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3 years ago

You deposit $5000 in an account earning 2% interest compounded monthly. How much will you have in the account in 10 years?

Mathematics

1 answer:

sineoko [7]3 years ago

4 0

Answer:

6000 dollars

Step-by-step explanation:

yadda yadda yadda that is the answer

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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

2 years ago

Read 2 more answers

What is the arc measure of \stackrel{\LARGE{\frown}}{AC}

algol [13]

Answer:

72°

Step-by-step explanation:

Given that the radius(r) of the circle is 10 units and the length of arc ABC is 16π

The length of arc ABC = $\frac{\theta}{360}*2\pi r$

Where θ is the central angle in degrees.

Since the length of arc ABC is 16π,

$16\pi=\frac{\theta}{360}*2\pi r\\16\pi=\frac{\theta}{360}*2\pi *10\\\theta=\frac{16\pi *360}{2 \pi *10} \\\theta=288^0$

The angle in a circle = 360°, therefore:

Central angle for arc AB (θ) = 360 - Central angle for arc ABC = 360 - 288 = 72°

Therefore the arc measure of arc AB is 72°

5 0

3 years ago

Whats 4.8 as a mixed number in simplest form?

julia-pushkina [17]

Answer:

4 4/5

Step-by-step explanation:

5 0

3 years ago

You have some money in your wallet. You don't know the exact amount, but you think you have 60 dollars give or take 15 dollars.

Karolina [17]

Answer:

The least amount is 75 dollars.

The biggest amount is 125 dollars

Step-by-step explanation:

The absolute value function will help us determine a range of possible values since we do not know the exact amount of money.

Defining the function.

Let x be the exact amount of money in my pocket, we can define the equation

And we know that the difference between the exact amount of money with 100 dollars must be either 25 dollars more than what we estimated, or 25 dollars less than the estimation. So we can write:

We have a difference inside an absolute value, since we know the difference must be either +25 or -25.

Solving for x

Using the definition of absolute value we have

So if the inside of the absolute value is positive we have the first line of the piece-wise function, that is

Solving for x give us

If the inside of the absolute value is negative we have to use the second line of the piece-wise function definition

Solving for x give us

So the least amount of money in my pocket is 75 dollars and the biggest amount is 125 dollars.

6 0

1 year ago

|x+2|+4=11<br> A) x=5,-9

Lisa [10]

Answer:

the mod always gives positive answers

so the answer will be

Step-by-step explanation:

x+2+4=11

x+6=11

x=11-6

x=5

answer is x is 5

8 0

2 years ago

Read 2 more answers