A universal set U consists of elements. If sets A, B, and C are proper subsets of U and n(U), n(A B)n(A C)n(B C), n(A B C), and n(A B C), determine each of the following.
a. n(AUB)
b. n(A'UC)
c. n(AnB)'
Answers
Answer:
[tex]n(A\ u\ B) = 10[/tex]
[tex]n(A'\ u\ C) = 10[/tex]
[tex]n(A\ n\ B)' = 6[/tex]
Step-by-step explanation:
Given
[tex]n(U) = 12[/tex]
[tex]n(A\ n\ B) =n(A\ n\ C) = n(B\ n\ C) =6[/tex]
[tex]n(A\ n\ B\ n\ C)=4[/tex]
[tex]n(A\ u\ B\ u\ C)=10[/tex]
Required
Solve a, b and c
There are several ways to solve this; the best is by using Venn diagram (see attachment for diagram)
Solving (a):
[tex]n(A\ u\ B)[/tex]
This is calculated as:
[tex]n(A\ u\ B) = n(A) + n(B) - n(A\ n\ B)[/tex]
From the attachment
[tex]n(A) = 0+2+4+2 = 8[/tex]
[tex]n(B) = 0+2+4+2 = 8[/tex]
[tex]n(A\ n\ B) = 4 +2 = 6[/tex]
So:
[tex]n(A\ u\ B) = 8 + 8 - 6[/tex]
[tex]n(A\ u\ B) = 10[/tex]
Solving (b):
[tex]n(A'\ u\ C)[/tex]
This is calculated as:
[tex]n(A'\ u\ C) = n(A') + n(C) -n(A'\ n\ C)[/tex]
From the attachment
[tex]n(A) = n(U) - n(A) = 12 - 8 = 4[/tex]
[tex]n(C) = 0+2+4+2 = 8[/tex]
[tex]n(A'\ n\ C) = 2[/tex]
So:
[tex]n(A'\ u\ C) = 4 + 8 - 2[/tex]
[tex]n(A'\ u\ C) = 10[/tex]
Solving (c):
[tex]n(A\ n\ B)'[/tex]
This is calculated as:
[tex]n(A\ n\ B)' = n(U) - n(A\ n\ B)[/tex]
[tex]n(A\ n\ B)' = 12- 6[/tex]
[tex]n(A\ n\ B)' = 6[/tex]
Related Questions
Which summation properties or formulas must be used to evaluate this summation? Check all that
apply
Answers
Given:
Summation problem is:
[tex]\sum\limits_{n=1}^{35}n(n^2+1)[/tex]
To find:
The properties or formulas must be used to evaluate the given summation.
Solution:
We have,
[tex]\sum\limits_{n=1}^{35}n(n^2+1)[/tex]
In can be rewritten as:
[tex]\sum\limits_{n=1}^{35}n(n^2+1)=\sum\limits_{n=1}^{35}(n^3+n)[/tex]
[tex]\sum\limits_{n=1}^{35}n(n^2+1)=\sum\limits_{n=1}^{35}n^3+\sum\limits_{n=1}^{35}n[/tex] [tex]\left[\because \sum\limits_{i=1}^n(a_i\pm b_i)=\sum\limits_{i=1}^na_i\pm \sum\limits_{i=1}^nb_i\right][/tex]
[tex]\sum\limits_{n=1}^{35}n(n^2+1)=\left[\dfrac{35(35+1)}{2}\right]^2+\dfrac{35(35+1)}{2}[/tex] [tex]\left[\because \sum\limits_{i=1}^ni=\dfrac{n(n+1)}{2},\sum\limits_{i=1}^ni^3=\left[\dfrac{n(n+1)}{2}\right]^2\right][/tex]
[tex]\sum\limits_{n=1}^{35}n(n^2+1)=\left[\dfrac{35(36)}{2}\right]^2+\dfrac{35(36)}{2}[/tex]
[tex]\sum\limits_{n=1}^{35}n(n^2+1)=\left[630\right]^2+630[/tex]
[tex]\sum\limits_{n=1}^{35}n(n^2+1)=396900+630[/tex]
[tex]\sum\limits_{n=1}^{35}n(n^2+1)=397530[/tex]
Therefore, the properties and formula used are:
[tex]\sum\limits_{i=1}^n(a_i\pm b_i)=\sum\limits_{i=1}^na_i\pm \sum\limits_{i=1}^nb_i,\\\sum\limits_{i=1}^ni=\dfrac{n(n+1)}{2},\\\sum\limits_{i=1}^ni^3=\left[\dfrac{n(n+1)}{2}\right]^2[/tex]
Answer: see attachment below
Step-by-step explanation:
HELP THIS IS FOR MY FINAL GRADE
Ida's ice-cream stand has increasing profits each week during the hot summer months. Ida finds that each week during the summer her profits increase by 15% over what they were the previous week. In her first week of business, her profits were $600. How much money will she make in all over 5 weeks?
Answers
Answer:
Ida makes $ 6960 in 5 weeks.
Step-by-step explanation:
Let the profit of the first week is p.
p = $ 600
Total profits of the five weeks
= p + (p + 0.15p) + (p + p +0.15 p) + (p + p + p + 0.15 p) + (p + p + p + p + 0.15 p)
= 11 p + 0.6 p
= 11 x 600 + 0.6 x 600
= 6600 + 360
= $ 6960
So, Ida makes $ 6960 in 5 weeks.
Which rule explains why these triangles are congruent?
Answers
hope this helps!!
10) Using Limit Comparison Test (LCT), the following series
+00
M:
-1 + 2n5
n6 + 1
n=1
Answers
Compare to the divergent series,
[tex]\displaystyle\sum_{n=1}^\infty\frac1n[/tex]
Then by the limit comparison test, the given series also diverges, since the limit
[tex]\displaystyle\lim_{n\to\infty}\frac{\frac{2n^5-1}{n^6+1}}{\frac1n} = \lim_{n\to\infty}\frac{2n^6-n}{n^6+1}=\lim_{n\to\infty}\frac{2-\frac1{n^5}}{1+\frac1{n^6}}=2[/tex]
is positive and finite.
HELP! Please!
Create an equation to model a population of cells which starts with 10 cells and doubles in size every day. How many days will it take to reach 1,000,000 cells?
Answers
Answer:
it will take 100,000 more days.
you can do this by dividing 10 and 1,000,000
Please help please and thanks
Answers
what are the prime factors of the greatest 4 digit number?
Answers
Answer:
The prime factors of the greatest 4 digit number are 3, 11 and 101.
Step-by-step explanation:
Hope it helps
A local dealership provides you with statistics that show the number of each color car they sold last year along with the percentages that those sales represented relative to their inventory for that color car.
For each color, how many cars did the dealership have in its inventory before they started selling them?
Answers
Answer:
red: 20
white: 30
black: 25
silver: 40
other: 12
Step-by-step explanation:
To find the original number of cars per color in the inventory, divide the sold number of cars by the percent of the inventory.
red: 20 = 10/0.5
white: 30 = 21/0.7
black: 25 = 19/0.76
silver: 40 = 10/0.25
other: 12 = 4/0.33
The y value is two less than twice the x-value
Answers
7) Point P is located at (4,8) on a coordinate plane. Point P will be relfected over y = x. What will bee
the coordiantes of the image of point P?
A. (28,4)
B. 24,8)
C. (4,28)
D. (8,4)
Answers
Write a statement that indicates that the triangles in each pair are congruent. NO LINKS!!
Answers
Answer:
23
UVW congruent to WFG
and
24
FHG congruent to LMN
Answer:
23 ) UVW is congruent to WGF
24 ) FHG is congruent to LMN
Use the Pythagorean theorem to find the value for ( show work )
Answers
Answer:
x = 12
Step-by-step explanation:
x^2 + (x - 7)^2 = (x + 1)^2
x^2 + x^2 - 14x + 49 = x^2 + 2x + 1
x^2 - 16x + 48 = 0
(x - 4)(x - 12) = 0
x - 4 = 0 or x - 12 = 0
x = 4 or x = 12
One side has length x - 7.
For x = 4, x - 7 = 4 - 7 = -3.
Since a side of a triangle cannot have a negative length, x = 4 must be discarded.
Answer: x = 12
Delia bought 32 fluid ounces of fruit juice. How many gallons of juice did she buy?
A. 1
B. 0.5
C. 0.25
D. 0.2
Answers
Answer:
the answer is C. 0.25.
Step-by-step explanation:
simply converting the fluid oz into gallons.
Find the surface area of the prism. 13 in. 3 in 7 in.
Answers
Answer:
182+78+42=302 ... 302's ya answer...Give me brainiest answer to say ty! :)
Step-by-step explanation:
Which completely describes the polygon ? equilateral equiangular regular congruent
Answers
Explanation:
Any regular polygon is both equilateral and equiangular.
Equilateral = all sides are equal
Equiangular = all angles are equal
The stock of Company A gained 6% today to $87.45. What was the opening price of the stock in the beginning of the day?
25 POINTS!!!!!!!!!!!!!!!!
Answers
Answer:
$82.50
Step-by-step explanation:
gainsd 6%=106%
$87.45×100%/106%=$82.50
Hope can help!!!
Answer:
$82.50
Step-by-step explanation:
gained6%=100%+6%
100%+6%=$87.45
100%=?
solution :
$87.45×100/106=$82.50
Find the difference,
(20m+ 3) - (7m - 5)
A. 27m - 2
B. 13m +8
C. 27m +8
D. 13m - 2
SUBMU
Answers
Answer:
B 13m+8
Step-by-step explanation:
(20m+3) - (7m-5)
20m+3-7m+5
13m+8
John made a small rectangular table for his workroom. If the sides of the table are 32 inches and 26 inches, what should the table measure diagonally?
Answers
Answer:
The table should measure diagonally about 41.23 inches.
Step-by-step explanation:
To find the diagonal of a rectangle we use the formula :
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
A and B both represent the side lengths of the rectangle, while C is the diagonal part. Knowing this formula, let's plug in the values for A and B and see what happens.
[tex]32^{2}[/tex] + [tex]26^{2}[/tex] = [tex]c^{2}[/tex]
1024 + 676 = [tex]c^{2}[/tex]
1700 = [tex]c^{2}[/tex]
The square root of 1700 is (rounded to the hundreth's place) = 41.23
Answer:
c41
Step-by-step explanation:
Suppose that your boss must choose four employees in your office to attend a conference in Jamaica. Because all 15 of you want to go, he decides that the only fair way is to draw names out of a hat. What is the probability that you, Kyle, Carol, and Adam are chosen? Enter a fraction or round your answer to 4 decimal places, if necessary.
Answers
Answer:
1 / 1365
Step-by-step explanation:
Given that :
Number of employees to choose from = 15
Number of employees to be chosen = 4
Probability of choosing You, Kyle, Carol and Adam
Recall ;
P(A) = number of required outcome / Total possible outcomes
Number of required outcome = 4C4
Total possible outcomes = 15C4
nCr = n! ÷ (n-r)!r!
Using calculator to save computation time :
15C4 = 1365
4C4 = 1
P(choosing you, Kyle, Carol and Adam) :
1 / 1365
what is 5a +14=3(a +2)
Answers
Answer:
a=-4
Step-by-step explanation:
See image below:)
Find the value of the expression (4x – 12)+(1/3xy – 5) when x = 6 and y=2
Answers
Answer:
11
Step-by-step explanation:
GIVEN
x = 6
y = 2
STEPS
(4x - 12) + (1/3xy - 5 )
(4(6) - 12 ) + ( 1/3(6x2) - 5)
(24 - 12) + ( 1/3(12) - 5)
12 + (4 - 5)
12 + (-1)
(12 - 1)
11
The average height of corn stalks in a field is 71 inches with a standard deviation of 4.3 inches. Sketch a normal curve labeling the horizontal axis at one, two, and three standard deviations from the mean.
Answers
Answer:
The answer is below
Step-by-step explanation:
The empirical rules states that for a normal distribution, 68% of the data falls within one standard deviation from the mean, 95% falls within two standard deviation from the mean and 99.7% falls within three standard deviations from the mean.
Given that:
mean (μ) = 71 inches, standard deviation (σ) = 4.3 inches
One standard deviation = μ ± σ = 71 ± 4.3 = (66.7, 75.3)
Two standard deviation = μ ± 2σ = 71 ± 2*4.3 = (62.4, 79.6)
Three standard deviation = μ ± 3σ = 71 ± 3*4.3 = (58.1, 83.9)
The graph is attached
HELP DUE SOON 20 POINTS
Answers
Answer:
x = 10
Step-by-step explanation:
m∠KNL = 90
10x - 10 = 90
10x = 100
x = 10
3p(2p - 9) - 2p(-9 + p)
Answers
Answer:
4p² - 9p
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
3p(2p - 9) - 2p(-9 + p)
Step 2: Simplify
[Distributive Property] Distribute 3p: 6p² - 27p - 2p(-9 + p)[Distributive Property] Distribute -2p: 6p² - 27p + 18p - 2p²[Subtraction] Combine like terms (p²): 4p² - 27p + 18p[Addition] Combine like terms (p): 4p² - 9p6p -27p -2p^2+12p
4p^2 -27p+18p
Combine like terms
Your answer is 4p^2 -9p
PLS HELP!! I NEED TO FIND THE SURFACE AREA OF THIS CYLINDER!!!!!
Answers
Answer:
Step-by-step explanation:
you have two disks, and one rectangle
area of the disk = π [tex]r^{2}[/tex]
47 π x 2 = 94 π (for the two disks....
rectangle area = L x W
width = 14
Length = 2*π*r = 14π
area = 14*14π = 196 π
total = 196 π + 94 π = 290 π
Answer:
The surface area of this cylinder is about 923.63 [tex]inches^{2}[/tex].
Step-by-step explanation:
The formula for the surface area of a cylinder is this :
[tex]A = 2\pi rh+2\pi r^{2}[/tex]
"R" is 7, and "h" is 14. Knowing these values, let's solve.
[tex]A = 2\pi rh+2\pi r^{2}[/tex] = 2 · π · 7 · 14 + 2 · π ·72 ≈ 923.62824
The surface area of this cylinder is about 923.63 [tex]inches^{2}[/tex].
Hope this helps, please mark brainliest! :)
What is the measure of angle AIN?
O
A. 95°
B. 125°
C. 55
o
O
D. 30°
Answers
Answer:
30
Step-by-step explanation:
AIN is a vertical angle to FIL, which means they ae equal
FIL = 30 so AIN = 30
What is the sum of the polynomials?
(m + n + 3) + (m + n + 4)
Answers
Answer:
i honestly dk but need help
Step-by-step explanation:
ls
Answer:
2m+2n+7
Step-by-step explanation:
See image below:)
I just need to know what is m=
Answers
Answer:
- 2
Step-by-step explanation:
Given :
Point A = (-1, 4)
Point B = (1, 0)
x2 = - 1 ; y2 = 4 ; x1 = 1 ; y1 = 0
Rise = (y2 - y1) = 4 - 0 = 4
Run = (x2 - x1). = - 1 - 1 = - 2
Slope = Rise / Run = 4 / - 2 = - 2
The slope, m = - 2
What are the coordinates of the point plotted on this graph?
Answers
Answer:
C
Step-by-step explanation:
Correct answer
if the given ordered pair equal then find value of x and y
(3x+5)=(x+2)
and (4y+7)= (y+3)
Answers
Answer:
3x+5 =x+2
3x-x=2-5
2x= –3
x=-3/2
4y+7=y+3
4y–y =3-7
3y=–4
y= —4/3