Suppose 80% of people enjoy swimming. Suppose 70% of people enjoy running.

Suppose 55% of people enjoy doing both. What percentage of people enjoy swimming

and/or running?

Answers

Answer 1

Answer:

95%

Step-by-step explanation:

In this case we can apply a formula that tells us that:  

# (AUB) = #A + #B - #AnB  

Where A would be the ones who enjoy swimming and B would be the ones who enjoy running. AnB is the intersection of both sets, that is, those who enjoy doing both things, these values we have, if we replace them we have left:

#(AUB) = 80% + 70% - 55%

#(AUB) = 95%

Which means that 95% of people enjoy either swimming or running

Answer 2

The percentage of people who enjoy swimming and/or running is calculated to be 95%.

We have 80% of people who enjoy swimming, and 70% who enjoy running, with a 55% overlap of people who enjoy both.

The formula for the principle of inclusion-exclusion is:

Union = A + B - Intersection

Therefore, the percentage of people who enjoy swimming and/or running is:

Union = 80% + 70% - 55% = 95%

Hence, 95% of people enjoy at least one of the two activities.


Related Questions

Lines AB and CD are parallel. If 6 measures (3x - 34)°, and 8 measures 145°, what is the value of x?

Answers

Answer:

x=23

Step-by-step explanation:

180-145= 35 so you have to set the equation to 35. 3x-34=35. add 34 to each side. now you have 3x=69. divide 3 on each side and you get x=23

In the triangle shown below, what is the approximate value of x?
O
A. 24.25 units
O
B. 14 units
O
C. 21 units
O
D. 31.30 units

Answers

Answer:

24.25 units for a.pe.x if the triangle has the sides x,14, and 28

Step-by-step explanation:

The value of the labeled side , x is 24.25 units.

From pythagoras :

Adjacent side = √hypotenus² - Opposite²

From the question given:

hypotenus = 28Opposite = 14

Now we have ;

Adjacent = √28² - 14²

Adjacent = √(784 - 196)

Adjacent = √588

Adjacent = 24.248

Hence, the value of x = 24.25 units.

Learn more on Pythagoras: https://brainly.com/question/231802

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30 points for answering

Answers

Answer:

1) d

2) f

3) a

Step-by-step explanation:

1) 6² = 36 cm²

2) ½ (pi × (6/2)²)

= 14.14 cm²

3) 36 + 4(14.14)

= 92.56 cm³

If you can buy four bunches of seedless black grapes for $10, then how many can you
buy with $5?

Answers

Hope this will help u ...

Simplify log5 + 1/2 log x ? First answered will be the brainiest

Answers

5 1/2 Im sorry this is probably not correct

• A discount movie pass costs $14. With the
pass, movie tickets cost $6 each. Fern
spent a total of $68 on the pass and movie
tickets. How many movies did he see?

Answers

Answer:

He saw 9 movies :0

Step-by-step explanation:

First, you take the total cost and subtract the one time cost from it ($68 - $14 = $54) Next, you take the $54 and divide it buy the cost of dollars per movie. ($54/$6 = 9)

So, 9 is your answer.

Hope this helps!!

Final answer:

To find the number of movies Fern saw, subtract the cost of the discount movie pass from the total amount she spent and then divide the result by the cost of each movie ticket. Fern saw 9 movies.

Explanation:

To find the number of movies Fern saw, we need to subtract the cost of the discount movie pass from the total amount she spent and then divide the result by the cost of each movie ticket.

The cost of the discount movie pass is $14, and Fern spent a total of $68. So, $68 - $14 = $54 is the amount she spent on movie tickets.

Since each movie ticket costs $6, we divide the amount she spent on movie tickets by the cost of each movie ticket: $54 ÷ $6 = 9.

Therefore, Fern saw 9 movies.

please help for brainliest

Answers

Answer:

525 people

Step-by-step explanation:

3000/200=15

You multiply 15 by 35

This equals 525.

Answer:

525

Step-by-step explanation:

heres why

because 35/200 is a fraction that can be used in decimal form to multipy with 3000 to find the total ammount of people that said that this was their first concert

the decimal used is .175 so multply that with 3000 and you get 525

If brainiest is earned its greatly Appreciated

Suppose that an individual has a body fat percentage of 17.8% and weighs 152
pounds. How many pounds of his weight is made up of fat? Round your answer to the nearest tenth.

Answers

Answer: The individual has 27.056 pounds of body fat to be exact, and rounded to the nearest tenth is 27.1 lbs of body fat.

a figure has been dilated by a scale factor of 2. which transformation could be used to prove the figures are similar using the AA similarity postulate ?

Answers

Answer:

translation maybe

Grade point averages can take on any numeric values between 0 and 4 . They are an example of a what variable

Answers

continuous i believe.

Please help solve this system of inequalities:

{2x-12>0
{3x<9

Thank you

Answers

Answer: 6,3

Step-by-step explanation: 3/3 and then 9/3=3 • 0+12=12, 12/2=6,

Please give brainliest

The system of inequalities consists of x > 6 and x < 3, which have no overlapping solution. No number can satisfy both conditions simultaneously; hence, there is no solution to the system.

To solve the given system of inequalities, let's solve each inequality separately:

For the first inequality 2x - 12 > 0, we add 12 to both sides to get:

2x > 12

Now, we divide both sides by 2:

x > 6

This inequality means that x must be greater than 6.

For the second inequality 3x < 9, we divide both sides by 3:

x < 3

This tells us that x must be less than 3.

If we look at both solutions, x > 6 and x < 3, there is no overlap between these two sets of numbers.

Therefore, there is no solution to the system, since no number can be both greater than 6 and less than 3 at the same time.

A DVD has a diameter of 34 centimeters. What is the area of the DVD? Round your answer to the nearest
hundredth. Use 3.14 for it.
The area of the DVD is about
cm

Answers

Answer:

907.46cm

Step-by-step explanation:

Area of Cirlce = πr^2

R= 17

R^2= 289

289 x 3.14 = 907.46

907.46cm

Answer:

Area of the circle = [tex]907.46\;cm^2[/tex]

Step-by-step explanation:

Diameter of the DVD = [tex]34\;cm[/tex]

[tex]Radius=\dfrac{34}{2}=17\;cm[/tex]

Area of the circle= [tex]\pi \times r^2[/tex]

      As,

         [tex]\pi =\dfrac{22}{7}=3.14[/tex]

Area is:

      [tex]=3.14\times 17\times 17\\\\=3.14\times 289\\\\=907.46\;cm^2[/tex]

Area of the circle is: [tex]907.46\;cm^2[/tex]


Elsa started eating lunch at 11:25 and finished at 11:45. Explain how to find
how long it took Elsa to eat lunch.

Answers

Answer:

20

Step-by-step explanation:

because they end with same hour just subtract 25 from 45

45 -25= 20

Factor the polynomial by its greatest common monomial factor.
20y^6-15y^4+40y^2=20y
6
−15y
4
+40y
2
=20, y, start superscript, 6, end superscript, minus, 15, y, start superscript, 4, end superscript, plus, 40, y, squared, equals

Answers

Answer:

[tex]5 {y}^{2} (4 {y}^{4} - 3 {y}^{2} + 8)[/tex]

Step-by-step explanation:

We want to factor the common monomial out of :

[tex]20 {y}^{6} - 15 {y}^{4} + 40 {y}^{2} [/tex]

The greatest common monomial fact is

[tex]5 {y}^{2} [/tex]

We factor to get:

[tex]5 {y}^{2} (4 {y}^{4} - 3 {y}^{2} + 8)[/tex]

The expression in the parenthesis has no common factor again since we factored the greatest common factor.

The greatest common factor of 20y^620y

6

20, y, start superscript, 6, end superscript, -15y^4−15y

4

minus, 15, y, start superscript, 4, end superscript, and 40y^240y

2

40, y, squared is 5y^25y

2

5, y, squared.

[Show me how to find the greatest common factor.]

Now we need to factor 5y^25y

2

5, y, squared out of 20y^6-15y^4+40y^220y

6

−15y

4

+40y

2

20, y, start superscript, 6, end superscript, minus, 15, y, start superscript, 4, end superscript, plus, 40, y, squared.

Hint #22 / 3

\begin{aligned} &\phantom{=}20y^6-15y^4+40y^2 \\\\ &=5y^2(4y^4)+5y^2(-3y^2)+5y^2(8) \\\\ &=5y^2\left(4y^4-3y^2+8\right) \end{aligned}

 

=20y

6

−15y

4

+40y

2

=5y

2

(4y

4

)+5y

2

(−3y

2

)+5y

2

(8)

=5y

2

(4y

4

−3y

2

+8)

Hint #33 / 3

In conclusion,

20y^6-15y^4+40y^2=5y^2\left(4y^4-3y^2+8\right)20y

6

−15y

4

+40y

2

=5y

2

(4y

4

−3y

2

+8)20, y, start superscript, 6, end superscript, minus, 15, y, start superscript, 4, end superscript, plus, 40, y, squared, equals, 5, y, squared, left parenthesis, 4, y, start superscript, 4, end superscript, minus, 3, y, squared, plus, 8, right parenthesis

Heather also buys 12 patio lights for $63. She estimates the cost of each light to be about $5.
She then calculates the actual cost of each light to be $2.40. Use the drop-down
boxes to explain whether her calculation is reasonable

Answers

Answer: yes her calculations were reasonable because : 63/12=5.25

Step-by-step explanation:

Final answer:

Heather's estimation that each light costs about $5 is closer to the actual cost of $5.25 per light. Her calculated cost of $2.40 per light is not reasonable as it significantly underestimates the actual cost.

Explanation:

The question is asking whether Heather's calculation for the actual cost of each patio light is reasonable. Initially, Heather estimated each light to cost about $5, but after calculation, she found the cost to be $2.40. To verify this, we can divide the total cost by the number of lights. So, the calculation is as follows:

Total cost for 12 lights = $63

Actual cost per light = Total cost / Number of lights

Actual cost per light = $63 / 12

Actual cost per light = $5.25

Based on this calculation, Heather's estimate of $5 per light was closer to the actual cost, which is $5.25 per light. Therefore, her calculation of $2.40 per light is not reasonable as it is quite far from the actual calculated cost.

What’s the median of 2, 4, 5, 7 ,7 , 15

Answers

Answer:

6

Step-by-step explanation:

the middle number of the given list

Answer:

median = 6

Step-by-step explanation:

5, 7 are in the middle.

You add these and divide by 2 to get the median.

The diameter of a penny is 19.05 mm and the thickness is 1.52 mm what is the approximate volume of the role of Penny to the nearest 10th

Answers

The volume of a cylinder is the area of the base circle times the height.

The area of a circle is [tex]\pi r^2[/tex]. Since the diameter is 19.05, the radius will be half that diameter:

[tex]r=\dfrac{d}{2}=\dfrac{19.05}{2}=9.525[/tex]

So, the base area is

[tex]A=\pi(9.525)^2[/tex]

Multiply this by the thickness and you'll get the volume.

Final answer:

The approximate volume of a roll of pennies can be calculated using the volume formula for a cylinder, considering the diameter and thickness of a penny, converting measurements to the same units, and then multiplying by the number of pennies in a roll.

Explanation:

To solve for the approximate volume of a roll of pennies, we can use the formula for the volume of a cylinder, which is V = πr^2h, where r is the radius and h is the height of the cylinder. In this case, the diameter of a penny is given as 19.05 mm, which means the radius is half of that, 9.525 mm or 0.9525 cm. The thickness of each penny is 1.52 mm or 0.152 cm. If we assume a roll of 50 pennies, the height of the roll would be 50 times the thickness of one penny.

First, we convert the radius into centimeters by dividing by 10: 0.9525 cm. Then we use the formula to calculate the volume: V = π * (0.9525 cm)^2 * (0.152 cm * 50), which provides the volume of the roll of pennies. As the question asks to approximate the volume to the nearest tenth, we can perform this calculation and round the result accordingly.

Volume calculation and unit conversion are crucial elements in this type of problem. Moreover, the accuracy of the estimation is important, which should be within an acceptable range like 5%.

After leaving camp for a three-day journey into the frozen tundra, Daniela has just returned to camp. The
three days of her journey can be described by displacement (distance and direction) vectors d , d), and dz.
where each vector indicates Daniela's displacement from the start of her day to the end of her day.
di = 8i +3
d, is not given
az = i +47
(Distances are given in kilometers, km.)
What distance did Daniela travel on day two?
kilometers
(Round your final answer to the nearest tenth.)
In what direction did Daniela travel on day two? Assume 0° is the rightward direction.
(Round your final answer to the nearest degree. Your answer should be between 0 and 360°.)

Answers

Answer:

  a) 8.7 km

  b) 187.6°

Step-by-step explanation:

Given

Travel vectors (distance)∠(direction) ...

d₁ = 8∠3°d₂ = unknownd₃ = 1∠47°total travel was a round trip

Find

(Rounded to the nearest tenth ...)

  a) |d₂|

  b) ∠d₂

Solution

In order for the sum of the three travel vectors to represent a round trip, their sum must be zero. That is, the value of d₂ must be the opposite of the sum of the other two vectors. A vector calculator can find the desired value easily. Here, we will show the calculation using the law of cosines and the law of sines.

__

a) A diagram can be helpful. Since we want to find the opposite of the sum of the given vectors, we can start by drawing their sum. In our diagram, d₁ is segment AB, and d₃ is segment BC. Their sum is the segment AC.

The internal angle ABC is the supplement of the difference of the angles for d₁ and d₃, so is 180° -(47° -3°) = 136°. Then the law of cosines gives length AC as ...

  AC² = AB² +BC² -2AB·BC·cos(B)

  AC² = 8² +1² -2·8·1·cos(136°) = 65 -16cos(136°) ≈ 76.5094

  AC ≈ √76.5094 ≈ 8.747

The distance traveled on day 2 is about 8.7 km.

__

b) Given the side lengths of a triangle and one angle, the law of sines can be used to find the other angles. Here, it is convenient to find the internal angle at A. The law of sines tells us ...

  sin(A)/BC = sin(B)/AC

  sin(A) = BC/AC·sin(B)

  A = arcsin(BC/AC·sin(B)) = arcsin(1/8.747·sin(136°)) ≈ 4.555°

The direction angle from C to A will be the sum of the 3° direction angle of AB and the internal triangle angle A we just found, added to 180°. That sum is ...

  ∠CA = 180° +3° +4.6° = 187.6°

  ∠d₂ = 187.6°

Answer:

Distance traveled 8.6 kilometers on day two

Daniela traveled in a direcrion of 234degrees on day two

Step-by-step explanation:

I had the same exact question and found the answers after having it incorrect

Six quarts of milk weigh 13 pounds .write three different proportions you could use to fin the weight of 10 quarts of milk

Answers

Answer:

1. 130/6

2. 65/3

3. 260/12

Step-by-step explanation:

The first thing is to calculate the weight of 10 quarts of milk, like this:

(13 pounds / 6 quarts) * 10 quarts = 130/6 pounds

The three fractions could be:

1. 130/6 pounds weigh 10 quarts of milk.

2. 65/3 pounds weigh 10 quarts of milk.

3. 260/12 pounds weigh 10 quarts of milk.

Samantha evaluates the expression -5.3 + 7.9 and gets an answer of 2.4

Answers

Answer:

Step-by-step explanation:

To the evaluate -5.3+7.9

We get

2.6

Therefore the error

=2.6-2.4

=0.2

Samantha is wrong the correct answer to -5.3 + 7.9 is 2.6

Two friends shop for fresh fruit. Elana buys a watermelon for $8.75 and 5 pounds of cherries. Taniy buys a pineapple for $4.25 and 4 pounds of cherries. Use the variable p to represent the price, in dollars, per pound of cherries. Write and simplify an expression to represent how much more Elana spent.​

Answers

Answer: 4.50 + p

Step-by-step explanation: For this problem we will write and simplify an expression to represent how much more Elana spent.

8.75 + 5p - (4.25 + 4p)        ---Distribute the negative sign to the numbers inside the parentheses.

8.75 + 5p - 4.25 - 4p            ---Combine like terms

8.75 - 4.25 + 5p - 4p

4.50 + p

So, the expression 4.50 + p represents how much more Elana spent.

Final answer:

Elana spent $4.50 plus the price of 1 pound of cherries more than Taniy. The expression representing this difference is simplified to $4.50 + p.

Explanation:

To find out how much more Elana spent than Taniy, we'll write an expression representing the total amount each person spent, using p as the variable for the price per pound of cherries. Elana's total spending is the cost of the watermelon plus the cost of cherries, expressed as 8.75 + 5p. Taniy's total spending is the cost of the pineapple plus the cost of cherries, expressed as 4.25 + 4p. To find the difference in their spending, we subtract Taniy's total from Elana's total.

The expression representing how much more Elana spent is:

(8.75 + 5p) - (4.25 + 4p)

Now we simplify the expression:

8.75 + 5p - 4.25 - 4p which simplifies to 4.50 + p.

Therefore, Elana spent $4.50 plus 1 pound of cherries more than Taniy.

An equation whose variables are polar coordinates is called a(n) ____ equation

Answers

polar equation i’m assuming g

The length of a rectangle is three times the width. What is the perimeter of the rectangle if the width is 17 inches?

51 inches

136 inches

204 inches

68 inches

Answers

Answer:

136 Inches

Step-by-step explanation:

One side will be x. The other will be 3x.

x=17

3x=51

It is asking for 8x

8x=136

Answer:

136 inches

Step-by-step explanation:

The perimeter of a rectangle can be found using:

p=l+l+w+w

We know the width is 17, and the length is 3 times the width, which is 17

p=(17*3)+(17*3)+17+17

p=51+51+17+17

p=136

So, the perimeter is 136 inches

find the acute angle formed by line 2y=x+1​

Answers

Answer:

26.57°

Step-by-step explanation:

[tex]2y = x + 1 \\ y = \frac{1}{2} x + 1 \\ equating \: it \: with \\ y = mx + b \\ slope \: m = \frac{1}{2} \\ \because \: \tan \theta = m \\ \therefore \: \tan \theta = \frac{1}{2} = 0.5 \\ \therefore \: \theta = {tan}^{ - 1} (0.5) \\\therefore \: \theta = {tan}^{ - 1} ( \tan \: 26.565051177 \degree) \: \\ \\ \huge \red{ \boxed{\therefore \: \theta = 26.57 \degree}}[/tex]

What is the solution set of {x | x > -5} u {x | x < 5}?

A) all numbers except -5 and 5
B) the numbers between -5 and 5
C) the empty set
D) all real numbers

Answers

Answer:

The answer is D

Step-by-step explanation:

The solution set of {x | x > -5} u {x | x < 5} is given by all real numbers. so option D is correct.

What is a solution set to an inequality or an equation?

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solutions to that equation or inequality. A set of such values is called a solution set to the considered equation or inequality.

We need to find the solution set of the following inequalities:

A set of {x | x > -5} u {x | x < 5} has the solution of all values of x greater than -5.

The solution is all values of x greater than -5.

This is the union of both the inequalities, therefore all the real numbers will justify the inequalities.

Then, the solution set of {x | x > -5} u {x | x < 5} is given by all real numbers. so option D is correct.

Learn more about inequalities here:

https://brainly.com/question/27425770

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what is the answer to this?

Answers

Answer:

s = -18

b is correct option

Step-by-step explanation:

[tex]\frac{4}{s} =\frac{-2}{9}[/tex]

By cross multiplication

4×9 = -2×s

0r

-2×s = 4×9

s = 36 ÷ -2

s = -18

I need help again lol....

A.) SSS Postulate


B.) ASA Postulate


C.) AAS Theorem


D.) SAS Postulate

Answers

Answer: C) AAS Theorem

Check out the diagram below. Note how for the left triangle, the side ZW is not between the marked angles V and W. So we do not use ASA and instead go with AAS. The order matters. If for instance, we knew that VW = WY, then we would go with ASA.

Larry rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total less than 8.

Answers

Answer:

7/12.

Step-by-step explanation:

The total possible outcomes = 6*6 = 36.

Possible outcomes for a total  8 or greater are :

2,6  6,2  3,5   5,3  3,6  6,3   4,4  4,5  5,4  4,6  6,4  5,5,  5,6  6,5  6,6 = 15.

So the number of outcomes for a sum < 8 = 36 - 15 = 21.

Answer is 21/36 = 7/12.

what is z=77674844/085447

Answers

Answer:

909.041207??

Step-by-step explanation:

Suppose 80% of people can swim. Suppose 70% of people can
whistle. Suppose 55% of people can do both. What percentage of people
can swim or whistle?

Answers

Answer:

95%

Step-by-step explanation:

Let the proportion who can swim be denoted by P(S) while the proportion that can whistle be denoted by P(W)

The proportion that can swim and whistle will be P(S and W)

The proportion that can swim or whistle will be P(S or W)

To get the proportion that can swim or whistle will be P(S or W), we use

P(S or W)=P(S)+P(W)-P(S and W)

Given that P(W) is 70%, P(S) is 80% and P(S andW) is 55% then

P(S or W)=80%+70%-55%=95%

Other Questions
NEED HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!ANSWER IF YOU SMART!!!1.The weather we experience occurs in what part of the atmosphere?exospherestratospherelife spheretroposphere2.Differential heating causes global air circulation that creates permanent winds and ocean currents on a global scale.TrueFalse3. If you place a bottle in warm water, the air pressure will increase as the molecules heat up. If the bottle is capped, the air pressure will increase because the air has nowhere to go. But, if you take off the cap, the air spreads out and the density decreases. If you replace the bottle cap with a balloon, you can see how the air pushes its way into the balloon.What causes the balloon to inflate?the ballon will inflate by itself over timethe humdity from the water caused the ballon to expand.the heating caused the air in the bottle to expand4.Changes in _______ cause air to move.densityoxygen contentheightbiological molecules5. The energy from the Sun heats different areas of the globe at different rates. What is this phenomenon called??differential heatingspace heatingconvection heatingthermal blanketing6. Earth's incoming solar energy is not balanced by the radiation that it reflects or reradiates.TrueFalse7.Short-wave solar radiation gets absorbed by the earth's surface and is reflected back to space as infrared radiation. 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If a total of 3250 tickets are sold and if the total amount of ticket sales was $ 160,045a) how many full-price tickets were sold? b) how many student tickets were sold? How does that way you live affect the environment? What can you do to protect and preserve the environment 2. What role does the national government play in protecting the suffragerights of citizens? There are four main types of mechanical weathering: frost wedging in which rocks are broken by water freezing within cracks, salt crystal growth in which rocks are broken by salt freezing within cracks, sheeting in which rocks dome upward and peel off, and biological activity in which living things such as tree roots break rocks apart. You will visually identify these types. Note that one of the images is not an example of mechanical weathering. in circle F, points A,B,C,D, and E are located on the circle such that measure of C=119, and BE is perpendicular AD. determine the measure of arc AE. show how you arrived at your answer. A uniform electric field exists in a region between two oppositely charged plates. An electron is released from rest at the surface of the negatively charged plate and strikes the surface of the opposite plate, 3.8 cm away, in a time 3.5 10-7 s. What is the magnitude of the electric field 1. Employees are not allowed to drink water in food-preparation areas.True or False2. Gloves should be changed after handling raw meat, seafood, or poultry and before handling ready-to-eat food.True or False3. If the food handler is wearing gloves, he or she does not need to worry about washing hands.True or False which equation will be parallel to y=6 A)Y= -6x B)X=6 C)y=1 D)Y=6x What is an advantage of matrix organization On January 1, 2021, White Water issues $450,000 of 6% bonds, due in 20 years, with interest payable annually on December 31 each year. Required: Assuming the market interest rate on the issue date is 6%, the bonds will issue at $450,000. Record the bond issue on January 1, 2021, and the first two interest payments on December 31, 2021, and December 31, 2022. (If no entry is required for a particular transaction/event, select "No Journal Entry Required" in the first account field.) Certain car manufacturers install a gauge that tells the driver how many miles they can drive until they will run out of gas. A study was conducted to test the accuracy of these gauges. Each driver was assigned a certain gauge reading until empty to watch for. When their car announced it had that many miles remaining until empty, they began to measure their distance traveled. After they ran out of gas, they reported the distance they were able to drive (in miles) as well as the gauge reading they were assigned (in miles). Here is computer output showing the regression analysis: Regression Analysis: Distance versus Gauge Reading Predictor Coef SE Coet Constant -0.7928 3.2114 -0.2469 0.8060 Gauge 1.1889 0.0457 26.0310 0.0000 B = 7.0032 R-39 = 0.9326 2-3q(adj) = 0.9312 Identify and interpret the slope of the regression line used for predicting the actual distance that can be driven based on the gauge reading. Problem 2. (4 points) Suppose A is a matrix of size 4 by 4. Which of the following statements must be TRUE? (I) If the rank of A is 4, then the matrix A must be invertible. (II) If the matrix A is invertible, then the rank of A is 4. (III) If A is invertible, then the nullity of A is 0. (A) I only (B) II only (C) III only (D) II and III only (E) I, II, and III