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2 years ago

Shaun is painting a fence. After finishing three-eighths of the length of the fence he finds that

Mathematics

2 answers:

Levart [38]2 years ago

5 0

Answer: x = 40

Step-by-step explanation:

let f be the total length of the fence:

(3/8)f = 15

divide both sides by 3/8

f = 15 x 8/3

f = 120/3

f = 40

faust18 [17]2 years ago

4 0

Answer: F = 40

Step-by-step explanation:

*Important: I do not know what the methods mentioned in 4b are, nor do I know its equation. Please take this into account.

What we know:

3/8 is equal to 15 ft
F is the total amount of fence painted
We need to set up and solve the equation

How we do this:

Using basic division, this equation is solveable.

Process:

Divide to find 1/8 15/3 = 5 (1/8f = 5)
Multiply to find total 5 x 8 = 40

(1/8 x 8 = 8/8)

Solution:

F = 40

8(5) = F

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Use the zero product property to find the solutions to the equation (x + 2) (x + 3) = 12

Inessa05 [86]

Answer:

The solution of the equations are -6 and 1

Step-by-step explanation:

* Lets explain how to solve the problem

- We want to find the solution of the equation (x + 2) (x + 3) = 12

- At first lets use the Foil method to multiply the two brackets

(x + 2) (x + 3) = (x)(x) + (x)(3) + (2)(x) + (2)(3)

(x + 2) (x + 3) = x² + 3x + 2x + 6 ⇒ add the like term

(x + 2) (x + 3) = x² + 5x + 6

∵ (x + 2) (x + 3) = 12

∴ x² + 5x + 6 = 12

- Subtract 12 from both sides

∴ x² + 5x - 6 = 0

- Factorize the left hand side

∵ x² = (x)(x)

∵ -6 = 6 × -1

∵ 6x + -1x = 5x

∴ (x + 6)(x - 1) = 0

- Lets use the zero product property

∵ (x + 6)(x - 1) = 0

∴ x + 6 = 0 ⇒ OR ⇒ x - 1 = 0

∵ x + 6 = 0

- Subtract 6 from both sides

∴ x = -6

∵ x - 1 = 0

- Add 1 to both sides

∴ x = 1

∴ The solution of the equations are -6 and 1

6 0

3 years ago

Read 2 more answers

G with the definition of covariance, prove cov[(ay − b),(cy − d)] = accov(x, y ), where x, y are random variables and a, b, c, d

____ [38]

By definition of covariance,

$\mathrm{Cov}(X,Y)=\mathbb E[(X-\mathbb E[X])(Y-\mathbb E[Y])]$

$\mathrm{Cov}(X,Y)=\mathbb E[XY-\mathbb E[X]Y-X\mathbb E[Y]+\mathbb E[X]\mathbb E[Y]]=\mathbb E[XY]-\mathbb E[X]\mathbb E[Y]$

We have

$\mathbb E[(aX-b)(cY-d)]=\mathbb E[acXY-adX-bcY+bd]$

$=ac\mathbb E[XY]-ad\mathbb E[X]-bc\mathbb E[Y]+bd$

$\mathbb E[aX-b]=a\mathbb E[X]-b$

$\mathbb E[cY-d]=c\mathbb E[Y]-d$

$\mathbb E[aX-b]\mathbb E[cY-d]=ac\mathbb E[X]\mathbb E[Y]-ad\mathbb E[X]-bc\mathbb E[Y]+bd$

Putting everything together, we find the covariance reduces to

$\mathrm{Cov}(aX-b,cY-d)=ac(\mathbb E[XY]-\mathbb E[X]\mathbb E[Y])=ac\mathrm{Cov}(X,Y)$

as desired.

5 0

3 years ago

margo is repaying a loan from her parents. she has already paid $315 and still owes them $1245. write an equation to find the or

ExtremeBDS [4]

Answer:

n-315=1245

Step-by-step explanation:

n stands for the original amount of the loan. Margo has paid $315, so the original number minus what Margo has paid, and the equality is the amount that Margo still owes.

6 0

2 years ago

What percent of 125 is 65

Arte-miy333 [17]

The answer is 52%. 65/125=0.52 * 100 = 52%

4 0

3 years ago

Read 2 more answers

A bag contains 12 red checkers and 6 black checkers. You will randomly select two checkers, one at a time, without replacement.

Mademuasel [1]

Answer:

Seestep by step explanation

Step-by-step explanation:

First Selection:

First branch P₁ = 12/18 P₁ = 4/6 P₁ = 2/3 (To pick a red one)

Second Branch P₂ = 6/18 P₂ = 1/3 ( To pick a black one)

Second Selection

We already have a red checker the we have 11 red checkers and 6 black checkers, then

First branch P₃ = 11/17

Second Branch P₄ = 6/17

But in case that our first checker was black then we have

First branch P₅ = 12/17

Second Branch P₆ = 5/17

8 0

3 years ago