If a function is defined as f(x)=2x+3 , find the value of f(4

1.a) The total revenue received for CD sales was $12,090,000.

1.b) The total revenue received for downloads was $2,499,000.

1.c) The total amount that Craze-K received in royalties last year was $1,240,065.

2) The total royalties that Mr. Pambruccian received last year were $45,210.01.

Commission = 8.5%

                                               CDs         Downloads      Total

Number of items sold     1.86 million      2.1 million

Selling price per unit       $6.50             $1.19

Total sales revenue      $12,090,000   $2,499,000   $14,5898,000

                                  (1.86 m x $6.50)  (2.1 m x $1.19)

Sales commission =      $1,027,650      $212,415        $1,240,065

Royalties = 4%

Selling price per book = $45.99

The total number of books sold = 24,576

The total revenue (sales) = $1,130,250,24 (24,576 x $45.99)

Royalties received = $45,210.01 ($1,130,250.24 x 4%)

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After four iterations of drawing and replacing balls, the probability that the urn contains three red and three blue balls is 1/3. so, the correct answer is D).

Let's consider the possible outcomes after each iteration of the process. We will use R and B to denote a red and blue ball, respectively.

After the first iteration, we have two possible outcomes:

R, R: The urn contains two red balls.

B, B: The urn contains two blue balls.

After the second iteration, we have four possible outcomes:

R, R, R, R: The urn contains four red balls.

R, R, B, B: The urn contains two red balls and two blue balls.

B, B, B, B: The urn contains four blue balls.

B, B, R, R: The urn contains two red balls and two blue balls.

After the third iteration, we have six possible outcomes:

R, R, R, R, R, R: The urn contains six red balls.

R, R, R, B, B, B: The urn contains three red balls and three blue balls.

R, R, B, B, R, R: The urn contains four red balls and two blue balls.

R, R, B, B, B, B: The urn contains three red balls and three blue balls.

B, B, B, B, B, B: The urn contains six blue balls.

B, B, R, R, B, B: The urn contains four blue balls and two red balls.

After the fourth iteration, we have six possible outcomes, one for each of the outcomes after the third iteration. In particular, we are interested in the outcomes where the urn contains three red balls and three blue balls, which occur in two of the six outcomes.

Therefore, the probability that the urn contains three balls of each color after the four iterations is 2/6 = 1/3, which is answer choice (d).

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--The given question is incorrect, the correct question is given

" an urn contains one red ball and one blue ball. a box of extra red and blue balls lie nearby. george performs the following operation four times: he draws a ball from the urn at random and then takes a ball of the same color from the box and returns those two matching balls to the urn. after the four iterations the urn contains six balls. what is the probability that the urn contains three balls of each color?(2020amc10b problem 18) (a) 16 (b) 1/5 (c) 1/4 (d) 1/3 (e) 12 "--

If the number of degrees of freedom for a chi-square distribution is 81, then the population mean and standard deviation is calculated to be 81 and 12.7279 respectively.

For a chi-square distribution with k degrees of freedom, the population mean and standard deviation are:

Population Mean = k

Population Standard Deviation = √(2k)

Therefore, for a chi-square distribution with 81 degrees of freedom:

Population Mean = k = 81

Population Standard Deviation = √(2k) = √(2×81) = √(162)

Population Mean = 81

Population Standard Deviation = 12.7279 (rounded to four decimal places)

So the population mean is 81 and the population standard deviation is approximately 12.7279.

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to the nearest whole percent, the percentage yield is 13%.

What is the percentage?

A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.

The percentage yield of a stock is calculated as follows:

Percentage Yield = (Annual Dividend / Stock Price) x 100%

Substituting the given values, we get:

Percentage Yield = (0.68 / 5.07) x 100% = 13.43%

Hence, to the nearest whole percent, the percentage yield is 13%.

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Answer:

Quintic

Step-by-step explanation:

the degree of a polynomial is determined by the variable with the largest exponent in the expression.

3h³ ← is of degree 3

6 ← is of degree 1

4h² ← is of degree 2

4[tex]h^{5}[/tex] ← is of degree 5

then the degree of the polynomial is 5 , or a Quintic

First, we need to calculate the monthly interest rate by dividing the APR by 12:

11.99% / 12 = 0.9992%

Next, we can use the formula for monthly interest on credit cards, which is:

(balance x monthly interest rate) + (payment - (balance x monthly interest rate)) = new balance

We can solve for the new balance each month, and then use the new balance to calculate the interest for the following month. Here's how it works:

Month 1:

(balance x 0.9992%) + ($350 - (balance x 0.9992%)) = $7,219.17 (new balance)

Month 2:

($7,219.17 x 0.9992%) + ($350 - ($7,219.17 x 0.9992%)) = $6,870.19 (new balance)

Month 3:

($6,870.19 x 0.9992%) + ($350 - ($6,870.19 x 0.9992%)) = $6,516.76 (new balance)

Month 4:

($6,516.76 x 0.9992%) + ($350 - ($6,516.76 x 0.9992%)) = $6,158.68 (new balance)

Month 5:

($6,158.68 x 0.9992%) + ($350 - ($6,158.68 x 0.9992%)) = $5,795.73 (new balance)

Month 6:

($5,795.73 x 0.9992%) + ($350 - ($5,795.73 x 0.9992%)) = $5,427.67 (new balance)

Month 7:

($5,427.67 x 0.9992%) + ($350 - ($5,427.67 x 0.9992%)) = $5,054.24 (new balance)

Month 8:

($5,054.24 x 0.9992%) + ($350 - ($5,054.24 x 0.9992%)) = $4,675.18 (new balance)

Month 9:

($4,675.18 x 0.9992%) + ($350 - ($4,675.18 x 0.9992%)) = $4,290.23 (new balance)

Month 10:

($4,290.23 x 0.9992%) + ($350 - ($4,290.23 x 0.9992%)) = $3,899.12 (new balance)

Month 11:

($3,899.12 x 0.9992%) + ($350 - ($3,899.12 x 0.9992%)) = $3,501.61 (new balance)

At the end of the 11th month, the balance is paid down to $3,501.61, and then at the end of the 12th month, it is paid off completely.

To calculate the total interest paid, we can add up the interest for each month:

$7,568.19 - $7,219.17 = $349.02

$7,219.17 - $6,870.19 = $348.98

$6,870.19 - $6,516.76 = $353.43

$6,516.76 - $6,158.68 = $358.08

$6,158.68 - $5,795.73 = $362.95

$5,795.73 - $5,427.67 = $368

I explained step by step.

Answer:

368

Step-by-step explanation:

The experimental probability of rolling the number 3 is approximately 0.2

Experimental probability is the ratio of the number of times an event occurs to the total number of trials or observations conducted in an experiment or a trial. It is an estimate of the probability of an event based on the actual outcome of a series of trials or experiments.

To find the experimental probability of rolling the number 3, we need to divide the number of times the number 3 occurred by the total number of rolls.

From the table, we can see that the number 3 occurred 45 times. The total number of rolls is

42 + 44 + 45 + 44 + 47 + 46 = 268

So, the experimental probability of rolling the number 3 is

45/268 = 0.168 (rounded to the nearest tenth)

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The given question is incomplete, the complete question is:

A class rolled number cubes. their results are shown in the table. what is the experimental probability of rolling the number 3? round your answer to the nearest tenth.

The circumference of the circle is approximately 31.42 cm and the area of the circle is approximately 157.08 cm².

A circle circumscribed about a square with sides of 10cm has a circumference of approximately 31.42 cm and an area of approximately 157.08 cm².

If a circle is circumscribed about a square, the diameter of the circle is equal to the diagonal of the square. In this case, the diagonal of the square is:

d = √(10² + 10²) = √(200) = 10√(2) cm

The radius of the circle is half the diameter, so:

r = 5√(2) cm

The circumference of the circle is:

C = 2πr = 10π√(2) cm

The area of the circle is:

A = πr² = 50π cm²

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The sequence's eighth partial total, then, is zero.

A series is a collection of things that is in order in mathematics. (or events). Similar to a group, it has individuals. (also called elements, or terms). The total length of the series is the number in ordered components (possibly endless).

The sequence is: 24, -24, 24, -24, ...

To find the 8th partial sum, we need to add the first 8 terms of the sequence.

S8 = 24 + (-24) + 24 + (-24) + 24 + (-24) + 24 + (-24)

Simplifying this expression, we see that every pair of adjacent terms cancels each other out, leaving us with:

S8 = 0 + 0 + 0 + 0

Therefore, the 8th partial sum of the sequence is 0.

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Consumer surplus and deadweight loss have decreased due to the price floor of $9.00 set by the government. The correct option is c.

To answer this question, we need to first understand what a price floor is and how it affects the market.

A price floor is a government-imposed minimum price that must be paid for a good or service.

In the context of a market, a price floor that is set above the equilibrium price will create a surplus of the good or service.

This is because the price floor creates a situation where the quantity supplied exceeds the quantity demanded.

Now, let's examine the diagram:

           ^

        | P=$9.00  <- price floor

  S    |  / \

        |  /  \

$10  | /     \

        |/        \

 $8   /           \

         |               \

$6   /|_________\

        |                      \

        |       Qd   Qs   |

        |___________|

                 Q

In this diagram, the price floor is set at $9.00, which is above the equilibrium price of $8.00.

As a result, there is a surplus of the good, with quantity supplied (Qs) exceeding quantity demanded (Qd).

Now, let's consider the impact on consumer surplus, producer surplus, and deadweight loss:

Consumer surplus is the difference between the price consumers are willing to pay and the actual price they pay. In this case, the price consumers are willing to pay is below the price floor, so consumer surplus is reduced. Therefore, option c.) "Consumer surplus and deadweight loss" is the correct answer.

Producer surplus is the difference between the price producers receive and the minimum price they are willing to accept. In this case, the price producers receive is above the equilibrium price, so producer surplus is increased. Therefore, option b.) "Consumer surplus and producer surplus" is incorrect.

Deadweight loss is the loss of economic efficiency that occurs when the quantity of a good that is bought and sold is below or above the equilibrium quantity. In this case, the price floor creates a surplus, which leads to deadweight loss. Therefore, option d.) "Only deadweight loss" is incorrect.

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Consider the diagram below. Which of the variables (consumer surplus, producer surplus, and deadweight loss) have decreased due to the price floor of $9.00 set by the government?

a.) Producer surplus and deadweight loss

b.) Consumer surplus and producer surplus

c.) Consumer surplus and deadweight loss

d.) Only deadweight loss

Based on the sample, the number of people whose favorite snack is cake are 589.

We learn languages ​​to communicate. In the world of mathematics, we express language based on algebraic formulas. Algebraic Expressions Simply put, defining an algebraic expression means combining numbers, letters, and operators to convey instructions or explanations. This is similar to forming sentences as a child learns to express himself in sentences.

Let,

The number of people whose favorite snack is cake = 31x

The number of people whose favorite snack is pretzels = 25x

The number of people whose favorite snack is cookies = 53x

The number of people whose favorite snack is other = 60x

Since the reception is been planned for 3200 people:

31x + 25x + 53x + 60x = 3200

169x = 3200

x = 3200/169

x = 18.93

x ≈ 19

As, The number of people whose favorite snack is cake:

= 31x

= 31 × 19

= 589

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The height of the building is 87.5 feet.

To find the height of the building, we will use similar triangles.
1. Draw a diagram with a right triangle formed by the basketball player, the mirror, and the top of the building.

Label the height of the building as 'h', the distance between the mirror and the building as 100 ft, and the distance between the mirror and the basketball player as 8 ft.
2. Draw another right triangle formed by the basketball player, the mirror, and the ground. Label the height of the basketball player as 7 ft.
3. Since the two triangles are similar, we can write the following proportion:

(height of the building) / (distance between mirror and building) = (height of basketball player) / (distance between mirror and basketball player)
4. Plug in the values: h / 100 = 7 / 8
5. To solve for the height 'h', multiply both sides by 100: h = (7 / 8) * 100
6. Calculate the value of 'h': h = 87.5 ft
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The 90% confidence interval for bmi is:  (27.998, 28.302)

The correct answer is an option (d) (27.97, 28.33)

We know that the formula for the confidencce interval is,

CI = [tex](\bar{x}\pm z\frac{s}{\sqrt{n} })[/tex]

where, Ci is the confidence interval

[tex]\bar{x}[/tex] is the sample mean

z is the confidence level value

s = sample standard deviation

n = sample size

Here we need to find 90% confidence interval for bmi in a sample of 3,326 adults, the mean bmi was 28.15 and the sample standard deviation was 5.32

n = 3326,  [tex]\bar{x}[/tex]  = 28.15 and σ = 5.32

We know that 1 - α = confidence interval

1 - α = 0.90

so, α = 0.10

α/2 = 0.05

And from the standard normal table [tex]z_{\alpha /2}[/tex] = 1.64

Using above formula of confidence interval,

CI = [tex](28.15 \pm 1.64\frac{5.32}{\sqrt{3326} } )[/tex]

CI = (28.15 ±0.152)

CI = (27.998, 28.302)

Therefore, the correct answer is an option (d) (27.97, 28.33)

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In order to determine the volume of a solid of revolution revolving around an axis that is alternatively the x or y-axis, the technique of cylindrical shells can be employed.

The general steps for doing this are as follows:

First, recognizing the area to revolve and the central axis must take place.

Second, an expression for the distance from the pivotal point to every single point within the region should be established; let us denote this distance as 'r'.

Then, discovering the measurement of each individual cylindrical shell can also be necessary by obtaining the distinction between two separate vertical points within the region; we shall refer to this tallest height identified as 'h.'

Lastly, setting up an integral expression for the volume of every encompassing cylindrical shell can bring forth more specific results.

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The recent study says 24% wage gap between nonmetropolitan and metropolitan workers can be attributed to differences in job opportunities, education and skill levels, cost of living, and economic development.

According to a recent study, the median earnings of nonmetropolitan workers in the United States was 24% less than the median earnings of metropolitan workers.

The most likely explanation for this phenomenon can be attributed to several factors.
1. Job opportunities: Metropolitan areas tend to have a higher concentration of job opportunities, particularly in higher-paying industries such as finance, technology, and professional services.

In contrast, nonmetropolitan areas often have fewer job options and may be dominated by lower-paying industries such as agriculture, retail, and hospitality.
2. Education and skill levels: Metropolitan areas generally have a larger pool of highly educated and skilled workers, which can lead to higher salaries.

Nonmetropolitan areas may have lower levels of education and skill among the workforce, which can result in lower earnings.
3. Cost of living: The cost of living is generally higher in metropolitan areas, which can lead to higher salaries to offset these expenses.

In nonmetropolitan areas, the cost of living is typically lower, which can result in lower wages as employers do not need to pay as much to maintain a reasonable standard of living for their workers.
4. Economic development: Metropolitan areas tend to have more robust economies with higher levels of economic development.

This can create a more competitive job market, which can lead to higher salaries for workers. Nonmetropolitan areas often have less economic development, which can result in fewer high-paying jobs and lower wages overall.
In summary, the 24% wage gap between nonmetropolitan and metropolitan workers can be attributed to differences in job opportunities, education and skill levels, cost of living, and economic development.

These factors contribute to the higher median earnings of metropolitan workers compared to their nonmetropolitan counterparts.

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The coefficient of [tex]x^{2}[/tex] in binomial expansion is 0

option is d .0

A binomial expansion is a method for expanding and simplifying algebraic statements of the type [tex](x+y)^{n}[/tex] into sum of terms of the form [tex]ax^{b} y^{c}[/tex].

An equation is a statement that determines the equivalence of two expressions joined by the equals sign "=". For instance, 5x - 9 = 10.

5x - 9 and 10 are expressions in this case. "=" is the sign that connects these two expressions.

According to the given information:

Given expanding term is [tex](2x+\frac{3}{x^{3} } )^{8}[/tex]

On cross multiplying and separating power numerator and denominator we get, [tex]\frac{(2x^{4} +3)^{8} }{(x^{3} )^{8} }[/tex]

Expanding the numerator we get [tex]256x^{32}+3072x^{28} +16128x^{24}+48384x^{20} +90720x^{16}+10884x^{12}+81648\\ x^{8}+34992x^{4}+6561[/tex]

Here there is no [tex]x^{2}[/tex],So co efficient of it is 0

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The pοpulatiοn οf bacteria will be apprοximately 104,320 bacteria 1,705 minutes frοm nοw.

Expοnential grοwth is a type οf grοwth in which a quantity increases at a rate prοpοrtiοnal tο its current value.

Tο sοlve the prοblem, we can use the fοrmula fοr expοnential grοwth, which is:

N = N₀ * [tex]2^{(t/d)[/tex]

where:

N₀ = initial pοpulatiοn

N = final pοpulatiοn

t = time elapsed

d = dοubling time

In this case, the dοubling time is 341 minutes. Sο, we can plug in the given values and sοlve fοr N:

[tex]N = 1630 * 2^{(1705/341)[/tex]

N ≈ 104,320

Therefοre, the pοpulatiοn οf bacteria will be apprοximately 104,320 bacteria 1,705 minutes frοm nοw.

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Answer:

diameter= 70

circumference= 219.8

Step-by-step explanation:

to find the diameter, es the doble of radius

35×2=

to fine circumference

πd

3.14× diameter

Answer:

y = -2x.

Step-by-step explanation:

The slope-intercept form of the equation of a line is:

y = mx + b

where m is the slope of the line, and b is the y-intercept.

In this case, the slope is -2, and the y-intercept is 0. So we can substitute these values into the slope-intercept form of the equation:

y = (-2)x + 0

Simplifying, we get:

y = -2x

the equation of the line in slope-intercept form is y = -2x.

The points that are in the solution set are (-1, -1) and (2, -1).

In order to determine which ordered pairs are valid and true solutions based on the given linear inequalities, we would have to test the given ordered pairs by substituting their values into each of the linear inequality as follows;

For ordered pair (0, 0), we have:

y ≤ -1

0 ≤ -1 (False).

For ordered pair (0, 0), we have:

3x + 4y < 4

3(0) + 4(0) < 4

0 < 4 (True)

For ordered pair (-1, -1), we have:

y ≤ -1

-1 ≤ -1 (True).

For ordered pair (-1, -1), we have:

3x + 4y < 4

3(-1) + 4(-1) < 4

-7 < 4 (True).

For ordered pair (2, -1), we have:

y ≤ -1

-1 ≤ -1 (True).

For ordered pair (2, -1), we have:

3x + 4y < 4

3(2) + 4(-1) < 4

-2 < 4 (True).

For ordered pair (-2, 2), we have:

y ≤ -1

2 ≤ -1 (False).

For ordered pair (-2, 2), we have:

3x + 4y < 4

3(-2) + 4(2) < 4

-6 + 8 < 4

2 < 4 (True).

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The probability that Joe will be accepted at one, and only one, the university is E. 0.45.

The probability that Joe will be accepted at one, and only one, university can be calculated using the following approach. First, we need to find the probability of Joe being accepted at each university individually and the probability of him not being accepted at each university. The acceptance rate for applicants with similar qualifications is 25 percent for University A and 40 percent for University B.

Let's use the following notations:

P(A) - probability of being accepted at University A

P(B) - probability of being accepted at University B

P(A') - probability of not being accepted at University A

P(B') - probability of not being accepted at University B

We are given:

P(A) = 0.25

P(B) = 0.40

To find the probability of not being accepted, we subtract the probability of being accepted from 1:

P(A') = 1 - P(A) = 1 - 0.25 = 0.75

P(B') = 1 - P(B) = 1 - 0.40 = 0.60

Now, we want to find the probability of Joe being accepted at one university and not at the other. There are two possibilities:

(1) he gets accepted at University A and not at University B or

(2) he gets accepted at University B and not at University A.

We can use the multiplication rule for independent events and the addition rule for mutually exclusive events to calculate this probability:

P(A and B') + P(A' and B)=

P(A) * P(B') + P(A') * P(B) =

(0.25 * 0.60) + (0.75 * 0.40) =

0.15 + 0.30 = 0.45

So, the probability that Joe will be accepted at one, and only one, university is 0.45. Therefore, the correct option is E. 0.45.

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To put the equation 3y - 9x = -6 into slope-intercept form, we need to isolate y on one side of the equation.

First, we will add 9x to both sides:

3y - 9x + 9x = 9x - 6

Simplifying the left side of the equation:

3y = 9x - 6

Next, we will divide both sides by 3:

y = 3x - 2

This is the equation in slope-intercept form, where the slope is 3 and the y-intercept is -2.

Step-by-step explanation: To find the cost of one taco, we can use a system of equations. Let x be the cost of one burger and y be the cost of one taco. Then we have:

2x + 4y = 22.50 x + 3y = 14.50

Multiplying the second equation by -2, we get:

-2x - 6y = -29 2x + 4y = 22.50

Adding the two equations, we get:

-2y = -6.50 y = 3.25

So one taco costs $3.25.

The expected value of the sample mean of mpg derived from a random sample of four passengers is 30.5 mpg.

The expected value of the sample mean can be calculated using the formula

E(x) = μ

where x is the sample mean, and μ is the population mean.

In this case, the population mean is given as 30.5 mpg. The standard deviation of the population is also given as 4.1 mpg.

The standard deviation of the sample mean can be calculated using the formula

σx = σ/√n

where σ is the population standard deviation and n is the sample size.

Substituting the given values, we get:

σx = 4.1/√4 = 2.05

So the expected value of the sample mean is

E(x) = μ = 30.5 mpg.

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The range of a set of numbers measures the spread or dispersion of the values in the set, and in the given set of numbers, the range is 4.1.

The range of a set of numbers is the difference between the largest and smallest numbers in the set.

The range can be a useful measure of the variability of a dataset, as it can tell us if the values are tightly clustered or widely spread out. However, the range can be influenced by extreme values, also known as outliers, which can distort the measure.

In the given set of numbers:

9, 6.9, 8.1, 7, 7.9, 7.1, 9, 7.6, 4.9

The largest number is 9, and the smallest number is 4.9.

So, the range is:

9 - 4.9 = 4.1

Therefore, the range of the given set of numbers is 4.1.

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Coach A can make 120 free throws in 3 minutes for number of free throws that Coach A can make varies directly with the amount of times she spends shooting the baskets.

A mathematical connection when two variables are involved in which the ratio of their values is constant is known as direct variation. Alternatively said, if one variable is multiplied by a specific amount, the second variable will also be multiplied by the same value. The two variables in this connection may be represented as a percentage, where the constant of proportionality is the ratio of their values, and the two variables are on opposite sides of an equal sign.

Given that, she can make 20 baskets in 30 seconds.

Thus, using proportion we have:

Free throws / Time = Free throws per unit time

20 baskets / 30 seconds = 2/3 baskets per second

Now, for 3 minutes or 3(60)n= 180 seconds we have:

Free throws = Time x Free throws per unit time

Free throws = 180 seconds x (2/3 baskets per second)

Free throws = 120 baskets

Hence, Coach A can make 120 free throws in 3 minutes.

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When skiing down a mountain with a vertical height of 1150 feet and a base-to-top distance of 2300 feet, the angle of elevation from the base to the top of the mountain is approximately 26.56 degrees.

When skiing down a mountain with a vertical height of 1150 feet and a base-to-top distance of 2300 feet, the angle of elevation from the base to the top of the mountain is given by tan⁻¹(1150/2300).

How to find the angle of elevation from the base to the top of the mountain?

The angle of elevation of an object from a point is the angle between the horizontal and the line of sight from the observer to the object above the horizontal. We can use the inverse tangent function to calculate this angle of elevation.

Step 1: Find the tangent of the angle of elevation: Let the height of the mountain be h and the distance from the base to the top of the mountain be d. Then tan(θ) = h/d.

Step 2: Inverse tangent of the height and distance of the mountain: Take the inverse tangent of the quotient to find the angle of elevation from the base to the top of the mountain. θ = tan⁻¹(h/d).Here, h = 1150 feet and d = 2300 feet. Substituting these values in the formula θ = tan⁻¹(1150/2300), we can find the angle of elevation from the base to the top of the mountain.θ = tan⁻¹(1150/2300) = 26.56 degrees.

So, the angle of elevation from the base to the top of the mountain is approximately 26.56 degrees.

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Answer:

100

Step-by-step explanation:

its impossable

The new volume of the cylinder is $100$ cubic feet.

Let the original radius and height of the cylinder be $r$ and $h$, respectively. Therefore, the original volume of the cylinder is given by $\pi r^2 h = 100$. After the radius decreases by $10%$ and the height increases by $10%$, the new radius and height become $0.9r$ and $1.1h$, respectively. The new volume of the cylinder can be calculated as $\pi (0.9r)^2 (1.1h) = 0.891\pi r^2 h$. Since $0.891\pi r^2 h = 100$, the new volume of the cylinder is $100$ cubic feet.

Therefore, the new volume of the cylinder is the same as the original volume, i.e., $100$ cubic fee

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The solution is A. 3/8. We can calculate it in the following manner.

According to the general equation for conditional probability,

P(A|B) = P(A and B) / P(B)

We are given that P(A|B) = 3/10 and P(B) = 2/5.

We need to find P(A and B) to solve for P(A|B).

Using the formula for conditional probability, we can rearrange the equation as:

P(A and B) = P(A|B) * P(B)

Substituting the given values, we get:

P(A and B) = (3/10) * (2/5) = 6/50 = 3/25

Now, we can find P(A|B) using the first equation:

P(A|B) = P(A and B) / P(B) = (3/25) / (2/5) = (3/25) * (5/2) = 3/10

Therefore, the answer is A. 3/8.

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