Finish labeling the number of elements in the regions in the Venn diagram shown to the right, where the subsets
A, B, and C of the universe, U, satisfy the following conditions.
n(U) = 100
n(ANB) = 14
n(A) = 40
n(BNC) = 13
n(B) = 50
n(ANC) = 14
n(C)= 30
n(ANBNC) = 7
q=
S=
t=
V=
w=
X=
Answers
Answer:
t=14
v=13
q=12
s=23
w=-4
x=28
Step-by-step explanation:
we know that the universal set =100
so, everything in it must add up to 100
first, from the information given to us,
t= n(A n C)= 14
v=n(B n C)= 13
to find q
we know from our guide that n(A) =40
which means everything inside A will add up to 40
therefore,
q + 7 + 7 + t = 40
and we already know that t = 14
so, that will be;
q + 7 + 7 + 14 = 40
therefore, q = 12
to find s,
we all know that n(B) = 50
which means that everything inside B will be equal to 50
therefore,
s + 7 + 7 + v = 50
and we know that v = 13
therefore,
s + 7 + 7 + 13 = 50
and s will end up to be = 23
to find w,
we know that n(C) = 30
so, everything in C end up to be all equal to 30
therefore,
t + 7 + w + v = 30
from our solution, t = 14, v = 13
so,
14 + 7 + w
q = 19, s = 30, t = 7, v = 6, w = 10, x = 7.
What is a set ?A set is a collection of well defined objects.
According to the given question of Venn diagram given,
n(U) = 100, n(A∩B) = 14, n(A) = 40, n(B∩C) = 13, n(B) = 50, n(A∩C) = 14, n(C) = 30 and n(A∩B∩C) = 7.
t = n(A∩C) - n(A∩B∩C).
t = 14 - 7
= 7.
q = n(A) - [ n(A∩B) + t ]
q = 40 - ( 14 + 7 )
q = 40 - 21
q = 19.
v = n(B∩C) - n(A∩B∩C)
v = 13 - 7
v = 6.
s = n(B) - [ n(A∩B) + v ]
s = 50 - ( 14 + 6 )
s = 30.
w = n(C) - [ n(A∩C) + v ]
w = 30 - ( 14 + 6 )
w = 10.
We know x = n(U) - q - s - w - n(A∩B) - n(B∩C) - n(A∩C) + n(A∩B∩C).
x = 100 - 19 - 30 - 10 - 14 - 13 - 14 + 7.
x = 7.
learn more about sets here :
https://brainly.com/question/18877365
#SPJ2
Related Questions
Find the graphed solution to the inequality. 3(x-9) < -18
Closed or open, left or right?
Answers
Answer:
open left
Step-by-step explanation:
We can distribute the left side to get [tex]3x-27<-18[/tex].
We can then add [tex]27[/tex] to both sides of the equation to get [tex]3x<9[/tex].
We can finally divide both sides of the equation to get [tex]x<3[/tex].
Because it's a [tex]<[/tex] and not a [tex]<=[/tex], it is closed. And because the inequality opens to the right, it faces to the left.
So, it is a open left graph.
-3 = -11 # -10 H + 05 > -15 -5 10 15 Stuck? Review related articles/videos or use a hint.
Answers
weooooooooooooooooooooooooooooooooooooo9ooooooooooow
Simplify and solve step by step 4x -2x -20x + x
Answers
Answer:
-17x
Step-by-step explanation:
okay yes okay yes yes okay
Hey there! Let's combine like terms! ;)
4x-2x-20x+x
First, let's do 4x-2x:
4x-2x=2x
2x-20x+x`
2x-19x
-17x
Hope it helps!
PLEASE HELP Enter your answer and show all the steps that you use to solve this problem in the space provided. Bernadette bought two pieces of ribbon. One piece is 6 1/4 feet long, and the other is 11 1/2 feet long. Find the total length of the ribbon.
Answers
Answer:
17 3/4 feet long
or
17.75 feet long
Step-by-step explanation:
11 1/2 -> 11 2/4 (just multiplying numerator/denominator by 2
11 2/4 + 6 1/4 = 17 3/4
Answer:
17 3/4
Step-by-step explanation:
Convert 6 1/4 to an improper fraction (25/4)
Convert 11 1/2 to an improper fraction (23/2)
Multiply 23/2 by 2/2 to get a common denominator
which makes 25/4 +23x2/4
And 25+46=71
So 71/4
Then to change it back into a mixed number you divide 71 by 4 and get
17 3/4
The mapping shows a relationship between input and
output values.
Input
Output
Which ordered pair could be removed to make this
relation a function?
0 (-5,0)
0 (-1, -3)
(4.-2)
(6.-1)
-5
2
-3
up N Ţ to
-1
ī p q no
-2
4
2
6
Answers
Answer:
(4,-2)
Step-by-step explanation:
How would i graph the solution set for 1/3x (greater than or equal to) y+2?
Answers
You’ll have to transform the equation into its slope-intercept form, y = mx + b, so that you could graph the line. Set y to “=“
1/3x = y + 2
Subtract 2 from both sides
1/3x -2 = y + 2- 2
1/3x - 2 = y or y = 1/3x - 2
Next, to graph the solid line, you need at least two points to plot. We can start with the y-intercept, (0, -2). Another point to use is the x-intercept. To solve for the x-intercept, (a, 0), set y = 0:
0 = 1/3x - 2
Add 2 on both sides:
0 + 2 = 1/3x - 2 + 2
2 = 1/3x
Multiply both sides by 3 to solve for x:
2(3) = (3) 1/3x
6 = x
Therefore, the x-intercept = (6,0).
Plot the intercepts on the graph and connect those two points to create line.
Next, to identify which half-plane region to shade, choose a convenient test point (not on the line) to see whether it part of the solution. We could use the point of origin, (0, 0). Substitute its values into the linear inequality:
1/3x ≥ y + 2
1/3(0) ≥ (0) + 2
0 ≥ 2 (false statement). Therefore, you must shade the half-plane region where it doesn’t contain the test point, (0, 0).
Attached is the graph where it shows that the shaded lower half-plane region.
Please mark my answers as the Brainliest if you find my explanations helpful :)
o differences between constructing an inscribed regular hexagon and constructing an inscribed square.
Answers
Answer:
a daddy
Step-by-step explanation:
What is your weight on Jupiter? (g = 26.0 m/s^2)
Answers
Answer:
depends on how much you weigh
What would be the all step you would take to solve the equation 2x + 1 = 10 - x?
Answers
Answer:
3
Step-by-step explanation:
Move the terms : 2x + 1 =10 -x
Collect like terms
Calculate : 2x + x=10-1
Divide both sides
3x = 9
x = 3
please help me asap and show your work
Answers
Answer:
1) x = 5 because square root of 25 is 5
2)x = 3 because cubed root of 27 is 3
3) No exact solution because square root 12 is 2root3
4)No exact solution because cubed root 12 is 2.2
What is the main idea or topic of a story called?
A. plot
B. theme
C. character
D. dialogue
Answers
Answer:
the answer is B. Theme. Hope this helps
Explanation
The theme is what the story’s topic is about
It’s also the main idea
PLEASE HELP ME
(Part 1) A line goes through the points (1, 6) and (–2, 8). Write the equation of the line in Point-Slope form. Show your work algebraically for full credit. Circle your answer
(Part 2) A line goes through the points (1, 6) and (–2, 8). Write the equation of the line in Slope-intercept form. Show your work algebraically for full credit. Hint: this is the same line as in #1. Circle your answer.
Answers
Answer:
48
Step-by-step explanation:
A step-by-step solution to 1/6 plus 2/8, with the answer in fraction form.Now we multiply 1 by 8, and get 8, then we multiply 6 by 8 and get 48.
8(b+1) = -11-3b. what is the answer
Answers
Answer:
B= -19/11 (negative 19 over 11)
A baseball game has a total of 9 innings in each inning
Answers
Answer:
it is d.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
2 teams have to play a total of 18 innings and each inning needs 3 outs, and then you take it in a 9-inning scenario.
WILL MARK BRAINLIEST Select the correct answer.
What is the slope of the line in this graph?
y 10
9
8
00
17
6
5
5
w
3
-2
N
X
1
2
3
5
ch
6
7
7
GO
9
10
ОА.
OB &
C.
9
OD
Answers
Hope this helps you !! :)
The solution is, the slope of the line in the graph is 5/7.
What is slope?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
here, we have,
from the given graph, we get,
the line is passing through the points ( 0,0) and, (5,7).
now, we know that
slope of a line is,
m = x1 - x2 / y1 - y2
so, we have,
here,
Slope(m) = 5-0/7-0
= 5/7
Hence, The solution is, the slope of the line in the graph is 5/7.
To learn more on slope click:
brainly.com/question/3605446
#SPJ7
PLEASE HELP ITS MATH THANK YOUUUU
Answers
Answer:
4 Kilometers
Step-by-step explanation:
if 2 centimeters = 1 kilometer than 8 centimeters = 4 kilometers
1 1.2.4 Quiz: Paying Taxes Question 7 of 10 Income tax is calculated based on: A. gross income minus deductions, B. net income minus profits C. gross income. D. net income minus deductions,
Answers
Income tax is calculated based on: A. gross income minus deductions
What is Income Tax?Income tax is defined as the levy that the government places on income earners for a specific period of time, which is usually a month or a year as the case may be.Income tax = gross profit less a fixed percentage charged on the taxable income of the payer.Therefore, income tax is calculated based on: A. gross income minus deductions
Learn more about income tax on:
https://brainly.com/question/547727
Answer:
The answer is A. Gross income minus deductions
Step-by-step explanation
I looked it the answer and read through the notes to find my answer
Evaluate.
(jk−1) ÷j when j=−4 and k=−0.8
Enter your answer as a decimal in the box.
Answers
Step-by-step explanation:
(jk−1) ÷j
[(-4)(-0.8) -1] ÷ (-4)
=[ 3.2 -1] ÷ (-4)
=2.2 ÷ (-4)
= -0.55
The solution of the expression "[tex]\frac{jk-1}{j}[/tex]" is "-0.55".
The given values are:
j = -4k = -0.8→ [tex]\frac{jk-1}{j}[/tex]
By putting the value of "j" and "k" in the given expression, we get
→ [tex]\frac{(-4)(-0.8)-1}{-4}[/tex]
By solving the brackets, we get
→ [tex]\frac{3.2-1}{-4}[/tex]
→ [tex]\frac{2.2}{-4}[/tex]
→ [tex]-0.55[/tex]
Thus the above response is correct.
Learn more:
https://brainly.com/question/25032806
¿Es 42.497.365 divisible por 6?
Answers
No, 42,497,365 is not divisible by 6.
Hope it helps you! :)
[tex]GraceRosalia[/tex]
Which number line shows the location
of 0.3?
Answers
There is no picture attached :)
Which of these is a correct statement about the function graphed below?
5
A. Its equation is y = 2x, so it is not a linear function.
B.
Its equation is y = 2x, so it is a linear function.
c. Its equation is y
2", so it is not a linear function.
D. Its equation is y
2", so it is a linear function
Answers
Answer:
C
Step-by-step explanation:
It curves so it automatically means it isn't any of the answers that say it is.
Numbers with variable powers are NEVER linear, so it is C.
Find the surface area of a right cone that has a radius of 9 inches and a height of 12 inches. Round your answer to the nearest hundredth.
Answers
Answer:
SA= 678.24 in^2
Step-by-step explanation:
SA = (pi)(r^2) + (pi)(r)(l)
r = radius
h = height
l = slant height
Pi = 3.14
Slant height:
l^2 = h^2 + r^2
l = sqrt (144+81)
= 15
SA = (pi)(9^2) + (pi) (9) (15)
SA = 254.34 + 423.9
SA= 678.24 square inches
If the slant height of the cone is 15 inches. Then the surface area of the cone will be 678.58 square inches.
How do find the surface area of some object?Find the area that its outer surfaces possess. The Sum of all those surface areas is the surface area of the considered object.
If a right cone has a radius of 9 inches and a height of 12 inches.
Then the surface area of a right cone will be
The slant height is given as
l² = 9² + 12²
l² = 81 + 144
l² = 225
l = 15
Then the surface area will be
Surface area = πr² + πrl
Surface area = π x 9² + π x 9 x 15
Surface area = 81π + 135π
Surface area = 216π
Surface area = 678.58 square inches
Learn more about the surface area here:
https://brainly.com/question/15096475
#SPJ2
Jose has scored 533 points on his math tests so far this semester. To get an A for the semester, he must score at least 616 points. Part 1 out of 2 Enter an inequality to find the minimum number of points he must score on the remaining tests in order to get an A. Let n represent the number of points Jose needs to score on the remaining tests.
Answers
Answer:
The answer is 612-533=n
There was 5/8 of a pie in the fridge. Daniel ate 1/4 leftover. How much of a pie did he have
Answers
Answer:
Therefore, 15 / 32 of the pie is left in the fridge.
What is the slope of the line shown in the graph? Express your answer as an improper fraction or as an integer
Answers
Answer:
y= 3/2x + 1
Step-by-step explanation:
Rise over run to find slope: Rise: 3 Run:2
Y-intercept is at +1
Step-by-step explanation:
slope is the same as gradient,m
m= y2- y1
x2 - x1
(2,4) (0,1)
x2,y2 x1,y1
m= 4 - 1
2 - 0
m= 3
2
These triangles are scaled copies of each other.
For each pair of triangles listed, the area of the second triangle is how many times larger than the area of the first?
a. Triangle G and Triangle F Response area
b. Triangle G and Triangle B Response area
c. Triangle B and Triangle F Response area
d. Triangle F and Triangle H Response area
e. Triangle G and Triangle H Response area
f. Triangle H and Triangle B Response area
Answers
Answer:
a. 4
b. 1/4
c. 16
d. 1/9
e. 4/9
f. 9/16
Step-by-step explanation:
The ratio of the areas is the square of the ratio of the lengths of the sides.
a. Triangles G and F
Select a side in triangle G and the corresponding side in triangle F:
side in F: 10
corresponding side in G: 5
ratio of lengths of F to G = 10/5 = 2
ratio of areas of G to F: (2)^2 = 4
b. Triangles G and B
Select a side in triangle G and the corresponding side in triangle B:
side in G: 5
corresponding side in B: 5/2
ratio of lengths of B to G = (5/2)/5 = 1/2
ratio of areas of B to G: (1/2)^2 = 1/4
c. Triangles B and F
Select a side in triangle B and the corresponding side in triangle F:
side in B: 5/2
corresponding side in F: 10
ratio of lengths of F to B = 10/(5/2) = 4
ratio of areas of F to B: (4)^2 = 16
Do the same for the other 3 pairs of triangles.
The answers are:
d. 1/9
e. 4/9
f. 9/16
The ratio of the areas is the square of the ratio of the lengths of the sides.
Let's find the ratio of areas one by one:
A. Triangles G and F
Select a side in triangle G and the corresponding side in triangle F:
Side in F= 10
Corresponding side in G= 5
The ratio of lengths of F to G = 10/5 = 2
The ratio of areas of G to F= (2)^2 = 4
B. Triangles G and B
Select a side in triangle G and the corresponding side in triangle B:
Side in G= 5
Corresponding side in B= 5/2
The ratio of lengths of B to G = (5/2)/5 = 1/2
The ratio of areas of B to G: (1/2)^2 = 1/4
C. Triangles B and F
Select a side in triangle B and the corresponding side in triangle F:
Side in B= 5/2
Corresponding side in F= 10
The ratio of lengths of F to B = 10/(5/2) = 4
The ratio of areas of F to B: (4)^2 = 16
D. Triangles F and H
Select a side in triangle F and the corresponding side in triangle H:
Side in F= 10
Corresponding side in H= 10/3
The ratio of lengths of H to F = (10/3)/10 = 1/3
The ratio of areas of H to F: (1/3)^2 = 1/9
E. Triangles G and H
Select a side in triangle G and the corresponding side in triangle H:
Side in G= 5
Corresponding side in H=10/3
The ratio of lengths of H to G = (10/3)/5 = 2/3
The ratio of areas of H to G: (2/3)^2 = 4/9
F. Triangles H and B
Select a side in triangle H and the corresponding side in triangle B:
Side in H=10/3
Corresponding side in B= 5/2
The ratio of lengths of B to H = (5/2)/(10/3) = 3/4
The ratio of areas of H to G: (3/4)^2 = 9/16
The final answers are:
a. 4
b. 1/4
c. 16
d. 1/9
e. 4/9
f. 9/16
To learn more about the ratio of areas,
brainly.com/question/7071992
Alex and her friends went out to lunch at the diner. The bill for lunch was $34.56 which included an 8% sales tax. How much was the price of the lunch before tax?
Answers
Answer:
34.48
Step-by-step explanation:
8% as a decimal is 0.08
34.56 - 0.08 = 34. 48
3[(5x + 1) - 2) = 2(4x - 3)
Answers
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
Step-by-step explanation:
Exact Form:
x=−3/7
Decimal Form:
x=−0.¯¯¯¯¯¯¯¯¯¯¯428571
How would you write about 100 meters
in 10 seconds as a unit rate?
Remember, unit rate is when the
denominator is 1, so you need to
reduce.
Answers
Answer:
10m/s
Step-by-step explanation:
unit rate just means how many meters you go in 1 second. that's why the denominator is only 1.
100metters/10 seconds
10meters/sec
Alex bought two hots dogs, fries, and a water at the food truck. The hot dogs were
$2.35 each and the fries were $1.25. When he paid with a $10 bill he received $1.45 in
change. How much was the water?