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: 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') = 36Draw 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.
Related Questions
–5(–2) also i checked and apparently its not -7
Answers
Answer:
Im pretty sure you need to multiply answer is 10
Step-by-step explanation:
because the -5and -2 are right next to each other and if -7 doesn't work thats the next best thing.
Factor the expression 49t4 - 25 using the polynomial identity (x2 - y2) = (x - y)(x + y)
Answers
Answer:
Step-by-step explanation:
49t^4-25
(7t^2-5)(7t^2+5)
if 4 shirts and 3 ties cost 241. and 3 shirts and 4 ties cost 200. what is the cost of 1 shirt and 1 tie?
Answers
Answer:
cost of 1 tie = 11
cost of 1 shirt = 52
Step-by-step explanation:
What is the simplest form of the expression?
✓4502 +502 + 425
Assume all variables are positive.
Answers
Answer:
A. [tex] 8x\sqrt{5} [/tex]
Step-by-step explanation:
Given:
[tex] \sqrt{45x^2} + \sqrt{5x^2} + 4x\sqrt{5} [/tex]
Required:
Simplify
[tex] \sqrt{9*5*x^2} + \sqrt{5*x^2} + 4x\sqrt{5} [/tex]
[tex] 3x\sqrt{5} + x\sqrt{5} + 4x\sqrt{5} [/tex]
Add like terms
[tex] 8x\sqrt{5} [/tex]
Henri challenges Emile to a walking race. Because Emile's walking rate is faster, Emile gives Henri a 45-meter head start. Emile knows his brother would enjoy winning the race, but he does not want to make the race so short that it is obvious his brother will win. How long should the race be so that Henri will win in a close race?
Answers
Answer:
about 29 seconds and 74 meters
Step-by-step explanation:
Suppose weights of the checked baggage of airline passengers follow a nearly normal distribution with mean 46 pounds and standard deviation 3.7 pounds. Most airlines charge a fee for baggage that weigh in excess of 50 pounds. Determine what percent of airline passengers incur this fee. (Round your answer to two decimal places.)
Answers
Answer:
85.99% of airline passengers incur this fee.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Mean 46 pounds and standard deviation 3.7 pounds.
This means that [tex]\mu = 46, \sigma = 3.7[/tex]
Most airlines charge a fee for baggage that weigh in excess of 50 pounds. Determine what percent of airline passengers incur this fee.
As a proportion, this is 1 subtracted by the pvalue of Z when X = 50. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{50 - 46}{3.7}[/tex]
[tex]Z = 1.08[/tex]
[tex]Z = 1.08[/tex] has a pvalue of 0.8599
0.8599*100% = 85.99%
85.99% of airline passengers incur this fee.
14) x - 27 0
3
X^3-27=0
X^3-27=0
Answers
Answer:
For the top equation, x = 27 (I think you meant to put x - 27 = 0. If not, I can always edit my answer for you)
For the bottom, x = 3
Hope this helps! Have a grrrreat day lol
The ratio of the three angles of a triangle is 2:4:6. What is the measure of the
SMALLEST angle?
Answers
Explanation:
I assume the question should read "the measures of the ANGLES of the triangle are in the ratio 2:4:6.
If the angles are in the proportion 2:4:6, the measures of the angles have the same scale factor
x
. And, the sum of the measures of the angles of a triangle is
180
.
⇒
2
x
+
4
x
+
6
x
=
180
12
x
=
180
12
x
12
=
180
12
x
=
15
The measures of the angles are:
2
x
=
2
(
15
)
=
30
4
x
=
4
(
15
)
=
60
6
x
=
6
(
15
)
=
90
1 4/5 divided by 2 7/10
Answers
Answer:
2/3Step-by-step explanation:
In order to divide fractions, you'll have to multiply the first number by the second number's reciprocal.
So it would be 1 4/5 times the reciprocal of 2 7/10.
Reciprocal of 2 7/10 = Reciprocal of 27/10 = 10/27.
So 1 4/5 x 10/27 = 2/3
Answer:
2/3
Step-by-step explanation:
1 4/5 ÷ 2 7/10
Convert these into improper fractions
(Denomintaor × whole number + numerator)/denoninator
(5 × 1 + 4)/5
9/5
(10 × 2 + 7)/10
27/10
Now the equation says:
9/5 ÷ 27/10
Use the method copy dot flip, meaning rewrite the first fraction, change the division sign to multiplication, and use the reciprocal of the last fraction
9/5 × 10/27
Multiply the numerators and denominators separately
(9 × 10)/(5 × 27)
90/135
Simplify
Both 90 and 135 can evenly fit 15
90 ÷ 15 = 6
135 ÷ 15 = 9
6/9
This can still be simplified further
Both 6 and 9 can evenly fit 3
6 ÷ 3 = 2
9 ÷ 3 = 3
2/3
This cannot be simplified any further
Entry to a certain University is determined by a national test. The scores on this test are known to be normally distributed with a mean of 725 and a standard deviation of 115. Harriet wants to be admitted to this university and she knows that she must score better than at least 75% of the students who took the test. Harriet takes the test and scores 874.5. 1. (2pts) What percentile did Harriet score in? 2. (2pt) Will Harriet be admitted? Wh
Answers
Answer:
She scored in the 90th percentile.
90th percentile is better than 90% of the students who took the test, so yes, she will be admitted.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
The scores on this test are known to be normally distributed with a mean of 725 and a standard deviation of 115.
This means that [tex]\mu = 725, \sigma = 115[/tex]
She must score better than at least 75% of the students who took the test.
So her z-score should have a pvalue of at least 0.75.
Harriet takes the test and scores 874.5. 1. (2pts) What percentile did Harriet score in?
We have to find the pvalue of Z when X = 874.5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{874.5 - 725}{115}[/tex]
[tex]Z = 1.3[/tex]
[tex]Z = 1.3[/tex] has a pvalue of 0.9032
She scored in the 90th percentile.
Will Harriet be admitted?
90th percentile is better than 90% of the students who took the test, so yes, she will be admitted.
Tina buys a briefcase online for 62.95. If shipping and handling are an additional 20% of the price, how much shipping and handling will Tina pay?
Answers
Answer:
Tina will pay $12.95 for shipping and handling.
Step-by-step explanation:
Because you literally just have to multiply $62.95 by .2 and you have your answer.
It is important to comparison shop when purchasing a car.
What does comparison shop mean?
-Always buy from a
local dealership
-Take several photos to
use for comparison
-Compare the price &
quality from different
vendors
-Compare the true
market value of every
vehicle
Answers
Answer:
Compare price and quality
Step-by-step explanation:
I did this test
Answer:
option c
Step-by-step explanation:
comparing the price and quality from different vendors is important as we are giving a money we should be sure enough that quality is also as much the money
Can someone please help me understand this and the answer
Answers
Answer:
x ≤ 2
Step-by-step explanation:
Simplify the expression 2(10) + 2(x-4)
Answers
Answer:
Hello! :) have a good day!
2x + 12
Answer:
First: Multiply the numbers
2 x 10 + 2 (x -4)
20+2(x-4)
Secondly: Distribute
20+2(x-4)=
20 + 2x - 8
Thirdly: Subtract the numbers
20 + 2x - 8=
12 + 2x
Lastly: Rearrange terms
12 + 2x
2x + 12
And that would leave us with our answer 2x + 12!
A restaurant has 23 tables. Some of the tables seat 4 persons and the rest seat two persons. In all, 76 persons can be seated at once. How many tables of each kind are there?
Answers
Answer:
15 tables with 4 seats and 8 tables with 2 seats.
Step-by-step explanation:
x = 4 seated tables
y = 2 seated tables
x + y = 23
4x + 2y = 76
Multiply first equation by -2 to cancel y's:
-2x - 2y = -46
4x + 2y = 76
2x = 30
x = 30 / 2
x = 15
And we said 23 tables so:
23 - 15 = 8
x = 15
y = 8
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
48/96 in its simplest form
Answers
Answer:
1/2
Step-by-step explanation:
just divide it I guess
1/2
48/2
=24/2
=12/2
=6/2
=3
Hope this helps :D
What is 2/7+7/8
Help
Answers
Answer:
65/56 = 1 9/56
Step-by-step explanation:
Answer:
Step-by-step explanation:
16/56 + 49/56 = 65/56= 1 9/56
pls help 100 points helphelp
Answers
Answer:
Some kind of evadence
Step-by-step explanation:
Answer:
Im pretty sure it would be C.
Step-by-step explanation:
Sine a signature, photograph and quotes are all pieces of evidence, you can rule them out and infer that c would be the most reliable answer.
Charlotte used a calculator to subtract.
She copied her answers from the display, but her teacher said her answers were wrong! Tell how Charlotte got each wrong answer.
1. 204.59 – 23.67 = 0.92
2. 936.4 – 15.85 = 77.79
3. 56.3 – 27.04 = 19.26
Answers
Answer:
Step-by-step explanation:
1. She omitted the 0 from the minuend, entering 24.59 instead of 204.59
2. She misplaced the decimal point of the minuend, entering 93.64 instead of 936.4
3. She typed 4 instead of 5 in the minuend, entering 46.3 instead of 56.3
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
IM GIVING 40 POINTS !! DONT SKIP :((.
Answers
x to the third power =8/27
Answers
Answer:
2/3
Step-by-step explanation:
2/3
describe the graphs of 3x - y = 4 and y = 3x + 2?
Answers
Answer:
3X-y=4
3x=4+y
3x-4=y
y=3x-4
Step-by-step explanation:
y=3x+2
y-2=3x
3x=y-2
x=y-2/3
I hope this answer help you
First try was incorrect
Hall is baking a pie. The radius of the pie is 17 inches. What is the
area of the pie?
Use 3.14 for pi and round your answer to the nearest tenth.
label required
Answers
Answer:
907.5
Step-by-step explanation:
Formula to find the area of a circle: πr²
πr² = 3.14 x 17²
= 3.14 x 289
= 907.46
≈ 907.5
Hope this helps :)
Substitute w = 1 and w = 3 to determine if the two expressions are equivalent.
Answers
Answer:
mineeeeeeeeeeee
Step-by-step explanation:
6p² equals to..................
Answers
Answer:
36p is the correct answer
Which statement is true about this data set?
3,1, 6, 4, 4, 4, 3, 2, 5, 3
Answers
Answer:
What statements?
Step-by-step explanation:
Is there a list of statements for this question? I would love to help!
4.) A customer at a concession stand bought 2 boxes of popcorn & 3
drinks for $12. Another customer bought 3 boxes of popcorn & 5
drinks for $19. How much does a box of popcorn cost? How much does
a drink cost? Write and solve a system of equations
Equation 1 :
Equation 2:
Popcorn
Drink:
Answers
Answer:
10$ each
Step-by-step explanation:
Plz help me I’m stuck
Answers
Answer:
$10.50
Step-by-step explanation:
15% of 70 = $10.50
Hope that helps! (Can you give me a brainliest please? It's ok if you don't!)
Answer: $10
Step-by-step explanation:
15%= 0.15
67.37×0.15= 10.1055 ≈ $10 when rounded to the nearest ten.
1. Is a triangle with side lengths 6, 4, 3 a right triangle? Why or why
not?
Answers
Answer:
no
Step-by-step explanation:
Using the converse of Pythagoras' identity.
If the square of the longest side is equal to the sum of the squares on the other 2 sides then the triangle is right.
longest side = 6 , then 6² = 36
4² + 3² = 16 + 9 = 25
Since 4² + 3² ≠ 6² then triangle is not right.