The Venn diagram here shows the cardinality of each set. Use this to find the cardinality of the given set.
Answers
n(A ∩ B ∩ C^c) = 15 there are 15 elements in the intersection of sets A and B but not in set C.
What is a circle?
A circle is a two-dimensional geometric figure that consists of all the points in a plane that are equidistant from a given point called the center. The distance from the center to any point on the circle is called the radius, which is denoted by the letter "r".
To find the cardinality of n(A∩B∩C^c), we need to know the number of elements that are in the intersection of A and B but not in C.
One way to approach this is to use the principle of inclusion and exclusion. This states that:
n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(A ∩ C) - n(B ∩ C) + n(A ∩ B ∩ C)
We can rearrange this formula to solve for n(A ∩ B ∩ C^c):
n(A ∩ B ∩ C^c) = n(A ∩ B) - n(A ∩ B ∩ C) - n(B ∩ C) + n(A ∩ C) + n(B) + n(C) - n(A)
Plugging in the values we have been given, we get:
n(A ∩ B ∩ C^c) = 4 - 3 - 9 + 7 + 11 + 15 - 10
Simplifying this expression, we get:
n(A ∩ B ∩ C^c) = 15
Therefore, there are 15 elements in the intersection of sets A and B but not in set C.
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Related Questions
Expand the expression.
t(–1.2w + 3)
Answers
Answer:
-2.5
Step-by-step explanation:
srry if I'm wrong...........
The expression t(–1.2w + 3) can be expanded as -1.2wt + 3t.
What is an expression?An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.
Given expression,
t (-1.2w + 3)
Using distributive property
-1.2wt + 3t
Hence, -1.2wt + 3t is the expanded form of the expression t(–1.2w + 3).
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A sphere and its dimension are shown in the diagram 15 inches
Answers
The measurement that is closest to the volume of the sphere is given as follows:
1,767.1 in³.
What is the volume of an sphere?The volume of an sphere of radius r is given by the multiplication of 4π by the radius cubed and divided by 3, hence the equation is presented as follows:
\(V = \frac{4\pi r^3}{3}\)
From the image given at the end of the answer, we have that the diameter is of 15 units, hence the radius of the sphere, which is half the diameter, is given as follows:
r = 0.5 x 15
r = 7.5 units.
Then the volume of the sphere is given as follows:
V = 4/3 x π x 7.5³
V = 1,767.1 in³.
Missing InformationThe sphere is given by the image presented at the end of the answer.
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Which one should I choose
Answers
0.How many elements doesA contain if it has:
a.64 subsets?
b.31 proper subsets?
c.No proper subset?
d.255 proper subsets?
Answers
convert 565900 seconds into days
Answers
Answer:
1 day = 86400 seconds
565900 divided by 86400 =
Step-by-step explanation:
a little more than 6 days
plz mark brainliest
Evaluate : 9⁴xa⁷b⁴/ 3⁵xa⁴b⁴
Answers
Answer:
27a³
Step-by-step explanation:
9⁴xa⁷b⁴ / 3⁵xa⁴b⁴
(3²)⁴xa⁷b⁴ / 3⁵xa⁴b⁴
3⁸xa⁷b⁴ / 3⁵xa⁴b⁴
3³a³
27a³
What is the volume of the composite figure? ASAP PLEASE!!!!
Answers
Answer:
74ft³
Step-by-step explanation:
Okay, so it's basically 3 rectangular figures smashed together so:
We'll do the 2 biggest one's first:
the formula for the volume of a rectangular figure is base x height so we first have to find the base:
4 x 3 = 12
So then we just plug our stuff in here:
12 x 3 = 36
Now there's 2 of these rectangles though so:
36 x 2 = 72
Now we're going to do the one in the middle:
1 x 2 = 2
2 x 1 = 2
Now we add that all together:
72 + 2 = 74
So, the volume of the composite figure is 74ft³
hope this helps:)
Last year, Adele went bowling several times and earned an average score of 95 points.
This year, after taking a class at school, she improved her score to an average of 133 points.
What is the percent of increase in Adele's average score?
Answers
Answer:
40 percent increase
Step-by-step explanation:
Starting point - 95
End point - 133
133-95 = 38
38/95 = 0.4
0.4*100=
40
Answer:
40%
Step-by-step explanation:
(133 - 95)/95 x 100 = (38/95) x 100 = 40%
Type < or > to make this statement true -a___-b
Answers
The comparisons that are true are 11. -5 < 0 12. 9 > -8 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51 19. 17 < 23 20. 18 > -36 and that is not true are 13. -7 = -7 (not true) 18. -32 > 4 (not true)
To make each statement true, write < or >. We need to compare two values for each statement to determine whether it is true or false.
To indicate that the first value is less than the second value, write <.
Alternatively, to indicate that the first value is greater than the second value, write >.
Below are the comparisons: 11. -5 < 0 12. 9 > -8 13. -7 > -7 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51 18. -32 > 4 19. 17 > 23 20. 18 > -36
To determine the direction of inequality, we need to compare the values.
We used inequality signs such as > (greater than) or < (less than) to indicate which value is larger or smaller than the other.
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The correct question would be as
Write > or < to make each statement true.
11. -5 0
12. 9 -8
13. -7 7
14. 55 -75
15. -32 -24
16. 89 73
17. -58 -51
18. -32 4
19. 17 23
20. 18 -36
Evaluate the expression: −(8 − 12) + 60 + (−4)2.
Answers
Answer: 80
Step-by-step explanation:
⇒ −(8 − 12) + 60 + (−4)²
⇒ -(-4) + 60 + 16
⇒ 4 + 60 + 16
⇒ 80
Match the given slope (m) and y-intercept (b) with the equation of the line in slope-intercept form.
Answers
The slope (m) and y-intercept (b) with the equation of the line in slope-intercept form are given as: m = 2 and b = 5 is y = 2x + 5; m = 3 and b = 5 is y = 3x + 5; m = 5 and b = 4 is y = 5x + 4.
How to Write the Equation of a Line in Slope-intercept Form?If m represents the slope of a line and b represents its y-intercept, the equation of the line in slope-intercept form is written as: y = mx + b.
Where m = 2 and b = 5, the equation of the line would be expressed as: y = 2x + 5.
Where m = 3 and b = 5, the equation of the line would be expressed as: y = 3x + 5.
Where m = 5 and b = 4, the equation of the line would be expressed as: y = 5x + 4.
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Solve the system of equations.
4x - 4y = 8
y + 4x = 2.5
Answers
x = -1.5
y = 8.5
hope it helps....!!!
\(4x-4y = 8~~~....(i)\\\\y+4x = 2.5~~~...(ii)\\\\(i)-(ii)\\\\~~~~4x-4y-y-4x = 8-2.5\\\\\implies -5y = 5.5\\\\\implies y = -\dfrac{5.5}5\\\\\implies y= -1.1\\\\\text{Substitute y= -1.1 in eq (i):}\\ \\~~~~4x-4(-1.1) = 8\\\\\implies 4x +4.4. =8\\ \\\implies 4x = 8-4.4\\\\\implies 4x = 3.6\\\\\implies x = \dfrac{3.6}4\\\\\implies x =0.9\\ \\\text{Hence,}~~ (x,y) = (0.9, ~-1.1)\)
The table shows information about the masses of some dogs.
a) Work out the minimum number of dogs that could have a mass of more than 24 kg.
b) Work out the maximum number of dogs that could have a mass of more than 24 kg.
Answers
a) A minimum of number of dogs that could have a mass of more than 24 kg is 6.
b) The maximum number of dogs that could have a mass of more than 18 kg is 20.
What do minimum and maximum value mean?Rearrange the function using fundamental algebraic concepts to get the value of x when the derivative equals 0. This response gives the x-coordinate of the function's vertex, which is where the maximum or minimum will occur. To find the minimum or maximum, rewrite the solution into the original function.
The minimum of the values present in the interval 20 to 40 is 6
The maximum of the values present in the interval 20 to 40 is (12+6) = 18
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You purchase a TV for $2,750.
The sales tax is 7.5%. What is the
total price including sales tax?
Answers
Sales tax: $206.25
■ Cost/Price before ST: $2,750.00
■ Total Cost/Price including ST: $2,956.25
For Field Day, the 72 students in fourth grade will be divided into tears with the same number of students on each team. The 60 students in third grade will be divided into teams that each have the same number of students as the fourth grade teams. What is the largest number of students that a team could have? Help meeee
Answers
We do this because the factors are the numbers determining the number of people and the number of teams, for example if they used the factors 6 and 10 for 60, they would make 6 teams of 10 people. And since factors are whole numbers, it makes sense for people and doesn’t cut ppl in half.
So the greatest factor that 72 and 60 gave have in common is 12, bc 5 x 12 is 60 and 6 x 12 is 72, and they don’t have other factors in common that are higher than 12.
This means that 12 is the answer, bc it’s the largest number of students that a team could have, in both the fourth and third grades.
Tickets to the movie theater cost $12 per person. Write an expression to represent the total cost of tickets for a group of people
Answers
What’s the answer to If =3+23
, what is
when =1
and =2
?
Answers
The value of y when a = 1 and b = 2 is 22.
How to solve an equation?The equation of can be solved as follows: We will substitute the value of a and b in the equation to find the value of y.
Therefore,
y = 3ab + 2b³
Let's find y when a = 1 and b = 2
Hence,
y = 3(1)(2) + 2(2)³
y = 6 + 2(8)
y = 22
Therefore,
y = 22
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Which is more, 1 pound or 22 ounces?
Answers
Answer:
22 ounces is more
Step-by-step explanation:
1 pound is equal to 16 ounces
Answer:
1 pound
Step-by-step explanation:
1pound=16oz 22oz= 1.375pound
PLEASE HELP DUE TOMORROW
Answers
Step-by-step explanation:
please mark me as brainlest
Please A milligram is a small unit of measure for mass in the metric system. There are 1,000 milligrams in 1 gram. btw
Which amount is greater than 12 grams?
1,200 milligrams
1,300 milligrams
12,000 milligrams
13,000 milligrams
Answers
Answer:n the metric system, "milli" means 1/1,000 and "kilo" means 1,000. This means that a milligram is 1/1,000 of a gram, and a kilogram is 1,000 grams. So a kilogram is much heavier than a milligram; in fact, a kilogra
Step-by-step explanation:
An experiment consists of spinning a spinner. Use the results in the table to find the experimental probability that the spinner does not land on yellow. Express your answer as a fraction in simplest form.
Red = 12
Blue = 10
Yellow = 6
A. 11/14
B. 3/7
C. 4/7
D. 3/14
Answers
Answer:
A. 11/14
Step-by-step explanation:
i hope this helps :)
The Probability of an Event P(E) is that the spinner does not land on yellow is 11/7.
An experiment consists of spinning a spinner.
Red = 12
Blue = 10
Yellow = 6
We have to determine,
The experimental probability is that the spinner does not land on yellow.
The total number of spinner= 12+10+6
The total number of spinner=28.
What is the formula for the experimental probability?Probability of an Event P(E) = Number of times an event occurs / Total number of trials.
The number of trials to not land on yellow is,
12+10=22
Therefore the Probability of an Event P(E) is given by,
\(P(E)=\frac{22}{28}\)
\(P(E)=\frac{11}{14}\)
Therefore option A is correct.
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$35.24
with a
20% tip
Answers
Multiply $35.24 by .2 and add that to the original bill.
Answer:
$42.288
Step-by-step explanation:
20%=0.2
0.2*35.24=7.048
35.24+7.048=42.288
an Expression for difference of a number s and -6
Answers
After answering the given query, we can state that The expression for the difference between a number s and -6 is: s - (-6) or s + 6
what is expression ?In numbers, you can multiply, split, add, or take away. The following is how a phrase is made together: Numeric number, expression, and arithmetic operator The elements of a mathematical expression are integers, factors, and functions. It is feasible to use contrasting words and terms. Any mathematical declaration containing variables, integers, and a mathematical action between them is known as an expression, also known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the provided equation, which are all separated by the mathematical symbol +.
The expression for the difference between a number s and -6 is:
s - (-6)
or
s + 6
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Consider the function below.
g(x) = 2x - 1
Find the difference quotient below (where h = 0) and simplify your answer.
g(x + h) - g(x) / h
Answers
Answer:
Step-by-step explanation:
please answer fast...............................
Answers
The coordinate of point R after the rotation is determined as = ( - 4, 7).
option A.
What is the rotation of a figure?A rotation is a transformation that turns the figure in either a clockwise or counterclockwise direction.
You can turn a figure 90°, a quarter turn, either clockwise or counterclockwise. When you spin the figure exactly halfway, you have rotated it 180°. Turning it all the way around rotates the figure 360°.
When a figure is rotated 180 degrees, each point of the figure is moved to a new position that is exactly opposite its original position with respect to a fixed center of rotation.
The initial coordinate of point R = ( 4, 7),
The new coordinate of point R after the rotation = ( - 4, 7)
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Jason and Eddy are traveling from Atlanta to Savannah, which is a distance of 248 miles. It took them two hours and 30 minutes to get to Macon, Georgia. Then, they made it from Macon to Savannah in 3 hours
and 15 minutes. What would be Jason and Eddy's average speed for this entire trip in mi/hr?
Answers
Answer:
43.13 mphStep-by-step explanation:
Average speed is:
s = d/t, where d- total distance, t - total timeFind the total time:
2 h 30 min + 3 h 15 min = 5 h 45 min = 5 45/60 h = 5.75 hFind the average speed:
s = 248 / 5.75 = 43.13 mphA doctor has 53 ccs of a 40% solution of a pain killer. How much sterilized water should be added to get a 27% solution?
Answers
Answer:
35.775
Step-by-step explanation:
So, 53 is the amount of ccs that makes a 40% solution.
How can we find the ccs of 27% solution?
Well, we should first find teh amount of ccs per 1%.
To do this, divide 53 by 40:
53/40
=
1.325
Now multiply this by 27 to get the amount of ccs for 27%:
27*1.325
=
35.775
Hope this helps! :)
If anyone help me with my entire test I’ll mark you brainliest
Answers
Help me please its urgent I need it done asap I need help if anyone could help me solve these problems that would be very helpful! (I'll give brainliest if you can solve all of them!) A company designs a circular dartboard such that the target area in the center is surrounded by a safety margin. Federal law requires that the area of the safety margin must be twice the area of the actual target in the center. If the total radius of the dartboard is 3 feet, what is the radius of the circular target in the center? (you must show the algebra for full credit)
Answers
Answer:
the radius of the circular target in the center is 2.12 feet
Step-by-step explanation:
the total area of the dartboard is
π x r² = π x 3² = 9π (28.27 ft²)
The area of the actual target in the center needs to be half of the dartboard (4.5 π) (14.14 ft²)
(Small area : 4.5π = π x r²
Divide both sides by π
4.5 = r²
√4.5 = r
r= 2.12132034....... (2.12 feet)
Please, help it is geometry
Answers
Answer:
WR ≈ 13.862
Step-by-step explanation:
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is
WR² + RT² = WT²
WR² + 12.1² = 18.4²
WR² + 146.41 = 338.56 ( subtract 146.41 from both sides )
WR² = 192.15 ( take the square root of both sides )
WR = \(\sqrt{192.15}\) ≈ 13.862 ( to the nearest thousandth )