Please explain the answer, no links or random words or I will report you.

Find the simplified form of the expression. Give your answer in scientific notation. (4 x 10^10)(9 x 10^5) 3.6 x 10^4 3.6 x 10^4

mezya [45]

It's simple arithmetic. The Answer is 604661760000000000000000000000000000000000000000000000000000000000000000000000000000 and in scientific notation
60466176 x 10⁸³

4 0

3 years ago

Figure ABCD is translated down by 6 units:

ElenaW [278]

Answer:

ABCDEFG NM,

Step-by-step explanation:

6 0

3 years ago

22 g(x) = *+ +7 What is the average rate of change of g over the interval —2, 4):

kobusy [5.1K]

Answer:

$Rate = 1$

Step-by-step explanation:

Given

$g(x) = x + 7$

Interval: (-2,4)

Required

Determine the average rate of change

This is calculated using:

$Rate = \frac{g(b) - g(a)}{b-a}$

Where:

$(a,b) = (-2,4)$

So, we have:

$Rate = \frac{g(4) - g(-2)}{4-(-2)}$

$Rate = \frac{g(4) - g(-2)}{4+2}$

$Rate = \frac{g(4) - g(-2)}{6}$

Calculate g(4) and g(-2)

$g(4) = 4 + 7 = 11$

$g(-2) = -2 + 7 = 5$

So:

$Rate = \frac{11 - 5}{6}$

$Rate = \frac{6}{6}$

$Rate = 1$

Hence, the average rate of change is 1

8 0

3 years ago

A home improvement contractor is painting the walls and ceiling of a rectangular room. The volume of the room is 875.00 cubic fe

Reika [66]

Answer:

The room dimensions for a minimum cost are: sides of 10 feet and height of 8.75 feet.

Step-by-step explanation:

We have a rectangular room with sides x and height y.

The volume of the room is 875 cubic feet, and can be expressed as:

$V=x^2y=875$

With this equation we can define y in function of x as:

$x^2y=875\\\\y=\dfrac{875}{x^2}$

The cost of wall paint is $0.08 per square foot. We have 4 walls which have an area Aw:

$A_w=xy=x\cdot \dfrac{875}{x^2}=\dfrac{875}{x}$

The cost of ceiling paint is $0.14 per square foot. We have only one ceiling with an area:

$A_c=x^2$

We can express the total cost of painting as:

$C=0.08\cdot (4\cdot A_w)+0.14\cdot A_c\\\\C=0.08\cdot (4\cdot \dfrac{875}{x})+0.14\cdot x^2\\\\\\C=\dfrac{280}{x}+0.14x^2$

To calculate the minimum cost, we derive this function C and equal to zero:

$\dfrac{dC}{dx}=280(-1)\dfrac{1}{x^2}+0.14(2x)=0\\\\\\-\dfrac{280}{x^2}+0.28x=0\\\\\\0.28x=\dfrac{280}{x^2}\\\\\\x^3=\dfrac{280}{0.28}=1000\\\\\\x=\sqrt[3]{1000} =10$

The sides of the room have to be x=10 feet.

The height can be calculated as:

$y=875/x^2=875/(10^2)=875/100=8.75$

The room will have sides of 10 feet and a height of 8.75 feet.

4 0

3 years ago

A business has a savings account that earns a 3% annual interest rate. At the end of 1996, the business had $4,000 in the accoun

olya-2409 [2.1K]

Answer:

The amount the business initially invested in 1991 is approximately;

A. $3,450

Step-by-step explanation:

The question relates to investment and finance

The parameters given are;

The annual interest rate on the business savings account = 3%

The amount the business had in the account at the end of 1996 = $4,000

The given formula used to determine the final amount in the savings account, $F = p \cdot \left(1 + \dfrac{r}{100} \right )^t$

Where;

F = The final amount

p = The initial (principal) investment

r = The annual interest rate

t = The time in years

Therefore, we have;

The required information = The initial amount, 'p', the business invested in 1991

The time in years, 't', from 1991 to 1996 = 1996 - 1991 = 5

∴ The time in years from 1991 to 1996, t = 5 years

The final amount in 1996, F = $4,000

r = 3%

Plugging in the values in the given equation gives;

$4000 = p\cdot \left(1 + \dfrac{3}{100} \right )^5$

Therefore;

$p = \dfrac{4000}{\left(1 + \dfrac{3}{100} \right )^5} = 3,450.43513754$

To the nearest dollar, the initial amount the business invested in 1991, p ≈ $3,450.

3 0

3 years ago