n(U) = 147, n(A) = 48, n(B) = 68, n(A ∩ B) = 19, n(A ∩ C) = 22, n(A ∩ B ∩ C) = 10, n(A' ∩ B ∩ C') = 39, and n(A' ∩ B' ∩ C') = 36.
Find n(C).
A) 26
B) 14
C) 30
D) 46

Answers

Answer 1

Answer:  D) 46

===========================================================

Explanation:

We have these 8 given facts

N(U) = 147n(A) = 48n(B) = 68n(A ∩ B) = 19n(A ∩ C) = 22n(A ∩ B ∩ C) = 10n(A' ∩ B ∩ C') = 39n(A' ∩ B' ∩ C') = 36

Draw out a rectangle to represent the universal set U. Inside this rectangle, draw three overlapping circles. Refer to the diagram below (imagine that none of the values have been written down just yet). These circles are A, B, and C.

Now we'll focus on the 8 facts above. To start off, we'll look at fact 6 which says n(A ∩ B ∩ C) = 10. This means there are 10 items inside all three sets. This is the middle most region where all three circles overlap with one another.

Then move to fact 4 and we see that 19 items are in sets A and B at the same time. Subtract off those 10 items in all three sets and we have 19-10 = 9 items in set A and B, but not set C. We can write this as n(A ∩ B ∩ C') = 9 if you wanted to stay consistent with this math notation. Write "9" in the overlapped region between A and B, but not inside circle C.

Now go to fact 5. We have n(A ∩ C) = 22 telling us there are 22 items in both sets A and C at the same time. Subtract off the 10 in all three sets and we're left with 22-10 = 12 items in set A and set C, but not set B. We can write this as n(A ∩ B' ∩ C) = 12. Write "12" in the region between A and C, but outside of circle B.

If you're stuck anywhere, refer to the diagram below. Imagine that not all of the values have been filled in just yet.

---------------------------

So far you should have the numbers 10, 9 and 12 written in those positions I mentioned. Circle A is mostly filled out. We're missing the region that's inside A but outside both B and C; however, we can find that to be 17. Why is this? Well because n(A) = 48 and the other values (10, 9 and 12) add to 10+9+12 = 31. Then note how 31+17 = 48. So we must have 17 items in circle A but outside the other circles. We can write this as n(A ∩ B' ∩ C') = 17

In short, all of the values in circle A must add to 48. We have 17+10+9+12 = 48.

From fact 7, we can see that n(A' ∩ B ∩ C') = 39 meaning there are 39 items in circle B and not in any other circle. So we'll fill this value in as well.

The last value to fill in is the 36 from fact 8. This goes outside all of the circles.

The venn diagram below shows all of these values filled in that I mentioned so far. The missing two blank regions in circle C can be thought of as one region for the sake of simplicity.

---------------------------

Using that diagram of filled in values, add up every number written down:

17+9+39+12+10+36 = 123

We have 123 items so far in the universal set

We're told that n(U) = 147, meaning there are 147 items total in the universal set.

This must mean that 147-123 = 24 items are in the two blank regions of circle C. We don't need to break down how the 24 splits up.

That 24 adds to the other numbers inside circle C to get to the final answer

12+10+24 = 46

Choice D is the answer.

Side note: you could use n(B) = 68 to help break down those two blank regions of circle C, but that's just unnecessary extra work.

N(U) = 147, N(A) = 48, N(B) = 68, N(A B) = 19, N(A C) = 22, N(A B C) = 10, N(A' B C') = 39, And N(A'

Related Questions

Please help it’s urgent

Answers

Answer:

1750 sq m

Step-by-step explanation:

100 x 85 = 8500 and 90 x 75 = 6750, so take away 6750 from 8500, 8500 - 6750 = 1750 sq m

Solve the image, and you get points.

Answers

The 3rd one is equivalent

Five students in the chess club went to the state tournament. If 20% of the chess club went to the tournament, how many students are in the chess club?

Answers

Answer:

25 students are in the chess club

Step-by-step explanation:

100×5=500

500÷20=25

I hope it's correct:)

Answer:

25 students

and how?

its 2          5         S       T      U       D          E         N        T         S

Anyone need help? :D

Answers

Answer:

yeah why? are you going to help?me

Answer:

Yes i actually do.

Step-by-step explanation:

Ples help i will give you the best

ITS 10 POINTS
Can u tell me how to slove

Answers

Answer:

1024.

Step-by-step explanation:

4^5=4x4x4x4x4=1024.

4x4x4x4x4

Explanation: it's just 4 five times

234235342421323254123+323546534311234

Answers

Answer:

I gotchu.

Step-by-step explanation:

234235342421323254123+323546534311234 = 2.34235666E20

Have a good day! :)

Evaluate the expression when c=2 and y=-6.
-c+by
0
Х
?

Answers

Answer:

-38

Step-by-step explanation:

-c + 6y

= -(2) + 6 (-6)

= -2+(-36)

= -2 - 36

= -38

the answer to this question is -38

The circumference of a circle is _______

A. the length of the radius
B. the distance around the circle
C. the length of the diameter
D. 270​

Answers

Answer:

B. the distance around the circle

Step-by-step explanation:

To easily answer this question, take a closer look at the given answer choices.

A says, "the length of the radius." Don't let the extra words trick you! This answer choice is just describing a radius. The term, "the length of--" is just there to trick you and to make you overthink. This answer choice is not correct because a radius =/= a circumference.

C says, "the length of the diameter." This is the exact same trick in choice A. Once you ignore the term, "the length off," you see that this answer choice is just describing a diameter. This answer is also incorrect because a diameter =/= a circumference.

D just says "270." This answer choice should not be considered, as there's no numbers involved in the question. The question is just looking for the definition of a circumference. Continually, not every circle's circumference is going to be 270. For these reasons, D is also an incorrect choice.

This leaves answer choice B. After eliminating the other answers, B becomes the remaining and correct choice. "The distance around the circle," is the only and correct definition of a circumference!

Answer:

Solution :

B

Know More :

The length of radius is not known as circumference.

Circumference or perimeter is same.

Area of circle = πr²

Perimeter of circle = 2πr

[tex] \\ [/tex]

F(x) = 3 + 4x G(x) = 6x + 7

I) find fg(x)

Answers

Answer:

See the attached document

Is this correct? Geometry Math Question

Answers

QW= 140°

hope that helped^^

A table is 2 feet wide. It is 6 times as long as it is wide.

Answers

Answer:

The table is 12 feet in length

Step-by-step explanation:

2 * 6 = 12

12 feet in length

The area of a rectangle is given as:

Area = Length x width

The perimeter of a rectangle is given as:

Perimeter = 2 (length + width)

The area of the table is 24 square feet.

The perimeter of the table is 28 feet.

What is a rectangle?

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

The perimeter of a rectangle is given as:

Perimeter = 2 (length + width)

We have,

Table:

Width = 2 feet

Length = 6 x 2 feet = 12 feet

We will assume that the table is a rectangle.

The area of the table:

= Length x width

= 12 x 2

= 24 square feet.

The perimeter of the table:

= 2 (length + width)

= 2 (12 + 2)

= 2 x 14

= 28 feet

Thus,

The area of the table is 24 square feet.

The perimeter of the table is 28 feet.

Learn more about rectangles here:

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equation for the area of a circle with a diameter of 31.6 cm. Use 3.14 for
[tex]\pi[/tex]

[tex] [/tex]

Answers

Answer:

783.8696

Step-by-step explanation:

The way to find the area of a circle is to find the radius, multiply it by itself, then multiply by pi. The diameter is double the radius so we have to divide the diameter by 2 to find the radius. 31.6/2 is equal to 15.8, and if we plug it into our formula, we can find that the area is 15.8 * 15.8 * pi, and since we use 3.14 for pi, the area is 15.8 * 15.8 * 3.14. We can use a calculator for this part and find that the area of this circle is 783.8696.

Area of a circle is PI x r^2

You are given the diameter, the radius is half the diameter:

Area - PI x 1/2(diameter)^2

Area = 3.14 x 1/2(31.6)^2

Area = 3.14 x 15.8^2

Area = 3.14 x 249.64

Area = 783.8696 sq. cm. ( Round answer as needed)

David's overtime rate is $20. This week, he worked 3 overtime hours. How much will he get paid for overtime?
A. $30
B.$45
C$60

Answers

Answer:

$60

Step-by-step explanation:

3x20=60

It’s 60 because 20x3 is 60

19 cm
6 cm
30 cm
The container is 2/3 full of water.
A cup holds 275 ml of water.
What is the greatest number of cups that can be completely filled with water from
the container? (4)

Answers

Answer:

A total of  8 (eight) completely filled cups.

Step-by-step explanation:

Recall that 1 milliliter is the SAME as 1 cubic cm. Therefore, the 275 ml cup holds exactly 275 cm^3 of water.

Now calculate the volume of water in the container. Since the container measures 19 cm x 6 cm x 30 cm, its total volume is:

Volume = 19 x 6 x 30 = 3420 cm^3

The amount of water in it fills 2/3 of its volume, then:

amount of water = 2/3 (3420) = 2280 cm^3

Now to find how many cups can be filled with such amount of water, we do the division:

2280 / 275 = 8.29

Then the maximum number of completely filled cups is: 8

(+4) + (+9) + (+8) =

(+4) + ( -6) + (+8) =

5 ) ( -2) + (+5) + (+2) =

(+7) + (+2) + ( 0) =

Answers

Answer:

Question 1: 21

Question 2: 6

Question 3: -3

Question 4: 9

3. A game console originally is priced at $120. Demand increases the cost by 75%. What is the new price? Show your work ​

Answers

Answer:

New price = $210

Step-by-step explanation:

Given:

Original price = $120

Increase in cost = 75%

Find:

New price

Computation:

New price = Original price + Increase in cost

New price = 120 + 120(75%)

New price = 120 + 90

New price = $210

There are 23 bears in Yellow Park. There are 5 times as many bears in Green Park. Which equation will help us find out how many bears are in Green Park?
A. b=23+5
B. b=23*5
C. b=23/5
D. b=23-5

Answers

Answer:

B

Step-by-step explanation:

"5 times as many bears"

A would be 5 more bears than,

B would be 5 times more bears than,

C would be 5 times less bears than, and

D would be 5 less bears than.

Answer:

B. b = 23 * 5

Step-by-step explanation:

Yellow Park: 23 bears

Green Park: 5 times as many bears as in Yellow Park

5 times 23 bears is is 5 * 23 or 23 * 5

Answer: B. b = 23 * 5

Evaluate the expression.


2.2

(

2
)
÷
(

1
4
)

5
−2.2⋅(−2)÷(−
4
1

)⋅5

Answers

um is this all one equation?

like -2.2×(-2)÷(-14)×5-2.2×(-2)÷(-41)×5?

Which graph shows u + v for the given vectors u and v?

Answers

Answer:

The answer is A

Step-by-step explanation:

When you move v's tail to u's head, you see that the vectors align up.

The graph shows (u + v) for the given vectors u and v will be Graph A.

What is vector ?

A vector is an object that has both a magnitude and a direction. Magnitude defines the size of the vector. It is represented by a line with an arrow, where the length of the line is the magnitude of the vector and the arrow shows the direction.

We have,

Four graphs and we have to tell which is the correct graph for (u + v).

So,

To add two vectors, add the corresponding components.

i.e. The sum of u and v  vector = ( u₁ + v₁, u₂ + v₂)

i.e.

Let u = (u₁, u₂)  and

v = (v₁, v₂)

Now,

(u + v) = ( u₁ + v₁, u₂ + v₂)

So,

From Graph A,

We have,

u = (1, 4) and v = (2, -2)

i.e.

u₁ = 1,

u₂ = 4,

v₁ = 2,

v₂ = -2

So,

Using the addition method of vector,

i.e.

(u + v) = ( u₁ + v₁, u₂ + v₂)

Substituting values,

(u + v) = [( 1 + 2), (4 + (-2))]

We get,

(u + v) = (3, 2)

So,

The graph A represents the correct points of (u +v).

Hence, we can say that the graph shows (u + v) for the given vectors u and v will be Graph A.

To know more about vectors click here

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Which do the following options represent the measure of arc RA

A.38.6
B.65.6
C.71.4
D.77.2

Answers

Answer:

77.2°

Step-by-step explanation:

Consider the triangle JKR.

∠KJR=108.6 (lies on the same line as ∠RJA, angles on a straight line add up to 180)

All the angles in a triangle add up to 180, so:

∠JKR+∠KJR+∠JRK=180

∠JKR+108.6+32.8=180

∠JKR=38.6=∠RKA

Consider ∠RKA. This angle stands on the same arc as ∠RCA.

Since the angle at centre is twice the angle at circumference, 2(∠RKA) = ∠RCA.

2(∠RKA) = ∠RCA

2(38.6)=∠RCA

∠RCA=77.2°

The total points scored in the games of an NBA playoff series: 195 177 215 200 189 232 201 199 192 201

Answers

Step-by-step explanation:

something is missing. maybe mean, median

Draw a picture using the rectangular fraction model and write the answer. When possible, write your answer as a mixed number. 3/4 + 2/3 =

Answers

Answer:

yesss sirrrrrrrr

Step-by-step explanation:

l am out eyyyyyy

Which graph represents the inequality ?

Answers

Answer:

if there is a pic i need to to help so since there is no pic i can not help

Step-by-step explanation:

Please help this is due today!

Do not answer this with one answer ,blank, or a ridiculous answer.... this is serious please.

Answers

Answer:

perdita is correct

Step-by-step explanation:

perdita is correct because A isoceles triangle has two of the same. The triangle will just be very very thin

fill in the blanks #7 and #8 plzzzzz

Answers

Answer:

7.Always 8.Never

Step-by-step explanation:

7. A linear pair are 2 angles that forms 180 degree angles. Supplementary Angles are angles that form 180 degrees. 180=180 so it is always

8. Vertical angles share a common vertex but like adjacent angles but unlike vertical angles they dont overlap so Vertical angles are non adjacent angles.Also adjacent angles aren't always equal either. So never

Evaluate Square root b2 - 4ac when a = 1, b = -6, and c = 9.

Answers

Answer:

[tex]x=3[/tex]

. Resolver la siguiente inecuación, utilizar la notación de intervalos y representar el conjunto
solución en la recta real:

3x-1 + x+7 < 2x+5 + 7
5 2 3 ​

Answers

Answer:

bat di mo masagotan bobo kaba ikaw somagot nyan kasi dapat nagaaral kanangmabuti hayop ka wag kang mag patolong

If you answer these questions i will give you free point's. (Answer all of them pls)


1. I am 50% of a quarter of 32.
2. I am two thirds of 60.
3. I am exactly half-way between 25% of 80 cm and 40% of 120cm.
4. I am one-quarter of 50% of 88kg.
5. I am 3% of half of 600 pounds.
6. I am exactly halfway between one fifth of 25cm and 2% of 300 cm.
7. I am greater that 0.6 kg, less than one-third of 6 kg, and equal to four times 10% of 3kg.

Answers

Answer:

1. 4

2.40

3. 28

4.11

5.12

6. 1

7. 1200

Step-by-step explanation:

I used • instead of x to show you multiply.

1. 1/4 (one quarter) of 32 = 8.
50% of 8 = 4

2. 2/3• 60 = 120/3 = 40

3. 25% = 0.25, 40% = 0.40
So 0.25 • 80= 20
0.40 • 120 = 48
Then subtract: 48-20 = 28. Half of 28 is 14. Add that 14 to 20, and your answer is 34. It will probably be helpful to either write that on a number line, or picture it on a number line.

4. 50% of 88kg is half of that, which is 44. One quarter = 1/4, so 44/4 = 11

5. Half of 600 pounds is 300 pounds. 3% = 3/100 = 0.03. Multiply that by 300 to get your answer. 300 • 0.03 = 9

6. 1/5 of 25cm = 25/5= 5
2% of 300 = 300• 0.02= 6
What is exactly halfway between 5 and 6? 5.5

7. Start this one with the last statement. 10% (0.10) of 3kg = 3•0.10= 0.3. Four times that = 4•0.3= 1.2

Then check: is that greater than 0.6? Yes.

One third of 6kg = 6/3= 2

Is 1.2 less than 2? Yes.

resiprocal of (-3/7)^2!​

Answers

Answer:

[tex]\frac{49}{9}[/tex]

Step-by-step explanation:

Given

[tex](\frac{-3}{7})^{2!}[/tex]

Required

Determine the reciprocal

If a number is x, the reciprocal is: 1/x

So, the reciprocal of [tex](\frac{-3}{7})^{2!}[/tex] is:

[tex]\frac{1}{(\frac{-3}{7})^{2!}}[/tex]

[tex]2! = 2*1 =2[/tex]

So, we have:

[tex]\frac{1}{(\frac{-3}{7})^{2}}[/tex]

[tex]\frac{1}{(\frac{-3^{2}}{7^{2}})}[/tex]

Evaluate all exponents

[tex]\frac{1}{(\frac{9}{49})}[/tex]

Take inverse of 9/49

[tex]\frac{49}{9}[/tex]

Hence, the reciprocal of [tex](\frac{-3}{7})^{2!}[/tex] is [tex]\frac{49}{9}[/tex]

A set of nine books is arranged in orderly fashion on a Shelf. Each book has 100 pages that is sheets of paper with printing on both sides making 900 pages in all. A work starting on the first page of the book eats through to the last page of the last book how many pages does the worm eat​

Answers

Answer:

1( first page of volume 1) + 900 (900 book of 100 pages) + 1 (last page of the book)

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