Find the value of x. round your answer to the nearest tenth.

A standard piece of paper is 0.05 mm thick. Let's imagine taking a piece of paper and folding the paper in half multiple times.

tatyana61 [14]

Answer:

(a) $g(n)=0.05\cdot 2^n$

(b) $g^{-1}(n)=\log_{2}20g(n)$

(c)43 times

Step-by-step explanation:

Part A

The paper's thickness = 0.05mm

When the paper is folded, its width doubles (increases by 100%).

The thickness of the paper grows exponentially and can be modeled by the function:

$g(n)=0.05(1+100\%)^n\\\\g(n)=0.05\cdot 2^n$

Part B

$g(n)=0.05\cdot 2^n\\2^n=\dfrac{g(n)}{0.05}\\ 2^n=20g(n)\\$Changing to logarithm form, we have:\\\log_{2}20g(n)=n\\$Therefore:\\g^{-1}(n)=\log_{2}20g(n)$

Part C

If the thickness of the paper, g(n)=384,472,300,000 mm

Then:

$g^{-1}(n)=\log_{2}20g(n)\\g^{-1}(n)=\log_{2}20\times 384,472,300,000\\=\dfrac{\log 20\times 384,472,300,000}{\log 2} \\g^{-1}(n)=42.8 \approx 43\\n=43$

You must fold the paper 43 times to make the folded paper have a thickness that is the same as the distance from the earth to the moon.

3 0

3 years ago

A survey of pet owners found that on average, they spend $1,225 annually per pet, with a standard deviation of $275. Between whi

earnstyle [38]

Answer:

B.$675 and $1,775

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Enter an equation of the form y= mx for the line that passes through the

hammer [34]

Answer:

y = 13x

Step-by-step explanation:

gradient = 13

x = 0

y = 0

$\frac{Δy}{Δx}$

so $\frac{y - 0}{x - 0}$ = 13

cross multiply and you get

y = 13x

5 0

3 years ago

Write an equation that represents the line. (1,-1),(3,-5)

geniusboy [140]

Answer:

x+y=0

Step-by-step explanation:

slope m of given equations is

(-5+1)÷(3+1)

=-1

then the equations of this line is

y-(-1)=m(x-1)

or, y+1=-1(x-1)

or, y+1= -x+1

or, x+y=0

x+y=0 is required equation of line.

6 0

3 years ago

Find QN. Please show all the work on how you got your answer

Effectus [21]

QN = 28

Solution:

Given MNPQ is a parallelogram.

QT = 4x + 6 and TN = 5x + 4

To find the length of QN:

Let us solve it using the property of parallelogram.

Property of Parallelogram:

Diagonals of the parallelogram bisect each other.

Therefore, QT = TN

⇒ 4x + 6 = 5x + 4

Arrange like terms together.

⇒ 6 – 4 = 5x – 4x

⇒ 2 = x

⇒ x = 2

Substitute x = 2 in QT and TN

QT = 4(2) + 6 = 14

TN = 5(2) + 4 = 14

QN = QT + TN

= 14 + 14

QN = 28

The length of QN is 28.

3 0

4 years ago