MATHEMATICS
MIDDLE SCHOOL

-4x+7y=20

y=3x+15

Answer:

Answer:

Solve by Substitution :

// Solve equation [2] for the variable y

[2] 5y = 15x - 4

[2] y = 3x - 4/5

// Plug this in for variable y in equation [1]

[1] 15x - 20•(3x-4/5) = 7

[1] -45x = -9

// Solve equation [1] for the variable x

[1] 45x = 9

[1] x = 1/5

// By now we know this much :

x = 1/5

y = 3x-4/5

// Use the x value to solve for y

y = 3(1/5)-4/5 = -1/5

Solution :

{x,y} = {1/5,-1/5}

MIDDLE SCHOOL

Simplify 2(x + 4) + 7(x – 5) + 3. Show each step of your work.

2x + 8 + 7x - 35 + 3

2x + 7x - 27 + 3

9x - 24

2x + 7x - 27 + 3

9x - 24

2(x + 4) + 7(x – 5) + 3

2x + 8 + 7x - 35 + 3 //distributive property.

9x - 23 // combine like variables

2x + 8 + 7x - 35 + 3 //distributive property.

9x - 23 // combine like variables

HIGH SCHOOL

Evaluate x – 2y if x = –3 and y = –6.

For given x and y value, the value of expression is 9. Therefore, option C is the correct answer.

Given that, x - 2y if x = -3 and y = -6.

What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Substitute x = -3 and y = -6 in the given expression, we get

-3 - 2(-6)

= -3+12

= 9

For given x and y value, the value of expression is 9. Therefore, option C is the correct answer.

To learn more about an expression visit;

brainly.com/question/28170201.

#SPJ2

X - 2y

x = -3 and y = -6

-3 - 2(-6)

-3 + 12

9

Answer: 9

x = -3 and y = -6

-3 - 2(-6)

-3 + 12

9

Answer: 9

MIDDLE SCHOOL

A team has P points. P = 3W + D

W = Wins

D = Draws

B) After 35 games a different football team has 50 points. 14 games were draw. How many games has this team lost

You would just plug it in and solve for w.

p = 3w + d

50 = 3w + 14 -subtract the 14 from both sides

36 = 3w - divide both sides by 3

12 = w

There were 12 wins. If they played 35 games, 12 were won and 14 were draw, you just subtract them from 35 and you get 9. The team lost 9 games.

p = 3w + d

50 = 3w + 14 -subtract the 14 from both sides

36 = 3w - divide both sides by 3

12 = w

There were 12 wins. If they played 35 games, 12 were won and 14 were draw, you just subtract them from 35 and you get 9. The team lost 9 games.

Sub in the values and solve for W

50=3W+14

50-14=3W

36=3W

12=W

The team won 12 games.

12+14=26 (games drawn and won)

35-26=9

Therefore they lost 9 games

50=3W+14

50-14=3W

36=3W

12=W

The team won 12 games.

12+14=26 (games drawn and won)

35-26=9

Therefore they lost 9 games

COLLEGE

What points are on the graph -3x+6y+5=-7

The slope 1/2 y -intercept -2

HIGH SCHOOL

How many different 6-digit numbers can be formed by arranging the digits in 332345?

Choose the three digits out of the 6 digits to form a three-digit number are given below.

Thus, there are 120 different ways by which a three-digit number can be formed.

What are Permutation and combination?A permutation is an act of arranging the objects or elements in order. Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.

Given

The sample is (3, 3, 2, 3, 4, 5).

How many different 6-digit numbers can be formed by arranging the digits in 3,3,2,3,4,5?Choose the three digits out of the 6 digits to form a three-digit number are given by

Thus, there are 120 different ways by which a three-digit number can be formed.

More about the permutation and combination link is given below.

brainly.com/question/11732255

Answer- 120

Solution-

There are digits to be arranged,they are {3,3,2,3,4,5}. And from those ,3 digits are repeated .

so the total number of distinct number that can be formed = = = 120 (ans)

HIGH SCHOOL

Lisa purchased a hat for $10, a purse for $20, and a book for $23.The sales-tax rate was 7.2 percent. What was the total amount she paid?

From information given Lisa bought three items.

10 + 20 + 23 = 53 dollars ( which is total pre- tax cost)

The sales tax rate is at 7.2% . Value of this tax in dollars will be:

7.2 % of 53 → (7.2 / 100) × 53 → 0.072 × 53 = 3.816

So the tax rate value is 3.816

Total cost of items will be 53 + 3.816 = 56. 816

Rounded off to the nearest cent 56.816 = 56.80

Therefore Lisa paid a total of $ 56.80

MIDDLE SCHOOL

Solve for x 2(x+9)=x+21

Answer: x = 3

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

2(x+9)=x+21

(2)(x)+(2)(9)=x+21 (Distribute)

2x+18=x+21

Step 2: Subtract x from both sides.

2x+18−x=x+21−x

x+18=21

Step 3: Subtract 18 from both sides.

x+18−18=21−18

x=3

MIDDLE SCHOOL

HELP!!!!!!!!!!!!!! When i go to search a question and i click on it it signs me out of brainly

Answer: sometimes it dose that if u have ether not been on brainly in a while or if u do a sertan type of question it logs u out and then you will have to re log in and if it dose that all the time u click on a question you might need to report a bug to brainly hope i helped :)

COLLEGE

A die is rolled. If you roll a 1, 2 or 3, you will toss 10 coins. If you roll a 4, 5 or 6, you will toss 20 coins. Let X denote the number of heads tossed. a) Determine the support of X. b) Determine the mean of X. c) Determine the variance of X.

Answer:

a) The support of X is {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}

b) The mean of X is 7.5

c) The variance of X is 10

Step-by-step explanation:

a) Since you can toss up to 20 coins, and from that you can obtain any number of heads from 0 to 20, then the support of X {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}.

b) To compute the mean of X, we need to see how is the behavior of X. Since 3 dices will gives 10 coins to toss and the other 3 will give us 20, then there is a probability of 1/2 that we tossed 10 coins and a probability of 1/2 that we tossed 20.

The random variable X, conditioned to the event 'The dice is 1,2 or 3' (or equivalently, 10 coins are tossed), will have a binomial distribution with paramenters n = 10, p = 1/2. The mean of X in this case is np = 5. If X is conditioned to the event 'The dice is 4,5 or 6', then X will have also binomial distribution, but this time with paramenters n = 20, p = 1/2. The mean of X in this case is 20*1/2 = 10.

Since each event we conditioned in had probability 1/2 to occur, then E(X) = 1/2 * 5 + 1/2 * 10 = 7.5.

c) Remember that V(X) = E(X²)- E(X)². Since we alredy know the mean of X, we just need to compute the mean of X squared.

The variance of a binomial distribution Z with paramenters n and p is

V(Z) = np(1-p)

since V(Z) = E(Z²)- E(Z)² = E(Z²)- n²p², then

E(Z²) = V(Z) + E(Z)² = np(1-p) + n²p² = p²(n²-n) + np

Therefore

E(X²) = E(X² | 10 coins are tossed) * 1/2 + E(X² | 20 coins are tossed) * 1/2 =

1/2*(0.5²(10²-10) + 5) + 1/2*(0.5²(20²-20) + 10) = 13.75 + 52.5 = 66.25

As a consecuence

V(X) = 66.25 - 7.5² = 10

The variance of X is 10.

Answer:

Step-Answer:

a) The support of X is {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}

b) The mean of X is 7.5

c) The variance of X is 10

Step-by-step explanation:

a) Since you can toss up to 20 coins, and from that you can obtain any number of heads from 0 to 20, then the support of X {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}.

b) To compute the mean of X, we need to see how is the behavior of X. Since 3 dices will gives 10 coins to toss and the other 3 will give us 20, then there is a probability of 1/2 that we tossed 10 coins and a probability of 1/2 that we tossed 20.

The random variable X, conditioned to the event 'The dice is 1,2 or 3' (or equivalently, 10 coins are tossed), will have a binomial distribution with paramenters n = 10, p = 1/2. The mean of X in this case is np = 5. If X is conditioned to the event 'The dice is 4,5 or 6', then X will have also binomial distribution, but this time with paramenters n = 20, p = 1/2. The mean of X in this case is 20*1/2 = 10.

Since each event we conditioned in had probability 1/2 to occur, then E(X) = 1/2 * 5 + 1/2 * 10 = 7.5.

c) Remember that V(X) = E(X²)- E(X)². Since we alredy know the mean of X, we just need to compute the mean of X squared.

The variance of a binomial distribution Z with paramenters n and p is

V(Z) = np(1-p)

since V(Z) = E(Z²)- E(Z)² = E(Z²)- n²p², then

E(Z²) = V(Z) + E(Z)² = np(1-p) + n²p² = p²(n²-n) + np

Therefore

E(X²) = E(X² | 10 coins are tossed) * 1/2 + E(X² | 20 coins are tossed) * 1/2 =

1/2*(0.5²(10²-10) + 5) + 1/2*(0.5²(20²-20) + 10) = 13.75 + 52.5 = 66.25

As a consecuence

V(X) = 66.25 - 7.5² = 10

The variance of X is 10.by-step explanation: