I need help with this and I need it in 30 minutes please

The original price of the product was approximately $98.00.

To determine the original price before the 15.5% decrease, we can use the following equation:

Original price - (15.5% of original price) = $82.81

Let's solve for the original price:

Original price - (0.155 * Original price) = $82.81

Simplifying the equation:

0.845 * Original price = $82.81

Dividing both sides by 0.845:

Original price = $82.81 / 0.845

Calculating the original price:

Original price ≈ $98.00

Therefore, the original price of the product was approximately $98.00.

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Points lie on the graph of the inverse of f(x)=5x−2.

Hence, the correct option is C,E,F.

To find the points on the graph of the inverse of f(x), we need to switch the x and y coordinates of each point on the graph of f(x). Then, we can simplify the equation to isolate y and get the inverse function.

f(x) = 5x - 2

y = 5x - 2 (replace f(x) with y)

x = 5y - 2 (switch x and y)

x + 2 = 5y (add 2 to both sides)

y = (x + 2)/5 (divide both sides by 5)

So, the inverse function of f(x) is

[tex]f^{-1}[/tex](x) = (x + 2)/5

Now, we can substitute each point from the given options into the inverse function to see if it lies on the graph of the inverse of f(x).

1. (0, -2)

[tex]f^{-1}[/tex](0) = (0 + 2)/5 = 2/5

No, this point does not lie on the graph of the inverse of f(x).

2. (1, 3)

[tex]f^{-1}[/tex](1) = (1 + 2)/5 = 3/5

No, this point does not lie on the graph of the inverse of f(x).

3. (-2, 0)

[tex]f^{-1}[/tex](-2) = (-2 + 2)/5 = 0

Yes, this point lies on the graph of the inverse of f(x).

4. (2/5, 1)

[tex]f^{-1}[/tex](2/5) = (2/5 + 2)/5 = 6/25

No, this point does not lie on the graph of the inverse of f(x).

5. (0, 2/5)

[tex]f^{-1}[/tex](0) = (0 + 2)/5 = 2/5

Yes, this point lies on the graph of the inverse of f(x).

6. (3, 1)

[tex]f^{-1}[/tex](3) = (3 + 2)/5 = 1

Yes, this point lies on the graph of the inverse of f(x).

Therefore, the points that lie on the graph of the inverse of f(x) are (-2, 0),  (0, 2/5) and (3, 1),

Hence, the correct option is C,E,F.

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(a) To find the slope of the curve where it meets the right-hand pole, we need to differentiate the given equation with respect to x. y = 17cosh(x/17) - 12.

Using the chain rule, we get dy/dx = (17/17)sinh(x/17) = sinh(x/17). Therefore, at x = 7, the slope of the curve is sinh(7/17) ≈ 0.6968.

(b) To find the angle theta between the line and the pole, we can use trigonometry. The slope of the curve at the right-hand pole is the same as the tangent of the angle theta.

Therefore, tan(theta) = 0.6968. Taking the inverse tangent of both sides, we get theta = arctan(0.6968) ≈ 34.33 degrees. Therefore, the acute angle formed by the right pole and the hanging line is approximately 34.33 degrees.

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To find the average rate of change of a function in a given interval, we need to calculate the difference in the function values at the endpoints of the interval and divide it by the length of the interval.

In this case, the interval is (0,2) and the function is f(x) = x^2 - 3x.

At the left endpoint, x=0, we have f(0) = 0^2 - 3(0) = 0.

At the right endpoint, x=2, we have f(2) = 2^2 - 3(2) = -2.

Therefore, the difference in the function values is f(2) - f(0) = -2 - 0 = -2.

The length of the interval is 2 - 0 = 2.

So the average rate of change of f(x) over the interval (0,2) is:

(-2)/2 = -1

Therefore, the average rate of change of f(x) over the interval (0,2) is -1.
Hi! To find the average rate of change in the interval (0, 2) for the function f(x) = x^2 - 3x, you can use the following formula:

Average Rate of Change = (f(b) - f(a)) / (b - a)

In this case, a = 0 and b = 2. First, calculate the function values at these points:

f(0) = (0)^2 - 3(0) = 0
f(2) = (2)^2 - 3(2) = 4 - 6 = -2

Now, apply the formula:

Average Rate of Change = (f(2) - f(0)) / (2 - 0) = (-2 - 0) / (2) = -2 / 2 = -1

So, the average rate of change in the interval (0, 2) for the function f(x) = x^2 - 3x is -1.

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For March 2020, the equivalent units of production for conversion costs are 30,750, rounded to the nearest whole number.

To determine the equivalent units of production for conversion costs in March 2020 for Dorchester Company, we need to follow these steps:
Calculate the equivalent units for the beginning work in process inventory:
Beginning WIP units = 6,000
Completion percentage for conversion costs = 50%
Equivalent units for beginning WIP = 6,000 * 50% = 3,000
Calculate the equivalent units for the units started and completed during March:
Units started and completed = 24,500
Completion percentage for conversion costs = 100%
Equivalent units for started and completed units = 24,500 * 100% = 24,500
Calculate the equivalent units for the ending work in process inventory:                                                                         Ending WIP units = 6,500
Completion percentage for conversion costs = 50%
Equivalent units for ending WIP = 6,500 * 50% = 3,250
Sum up the equivalent units from steps 1, 2, and 3:
Total equivalent units for conversion costs = 3,000 (beginning WIP) + 24,500 (started and completed units) + 3,250 (ending WIP) = 30,750
So, for March 2020, the equivalent units of production for conversion costs are 30,750, rounded to the nearest whole number.

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The area of the parallelogram is approximately 21.2 square feet, rounded to the nearest tenth of a square foot.

To find the area of a parallelogram, we need to multiply the base by the height. In this case, the two sides given (9.5 feet and 6.1 feet) are the base and height respectively, because they are perpendicular.

To find the area, we first need to find the length of the other two sides. Since a parallelogram has opposite sides that are equal in length, we know that the other two sides are also 9.5 feet and 6.1 feet.

Next, we can use the given angle (20°) to find the height of the parallelogram. We can use trigonometry, specifically the tangent function, to do this:

tan(20°) = height / 6.1 feet

height = 6.1 feet * tan(20°)

height ≈ 2.23 feet

Now we can find the area:

area = base * height

area = 9.5 feet * 2.23 feet

area ≈ 21.185 square feet

Rounding to the nearest tenth of a square foot, the area is approximately 21.2 square feet.

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The correct graph to display the data is: C. Bar graph with the title "favorite sport" and the x-axis labeled "sport" and the y-axis labeled....

A bar graph is an appropriate choice for displaying the data collected from the middle school students because it allows us to compare discrete categories (in this case, sports) and their corresponding frequencies (number of students).

In this case, the data is as follows:

The correct bar graph has the title "Favorite Sport" to indicate the subject of the data being represented.

The x-axis is labeled "Sport" and lists the four sports - basketball, baseball, soccer, and tennis - in separate, distinct categories. The y-axis is labeled "Number of Students" and displays the frequency or count of students who chose each sport as their favorite.

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Therefore , the solution of the given problem of unitary method comes out to be (Sum of Daily Balances) / Average Daily Balance (Number of Days in Period).

The well-known minimalist approach, current variables, and any crucial elements from the initial Diocesan tailored query can all be used to accomplish the work. In response, you can be granted another chance to utilise the item. If not, important impacts on our understanding of algorithms will vanish.

Here,

You must be aware of an account's daily balance over a specific time period in order to determine the average daily amount. how to get an average daily balance:

The time frame for which you wish to compute the average daily balance should be chosen. This could, for instance, be a month, a quarter, or a year.

Find the account balance at the end of each day during the specified period.

Sum up each day's balance for the duration.

By the number of days in the time frame, divide the sum. You are then given the daily average balance.

The formula for determining the typical daily balance is as follows:

=> (Sum of Daily Balances) / Average Daily Balance (Number of Days in Period)

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Answer: 50

Step-by-step explanation:

37 is 74 percent of what number

We already have our first value 37 and the second value 74. Let's assume the unknown value is Y which answer we will find out.

As we have all the required values we need, Now we can put them in a simple mathematical formula as below:

STEP 1   37 = 74% × Y

STEP 2   37 = 74/100× Y

Multiplying both sides by 100 and dividing both sides of the equation by 74 we will arrive at:

STEP 3     Y = 37 × 10074

STEP 4     Y = 37 × 100 ÷ 74

STEP 5     Y = 50

Finally, we have found the value of Y which is 50 and that is our answer.

The smallest number of digits that should be used to label the population is 4, since there are 1,020 students in the school.

To determine the smallest number of digits needed to label the population, we will follow these steps:

1. Determine the total number of students in the population.
2. Identify the number of digits needed to represent the largest student number.
3. Apply this number of digits to all student labels.

Let's apply these steps to your question:

1. The total number of students is 1,020.
2. The largest student number is 1,020, which requires 4 digits (since it has four numbers: 1, 0, 2, and 0).
3. To label the entire student population consistently, use 4 digits for all student labels.

So, the smallest number of digits that should be used to label the population is 4.

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To satisfy the conditions that the mode is larger than the median, and the median is larger than the mean, one possible set of frequencies is 1 person chooses 1, 3 people choose 2, 4 people choose 3, 1 person chooses 4 and 11 people choose 5 This results in a mode of 5, a median of 4, and a mean of approximately 3.75.

Since we are given that the mode is larger than the median, that means that at least 11 people must choose the same number. Let's assume that 11 people choose the number 5.

Now, since the median is larger than the mean, we want to make sure that the remaining 9 people choose numbers that are smaller than 5. If they all choose 1, 2, or 3, then the median will be 3, which is larger than the mean. Therefore, we need to make sure that at least one person chooses 4.

So one possible set of frequencies could be

1 person chooses 1

3 people choose 2

4 people choose 3

1 person chooses 4

11 people choose 5

This set of frequencies gives us a mode of 5 (since 11 people choose 5), a median of 4 (since the middle value is 4), and a mean of

(11 + 32 + 43 + 14 + 11*5) / 20 = 3.7

Since the median is larger than the mean, this set of frequencies satisfies all the given conditions.

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The type of triangle formed from the side lengths of a triangle 2, 10, 11 is a scalene triangle.

Based on the given side lengths of a triangle (2, 10, 11), we can determine the type of triangle formed by examining their relationships. First, let's check if these side lengths can form a valid triangle using the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides must be greater than the length of the remaining side. In this case, 2 + 10 > 11, 2 + 11 > 10, and 10 + 11 > 2, so a triangle can be formed.

Now let's identify the type of triangle. There are three main categories to consider: equilateral, isosceles, and scalene. An equilateral triangle has all three sides equal in length, which doesn't apply here. An isosceles triangle has two sides with equal lengths, but in this case, all three sides have distinct lengths. Therefore, the triangle is a scalene triangle, meaning it has no sides of equal length.

In summary, the triangle formed by side lengths 2, 10, and 11 is a scalene triangle because all three sides have different lengths and satisfy the Triangle Inequality Theorem.

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Sam increase the amount of protein she eats by a percentage of 30%.

To find the percentage increase, we can use the formula: (change in amount / original amount) x 100%.

Percentage is a way to express a number as a fraction of 100. It is a convenient method for comparing ratios or proportions because it standardizes them to a common denominator of 100. In this case, we want to find the percentage increase in Sam's daily protein consumption.

First, we need to determine the change in amount. This can be found by subtracting the original amount from the new amount: 58.5g - 45g = 13.5g.

Next, we'll divide the change in amount by the original amount: 13.5g / 45g = 0.3. To express this as a percentage, we'll multiply by 100: 0.3 x 100% = 30%.

Therefore, Sam increased her daily protein intake by 30%. This percentage helps us understand the relative change in her protein consumption compared to her initial intake.

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An equation that could be used to determine M, the unknown side length of the logo is X = (36/5) x M

Let's assume that the unknown side length of the logo is 'M'. The logo is a rectangle, and the area of a rectangle is given by multiplying its length and width. Since we know the length of the logo is 7(1)/(5) feet, we can write the equation:

A = L x W

where A is the area of the logo, L is the length of the logo, and W is the width of the logo.

Substituting the given values, we get:

A = (7(1)/(5)) x M

or

A = (36/5) x M

Now, we know that the area of the logo is exactly the maximum area allowed by the building owner. Let's assume this maximum area is 'X'. So, we can write another equation:

A = X

Combining both equations, we get:

X = (36/5) x M

This is the required equation that could be used to determine the unknown side length 'M' of the logo if we know the maximum area allowed by the building owner 'X'.

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Answer:

The answer to your problem is, F = 15N

Step-by-step explanation:

You have: F = ka

Where F is the force acting on the object, A is the object's acceleration and is the constant of proportionality.

Which will be our letters that we will NEED to use for today.

You can calculate the constant of proportionality by substituting F = 18 and a = 6 into the equation and solving for k: Then we can now figure out the “ formula of expression “

18 = k6

k = [tex]\frac{18}{6}[/tex]

K = 3

We would need to calculate the force when the acceleration of the object becomes 5 m/s², as following: F = 3 x 5 ( Basic math )

= F = 15

Thus the answer to your problem is, F = 15N

In 2002, the average price of a two-bedroom apartment in the uptown area was approximately $0.316 million, and it was increasing at a rate of about $0.0328 million per year.

To find the average price of a two-bedroom apartment in 2002 (t=8), you need to evaluate the given function p(t) = 0.17e^(0.10t) at t=8:

p(8) = 0.17e^(0.10 * 8)

p(8) = 0.17e^0.8 ≈ 0.316 million dollars

To find the rate at which the price was increasing in 2002, you need to find the derivative of the function p(t) with respect to t, and then evaluate it at t=8:

p'(t) = d/dt (0.17e^(0.10t))
p'(t) = 0.17 * 0.10 * e^(0.10t)

Now, evaluate p'(t) at t=8:

p'(8) = 0.17 * 0.10 * e^(0.10 * 8)
p'(8) ≈ 0.0328 million dollars per year

So, in 2002, the average price of a two-bedroom apartment in the uptown area was approximately $0.316 million, and it was increasing at a rate of about $0.0328 million per year.

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The correct answer is "Translated to the left 10 and down 3 and then reflected about the y-axis."

Transformation is a process that changes the position, orientation, size, or shape of a geometric object. Transformations are often described using matrices, vectors, or other mathematical operations.

Types of Transformations

From the problem statement, to move the center from (15,-2) to (-5,-5), we need to translate the circle to the left by 10 units and down by 3 units. So the first transformation is a translation to the left 10 units and down 3 units.

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To express u = (7, -10) as a linear combination u = rv + sw, where v = (2, 1) and w = (1,4), we need to find the values of r and s such that:

u = rv + sw

Substituting the given values, we get:

(7, -10) = r(2, 1) + s(1,4)

Using the symbolic notation, we can write this as a system of equations:

7 = 2r + s
-10 = r + 4s

We can solve this system of equations by using the elimination method:

Multiply the second equation by 2:

7 = 2r + s
-20 = 2r + 8s

Subtracting the first equation from the second, we get:

-27 = 7s

Dividing both sides by 7, we get:

s = -27/7

Substituting this value of s into the first equation, we get:

7 = 2r - 27/7

Multiplying both sides by 7, we get:

49 = 14r - 27

Adding 27 to both sides, we get:

76 = 14r

Dividing both sides by 14, we get:

r = 38/7

Therefore, u = (7, -10) can be expressed as the linear combination:

u = (38/7)(2,1) + (-27/7)(1,4)

Using fractions where needed, the answer is:

u = (76/7, 38/7) + (-27/7, -108/7)
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Answer:

  (x, y) = (5, 3)

Step-by-step explanation:

You want the solution to the system of equations ...

It is convenient to subtract the second equation from 3 times the first:

  3(4x -3y) -(5x -9y) = 3(11) -(-2)

  12x -9y -5x +9y = 33 +2

  7x = 35 . . . . . . . simplify

  x = 5 . . . . . . . . . . divide by 7

  4(5) -3y = 11 . . . . . substitute into the first equation

  9 = 3y . . . . . . . . add 3y-11 to both sides

  y = 3 . . . . . . . . divide by 3

The solution is (x, y) = (5, 3).

__

Additional comment

We find using a graphing calculator to be the easiest way to solve a pair of simultaneous equations. The attachment shows the solution is the one we found above.

The approach of "substitution" is straightforward, if error-prone. Basically, you solve one equation for either variable, then use that expression in the other equation. Here, for example, you can solve the first for x:

  x = (11 +3y)/4

Then use that in the second equation:

  5(11 +3y)/4 -9y = -2

  5(11 +3y) -36y = -8 . . . . eliminate the denominator

  55 +15y -36y = -8 . . . . . eliminate the parentheses

  -21y = -63 . . . . . . . . . . . simplify, subtract 55

  y = 3 . . . . . . . . . . . . divide by -21

  x = (11 +3(3))/4 = 20/4 = 5 . . . . find x

In the above, we used "elimination." We took advantage of the fact that the y-coefficients were related by a factor of 3. To cancel y-terms, we need to have the equations we "add" have opposite signs for the y-terms. Here, we do that by multiplying the first by 3 (to make -9y), then subtracting the second equation (which has -9y, so will cancel). We could have subtracted 3 times the first from the second, but that would make all the resulting coefficients be negative, which we like to avoid.

Or, we could have multiplied the first equation by -3 to make the y-coefficients opposite, then added the results. (Again, that would give negative coefficients in the sum.) Planning ahead can help avoid mistakes due to minus signs.

(A) ∠X is the largest angle in the given triangle as the side opposite is also the largest.

An angle is formed when two straight lines or rays meet at a single terminal.

The place where two points converge is known as an angle's vertex. The name "angle" comes from the Latin word "angulus," which means "corner."

Two lines that meet at the same point or two planes that meet at the same line form a geometric figure.

The angle in degrees separates these lines or planes.

So, we know that:

The side opposite to the largest angle is also the largest side of the triangle and vica-versa.

Remembering this we can easily conclude that ∠X is the largest angle as the largest is 9 units and X is opposite of the side YZ which measures 9 units.

Therefore, (A) ∠X is the largest angle in the given triangle as the side opposite is also the largest.

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Correct question:

Which angle in AXYZ has the largest measure?

A. ∠X

B. ∠Y

C. ​∠Z

D. Cannot be determined

Given two events E and F with Pr(E) = 0. 4, Pr(F) = 0. 5, and Pr(EnF) = 0. 3 then:

a) Pr(E|F) = 0.6

b) Pr(F|E) = 0.75

c) NO, E and F are not independent.

a) To find Pr(E|F), we use the formula: Pr(E|F) = Pr(EnF)/Pr(F). Substituting the given values, we get Pr(E|F) = 0.3/0.5 = 0.6.

b) Similarly, to find Pr(F|E), we use the formula: Pr(F|E) = Pr(EnF)/Pr(E). Substituting the given values, we get Pr(F|E) = 0.3/0.4 = 0.75.

c) We can check for independence by seeing if Pr(E) = Pr(E|F) or Pr(F) = Pr(F|E). However, since Pr(E) ≠ Pr(E|F) and Pr(F) ≠ Pr(F|E), we can conclude that E and F are not independent.

In other words, the occurrence of one event affects the probability of the other event occurring. Specifically, the fact that Pr(EnF) ≠ Pr(E)Pr(F) indicates that the events are dependent.

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Using probability, we can find probability of the random variable, x falling in the shaded region as to be 5/8.

Probability is the ratio of favourable outcomes to all other potential outcomes of an event. The symbol x can be used to express the quantity of successful outcomes for an experiment with 'n' outcomes. The following formula can be used to determine an event's probability.

Positive Outcomes/Total Results = x/n = Probability(Event)

Let's look at a simple example to better understand probability. Imagine that we need to predict whether it will rain or not. The right response to this question is "Yes" or "No." Whether it rains or not is uncertain. Probability is used to predict the outcomes when tossing coins, rolling dice, or drawing cards from a deck of cards.

Here in the question,

Total region = 8.

Shaded region = 5

So, probability of falling in the shaded region = 5/8

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Answer:

m = 6/5

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (3, 9) and (8, 15)

We see the y increase by 6 and the x increase by 5, so he slope is

m = 6/5

Answer:

The slope of the points is 6/5.

Step-by-step explanation:

SOLUTION :

Using slope of a line formula to find the slope of the points :

[tex]\quad\dashrightarrow{\sf{m = \dfrac{y_2 - y_1}{x_2 - x_1}}}[/tex]

Substituting all the given values in the formula to find the slope of the points :

[tex]\quad\dashrightarrow{\sf{m = \dfrac{y_2 - y_1}{x_2 - x_1}}}[/tex]

[tex]\quad\dashrightarrow{\sf{m = \dfrac{15 - 9}{8 -3}}}[/tex]

[tex]\quad\dashrightarrow{\sf{m = \dfrac{6}{5}}}[/tex]

[tex]\quad{\star\underline{\boxed{\sf{\red{m = \dfrac{6}{5}}}}}}[/tex]

Hence, the slope of the points is 6/5.

The effect of the student presenting such a monologue would be B. The mean will decrease.

Order the data points:

1. 5, 1. 5, 2, 2. 5, 2. 5, 2. 5, 3, 3. 5, 3. 5, 4

Find the mean ;

= (1. 5 + 1. 5 + 2 + 2. 5 + 2. 5 + 2. 5 + 3 + 3. 5 + 3. 5 + 4) / 10

= 27 / 10

= 2. 7

Then find the new mean after the student presents the monologue:

= ( 0. 5 + 1. 5 + 1. 5 + 2 + 2. 5 + 2. 5 + 2. 5 + 3 + 3. 5 + 3. 5 + 4) / 11

= 2. 5

The mean therefore reduced.

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Answer:

b

Step-by-step explanation:

The probability that more than 2 minutes pass before a sale is completed is approximately 0.895 or 89.5%.

The CDF of the exponential distribution is given by:

F(x) = 1 - e^(-λx)

where λ is the rate parameter, which is the reciprocal of the mean, λ = 1/18 in this case. The variable x is the time it takes for a sale to be completed.

To find the probability that more than 2 minutes pass before a sale is completed, we need to find the complement of the probability that a sale is completed within the first 2 minutes. That is:

P(X > 2) = 1 - P(X ≤ 2)

Substituting into the CDF formula:

P(X > 2) = 1 - F(2) = 1 - [tex](1 - e^{(-\lambda_2)} = e^{(-\lambda_2)}[/tex]

Plugging in the value of λ:

P(X > 2) = [tex]e^{(-(1/18)\times2)}[/tex] ≈ 0.895

This means that there is a high chance that it will take more than 2 minutes for a sale to be completed on the phone.

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Using the given information we can compute several financial ratios that help us evaluate the company's financial performance.

To calculate these ratios, we need to use information from the income statement and the additional information provided.

One important financial ratio is earnings per share (EPS), To compute EPS, we divide net income by the average number of common shares outstanding during the year. To find the average number of shares outstanding, we add the beginning and ending shares and divide by 2.

Net income = $122,100

Average number of common shares outstanding = (26,700 + 36,000) / 2 = 31,350

EPS = $122,100 / 31,350 = $3.89

Another important financial ratio is the price-earnings (P/E) ratio, To compute the P/E ratio, we divide the market price per share by the EPS.

Market price per share = $13

EPS = $3.89

P/E ratio = $13 / $3.89 = 3.34 times

The payout ratio measures the proportion of earnings that is paid out as dividends. To compute the payout ratio, we divide total dividends by net income. However, we need to adjust for the fact that some of the dividends were paid to preferred stockholders. To do this, we subtract the preferred dividends from the total dividends before dividing by net income.

Total dividends = $24,200

Preferred dividends = $6,600

Common dividends = $24,200 - $6,600 = $17,600

Net income = $122,100

Payout ratio = $17,600 / $115,500 = 15.24%

The times interest earned (TIE) ratio, To compute the TIE ratio, we divide earnings before interest and taxes (EBIT) by interest expense.

Interest expense = $16,200

EBIT = Gross profit - Expenses + Interest expense = $197,300 - $75,200 + $16,200 = $138,300

TIE ratio = $138,300 / $16,200 = 8.54 times

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Answer: 7x=30.5

Step-by-step explanation: If you were to answer this equation with the given information it would not be correct. 7(4.25)=29.75.  You need to go through BEDMAS to answer this.

You what you need to do is divide 30.5 by 7 to get the amount she needs to jog for a week, if you do that you get 4.37 miles each day to get to 30.5 in a week.

The probability of choosing exactly 13 students who dressed up as the 40s out of the 16 selected students is approx. 0.4334.

We can model this situation as a hypergeometric distribution, where we have a population of 19 students, 15 of whom dressed up as the 40s.

We want to choose a sample of 16 students and find the probability that exactly 13 of them dressed up as the '40s.

The probability of choosing exactly 13 students who dressed up as the 40s can be calculated:

(number of ways to choose 13 students who dressed up as the 40s) * (number of ways to choose 3 students who dressed up as other decades) / (total number of ways to choose 16 students)

The number of ways to choose 13 students who dressed up as the '40s is the number of combinations of 15 choose 13:

(15 choose 13) = 105

The number of ways to choose 3 students who dressed up as other decades is the number of combinations of 4 choose 3, which is:

(4 choose 3) = 4

The total number of ways to choose 16 students from 19 is the number of combinations of 19 choose 16, which is:

(19 choose 16) = 969

105 * 4 / 969 = 0.4334

Therefore, the probability of choosing exactly 13 students who dressed up as the 40s = 0.4334 (rounded to four decimal places)

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The volume of water the cup can hold is 25.12 inches³.

A water cup is in the shape of the cone. The diameter of the cup is 4 inches and the height is 6 inches.

Therefore, the volume of water the water cup can hold can be calculated as follows:

Hence,

volume of the cup = 1 / 3 πr²h

where

Therefore,

r = 4 / 2 = 2 inches

h = 6 inches

Therefore,

volume of the cup = 1 / 3 × 3.14 × 2²  6

volume of the cup = 1 / 3 × 3.14 × 4  × 6

volume of the cup = 75.36 / 3

volume of the cup = 25.12 inches³

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