(i) The number of students who registered for political science is 150
(ii) The number of students who registered for political science and geography but not economics is 50
(iii) The number of students who registered for economics and political science but not geography is 20
The Venn diagram for the question is shown in the attachment below.
E represents Economics
G represents Geography
and P represents Political science
From the question,
10 for economics only, that is, n(E∩G'∩P') = 10
150 from economics and geography, that is n(E∩G) = 150
90 from economics but not political science, that is, n(E∩P') = 90
210 from geography, that is, n(G) = 210
120 from political science and geography, n(P∩G) = 120
180 from economics, that is, n(E) = 180
Total of student registered for courses is 250, that is, n(ξ) = 250
Now from the given information,
n(E∩G∩P') = n(E∩P') - n(E∩G'∩P') = 90 - 10 = 80
n(E∩G∩P) = n(E∩G) - n(E∩G∩P') = 150 - 80 = 70
n(E∩P∩G') = n(E) - [n(E∩G'∩P') + n(E∩G∩P') + n(E∩G∩P)]
= 180 - [10+80+70] = 180 - 160 = 20
n(P∩G∩E') = n(P∩G) - n(E∩G∩P) = 120 - 70 = 50
n(G∩E'∩P') = n(G) - [n(E∩G∩P') + n(E∩G∩P) + n(P∩G∩E')]
= 210 -[80+70+50] = 210 - 200 = 10
All of these are shown in the Venn diagram
(i) To determine the number of students who registered for political science, we will first determine n(P∩G'∩E'), that is, those who registered for political science only.
Let n(P∩G'∩E') = x
Then, using the Venn diagram, we can write that
10 + 80 + 20 + 70 + 10 + 50 + x = n(ξ) = 250
240 + x = 250
x = 250 - 240
x = 10
n(P∩G'∩E') = 10
∴ 10 registered for political science only
Now, number of students who registered for political science n(P) is
n(P) = n(E∩P∩G') + n(E∩G∩P) + n(P∩G∩E') + n(P∩G'∩E')
n(P) = 20 + 70 + 50 + 10
n(P) = 150
∴ 150 students registered for political science
(ii) For the number of students who registered for political science and geography but not economics, that is, n(P∩G∩E')
As determined above and as shown in the Venn diagram,
n(P∩G∩E') = 50
∴ 50 students registered for political science and geography but not economics
(iii) For the number of students who registered for economics and political science but not geography, that is, n(E∩P∩G')
As determine above and as shown in the Venn diagram as well
n(E∩P∩G') = 20
∴ 20 students registered for economics and political science but not geography
Hence,
(i) The number of students who registered for political science is 150
(ii) The number of students who registered for political science and geography but not economics is 50
(iii) The number of students who registered for economics and political science but not geography is 20
Learn more here: https://brainly.com/question/15311191
A rectangular prism has a square base with edges measuring 8 inches each. Its volume is 768 cubic inches. Find the height and the surface area of the prism
Answer:
Height = 12in
Surface area = 320in²
Step-by-step explanation:
Given
Length of the square base = 8in
Volume of the prism = 768 cubic inches
Using the formula;
Volume of the prism = Base area * Height of prism
768 = 8² * H
768 = 64H
H = 768/64
H = 12in
Hence the height of the prism is 12in
Get the surface area
Surface area = 2l² + 2lh
Surface area = 2(8)² + 2 (8)(12)
Surface area = 128 + 192
Surface area = 320in²
Hence the Surface area of the prism is 320in²
What is the area of the right triangle below? A. 96 sq. units
B. 11 sq. units
C. 22 sq. units
D. 48 sq. units
Answer:
D. 48 sq. units
Step-by-step explanation:
Area of a triangle is
A = 1/2 bh where b is the base and h is the height
A = 1/2 ( 16) *6
A = 48
A simple random sample is drawn from a normally distributed population. The value of which of the following will not
known for certain but can be inferred?
o u
o-x
os
on
Help please I need 6 and 8
What is the value of the first term in the following arithmetic sequence?
-9, -2, 5, 12, ...
-9
7
9
-7
Answer:
-9
Step-by-step explanation:
the first number
hope it is well understood
the additive inverse of 5/9 is
Answer:
- 5/9
Step-by-step explanation:
The additive inverse can be broken down. Additive means we are adding something to it. Inverse means the opposite. Combined, it would be saying we are adding the opposite. The opposite of 5/9 would end up being -5/9, as when added together the sum is 0.
Which square root is between 4 and 5
10
14
24
32
They are divided by the way
Find the sum of 5x+y and (2xy + xy).
Answer:
6x^2y+2xy^2
Step-by-step explanation:
5x^2y + (2xy^2 + x^2y).
Combine like terms
6x^2y+2xy^2
[tex]\displaystyle\ \Large \boldsymbol 5\underline{x^2y}+2xy^2+\underline{x^2y}=5x^2y+x^2y+2xy^2=\boxed{6x^2y+2xy^2}[/tex]
The perimeter of an iPad Air is 820 mm. Its length is 100 mm less than twice the
width.
If x = the length of the iPad Air and y = the width of the iPad Air, the linear system of
equations that could be used to model this situations is,
2x + 2y = a
bx = cy-d
The value of a is:
A The value of b is:
A The value of c is:
Ą The value of d is:
1
Answer:
a = 820, b = 1, c = 2, d = 100
Step-by-step explanation:
Let x represent the length of the iPad Air and y represent the width of the iPad Air. Since the perimeter of an iPad Air is 820 mm, hence:
2(length + breadth) = 820
2(x + y) = 820
2x + 2y = 820 (1)
Also, the length is 100 mm less than twice the width. Therefore:
x = 2y - 100 (2)
Given that the equations be used to model this situations is:
2x + 2y = a
bx = cy-d
Therefore comparing this model with equation 1 and 2, we get that:
a = 820, b = 1, c = 2, d = 100
Evaluate (7.1x 10³)+(4.6 x 10⁶)²
Give your answer in standard form to 3SF
Answer:
2.12x10^13 is what I got
the simple interest $ Interest, on a sum of money , $P after T years at R% is given by the formula interest = PRT ÷100
a) make t subject of the formula
b) find t if interest = 51 , P =340 and R=2 1/2
Step-by-step explanation:
a)t=100×I÷PR
b)t=200×51÷340×5 (simplify)
therefore t=8670
thanks Hope It Help
Write an equation of the direct variation that includes the point (9, –12).
(A.) y = 1 1/3x (B.) y = - 1/12x (C.) y = 1 1/3x (D.) -3/4x ...?
Answer:
I think you have a typo in you choices...
y = -4/3 x is the answer...
which is the same as y = - 1 1/3 x
you don't have that choice, "A" and "C" are the same..
I think that one of them is "y = - 1 1/3 x "
y = kx
-12 = k 9
k = -12/9 = -4/3
Step-by-step explanation:
PLSSS HELPP I need the answers
Answer:
Step-by-step explanation:
t = 20
CROSS MULTPLICATION !
[tex]\frac{a}{b} = \frac{c}{d}[/tex]
in this situation ab = cd
[tex]\frac{16}{t} = \frac{80}{100}[/tex]
(16)(100) = 80t
1600 = 80t
1600/80 = t
t = 20
Answer:
11
Step-by-step explanation:
11
1
45
35x345 = 30
1
how do i work out the shaded area??
help!!!!
Answer:
Step-by-step explanation:
Remark
The method you would use is
find the area of the rectanglefind the area of the left trianglefind the area of the right triangleSubtract the two triangle's areas from the area of the rectangle.Area of the rectangle
Area = L * W
L = 3 + 14 = 17
W = 6
Area = 6 * 17 = 102
Area of Left triangle
H = 6
B = 3
Area = 1/2 * B * H
Area = 1/2 * 3 * 6
Area = 9
Area of the triangle on the right
H = 6
B = 17 - 7 = 10
Area = 1/2 * b * h
Area = 1/2 * 6 * 10 = 30
Area of the two triangles = 39
Area of the green area = 102 - 39 = 63
Corey and Courtney are 210 feet apart when they start walking toward one another. Courtney walks twice as fast as Corey so whenever Corey travels
x
feet, Courtney travels
2
x
feet. Let
x
represent the number of feet Corey has traveled since he started walking toward Courtney.
Write an expression in terms of x to represent the distance (in feet) between Corey and Courtney.
Answer:
210 - 3x
Step-by-step explanation:
SOMEONE HELP ME PLEASE
Answer:
3/5 * 3/5 = 9/25 = .36 = 36%
Step-by-step explanation:
To the nearest degree, find the measure of angle A?
Answer:
I would say 26 or 42 but i would o with 26
Step-by-step explanation:
Answer:
26
Step-by-step explanation:
[tex]arccos\left(\frac{18}{20}\right)[/tex] = 25.8
For the following right triangle, find the side length x
Answer:
x = 25
Step-by-step explanation:
b² + h² = x²
24² + 7² = x²
576 + 49 = x²
625 = x²
√625 = √x²
25 = x
Step-by-step explanation:
x² = 7² + 24²
x² = 49 + 576
x² = 625
x = 25
WILL GET BRAINLEST WILL HAVE TI ZOOM IN THI SHIW WORK TOO PLSSS ASAP
Answer:
sin = 1.333333
cos = 0.75
56 out of the 56 employees at the sports shop are part-time employees. What percentage of the employees at the sports shop work part-time?
Answer:
100%
Step-by-step explanation:
Since 56/56 employees at the sports shop work part time, that means 100% of them do, or all of them.
Can someone help me please like please I need to turn it in like in 10 minutes
Use linear combination to solve for x and y.
2x+4y=-4
3x+5y=-3
Dautienbanchuyenvexophuongtrinhthu1saudothevaophuontrinhthu2,thuchiencacbuoc
chuyenvedoidaularaketquanhe
If triangle BCD was reflected over the x-axis, what would be the coordinates of the new triangle's vertices?
A. (-1, 0), (-1, -2), (-4, 1)
B. (-1, 0), (-1, 2), (-4, 1)
C. (-1, 0), (-1, 2), (4, -1)
D. (1, 0), (-1, 2), (-4, 1)
on time 4 learning
Answer:
b the answer is B because
write the point-slope form of an equation of the line through the points (6,-1) and (5,7)
Answer:
y - 7 = -8 (x - 5)
Step-by-step explanation:
y2 - y1 / x2 - x1 7 - (-1) / 5 - 6 = -8
y - 7 = -8 (x - 5)
What is the multiplicative rate of change of the
exponential function shown on the graph?
81
2,
4
0
16
1
A
12
4
AN
8
1.
NI
-2.
2
-1.
9
x
(0,1)
1
-3 -2
-1
N
3
Answer:
The answer for thue would happened to be 2
-1.
Answer:
9/2
Step-by-step explanation:
During a sale, Cindy found boxes of dog biscuits on sale for $0.69 that had previously cost $2.23. What percentage is the discount?
Answer:
The dog biscuits are approximately 69% off.
Step-by-step explanation:
(1 - 0.69/2.23) * 100
(223/223 - 69/223) * 100
154/223 * 100 = 69%
yea...we most def ain't learn this in class
Answer:
F. 300,000
Step-by-step explanation:
logically, it is decreasing by 1.
Samantha found a great deal on sweatshirts at the mall and bought 5 sweatshirts at the
Super Duper sale price. Allison went the next day, but the sale was over, so she only bought
2 sweatshirts and paid $30 more per sweatshirt than Samantha. If the total cost of all 7
sweatshirts was $340, how much did one sweatshirt cost at the Super Duper sale price?
Answer:
$40
Step-by-step explanation:
You have two sweatshirts that cost $30 more the day after.
First, you do [tex]340 -(2*30)[/tex]
Second, you divide what you got above ($280), by 7 and voila, you have $40 per sweatshirt.
Which one of the following sets is real numbers?
A. |x| = -1
B. |x| < -1
C. |x| > -1
Use the parabola tool to graph the quadratic function f(x)=−(x−2)2+4.
Answer:Use demos it could give you the answer
Step-by-step explanation:
