The city of Joyville has 87,388 residents.

among a group of students 50 played cricket 50 played hockey and 40 played volleyball. 15 played both cricket and hockey 20 play

kondaur [170]

Answer:

Cricket only= 30

Volleyball only = 15

Hockey only = 25

Explanation:

Number of students that play cricket= n(C)

Number of students that play hockey= n(H)

Number of students that play volleyball = n(V)

From the question, we have that;

n(C) = 50, n(H) = 50, n(V) = 40

Number of students that play cricket and hockey= n(C∩H)

Number of students that play hockey and volleyball= n(H∩V)

Number of students that play cricket and volleyball = n(C∩V)

Number of students that play all three games= n(C∩H∩V)

From the question; we have,

n(C∩H) = 15

n(H∩V) = 20

n(C∩V) = 15

n(C∩H∩V) = 10

Therefore, number of students that play at least one game

n(CᴜHᴜV) = n(C) + n(H) + n(V) – n(C∩H) – n(H∩V) – n(C∩V) + n(C∩H∩V)

= 50 + 50 + 40 – 15 – 20 – 15 + 10

Thus, total number of students n(U)= 100.

Note;n(U)= the universal set

Let a = number of people who played cricket and volleyball only.

Let b = number of people who played cricket and hockey only.

Let c = number of people who played hockey and volleyball only.

Let d = number of people who played all three games.

This implies that,

d = n (CnHnV) = 10

n(CnV) = a + d = 15

n(CnH) = b + d = 15

n(HnV) = c + d = 20

Hence,

a = 15 – 10 = 5

b = 15 – 10 = 5

c = 20 – 10 = 10

Therefore;

For number of students that play cricket only;

n(C) – [a + b + d] = 50 – (5 + 5 + 10) = 30

For number of students that play hockey only

n(H) – [b + c + d] = 50 – ( 5 + 10 + 10) = 25

For number of students that play volleyball only

n(V) – [a + c + d] = 40 – (10 + 5 + 10) = 15

3 0

3 years ago

The area of a rectangle is 65 m2 , and the length of the rectangle is 3 m less than twice the width. find the dimensions of the

salantis [7]

X = <span>width
2x-3 = </span><span>length

</span> $x(2x-3) = 65\\
2x^2 - 3x - 65 = 0 \\ D=b^2-4ac=(-3)^2-4*2*(-65)=529\\
x_{1,2}= \frac{-bб \sqrt{D} }{2a}= \frac{3б 23}{4} \\ x_1=-5 \ \ \O \\ x_2=6.5 \ \$

width = 6.5 m
length = 2x-3 = 2*6.5 - 3 = 10 m

4 0

3 years ago

4. Two points on a line are (-10, 1) and (5, -5). If

Vsevolod [243]

Answer:

The x-coordinate of another point is zero

Step-by-step explanation:

step 1

Find the slope between the two given points

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

$(-10,1),(5,-5)$

substitute in the formula

$m=\frac{-5-1}{5+10}$

$m=\frac{-6}{15}$

Simplify

$m=-\frac{2}{5}$

step 2

Find the x-coordinate of another point

we have

(x,-3)

we know that

If the other point is on the line, then the slope between the other point and any of the other two points must be the same

so

Find the slope between the points

$(x,-3),(5,-5)$

Remember that

$m=-\frac{2}{5}$

substitute in the formula

$-\frac{2}{5}=\frac{-5+3}{5-x}$

$-\frac{2}{5}=-\frac{2}{5-x}$

the denominators must be the same

$5=5-x$

$x=0$

therefore

The x-coordinate of another point is zero

3 0

3 years ago

How do u find slope on the graph

Shkiper50 [21]

Answer:

you get 2 coordinates x one, y one, x two, and y two and then do rise over run which is y two - y one over x two - x one say x one is 4 and y one is 7 and x two is 8 and y two is 13 you say 13-7=6 and 8-4=4 so it is 6/4 hope that makes sense

7 0

2 years ago

Help!! Find the value of x

Romashka [77]

Answer:

x = 51

Step-by-step explanation:

The sum of internal angles for this rectangle is 360

x + 81 + 124 + 104 = 360 add like terms

x + 309 = 360 subtract 309 from both sides

x = 51

5 0

3 years ago

The city of Joyville has 87,388 residents.​

The city of Joyville has 87,388 residents.