The volume of the rain barrel is approximately 10,256.58 cubic inches.
To get the volume of the rain barrel, which is shaped like a right circular cylinder, you need to use the formula for the volume of a cylinder: V = πr²h. Here, V represents the volume, r is the radius, and h is the height of the cylinder.
The given diameter of the rain barrel is 22 inches. To find the radius (r), you need to divide the diameter by 2:
r = 22 / 2 = 11 inches.
The height (h) of the rain barrel is given as 27 inches.
Now, you can plug these values into the formula and use 3.14 for pi (π):
V = πr²h
V = 3.14 * (11²) * 27
V = 3.14 * (121) * 27
V = 3.14 * 3267
V ≈ 10,256.58 cubic inches
So, the volume of the rain barrel is approximately 10,256.58 cubic inches.
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Nataly compra una falda, una blusa y un saco con los precios de la lista son s/78,s/65 y s/240 pero al pagar la falda se la dejan a s/69,la blusa a s/52 y el sacon a s/198.¿cuánto se ahorró nataly?
Nataly saved s/64.
Nataly compró una falda, una blusa y un saco por s/78, s/65 y s/240, respectivamente. Pero compró la falda por s/69, la blusa por s/52 y el saco por s/198. ¿Cuánto se ahorró Nataly?The original prices for the items are:
Skirt: s/78
Blouse: s/65
Jacket: s/240
The discounted prices Nataly paid are:
Skirt: s/69
Blouse: s/52
Jacket: s/198
To find out how much Nataly saved, we need to calculate the difference between the original prices and the discounted prices, and then add them up:
savings = (78 - 69) + (65 - 52) + (240 - 198)
savings = 9 + 13 + 42
savings = s/64
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9 Real / Modelling Naomi rents a room to teach yoga to x people.
She uses this equation to work out her profit, y, in pounds:
y = 10x - 50
a Draw the graph of the line y = 10x - 50.
b i What is her profit when 0 people attend the class?
ii What does the y-intercept represent?
c How much does each person pay for the class?
Her profit when 0 people attend is -$50 and each person pays 10
Drawing the graph of the lineFrom the question, we have the following parameters that can be used in our computation:
y = 10x - 50.
The graph is added as an attachment
Her profit when 0 people attendThis means that
x = 0
So, we have
y = 10(0) - 50.
y = -50
She made a loss of 5-
What the y-intercept representsThis represents her profit when 0 people attend
How much each person pays per classThis represents the slope of the function
The slope of the function is 10
So, each person pays 10
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what are the ordered pairs of y>1/2x+3
The ordered pairs of the inequality expression is (0, 4)
What are the ordered pairs of the inequality expressionFrom the question, we have the following parameters that can be used in our computation:
The inequality expression y>1/2x+3
To determine the ordered pairs of the inequality expression, we set x - 0 and then calculate the value of y
Using the above as a guide, we have the following:
y > 1/2 * 0 + 3
Evauate
y > 3
This means that the value of y is greater than 3 say y = 4
So, we have (0, 4)
Hence, the ordered pairs of the inequality expression is (0, 4)
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0. 587. Write this value in
scientific notation.
. 0.587 in scientific notation is 5.87 x 10^-1.
Find out the scientific notation of the given value?Scientific notation is a way of writing numbers that are very large or very small in a compact and standardized way. In scientific notation, a number is expressed as a coefficient multiplied by 10 raised to some power.
For example, the number 0.587 can be written in scientific notation as 5.87 x 10^-1. The coefficient 5.87 is obtained by moving the decimal point one place to the right, while the negative exponent -1 indicates that the decimal point has been moved one place to the left, to the tenth place.
Scientific notation is commonly used in scientific and engineering fields where very large or very small numbers are often encountered, and it allows for easier calculation and comparison of these values.
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21. Marla is drawing a regular polygon. She has drawn two of the sides with an interior angle of 140°, as shown below. When Marla completes the regular polygon, what should be the sum, in degrees, of the measures of the interior angles?
The sum of the measures of the interior angles is 1260 degrees
What should be the sum of the measures of the interior angles?From the question, we have the following parameters that can be used in our computation:
An interior angle = 140 degrees
The sum of interior angles of a regular polygon is:
S = (n - 2) × 180
Where n is the number of sides of a polygon
Also, we have
S = 140n
Substitute the known values in the above equation, so, we have the following representation
140n = (n - 2) × 180
Expand
140n = 180n - 360
This gives
40n = 360
Divide
n = 9
Recall that
S = (n - 2) × 180
So, we have
S = (9 - 2) × 180
Evaluate
S = 1260
Hence, the sum of the measures of the interior angles is 1260 degrees
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70% of a class is at lunch what percentage is still studying?
Answer:
30%
Step-by-step explanation:
If there are only 2 categories:
Students at lunch and students studying, then the whole is 100%
100% - 70% = 30%
Helping in the name of Jesus.
Two circles, C1 and C2, intersect at point A and B. Passes through the center O of circle C2. The point P lies on circle C2 so that the line PAT is target to circle Ci and point A. Let ∠APB =.
The value of ∠APB = 180°. It is a straight line.
Given the information, we can deduce that the line passing through the center O of circle C2 and point A also passes through point B, as AB is the intersection of the two circles.
Now, consider the line segment AP. Since PAT is tangent to circle C1 at point A, we know that ∠APT = 90°. Additionally, since AB is a diameter of circle C1, we know that ∠ABP = 90°.
Using these angles, we can see that ∠APB is equal to the sum of ∠APT and ∠ABP. Therefore,
∠APB = ∠APT + ∠ABP = 90° + 90° = 180°.
So, we have shown that ∠APB is a straight line.
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PLEASE HELP ASAP (BRAINLIEST) 39 POINTS
Answer:
3x + 5 = 4x - 40
x = 45
5y - 50 = y
4y = 50
y = 25/2
The y-values that a function approaches when the x-values are extremely large or extremely small. this is called the function's ____ behavior.
The y-values that a function approaches when the x-values are extremely large or extremely small is called the function's asymptotic behavior.
When we talk about the asymptotic behavior of a function, we are referring to what happens to the values of the function as the input (x-values) either tends to positive infinity or negative infinity.
In other words, we are interested in how the function behaves when the input values become extremely large or extremely small.
To understand asymptotic behavior, let's consider two types of asymptotes: horizontal and vertical asymptotes.
Horizontal Asymptotes:
A horizontal asymptote is a horizontal line that a function approaches as the x-values become extremely large or extremely small. We usually denote horizontal asymptotes as y = c, where c is a constant.
For example, let's consider the function f(x) = (2x^2 + 3) / (x^2 - 1). As x approaches positive or negative infinity, we can observe the following behavior:
As x becomes extremely large or extremely small, the function becomes closer and closer to the line y = 2. Therefore, we say that y = 2 is a horizontal asymptote for this function.
Vertical Asymptotes:
A vertical asymptote is a vertical line that the function approaches as the x-values approach a particular value. It typically occurs when there is a division by zero or when the function tends to infinity at a specific point.
For example, consider the function g(x) = 1 / (x - 2). As x approaches 2 from either side (but never equal to 2), we can observe the following behavior:
As x approaches 2 from the left (x < 2), the function g(x) becomes increasingly negative, tending towards negative infinity.
As x approaches 2 from the right (x > 2), the function g(x) becomes increasingly positive, tending towards positive infinity.
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simplify and rearrange the equation to the form c=
For given equation x = (-b ± √(b²-4ac))/2a the equation in the form c= is: c = -x²(a/b) - x.
What is equation?
An equation is a mathematical statement that shows that two expressions are equal. It typically contains variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, and division.
What is goal of equation?
The goal of solving an equation is to determine the value or values of the variable that make the equation true. Equations are used extensively in mathematics and science to describe relationships between quantities and to solve problems.
According to given information:Starting with the equation:
x = (-b ± √(b²-4ac))/2a
We can simplify and rearrange it to the form c= as follows:
Multiply both sides by 2a to get rid of the denominator:
2a x = -b ± √(b²-4ac)
Add b to both sides:
2a x + b = ± √(b²-4ac)
Square both sides:
(2a x + b)² = b² - 4ac
Expand the left side:
4a² x² + 4abx + b² = b² - 4ac
Simplify:
4a² x² + 4abx = -4ac
Divide both sides by 4a:
x² + bx/a = -c/a
Rearrange to the form c=:
c = -x²(a/b) - x
Therefore, the equation in the form c= is:
c = -x²(a/b) - x
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A single number cube is rolled twice. The 36 equally-likely outcomes are shown to the right. What is the first step in finding the probability of getting two numbers whose sum is 12? Find the probability of getting two numbers whose sum is 12.
The probability of getting two numbers whose sum is 12 when rolling a single number cube twice is 1/36.
To find the probability of getting two numbers whose sum is 12 when a single number cube is rolled twice, we'll first need to identify the favorable outcomes.
A number cube has six faces, numbered from 1 to 6. When it is rolled twice, there are 6 x 6 = 36 equally-likely outcomes. To find the probability, we can use the formula:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
The first step is to identify the favorable outcomes, which are the pairs of numbers that add up to 12. Since we are dealing with a number cube that has faces numbered 1 to 6, there is only one possible pair that satisfies this condition: (6,6).
Now that we have determined the favorable outcome, we can find the probability:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
Probability = 1 (for the pair 6,6) / 36
Thus, the probability of getting two numbers whose sum is 12 when rolling a single number cube twice is 1/36.
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in a class, 12 students finished early. this represents 40% of the students. model this situation by evenly distributing the 12 students in the 4 shaded sections
Answer:Each of the shaded sections represents 25% of the total number of students in the class, and since we have evenly distributed the 12 students among them, each shaded section now represents 30% of the students (i.e., 25% + 5% = 30%).
Step-by-step explanation: To model this situation, we need to determine the total number of students in the class. We can use the given percentage to set up a proportion:
40% = 12 students / x total students
To solve for x, we can cross-multiply and simplify:
0.4x = 12
x = 12 / 0.4
x = 30
Therefore, there are 30 students in the class.
To evenly distribute the 12 students in the 4 shaded sections, we can divide 12 by 4 to get the number of students for each section:
12 students / 4 sections = 3 students per section
The mean number of days with 0. 01 inch or more precipitation per month for Lewiston, Idaho, is about 8. 7. Find the probability that in a given month
(a) There are exactly 9 days with 0. 01 inch or more precipitation.
(b) There are at most 9 days with 0. 01 inch or more of precipitation.
(c) There are more than 9 days with 0. 01 inch or more of precipitation
We will use the Poisson distribution, which is a probability distribution that models the number of events occurring in a fixed interval of time or space, given the average rate of occurrence and assuming that the events are independent and randomly distributed.
For this problem, we will assume that the number of days with 0.01 inch or more precipitation in Lewiston, Idaho, follows a Poisson distribution with parameter λ = 8.7.
(a) To find the probability that there are exactly 9 days with 0.01 inch or more precipitation, we can use the Poisson probability mass function:
P(X = k) = e^(-λ) * λ^k / k!
where X is the random variable representing the number of days with 0.01 inch or more precipitation, λ is the parameter of the Poisson distribution, and k is the number of events we are interested in.
Plugging in the values, we get:
P(X = 9) = e^(-8.7) * 8.7^9 / 9! ≈ 0.151
Therefore, the probability that there are exactly 9 days with 0.01 inch or more precipitation is approximately 0.151.
(b) To find the probability that there are at most 9 days with 0.01 inch or more precipitation, we can use the cumulative distribution function of the Poisson distribution:
P(X ≤ k) = ∑i=0^k e^(-λ) * λ^i / i!
Plugging in the values, we get:
P(X ≤ 9) = ∑i=0^9 e^(-8.7) * 8.7^i / i! ≈ 0.503
Therefore, the probability that there are at most 9 days with 0.01 inch or more precipitation is approximately 0.503.
(c) To find the probability that there are more than 9 days with 0.01 inch or more precipitation, we can subtract the probability of having 9 or fewer days from 1:
P(X > 9) = 1 - P(X ≤ 9) ≈ 0.497
Therefore, the probability that there are more than 9 days with 0.01 inch or more precipitation is approximately 0.497.
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Apple Inc. Stock closes at $109. 99 per share. The next day the stock goes up $1. 49. What is the new price per share? (Just type the amount of money. Do not type the words "per share". )
The new price per share is $111.48.
Stock price is the current market value of a share of a publicly traded company's stock. It represents the price at which buyers and sellers agree to trade shares in the open market. Stock prices are determined by a variety of factors, including the company's financial performance, industry trends, and overall market conditions. The stock price is often used as an indicator of investor sentiment about the company and its future prospects.
To find the new price per share, follow these steps:
1. Note the initial stock price: $109.99
2. Note the increase in stock price: $1.49
3. Add the increase to the initial stock price: $109.99 + $1.49 = $111.48
The new price per share is $111.48.
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Write (0,15) + (1,5) as a linear function and also as an exponential function
Answer: Linear Function: y = -10x + 15 Exponential Function:
y = 15(1/3)(to the power of x)
Step-by-step explanation:
Linear Function:
First we need to find the slope by using the slope equation: (y2 - y1)/(x2 - x1)
In which, it should be (5 - 15)/(1 - 0)
So, we know that the slope is -10, and we already know that the y-intercept is 15, so, we are going to plug it in to the slope-intercept formula, which is
y = mx + b,
In which, it would become y = -10x + 15
Exponential Function =
The exponential function is y = ab(to the power of x)
Let's list out the points onto the equation, 15 = ab(0) and 5 = ab(1)
Know let's solve for each variable.
1. 15 = ab(0)
2. 15/b(0) = a
3. 15 = a
Know we know that a is 15, we can solve for b.
1. 5 = (15)b(1)
2. 5/15 = b(1)
3. 1/3 = b
Know we know that b is equal to 1/3, let's plug it into the equation.
y = 15(1/3)(to the power of x)
Help me with homework
Therefore, the perimeter of the rectangle is 38 units that is option C.
What is coordinate?A coordinate is a set of numbers or values that specifies the position or location of a point or object in a space. In mathematics, coordinates are used to describe the position of a point in a plane, a space or a higher-dimensional object. Coordinates can be represented by ordered pairs or tuples, where the first value corresponds to the position on the horizontal axis, and the second value corresponds to the position on the vertical axis.
Here,
First, we need to find the distance between points A and B to determine the length of the rectangle:
Distance AB = |yB - yA|
= |8 - 2|
= 6
Next, we need to find the distance between points B and C to determine the width of the rectangle:
Distance BC = |xC - xB|
= |6 - (-7)|
= 13
Since opposite sides of a rectangle are equal in length, we know that the distance between points A and D is also 13, and the distance between points C and D is also 6.
Therefore, the perimeter of the rectangle is:
Perimeter = 2 * (length + width)
Perimeter = 2 * (13 + 6)
Perimeter = 2 * 19
Perimeter = 38
So the answer is (C) 38.
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The cost of manufacturing a certain type of headphone varies inversely as the number of headphones increases. If 8000 headphones can be manufactured for $8. 00 each, find the cost to manufacture 2000 headphones
The cost to manufacture 2000 headphones as the number of headphones varies inversely with the cost of manufacture is $32
Let x = number of headphones
y = cost of manufacturing headphones
The cost of manufacturing a certain type of headphones is inversely proportional to the number of headphones.
The equation for inversely proportional is
x₁ y₁ = x₂ y₂
x₁ = 8000 , y₁ = 8 , x₂ = 2000 y₂ = ?
Putting the value in the equation we get ,
8000 × 8 = 2000 × y₂
64000/2000 = y₂
y₂ = 32
Cost of manufacturing 2000 headphones is 32 .
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Parallel lines EN, BH, and RK, with transversal PW are shown. m/BMV-108 and m/KVS-72.
Part A: Based on the diagram above and the given information, what is the
m/WPN?
The value of measure of angle WPN is,
⇒ m ∠WPN = 108°
We have to given that;
Parallel lines EN, BH, and RK, with transversal PW are shown.
And, m ∠ BMV = 108° and m ∠KVS = 72°
Now, We get by definition of vertically opposite angle;
m ∠ BMV = m ∠PWN = 108°
Hence, By definition of alternate angle we get;
⇒ m ∠PWN = m ∠WPN = 108°
Thus, The value of measure of angle WPN is,
⇒ m ∠WPN = 108°
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PLEASE HELP ASAP!! The image is attached 30 points!!
Answer:
366 times
Step-by-step explanation:
Calculate the surface area of the rectangular prism shown. You do not need to provide units as they have been provided for you.
Surface Area = ___ yd2
rectangular prism with the base having all measurements of 7 yards and the height measuring 5 yards
Answer:
238 ft²
Step-by-step explanation:
Base area is l*w and there are two of these so 2(7*7) = 98
Then there 4 faces that have dimensions 4(7*5)=140
98+140=238
Find the perimeter of a rectangle whose vertices are (3,2), (13,2), (13,9), and (3,9).
The perimeter of a rectangle is 34 units.
To find the perimeter of the rectangle with vertices (3,2), (13,2), (13,9), and (3,9), you need to determine the lengths of its sides.
The distance between (3,2) and (13,2) is the length of the base: 13 - 3 = 10 units.
The distance between (3,2) and (3,9) is the height: 9 - 2 = 7 units.
The perimeter of a rectangle is given by the formula P = 2*(length + width). In this case, P = 2*(10 + 7) = 2*17 = 34 units.
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“The mode of a data set is one of the values in the data set.” This statement is ____________.
Leslie works for Blank Chemical Corporation. Her annual salary is $57,285. 50. She is
paid biweekly (26 weeks). Each pay period, Leslie's employer deducts $418. 63 for
federal tax withholding. City tax for Blank Chemical employees is 3. 65%. What is Leslie’s annual social security (6. 2%) deduction?
Leslie’s annual social security deduction is $3551.70.
How to determine Leslie’s annual social security deduction?Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.
Leslie’s annual salary is $57,285. 50 and her annual social security deduction is 6.2% of the annual salary. We can say:
Annual social security deduction = 6.2/100 * 57,285. 50
Annual social security deduction = $3551.70
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Question below, please help! this is part of my grade.. (30 points)
Answer:
y = 1 + 2√7 or y = 1 - 2√7
Step-by-step explanation:
To complete the square, you need to add and subtract the square of half of the coefficient of the y term.
First, you can factor out a 1 from the y^2 - 2y term:
y^2 - 2y - 27 = 0
y^2 - 2y = 27
Next, take half of the coefficient of the y term (-2/2 = -1) and square it (1):
y^2 - 2y + 1 - 1 = 27
The "+1 -1" doesn't change the value of the equation, it's just a way to add 0 to the equation so we can complete the square.
Now you can rewrite the left side as a perfect square:
(y - 1)^2 - 28 = 0
Add 28 to both sides:
(y - 1)^2 = 28
Take the square root of both sides (remembering to include both positive and negative square roots):
y - 1 = ±√28
y = 1 ± 2√7
So the solutions are:
y = 1 + 2√7
y = 1 - 2√7
Answer: y=± 2√7+1
6.29
Step-by-step explanation: Use the formula
(b/2)^2 in order to create a new term. Solve for y by using this term to complete the square.
50+30(2x+10) What is the value of x
Distribute
50+30(2x+10)
50+30×2x+30×10
50+60×+300
add the number
50+300+60×
350+60x
re arrange the term60x+350
common factors
10(6x+35)
1ST ONE TO ANSWER MY QUESTION WILL BE MARKED BRAINLIESTT! ANSWER 1 QUESTION!
2x²t + 7xy
Step-by-step explanation:To simplify, we will combine like terms.
Given:
5xy - x²t + 2xy + 3x²t
Reorder like terms:
5xy + 2xy + 3x²t - x²t
Combine like terms:
➜ 5 + 2 = 7
➜ 3 - 1 = 2
7xy + 2x²t
Reorder by degree:
2x²t + 7xy
(a) What is the mean of this stem and leaf plot? Show your work. What is the median of the data? Show your work
The mean of the given stem and leaf plot is 24.5 and the median of the data is 25.
The stem and leaf plot represents the given data as:
| 2 | 4, 5, 6, 9
| 3 | 1, 4, 5, 5, 7, 8
| 4 | 2, 5, 7, 8, 9
To find the mean, we need to add up all the values and divide by the total number of values.
Mean = (24 + 25 + 26 + 29 + 31 + 34 + 35 + 35 + 37 + 38 + 42 + 45 + 47 + 48 + 49) / 15
= 367 / 15
= 24.5
To find the median, we need to arrange the data in order and find the middle value. As there are 15 data points, the median will be the average of the 8th and 9th data points.
Data in order: 24, 25, 25, 26, 29, 31, 34, 35, 35, 37, 38, 42, 45, 47, 48
Median = (35 + 37) / 2
= 36.
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Simon bought a 10-pound bag of cat food. he give 0.3 pounds of food per day. write an equation in two variables to describe how the amount of cat food in the bag changes over time. explain variable in your equation represent
The equation in two variables that describes how the amount of cat food in the bag changes over time is: A = 10 - 0.3t
Where A represents the amount of cat food left in the bag after t days, and t represents the number of days that have passed since Simon bought the bag.
The variable A is the dependent variable because it depends on the value of t. As time passes and t increases, the amount of cat food left in the bag decreases. The variable t is the independent variable because it is the input that determines the value of A.
For example, after one day (t = 1), Simon will have used 0.3 pounds of cat food and there will be 9.7 pounds left in the bag (A = 10 - 0.3(1) = 9.7). After two days (t = 2), he will have used 0.6 pounds of cat food and there will be 9.4 pounds left in the bag (A = 10 - 0.3(2) = 9.4), and so on.
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A compound event may consist of two dependent events.
A. True
B. False
A. True. A compound event may consist of two dependent events. Dependent events are those in which the outcome of the first event affects the outcome of the second event. For example, drawing a card from a deck and not replacing it before drawing a second card would be an example of dependent events.
you purchase a computer for 875 plus 5% sales tax. you decide to finance it through the stores 0% program for 12 months. the terms state that you must pay
The amount of interest paid for missing the payment in the eight month would be C. $87.28
How to find the interest ?First, find the total cost of the computer including the sales price :
= 875 x ( 1 + 0. 05 )
= 875 x 1. 05
= $ 918. 75
Then, find the monthly rate of interest :
= 14. 25 / 12
= 1. 1875 %
This leads to an eight month interest rate of :
= 8 x 1. 1875 %
= 9. 5 %
The interest to be paid:
= 9. 5 % x 918. 75
= $ 87. 28
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Full question is:
You purchase a computer for $875.00 plus 5% sales tax. You decide to finance it through the store's 0% program for 12 months. The terms state that you must pay $100.00/month and that if you miss a payment, you will be assessed a late fee of $39.00 plus the interest accrued to that point at a 14.25% APR. If you miss a payment in the eighth month, how much interest will you be charged?. A. $83.13. B. $16.63. C. $87.28. D. 58.19