Write the equations of the lines on the grid.

Which of the following expressions is equivalent to a3 + b3?

lubasha [3.4K]

ANSWER
${a}^{3} + {b}^{3} = (a + b)( {a}^{2 } - ab + {b}^{2} )$

EXPLANATION

To find the expression that is equivalent to
${a}^{3} + {b}^{3}$
we must first expand
${(a + b)}^{3}$
Then we rearrange to find the required expression.

So let's get started.

${(a + b)}^{3} = (a + b) {(a + b)}^{2}$

We expand the parenthesis on the right hand side to get,

${(a + b)}^{3} = (a + b) ( {a}^{2} + 2ab + {b}^{2} )$

We expand again to obtain,

${(a + b)}^{3} = {a}^{3} + 3 {a}^{2}b + 3a {b}^{2} + {b}^{3}$

Let us group the cubed terms on the right hand side to get,

${(a + b)}^{3} = {a}^{3} + {b}^{3} + 3 {a}^{2}b + 3a {b}^{2}$

${(a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab (a+ b)$

We make the cubed terms the subject,

${(a + b)}^{3} - 3ab (a+ b) = {a}^{3} + {b}^{3}$

We factor to get,

$(a + b)({(a + b)}^{2} - 3ab ) = {a}^{3} + {b}^{3}$

We expand the bracket on the left hand side to get,

$(a + b)( {a}^{2} + 2ab + {b}^{2} - 3ab ) = {a}^{3} + {b}^{3}$

We finally simplify to get,

$(a + b)( {a}^{2} - ab + {b}^{2} ) = {a}^{3} + {b}^{3}$

5 0

3 years ago

Read 2 more answers

The circle with center O has a circumference of 36 units. What is

Alex777 [14]

I think the answer is D

6 0

3 years ago

It is known that diskettes produced by a cer- tain company will be defective with probability .01, independently of each other.

zheka24 [161]

Answer:

1.27%

Step-by-step explanation:

To solve this problem, we may consider a binomial distribution where a customer can either accept or reject (and return) the diskette package.

Lets consider some aspects:

1. From the formulation of the exercise we know that a package is accepted if it has at most 1 defective diskette. So our event A is defined as:

A = 0 or 1 defective diskette

2. The probability of a diskette being defective is 0.01

3. Each package contains 10 diskettes.

If X is defined as number of defective diskettes in the package, the probability of X is given by a binomial distribution with probability 0.01 and n=10

X ~ Bin(p=0.01, n=10)

Let us remember the calculation of probability for the binomial distribution:

$P(X=x)=nCx*p^{x}*(1-p)^{(n-x)}$ with x = 0, 1, 2, 3,…, n

Where

n: number of independent trials

p: success probability

x: number of successes in n trials

In our case success means finding a defective diskette, therefore

n=10

p=0.01

And for x we just need 0 or 1 defective diskette to reject the package

Hence,

$P(X=x)=10Cx*0.01^{x}*(1-0.01)^{(10-x)}$ with x = 0, 1

So,

$P(A)=P(X=0)+P(X=1)$

$P(A)=10C0*0.01^{0}*(1-0.01)^{(10-0)} + 10C1*0.01^{1}*(1-0.01)^{(9)}$

$P(A)=0.99^{10}+10*0.01*0.99^{9}$

$P(A)=0.9957$

Now, because we have 3 packages and we might reject just 1 of them, we can find this probability like this:

$3*(1-P(A))*P(A)*P(A) = (1-0.9957)*0.9957*0.9957=0.0127$

Finally, we have that the probability of returning exactly one of the three packages is 1.27%

3 0

3 years ago

A pizza is cut into twelve pieces. Describe the steps you would take to find the area of one slice of the pizza.

DanielleElmas [232]

Hey there!

First, you would need to find the area of the circle/pizza . . .

Formula of finding area → pi*r² (Pi * the radius of the circle/pizza²)
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Once you have found the area, you would need to divide the result by the number 12 since there is a total of 12 slices in the pizza.
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This is how you would find the area of one slice of pizza.
__________________
I hope this helps you.
Have a great day! :)

5 0

3 years ago

What number is 65% of 30?

muminat

65%=0,65

30×0,65=19,5 <-----------

7 0

3 years ago

Read 2 more answers