18 to the right by 3 units to obtain f(x) =[tex](x-3)^2[/tex] - 18. This can be done by replacing x with (x-3) in the function, which results in f(x) =[tex](x-3)^2[/tex]- 18.

Vertical stretching: Finally, we need to vertically stretch the graph of f(x) = [tex](x-3)^2[/tex] - 18 by a factor of -6 to obtain f(x) = [tex](x-3)^2[/tex] - 6x + 18. This can be done by multiplying the function by -6, which results in f(x) = -6[tex](x-3)^2[/tex] + 18 - 6x.

So, the series of transformations required to transform f(x) = [tex]x^{2}[/tex] into f(x) = [tex]x^{2}[/tex] - 6x + 18 is:

f(x) = [tex]x^{2}[/tex] -> f(x) =[tex]x^{2}[/tex] - 18 (translation) -> f(x) =[tex](x-3)^2[/tex] - 18 (horizontal translation) -> f(x) = -6[tex](x-3)^2[/tex]+ 18 - 6x (vertical stretching)

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Answer:

In each statement:

The rate is the percentage or ratio that relates the quantity being described to the base.

The base is the total quantity or amount that the rate is applied to.

The percent is the rate expressed as a percentage, or the part of the base that corresponds to the rate.

Answer:

421.875 ft³

Step-by-step explanation:

Since the length, width, and heigh are equal, this is a cube.

V = s³

V = (7.5 ft)³

V = 421.875 ft³

Answer:421.875 ft^3

Step-by-step explanation:

Answer:

(x - 5)^2 = 15 and (x + 13)^2 = 3

Step-by-step explanation:

Sure, I can help you with that.

Let's start with the first equation:

0 = x^2 - 10x + 10

To rewrite this equation in the form (x - p)^2 = q, we need to complete the square.

First, let's factor out the coefficient of x^2:

0 = 1(x^2 - 10x + 10)

Next, we want to add and subtract a value that will allow us to complete the square inside the parentheses. In this case, we will add and subtract (10/2)^2 = 25:

0 = 1(x^2 - 10x + 25 - 25 + 10)

Now we can rearrange the terms inside the parentheses and simplify:

0 = 1((x - 5)^2 - 15)

Finally, we can rewrite the equation in the desired form by adding 15 to both sides:

15 = (x - 5)^2

So the first equation in the form (x - p)^2 = q is:

(x - 5)^2 = 15

Now let's move on to the second equation:

x^2 + 26x + 167.5 = 0

Again, we need to complete the square to rewrite this equation in the form (x - p)^2 = q.

First, let's factor out the coefficient of x^2:

x^2 + 26x + 167.5 = 1(x^2 + 26x + 167.5)

Next, we want to add and subtract a value that will allow us to complete the square inside the parentheses. In this case, we will add and subtract (26/2)^2 = 169:

x^2 + 26x + 167.5 = 1(x^2 + 26x + 169 - 169 + 167.5)

Now we can rearrange the terms inside the parentheses and simplify:

x^2 + 26x + 167.5 = 1((x + 13)^2 - 1.5)

Finally, we can rewrite the equation in the desired form by adding 1.5 to both sides:

1.5 = (x + 13)^2 - 1.5

So the second equation in the form (x - p)^2 = q is:

(x + 13)^2 = 3

Answer:

27 cups of oats

Step-by-step explanation:

23
+ 4=27

In Δ PRQ, The value of the missing variable x is 4.8.

Calculating the area οf a triangle. Use the fοrmula area = 1/2 * base * height tο calculate the area οf a triangle. Select a side tο serve as the base and calculate the triangle's height frοm that pοint.

Cοrrespοnding sides in similar triangles are prοpοrtiοnal. As a result, using the infοrmatiοn prοvided, we can calculate the fοllοwing prοpοrtiοn:

As Δ PQS ≅ Δ PRQ

Then according to CPCT

PQ ≅ PR

and

PS ≅ PQ

Then we have

7 ≅ 5+ x

5 ≅  7

Then

[tex]$ \frac{7}{5 + x} = \frac{5}{7}[/tex]

Cross multiply

[tex]$ \frac{7}{5 + x} = \frac{5}{7}[/tex]

7 × 7 = 5(5+ x)

49 = 25 + 5x

49 - 25 = 5x

24 = 5x

x = 24/5

x = 4.8

Thus, In Δ PRQ, The value of the missing variable x is 4.8.

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Complete question:

Parts of similar triangle are given as the Δ PQS ≅ Δ PRQ. Find the value of x.

If Yin makes the maximum salary contribution to her 401(k), she will have made a total of $7,950.

Divide the part by the entire and multiply the result by 100 to obtain the percentage. A number can be expressed as a fraction of 100 by using the percentage, in other words.

If, for instance, there were 50 students in the class and 35 of them passed the test, and you want to know what percentage of those students passed the test, you may determine it by using the formula below.

% = (Number of students who passed / Total number of students) x 100 % = (35 / 50) x 100 % = 0.7 x 100 %

Percentage = 0.7 x 100

Percentage = 70%

If Yin may contribute up to 15% of her annual earnings to her 401(k) and her beginning salary is $50,000, her maximum annual contribution would be:

Maximum donation is = 15% of $50,000.

Maximum donation is 0.15 times $50,000.

Maximum annual contribution =  $7,500

Given that Yin's company will match up to 6% of her contributions, the maximum amount they might contribute annually is:

6% of $50,000 is the employer's contribution.

Employer contribution equals 0.6 times $50,000.

Annual employer contribution equals $3,000.

Hence, Yin's company will pay an additional $3,000 year if she contributes the maximum of $7,500 to her 401(k). Yin will contribute a total of $10,500 per year to her 401(k) ($7,500 + $3,000). (k).

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Answer:

Since the prism is completely filled with 96 cubes that have an edge length of 1/2 cm, we can find the volume of the prism by multiplying the number of cubes by the volume of each cube.

The volume of each cube is (1/2 cm)^3 = 1/8 cm^3.

The number of cubes is 96.

Therefore, the volume of the prism is:

volume = (number of cubes) x (volume of each cube)

volume = 96 x (1/8 cm^3)

volume = 12 cm^3

So, the volume of the prism is 12 cubic centimeters.

The length of OM, given that the triangles are similar to each other, is calculated as: 14.4.

Similar triangles are triangles that have the same shape but may have different sizes. They have the same angles, but the lengths of their sides are proportional. This means that corresponding sides of similar triangles are in proportion, and the ratio of their corresponding sides is constant.

Since triangle JKL is similar to triangle MNO, therefore:

JK/MN = JL/MO

Substitute:

5/24 = 3/x

Cross multiply:

5x = 72

5x/5 = 72/5

x = 14.4

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a. The shape οf the distributiοn οf the sample mean time is nοrmal.

b. The standard error is 0.5345.

Standard deviatiοn is: It is a measure οf hοw spread οut numbers are. It is the square rοοt οf the Variance, and the Variance is the average οf the squared differences frοm the Mean.

Given that:

μ =35

σ = 2

n = 14

a. The shape of the distribution of the sample mean time is normal.

b. To calculate the standard error of the mean time, we would apply this formula,

Standard error :

[tex]$ \rm SE = \frac{ \sigma}{\sqrt{(n)} }[/tex]

[tex]$ \rm SE = \frac{ 2}{\sqrt{(14)} }[/tex]

SE = 0.5345

Thus, the standard error is 0.5345.

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Complete question:

Majesty Videο Prοductiοn Inc. wants the mean length οf its advertisements tο be 30 secοnds. Assume the distributiοn οf ad length fοllοws the nοrmal distributiοn with a pοpulatiοn standard deviatiοn οf 2 secοnds. Suppοse we select a sample οf 16 ads prοduced by Majesty.

a. What can we say abοut the shape οf the distributiοn οf the sample mean time?

b. What is the standard error of the mean time?

The volume of the solid is 7.58 thousandths when rounded to the nearest thousandth.

Area is a measure of the size of a given space or the amount of a given surface. It can be measured in square feet, square meters, acres, hectares, and other units. Area can be used to describe the size of a two-dimensional shape or the surface area of a three-dimensional object. Area can also be used to calculate the amount of material needed to cover a given space, such as for a roof, carpet, or other covering.

To find the volume of the solid, we will use the following formula:
V=∫baπ(y2−(x−1)2)dx

Where b is the upper bound of the integral, a is the lower bound of the integral and y is the height of the solid.

Since the region R is the base of the solid, we can set a = 0 and b = 2, since this is the x-value at which the two functions intersect. Additionally, we can set y = ln(x) + 1 since this is the height of the solid.

Therefore, the volume of the solid is:
V = ∫02π(ln(x)2 + 12 − (x−1)2)dx

Calculating the integral, we get:
V = [π(xln(x)2 + x − 2xln(x) − x + 1)]02

Substituting the bounds of the integral, we get:
V = [π(22ln(2)2 + 2 − 4ln(2) − 2 + 1)] − [π(02ln(0)2 + 0 − 2ln(0) − 0 + 1)]

Simplifying the equation, we get:
V = π(ln(2)2 + 1 − 2ln(2))

Finally, substituting the value of ln(2) into the equation, we get:
V = 3.14159 (2.386294 + 1 − 4.772188) ≈ 7.58 thousandths

Therefore, the volume of the solid is 7.58 thousandths when rounded to the nearest thousandth.

In conclusion, the volume of the solid whose base is the region R and each cross section perpendicular to the a-axis is a semicircle is 7.58 thousandths when rounded to the nearest thousandth. This was calculated by integrating the equation V=∫baπ(y2−(x−1)2)dx with the bounds of integration a=0 and b=2 and the height of the solid y=ln(x)+1.

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Answer:

The inequality that represents this situation is 15x + 10y ≥ 1100, since Ezra needs to earn at least $1100 to buy the laptop.

To check if (60, 20) is a solution to this inequality, we need to substitute x = 60 and y = 20 into the inequality and see if it is true:

15(60) + 10(20) ≥ 1100

900 + 200 ≥ 1100

1100 ≥ 1100

Since 1100 ≥ 1100 is true, this means that (60, 20) is a solution to the inequality. This means that if Ezra works 60 hours mowing lawns and 20 hours walking dogs, he will earn enough money to buy the laptop.

The point (60, 20) represents the combination of hours worked for mowing lawns (x) and walking dogs (y) that will result in Ezra earning enough money to buy the laptop. The x and y values are the inputs or variables, while the inequality 15x + 10y ≥ 1100 is the constraint that must be satisfied. The solution (60, 20) is the output or result of the system of inequalities, and represents the combination of hours worked that will satisfy the constraint.

Answer:

10.01

Step-by-step explanation:

13 defective and 15 non defective calculators mean the total amount of calculators is 28

So there is a 13/28 chance that if we pull one calculator out, it will be defective

Since 3 calculators are pulled out, we cube 13/28

= (13/28)*(13/28)*(13/28)

= 2197/21952

=0.10008199708

as a percentage this is 10.008199708%

rounded -> 10.01

Answer: $28,383.68.

Step-by-step explanation:

The first step is to determine the number of monthly payments over the 5-year period, which is 5 years x 12 months/year = 60 months.

Next, we can use the formula for the future value of an annuity, which is:

FV = P * ((1 + r/n)^(n*t) - 1) / (r/n)

where:

FV is the future value of the loan (the amount owed at the end of the 5-year period)

P is the initial principal amount ($20,000 in this case)

r is the annual interest rate (6%)

n is the number of compounding periods per year (12 for monthly compounding)

t is the total number of years (5)

Plugging in these values, we get:

FV = $20,000 * ((1 + 0.06/12)^(12*5) - 1) / (0.06/12)

FV = $28,383.68

Therefore, the balance owed at the end of the 5-year period would be $28,383.68.

A ratio that can be used to determine the slope of this line include the following: D. [tex]\frac{7\;+\;2}{-5\;+\;-8}[/tex]

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the slope formula, we have the following;

Slope (m) = (7 - (-2))/(-5 - 8)

Slope (m) = (7 + 2)/(-5 - 8) ⇒ (Required ratio)

Slope (m) = 9/-13

Slope (m) = -0.6923.

In this context, we can reasonably infer and logically deduce that the slope of this line is equal to -9/13 or -0.6923.

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The value of x such that x - 4 and 2x + 1 are angles on a line is 61

x - 4 and 2x + 1 are angles on a line.

Using the theorem of sum of angles on a line that states that:

When two angles are on a line, they add up to 180 degrees.

So we have:

x - 4 + 2x + 1 = 180

Simplifying and solving for x:

3x - 3 = 180

So, we have

3x = 183

Divide both sides by 3

x = 61

Therefore, x = 61 is the value that makes x - 4 and 2x + 1 angles on a line.

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The equation to represent the situation is 96 = 12 + 8x and the number of hours she rent the boat is 10.5 hours.

During a vacation, Alice went fly-fishing. She rented a drift boat. Rick's Rental fishing rod drift boat cost $12 plus $8/hour.

She spent a total of 96 dollars. The equation to solve the situation can be calculated as follows:

Hence,

y = 12 + 8x

where

Therefore,

96 = 12 + 8x

8x = 96 - 12

8x = 84

divide both sides by 8

x = 84 / 8

x = 10.5 hours

Therefore,

hours she rented the boat = 10.5 hours

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Answer10 toooooooooooo the third poewedd

Step-by-step explanation:

Answer:

450

Step-by-step explanation:

Option A is correct. The circle graph  or pie chart have five parts as 5 ways of transportation labeled Subway 40%, bicycle 10%, car service 15%, bus 8%, and walk 27%

Let's create pie chart to show the parts of transportation, each transportation ways will be represented by their percent.

Total number of visitors from various transportation = 80 + 20 + 30 + 54 + 16 = 200

Percentage of ways of transportation for each type:

Subway: %

Bicycle: %

Car Service: %

Bus: %

Walk: %

So, the correct pie chart of different ways of transportation will have five parts named as Subway 40%, bicycle 10%, car service 15%, bus 8%, and walk 27%.

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The cost to operate Lee's Tv is 2.88 dollars.

Lee watches TV for 4 hours per day. During that time, the TV consumes 200 watts per hour. Electricity costs (12 cents)/(1 kilowatt-hour).

Therefore, the cost for Lee to operate in 30 days can be calculated as follows:

200 watt = 0.2 kilowatt

Therefore,

1 day = 4 hours

30 days = ?

cross multiply

number of hours = 120 hours.

Therefore, in 30 days he watches television for 120 hours.

Let's find the cost

0.12 dollars  = 12 cent

1 hour  = 0.2 kilowatt

120 hours =

kilowatt use in 30 days = 0.2 × 120 = 24 kilowatts

Therefore,

1 kilowatts = 0.12 dollars

24 kilowatts = ?

cost of Tv for a month of 30 days = 24 × 0.12

cost of Tv for a month of 30 days = 2.88 dollars

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No, if fit indicates that the bookcase's sides must be flush with the wall, which means that they must touch the wall and that the bookshelf is correctly positioned in that location.

A triangle is a polygon with three edges and three vertices.

It belongs to the basic geometric shapes.

A triangle having vertices A, B, and C is known as triangle ABC.

Any three locations in Euclidean geometry that are not collinear result in a distinct triangle and a distinct plane.

I've discovered that using the 3:4:5 triangle is the simplest way to determine for sure if an angle is 90 degrees.

This rule states that a triangle is a right triangle even if one of its sides is 3 and the other is 4 if the diagonal connecting its two points measures 5.

So, we must check to see if any of the bookcase's vertices measure 90 degrees because a square room will naturally have corners that do.

We may utilize Pythagorean Theorem to find the solution because every right triangle contains a 90° angle.

Pythagorean The a, b, and c are the legs, and the theorem states that a² + b² = c².

For our bookshelf, 10 and 12 are the legs, and 18 would be the hypotenuse if it were a right triangle as the hypotenuse is always the longest side.

To determine whether the equation is true or false, enter the values.

10² + 12² = 18²

100 + 144 = 324

244 ≠ 324

Thus, the bookshelf does not form a straight angle and cannot be placed in the room's corner.

Therefore, no, if fit indicates that the bookcase's sides must be flush with the wall, which means that they must touch the wall and that the bookshelf is correctly positioned in that location.

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Correct question:

A triangular bookshelf has a base of 10 inches,12 inches, and 18 inches. Will the bookshelf fit in the corner of a square living room?