A mathematical model was created and solved using linear programming. The optimal values were determined: x1 = 10 and x2 = 10. If one of the constraints is: 4x1 + 2x2 >= 55, you can conclude that:
A.this is a binding constraint, so there is no slack or surplus

B.there are 15 units of surplus

C.there are 15 units of slack

D.there are 5 units of slack

E.there are 5 units of surplus

Answers

Answer 1

In mathematics, linear programming is a technique for maximizing operations under certain restrictions.

Why does a mathematical model of a linear programming problem is important?

Using the mathematical modeling technique of linear programming, a linear function is maximized or minimized depending on the restrictions it is subjected to. This method has proved helpful for directing quantitative judgments in business planning, industrial engineering, and—to a lesser extent—in the social and physical sciences.

In mathematics, linear programming is a technique for maximizing operations under certain restrictions. Maximizing or minimizing the numerical value is the primary goal of linear programming. It comprises of linear functions that are subject to restrictions in the form of inequalities or linear equations.

Therefore, the correct answer is option A. this is a binding constraint, so there is no slack or surplus.

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Related Questions

Evaluate 9.1p + 8.9r when p = 6 and r =7.

Answers

Answer:

116.9

Step-by-step explanation:

9.1(6) + 8.9(7)

54.6+62.3

116.9

ten students are arranged in a row. every minute, a new student is inserted in the row (which can occur in the front and in the back as well, hence 11 possible places) with a uniform 1 11 probability of each location. then, either the frontmost or the backmost student is removed from the row (each with a 1 2 probability). suppose you are the eighth in the line from the front. what is probability that you exit the row from the front rather than the back?

Answers

The probability that you exit the row from the front rather than the back is 1/2.

How do you determine probability?

The probability is calculated by dividing the total number of outcomes by the number of possible ways the event could occur. Probability and odds are two separate ideas. Odds are the possibility of something happening divided by the likelihood that it won't happen.

What is fundamental probability in math?

A probability is a number that expresses the possibility or likelihood that a specific event will take place. In addition to being expressed as percentages ranging from 0% to 100%, probabilities can also be expressed as proportions between 0 and 1.

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Match the plot with a possible description of the sample.

60 70 80 90 100

Choose the correct answer below

A. Wait time (in minutes) for a sample of doctors offices

B.Ages (in years) of a sample of residents of a retirement home.

C. Highest yearly temperatures (F) for a sample of deserts.

D. Time (in hours_ spent watching TV in a day for a sample of teenagers.

Answers

Ages (in years) of a sample of retirement home inhabitants is option B. For the lowest wait time, the maximum frequency is anticipated to be right-skewed. A desert cannot have a maximum annual temperature of 60°F, and it is not conceivable to watch 60+ hours of TV in a single day.

Residents of senior living facilities are typically 84 years old. While there are many couples in these communities, the majority of people who live in independent living are women. Some people move in at or near the minimum age (often around 65), but most people do so between the ages of 75 and 84. Residents come from all different backgrounds.

Many people are choosing senior living in a community environment, including teachers, nurses, small business owners, big business CEOs, university professors, housewives, lawyers, engineers, musicians, and more. Current residents will attest that the rich diversity of origins fosters amazing interactions and relationships. And contrary to popular belief, the majority of residents of independent living are quite active.

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Correct Question:

Match the plot with a possible description of the sample.

60 70 80 90 100

Choose the correct answer below

A. Wait time (in minutes) for a sample of doctors offices

B. Ages (in years) of a sample of residents of a retirement home.

C. Highest yearly temperatures (F) for a sample of deserts.

D. Time (in hours_ spent watching TV in a day for a sample of teenagers.

Triangle PQR is similar to triangle STU. Find the measure of side ST. Figures are not
drawn to scale.

Answers

Answer:

ST = 2.6

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{ST}{PQ}[/tex] = [tex]\frac{SU}{PR}[/tex] ( substitute values )

[tex]\frac{ST}{18}[/tex] = [tex]\frac{5.2}{36}[/tex] ( cross- multiply )

36 × ST = 18 × 5.2 = 93.6 ( divide both sides by 36 )

ST = 2.6

the random variable x has mean 8 and standard deviation 2. the random variable w is defined as w=7 4x . what are the mean and standard deviation of w ?

Answers

The random variable x's mean and standard deviation are 8 and 2, respectively. W=7+ 4x is the formula for the random variable w. The mean of w is E(W) =39

Explain about the Mean?

A dataset's mean is calculated by dividing the sum of all values by the total number of values. The term "average" is frequently used to describe it because it is the most widely used central tendency metric.

Divide the entire number of values by the total number of numbers to find the average. A mean is the term used to describe the mathematical average of a set of two or more data values. Average is also referred to as mean or arithmetic mean.

The mean is the average value of the data. It's easy to calculate: just add up all the numbers, then divide by the total number of numbers. Or, to put it another way, it is equal to the sum divided by the quantity.

The mean is then determined as follows:

E(W) = E (7 + 4X)

This results

E(W) = 7 + 4 E (X)

We thus have:

E(W) = 7 + 4 x 8

E(W) =39

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Standard deviation = 8 and mean = 39.

What is standard deviation?

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection.

Given, the formula for mean is E(W) = 7 + 4(X)

∴ E(W) = 7 + 4E(X)

Mean, E(X) equals to 8, hence substituting in the above equation, we get,

E(W) = 7 + 4×8

⇒E(W) = 39

Since, E(W) = 7 + 4(X)

Var(W) = Var(7) + Var(4X)

Since, Var(constant)=0,

Var(W) = Var(4X)

Var(W) = 4²×Var(X), where Var(X)=σₓ²

⇒ Var(W) = 16×σₓ², where σₓ²=2²

⇒ Var(W) = 16×4

⇒ Var(W) = 64

Standard Deviation (SD) = √64 = 8

Thus, standard deviation = 8 and mean = 39.

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A regular polygon is shown, with one of its angle measures labeled a.

9 sided regular polygon with one angle labeled a

If m∠a = (5z + 65)°, find the value of z.

z = 15
z = 20
z = 23
z = 41

Answers

The measure of z in the polygon is (a) z = 15

How to determine the measure of z?

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

Shape = 9-sided polygon

Parameter to calculate = the measure of z

The sum of the interior angles is calculated using the following angle formula

The sum of the interior angles = ( n − 2 ) × 180 ∘ where n is the number of sides

In this case

n = 9

Substitute the known values in the above equation, so, we have the following representation

The sum of the interior angles = (9 − 2) × 180∘

Evaluate

The sum of the interior angles = 1260∘

So, the internal angle is

Angle = 1260/9

Evaluate

Angle = 140

This means that

5z + 65 = 140

So, we have

5z = 75

Divide by 5

z = 15

Hence, the angle is (a) z = 15

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give the equation of the line that goes through the point (5, -2) and has a slope of 0.

Answers

When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilised (0, b). B stands in for the y value of the y-intercept point in the formula.

How to calculated the slope intercept?

Determine the equation of the line with a slope of 2/3 and a y intercept of (0, 4).

Solution

Step 1: Replace the provided in the formula.

Provided that the slope, m, is given as 2/3 and the y intercept, (0, 4), b = 4.

y = mx + b

y = 2 3 x + 4

2 /3 x – y = - 4

(Note: You must multiply this by the LCD of 3 to fix this since the conventional form does not support fractional numbers.)

3( 2 /3x – y) = (- 4) (- 4)

3/2x – 3y = - 12

This is the line's determined equation.

Verify is the second step.

Utilizing the formula, plot two points. In this example, y1 = 2 and Y2 = -6. 2x - 3y = - 12 2x – 3y = - 12

Let y = 2 Let y = - 6

2x – 3(2) = - 12 2x – 3(-6) = - 12

2x – 6 = - 12 2x + 18 = - 12

2x = - 6 2x = - 30 \sx = - 3 x = - 15

P1 therefore equals (-3, 2) and P2 equals (-15, -6).

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Jason and his 3 brothers want to buy a gift for their mother. They have $314 saved. Each of them will save $17 a week until they have at least $515 for her gift. How much money will they save after 3 weeks? Will they have enough money to buy the gift?


A. What are the hidden questions?



B. Write an equation that can be used to answer each hidden question. Then solve.



C. Write and solve an equation to find how much money they will save after 3 weeks. Will they have enough to buy the gift? Explain

if u show points I give u 200 points

Answers

The equation to find how much money they will save after 3 weeks is y = 68x, and they will save $518, so yes they have enough money to buy the gift.

What is equation?

An assertion that two mathematical expressions have equal values is known as an equation. An equation simply states that two things are equal. The equal to sign, or "=," is used to indicate it.

Given:

Total money Jason and his 3 brothers have = $314,

Each of them will save $17 a week until they have at least $515,

At the end of three weeks, the money saved by Jason and his brothers,

Money saved = 17 × number of person × number of weeks

Assume the number of weeks is x and the money saved is y then,

y = 17x × 4

y = 68x

Money saved, y = 68 × 3

Money saved = $204

Total money after the end of three weeks = $314 + $204

Total money after the end of three weeks = $518

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Thomas increased the amount of water she gives her plants from 2 cups to 2 1/2 cups. By what percentage did Thomas increase the amount of water?

Answers

Ok so any % change is simply just final over initial. It would also be helpful to convert your fractions into decimals. So, 2.5/2 will give you 1.25. Move the decimal to the right twice, you get 125. So now it’s at 125% of the FULL value, so subtract 100 and it increased by 25%. :)

What is the length of the sides of this equilateral triangle?
3x + 6
6x - 3
9x - 12

Answers

Answer:

15

Step-by-step explanation:

In an equilateral triangle all the sides length are the same.  Set two sides equal to each other and solve for x

3x + 6 = 6x - 3    Subtract 3x from both sides

6 = 3x -3  Add 3 to both sides

9 = 3x  Divide each side by 3

3 = x

Now that we know x is 3, plug this into the expression for any side and find the side length

3x + 6

3(3) + 6

9 + 6 = 15

The Oakland Tigers are having team shirts made. One option is to pay Susan's Tees a $34 setup fee and then buy the shirts for $10 each. Another option is to go to City Printing, paying $23 for a setup fee and an additional $11 per shirt. The team parent in charge of the project notices that, with a certain number of shirts, the two options have the same cost. What is the cost? How many shirts is that?

Answers

To find the cost of the shirts, we need to set up a system of equations. Let x be the number of shirts.

Option 1: 34 + 10x = Option 2: 23 + 11x

We can solve this system of equations by subtracting the equations:

34 + 10x - 23 - 11x = 0

11x - 23 = 0

11x = 23

x = 23 / 11

Therefore, the cost is the same when the team orders 23/11 = 2 shirts.

find equations of both lines through the point (2, −3) that are tangent to the parabola y = x2 + x

Answers

The equations of the tangents that pass through (2,−3) are y=−x−1 and  y= 11x−25.

What is an equation?

In arithmetic,an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.

Main BODY:

The gradient of the tangent to a curve at any particular point is given by the derivative of the curve at that point. So for our curve (the parabola) we have

y=x²+x

Differentiating wrt x we get:

dy / dx = 2x +1

Let P(α,β) be any generic point on the curve. Then the gradient of the tangent at P is given by:

m=2α+1                   (using the derivative)

And as P lies on the curve we also have:

β=α²+α                    (using the curve equation)

And so the tangent at P passes through (α,α²+α) and has gradient 2α+1, so using the point/slope form y−y₁=m(x−x₁) the equation of the tangent at P is;

y−(α²+α)=(2α+1)(x−α)

if this tangent also passes through

(2,−3) then;

⇒-3−(α²+α)=(2α+1)(2−α)

⇒-3 −α²- α = 3α−2α²+2

⇒α²−4α−5=0

∴α=−1,5

If  α=−1⇒β=0

, and the tangent equation becomes:

y−0=(−1)(x+1)

∴ y=−x−1

If α=5⇒β=30

, and the tangent equation becomes:

y−30=(11)(x−5

∴y−30=11x−55

∴y=11x−25

Hence the equations of the tangents that pass through (2,−3) are y=−x−1 and  y= 11x−25.

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4700 people attended a football game. If 2% of the people who attended were
teenagers, how many teenagers attended the game?
Insert the values given in the problem then scale up or
down to find the missing value.
attendees
percent
100

Answers

The number of teenagers in the game are 94.

What is percentage?

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, 4700 people attended a football game.

Here, 2% of the people who attended were teenagers

So, the number of teenagers are

2% of 4700

= 0.02×4700

= 94

Therefore, there are 94 teenagers attended the game.

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There are 140 students in the seventh grade, and 25% are in the Environmental Club.
How many students are in the Environmental Club?

Answers

The answer is 35

140 times 0.25

Find the slope of every line that is perpendicular to this one.

Answers

Answer:

-4/7

Step-by-step explanation:

The slope of the given line is [tex]\frac{3-(-4)}{4-0}=\frac{7}{4}[/tex].

Perpendicular lines have slopes that are negative reciprocals of each other, so the answer is [tex]-4/7[/tex].

The slope of every line perpendicular to the line passing through (4, -3) and (0, -4) is -4.

We have,

Let's first find the slope of the given line passing through (4, -3) and

(0, -4):

slope = (change in y) / (change in x)

= (-4 - (-3)) / (0 - 4)

= (-4 + 3) / (-4)

= -1 / (-4)

= 1/4

The slope of the given line is 1/4.

Now, to find the slope of a line perpendicular to this line, we take the negative reciprocal of the slope:

[tex]slope_{perpendicular} = -1 / slope[/tex]

= -1 / (1/4)

= -4

Therefore,

The slope of every line perpendicular to the line passing through (4, -3) and (0, -4) is -4.

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write an equation in point-slope form of each line that passes through the given points. (4, 1), (-2, 7) ​

Answers

Answer: y=-x+5

Step-by-step explanation:

you’ve observed the following returns on yamauchi corporation’s stock over the past five years: −10 percent, 24 percent, 21 percent, 11 percent, and 8 percent.

Answers

The stock's average nominal risk premium is 6.70%, while its average real return is 7.47%.

What is meant by average real return?

The inflation rate can be obtained from the consumer price index or the GDP deflator. The real rate of return is the actual yearly rate of return after accounting for factors like inflation. It is computed by adding the nominal rate to the inflation rate and dividing the result by three.

The annual return factored in after taxes and inflation is known as the real rate of return. Taxes and inflation are not included in a nominal rate of return, which is what it is called. The same goes for a rate of return that is calculated using taxes or inflation.

From the information given, the average return will be calculated thus:

Average return = 0.540 / 5

                          = 0.108

Average return = 10.80%

Therefore, the average real return will be:

= [( 1 + Average return) / (1+ inflation rate)] - 1

substitute the values in the above equation, we get

= [(1+0.1080) / (1+0.081)] - 1

simplifying the above equation,

= 0.0747

= 7.47%

Also, the average nominal risk premium will be:

= Average Return - Risk free rate

= 0.1080 - 0.041

= 0.067

= 6.70%

Therefore, the stock's average nominal risk premium is 6.70%, while its average real return is 7.47%.

The complete question is:

You’ve observed the following returns on Yamauchi Corporation’s stock over the past five years: −10 percent, 24 percent, 21 percent, 11 percent, and 8 percent. The average inflation rate over this period was 3.1 percent and the average T-bill rate over the period was 4.1 percent. a. What was the average real return on the stock? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. What was the average nominal risk premium on the stock? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

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Given angle 1 is congruent to angle 3

prove angle 6 is congruent angle 4

Answers

Proof of  angle 6 is congruent to angle 4 is given.

What is congruent?

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Angles of equal measure are said to have congruent angles.

Given,

∠1 ≅ ∠3

And we know from the vertical angles, property;

The angles opposite each other when two lines cross.

They are always equal.

And here we have two pairs of vertical angles,

So, ∠1 = ∠4

and ∠3 = ∠6

And ∠1 ≅ ∠3 is given.

So,  ∠1 ≅ ∠4

and ∠3 ≅ ∠6

Comparing, we get

∠4 ≅ ∠6

Therefore, ∠4 ≅ ∠6 is proved.

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Differentiate 3x² over x³ +3

Answers

Answer:

[tex] \displaystyle{y' = \dfrac{ - 3x( {x}^{3} + 6) }{( {x}^{3} + 3)^{2} }}[/tex]

Step-by-step explanation:

We can use the quotient rule:

[tex] \displaystyle{y = \frac{u}{v} \to y '= \dfrac{u'v - uv'}{ {v}^{2} }}[/tex]

In this case, u and v both are functions. By applying formula above, we will have:

[tex] \displaystyle{y' = \dfrac{(3 {x}^{2})' ( {x}^{3} + 3) - (3 {x}^{2} )( {x}^{3} + 3)' }{( {x}^{3} + 3)^{2} }}[/tex]

Then apply power rule to derive functions, we have to know that:

[tex] \displaystyle{y = {x}^{n} \to y' = n {x}^{n - 1} } \\ \\ \displaystyle{y = c \to y' = 0 \: \: \: (c \in \mathbb{R})}[/tex]

Therefore, we will have:

[tex] \displaystyle{y' = \dfrac{6x ( {x}^{3} + 3) - (3 {x}^{2} )3 {x}^{2} }{( {x}^{3} + 3)^{2} }}[/tex]

Expand the terms in:

[tex] \displaystyle{y' = \dfrac{6 {x}^{4} + 18x - 9 {x}^{4} }{( {x}^{3} + 3)^{2} }} \\ \\ \displaystyle{y' = \dfrac{ - 3 {x}^{4} + 18x }{( {x}^{3} + 3)^{2} }} \\ \\ \displaystyle{y' = \dfrac{ - 3x( {x}^{3} + 6) }{( {x}^{3} + 3)^{2} }}[/tex]

Hence, that's the answer. You can keep in unfactored form or factored form as you desire!

40 times 3453 divided by 24=

Answers

Answer:

Step-by-step explanation:

57,555

Answer:5755

Step-by-step explanation: 40 X 3453 = 138,120

138,120 / 24 = 5755

For 44 points and due in 59 mins help!, Stewart loves playing Genshin Impact so much that he “forgets” to do his schoolwork. It’s really starting to impact his grades and he has 36 overdue assignments. The semester is almost over, and he really needs to improve his grades. He can realistically complete 4 overdue assignments each day.

Draw a graph to represent this situation.

Answers

The number of days required to complete his task is 9 days.

What is a graph?

The graph of a relation R is the set of all points (x, y) in a coordinate plane such that x is related to y through the relation R.

Stewart loves playing Genshin Impact so much that he “forgets” to do his schoolwork. It’s really starting to impact his grades and he has 36 overdue assignments. The semester is almost over, and he really needs to improve his grades. He can realistically complete 4 overdue assignments each day.

So he will complete 4 assignments each day and he has to complete the 36 overdue assignments.

The number of days required to do this = 36/4

                                                                  = 9 days.

Hence, the number of days required to complete his task is 9 days. and this relation can be expressed on the graph as

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the nth term of this sequence: 1/2,4/3,9/4,16/5
URGENT

Answers

Answer: [tex]\frac{n^{2} }{n+1}[/tex]

Step-by-step explanation:

The numerator (top digit) are squares. For example,

1 is [tex]1^{2}[/tex]

4 is [tex]2^{2}[/tex]

9 is [tex]3^{2}[/tex]

and so on.

The bottom digit increases by one.

Therefore, the Nth term would be that number (N) squared on the numerator, and n+1 on the denominator.

assuming that workers' salaries in your company are uniformly distributed between $10,000 and $60,000 per year, find the probability that a randomly chosen worker earns an annual salary between $45,000 and $50,000.

Answers

According to the uniform distribution, there is a 0.1= 10% chance that a worker selected at random will have an annual wage between $45,000 and $60,000.

Uniform Distribution:

In statistics, uniform distribution refers to a type of probability distribution in which all outcomes are equally likely. A deck of cards has within it uniform distributions because the likelihood of drawing a heart, a club, a diamond, or a spade is equally likely.

An uniform distribution has two bounds, a and b.  

The probability of finding a value between c and d is:

P(c ≤ X ≤ d) = [tex]\frac{d-c}{b-a}[/tex]

given that , workers' salaries in your company are uniformly distributed between $10,000 and $60,000 per year

a = 10,000 , b= 60,000 , c = 45,000 and d = 50,000

The probability is

P(45,000 ≤ X ≤ 50,000) = [tex]\frac{50,000-45,000}{60,000-10,000}[/tex]

                                       = 0.1

0.1 = 10% probability that a randomly chosen worker earns an annual salary between $45,000 and $60,000

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15) Translate 4 units down, and then reflect over the y-axis. Pre-image: (5, 15) (4, 12) (2, 18) mage: I need help ​

Answers

The image of the transformation is (-5, 11) (-4, 8) (-2, 14)

How to determine the image of the transformation

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

Pre-image: (5, 15) (4, 12) (2, 18)

Transformation: Translate 4 units down, and then reflect over the y-axis.

Mathematically, this can be expressed as

(x, y) = (-x, y - 4)

Substitute the known values in the above equation, so, we have the following representation

(5, 15) (4, 12) (2, 18) = (-5, 11) (-4, 8) (-2, 14)

Hence, the image is (-5, 11) (-4, 8) (-2, 14)

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how much do national football league players weigh on aerage in a random sample of 50 nfl players the average weight is 244.4 pounds

Answers

This statistic is based on an average of all players in the NFL. The average weight of a random sample of 50 NFL players may be slightly different.

This statistic is based on an average of all players in the NFL. It is not possible to accurately estimate the average weight of a random sample of 50 NFL players without actually measuring the weight of each individual player. The average weight of a random sample of 50 NFL players may be slightly different due to the randomness of the sample and individual player physical characteristics.

In order to accurately determine the average weight of a random sample of 50 NFL players, the weight of each individual player must be measured. The sample size of 50 players is relatively small, and the results may be significantly affected by the inclusion or exclusion of a single player. Additionally, the average weight of the sample may vary due to individual player physical characteristics such as height, body composition, and muscle mass. Furthermore, the average weight could be affected by the age and experience level of the players in the sample. All of these factors should be taken into consideration when attempting to determine the average weight of a random sample of NFL players.

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Which of the following quadrilaterals has four right angles and 4 congruent sides? A. parallelogram B. rectangle C. rhombus D. square

Answers

Answer:Square

Step-by-step explanation:

A square is a quadrilateral with four right angles and four congruent sides. All squares are rectangles and rhombuses.

Answer:

D. square

Step-by-step explanation:

As an explanation, I have attached a picture of the 4 quadrilaterals and their internal angles and sides.

⭐if this response helped you, please mark it the "brainliest"!⭐

Marcus has x songs downloaded on his phone. He downloads 20 more songs to his phone.

Enter an expression in the box to represent the number of songs Marcus now has on his phone.

Answers

x+20 marcus has x+20 songs

Answer:

x + 20 = y

Step-by-step explanation:

x + 20 = y

where x= number of songs

y = total songs marcus has

if antonella has 3 more quarters than nickels and they have a combined value of 225 cents, how many of each coin does she have?

Answers

Antonella have a number of coins of quaters and nickels whose total value is 250.

The number of coins of nickel is 10 and the number of coins of quarters is 7.

Nickel and quarters are the coin based form of currency in the United States. The value of one nickel is 5 cents, while that of one quarter is 25 cents. We have given that

Antonella has 3 more quaters than nickles.

Let she has "x" number of quaters and "y" be number of nickels .

According to question,

y = 3+ x ---(1)

Combined value of all is 225 cents .

i.e 25 × x + y× 5 = 225 cents

plug the value of y from equation (1) to equation(2) we get,

25 x + 5(3+x) = 225

solve the equation

=> 25x + 15 + 5x = 225

=> 30x = 210

=> x = 7

put the value of x in equation (1)

y = x + 3 = 10

Hence, the number of nickels coins is 10 and numbers of quaters are 7.

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whats the probabilty that a randomly selected dorm room has a tv but no refridgerator

Answers

Using the provided percentages, it is discovered that:

a) A randomly chosen dorm room has a 31% chance of having a TV but no refrigerator.

b) A randomly chosen dorm room has a 48% chance of having either a television or a refrigerator, but not both.

c) There is a 31% chance that a randomly chosen dorm room lacks both a refrigerator and a television.

How to find the Calculation?

Item a:

TVs were owned by 52% of people.

21% of them had a refrigerator as well.

52 - 21 = 31

A randomly chosen dorm room has a 31% chance of having a TV but no refrigerator.

Item b:

31% just have a TV.

Only 17% of people—38—have a refrigerator.

31 + 17 = 48

A randomly chosen dorm room has a 48% chance of having either a television or a refrigerator, but not both.

Item c:

The likelihood that at least one exists is:

P(A∪B) = P(A) + P(B) - P(A∩B)

Hence:

P(A∪B) = 0.52 + 0.38 - 21 = 0.69.

1 - 0.69 = 0.31

There is a 31% chance that a randomly chosen dorm room lacks a refrigerator or a television.

The Complete Question.

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Answer:

The probability that a randomly selected dorm room has a TV but no refrigerator is 0.31

What is Probability?

Probability is a branch of mathematics that quantifies the likelihood of an event occurring or the likelihood of a statement being true. The probability of an event is a number between 0 and 1, with approximately 0 indicating the improbability of the event and 1 indicating certainty.

According to question

The probability that a randomly selected dorm room has a TV but no refrigerator

Solution :

Suppose

A = event of having refrigerators,

B = event of having a TV,

We have,

P(A) = 34% = 0.34,

P(B) = 51% = 0.51,

P(A∩B) = 21% = 0.21

Therefore:

Probability of a TV but no refrigerator = P(A∩B')

= P(A) - P(A∩B)

= 0.34 - 0.21

= 0.31

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Calculate the volume of the figure. Use 3.14 for π

Answers

Volume=4/3x pie x radius^3
=4/3 x3.14 x8^3
=2143.57333…

Hope this helps
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