. a) In a group of 75 students, 20 liked football only, 30 liked cricket only and 18 did not like any of two games? (i) How many of them liked at least one game? (ii) Find the number of students who liked both the games. (iii) How many of them liked football? (iv) How many of them liked cricket? (v) Represent the result in a Venn diagram.​

Answer:

It is (x - 3)³ - 9x(3 - x)

Step-by-step explanation:

Express 27 in terms of cubes, 27 = 3³:

[tex] = {x}^{3} - {3}^{3} [/tex]

From trinomial expansion:

[tex] {(x - y)}^{3} = (x - y)(x - y)(x - y) \\ [/tex]

open first two brackets to get a quadratic equation:

[tex] {(x - y)}^{3} = ( {x}^{2} - 2xy + {y}^{2} )(x - y)[/tex]

expand further:

[tex] {(x - y)}^{3} = {x}^{3} - y {x}^{2} - 2y {x}^{2} + 2x {y}^{2} + x {y}^{2} - {y}^{3} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3x {y}^{2} - 3y {x}^{2} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3xy(y - x) \\ \\ { \boxed{( {x}^{3} - {y}^{3} ) = {(x - y)}^{3} - 3xy(y - x)}}[/tex]

take y to be 3, then substitute:

[tex]( {x}^{3} - 3^3) = {(x - 3)}^{3} - 9x(3 - x)[/tex]

Answer:

y = -6x -6

Step-by-step explanation:

The general form of the equation of a line in the slope-intercept form may be given as

y = mx + c where

m is the slope and c is the intercept

Hence given the equation

18x + 3y = -18

subtract 18x from both sides

3y = -18x - 18

Divide both sides of the equation by 3

y = -6x -6

This is the equation in the slope - intercept form with -6 as the slope and -6 as the intercept

Answer:

x< - 8

Step-by-step explanation:

3x <-24

x < - 24

3

x< - 8

x < - 8

Step-by-step explanation:

3x < - 24

Divide 3 on both sides,

3x / 3 < - 24 / 3

x < - 8

Answer:

yes it is. a polygon is any closed shape with at least 3 connected lines (eg. triangle, square, pentagon, hexagon, heptagon, octagon, etc)

Step-by-step explanation:

Answer:

5/8 ft^2

Step-by-step explanation:

The area of a rectangle is given by

A = l*w  where l is the length and w is the width

A = 5/6 * 3/4

A = 3/6 * 5/4

A = 1/2 * 5/4

A = 5/8 ft^2

Answer:

2.3

Step-by-step explanation:

.5 - .3 = .2

.8 - .5 = .3

1.2 - .8 = .4

1.7 - 1.2 = .5

We should add .6 next

1.7+.6 = 2.3

Answer:

0.0071164

Step-by-step explanation:

Answer:

Distance = 7 7/9 Km

Step-by-step explanation:

Given the following data;

Distance = 2⅔ = 8/3 Km

Time = ⅗ hour

First of all, we would find her speed;

Speed = distance/time

Speed = (8/3)/(3/5)

Speed = 8/3 * 5/3

Speed = 40/9 km/h

Next, we would find the distance covered when time = 1¾ hours

Distance = speed * time

Distance = 40/9 * 1¾

Distance = 40/9 * 7/4

Distance = 10/9 * 7

Distance = 70/9

Distance = 7 7/9 Km

Answer:

Option (a)

Step-by-step explanation:

[tex]\sqrt[6]{1000m^{3} n^{12} } = \sqrt[6]{10^{3} } \sqrt[6]{m^{3} } \sqrt[6]{n^{12} } =\\\sqrt{10} \sqrt{m} n^{2} = n^{2} \sqrt{10m}[/tex]

Answer:770

Step-by-step explanation:

There are a total of 6 faces, so we shall calculate the area of each face then add them

=(11×12) +(11×12) +(11×11)+(11×11)+(11×12)+(11+12)

=770cm^2

The total surface area of the given box will be 770 cm² hence correct option will be option (B).

The quantity of space enclosing a three-dimensional shape's exterior is its surface area.

In another meaning, if we say side square then it is an area of the square but for a cuboid, there are 6 faces so the surface area will be external to all 6 surfaces area.

Given that the box has 6 faces with sides

2 face has dimension = 11cm and 12 cm

2 face has dimension = 11cm and 11cm

2 face has dimension = 11cm and 12 cm

Total surface area = 2(11 × 12) + 2(11 × 11) + 2(11 × 12) = 770 cm²

Hence, the total surface area will be 770 cm².

To learn more about surface area,

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Answer:

50

Step-by-step explanation:

Sum Even numbers

n = 50

d = 2

a1 = 2

The last number is

an = a1 + (n-1)d

an = 2 + (50 - 1)*2

an = 2 + 49 * 2

an = 2 + 98

an = 100

Sum of the even numbers

Sum = (a1 + a50)*n/ 2

Sum = (2 + 100)*50/2

sum = 102 * 25

sum = 2550

Sum of the first 50 odd numbers

a1 = 1

n = 50

d = 2

l = ?

Find l

l = a1 + (n - 1)*2

l = 1 + 49*2

l = 99

Sum

Sum = (1 + 99)*50/2

Sum = 2500

The difference and answer is 2550 - 2500  = 50

Answer:

c

Step-by-step explanation:

12/18 = 2/3

Answer:c

Step-y-step explanat:c

Answer:

ok so you take m time h then like you count to h like a b c d e f g h and tgen with that you count 1 2 3 4 5 6 7 till h than you multiply that with 3

Your question is not complete but I guess you want to know the total price to be paid. This will be:

= $145 + (5.5% × $145)

= $145 + (0.055 × $145)

= $145 + $7.975

= $152.975

Answer:

Correct answer is 4 because the last 2 terms can be combined:

Step-by-step explanation:

4x3 + 9y2 – 3x + 2 – 1 = 4x3 – 3x + 9y2 + 1.

Answer:

1. 1.66in

2. 6.66in

3. 3.33in

4. 1inch

Step-by-step explanation:

the area of a rectangle is found by multiplying the length times width or the two sides.

5 x 1/3 is about 1.66 inches

5 x 4/3 is about 6.66 inches

5/2 x 4/3 is about 3.33 inches

and 7/6 x 6/7 is 1 inch

Answer:

2 sin(2x)

Step-by-step explanation:

sin x stretched vertically by a factor 2 and compressed horizontally by a factor 2.

The solution is : A. y = cos(x) - 2, is the equation of the sinusoidal function shown.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

The word "sinusoid" means the graph has a shape of the sine function that smoothly goes up and down.

so, we get,

However, the cosine function also has the same shape but the only thing is that it is horizontally translated. Thus, the cosine function is the sinusoid.

Hence, The solution is : A. y = cos(x) - 2, is the equation of the sinusoidal function shown.

To learn more on function click:

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Answer:

A

Step-by-step explanation:

Its not a linear function; there is no consistent rate of change between each of the points.

Answer:

[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]

Step-by-step explanation:

There's a handy formula we can use to find the sum of a geometric sequence, and here it is

[tex]S_n = \frac{a_1 (1 - r^n)}{1 - r}[/tex]

The value n represents the amount of terms you want to sum in the sequence. The variable r is known as the common ratio, and a is just some constant. Let's find those values.

First lets visualize this sequence

[tex]n_1 = 1\\n_2 = 1 + 3\\n_3 = 1 + 3 + 3^2\\n_4=1+3+3^2+3^3\\...[/tex]

Okay so there's clearly a pattern here, let's write it a bit more concisely. For each n, starting at 1, we raise 3 to the (n-1) power, add it to what we had for the previous term.

[tex]S_n = \sum{3^{n-1}} = 3^{1 - 1} + 3^{2 - 1} + 3^{3-1} ...[/tex]

Our coefficients of r, and a, are already here! As you can see below, r is just 3, and a is just 1.

[tex]S_n = \sum{a*r^{n-1}}[/tex]

To finish up lets plug these coefficients in and get our sum after 10 terms.

[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]

Answer:

Table C

Step-by-step explanation:

r = j+3

In table A

j = 12 so r = 12+3 = 15  not true so it does not fit the equation

In table B

j = 3 so r = 3+3 = 6  not true so it does not fit the equation

In table C

j = 6 so r = 9+3 = 9 this could be the table

In table D

j = 27 so r = 27+3 = 30  not true so it does not fit the equation

Answer:

There are 750 more drama movies that children's movies.

Step-by-step explanation:

There are 1003 drama movies, and 253 children's movies.

1003 - 253 = 750

Answer:

655.35

Step-by-step explanation:

got it right on edmentum

Answer:

The correct answer is - $720 or 20%.

Step-by-step explanation:

Given:

Total expense = 3600

Electric=30%

Heating and gas=50%

Water and sewer=X%

Solution:

For electric: 3600*30/100 = 1080

for heating and gas: 3600*50/100 = 1800

Left money for expense of water and shower = total - (electric and heating)

= 3600-1880

= 720

Percentage of water and shower = 720*100/3600

= 20%

Answer:

Correct!

Step-by-step explanation:

Thank you this is correct :) I took the test

Answer:

Bro what to do in this question I am not able to understand Hope you understand me

Answer:

x=13

Step-by-step explanation:

f(x) = sqrt(x-11)

The square root must be greater than or equal to zero

sqrt(x-11)≥0

Square each side

x-11≥0

x ≥11

The only answer that is greater than or equal to 11 is

x=13

Answer:

The right solution is "68%".

Step-by-step explanation:

The empirical rule is:

[tex]X\sim N(8.43, 1.5)[/tex]

According to the question,

= [tex]P(6.93< \mu < 9.93)[/tex]

= [tex]P(\frac{6.93-8.43}{1.5} < \frac{\mu -8.43}{1.5} < \frac{9.93-8.43}{1.5} )[/tex]

= [tex]P(z(1)-P(z(-1))[/tex]

= [tex]68[/tex] (%)

Thus the above is the right solution.

Step-by-step explanation:

tan Z=p/b

=48/14

=24/7

Keep smiling and hope u are satisfied with my answer.Have a good day :)

Answer:

see below

Step-by-step explanation:

{1} x+(y-z)=(x+y)+z   associative property of addition

2} (pq) * 1 = pq D  multiplicative identity

3} (5x)y-5(xy) H   associative property of multiplication

4} a+5b = 5b + a   commutative property of addition

5} a+0=a  I   additive identification property

6} gh - hg   C commutative property of multiplication

7} 8 + (-8)=0   A  additive inverse property

8} x * 0 = 0   J   zero property

9} 5 * (1/5)=1   B   multiplicative inverse property

10} 2(a+b)=2a * 2b   G  distributive property

Let's see

#a

x+(y-z)=(x+y)+z

#b

(pq) * 1 = pq

#c

(5x)y-5(xy)

#d

a+5b = 5b + a

#e

a+0=a

#f

gh - hg

#g

8 + (-8)=0

#h

x * 0 = 0

#i

5 * (1/5)=1

#j

2(a+h)=2a * 2b

Answer:

don't know...........

Equation:- 2y-x=10

For L to intersects Y axis then X cordinate must be zero

so put value of X as zero (0)

2y=10

So Y cordinate is equal to 5

Cordinate:- (0,5)