PLZ HELP

The function g has an inverse. The function g − 1 determines the number of folds needed to give the folded paper a thickness of

Amanda [17]

Answer:

$\mathbf{g^{-1} (t) = log _2 \ 20 \ t}$

Step-by-step explanation:

Here is the full question

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. We'll assume we can make "perfect folds," where each fold makes the folded paper exactly twice as thick as before - and we can make as many folds as we want.

Write a function g that determines the thickness of the folded paper (in mm) in terms of the number folds made, n. (Notice that g(0) 0.05,)

$g(n )= (05)2^n$

The function g has an inverse. The function g⁻¹ determines the number of folds needed to give the folded paper a thickness of t mm. Write a function formula for g⁻¹).

<u>SOLUTION:</u>

If we represent g(n) with t;

Then

$\mathbf{t = (0.05)2^n} \\ \\ \mathbf{\dfrac{t}{0.05} = 2^n} \\ \\ \mathbf{\dfrac {100 \ t }{ 5} = 2^n} \\ \\ \mathbf{20 t = 2^n}$

Taking logarithm of both sides; we have :

$\mathbf{log (20 t) = n log 2} \ \ \ \mathbf{(since \ , log \ a^b = b \ log \ a) } \\ \\ \mathbf{n = \dfrac{log \ 20 t }{log \ 2 }} \\ \\ \mathbf{g^{-1} (t) = \dfrac{log \ 20 t }{log \ 2 }} \\ \\ \mathbf{g^{-1} (t) = log _2 \ 20 \ t}$

4 0

4 years ago

Find the equation of a line with a slope of −2 and a y-intercept of (0,o).

kari74 [83]

The equation should be y=-2x .

6 0

4 years ago

4’1” - 1’ 10” whats is

cluponka [151]

Since inches are out of 12 this would be

4 ft - 1 ft = 3 ft

3' 1" - 1 " = 3 '

3 feet is also 2 ft and 12 inches

2' 12" - 9 " = 2' 3"

So the answer is 2 feet and 3 inches

Hope this helps

-GoldenWolfX

7 0

4 years ago

The price p of a gallon of gas goes up to $0.05 cents on Friday. On Saturday the price goes down $0.03. Write a expression with

m_a_m_a [10]

Answer:

The expression with three terms to show the price of a gallon of gas on Saturday is ⇒ $p+0.05-0.03$

Step-by-step explanation:

Given:

Price of a gallon of gas in dollars = $p$

On Friday, the price goes up by = $0.05

On Saturday, the price goes down by = $0.03

To write an expression with three terms to show the price of a gallon of gas on Saturday.

Solution:

Initial price of a gallon given in dollars was = $p$

On Friday the price increased by $0.05.

So, the price on Friday in dollars can be given as = $p+0.05$

On Saturday, the price decreased by $0.03

So, the price on Saturday in dollars can be given as = $p+0.05-0.03$

Thus, the expression with three terms to show the price of a gallon of gas on Saturday is ⇒ $p+0.05-0.03$

4 0

3 years ago

Quit Smoking: The New England Journal of Medicine published the results of a double-blind, placebo-controlled experiment to stud

Juliette [100K]

Answer:

Option A is correct.

In this experiment the nicotine treatment had a higher success rate than the placebo group, but the improvement was less than 1%. It was exactly 0.8%

Step-by-step explanation:

In a drug treatment experiment, there are usually two groups.

- The treatment group; they get the full dosage and content of the drug to be tested.

- The placebo group; here, they sort of serve as the control group. They get the dosage of the drug to be tested with the active ingredient of the drug removed.

Double blind means that both the participants and the conductors do not know which members belong to which treatment group. It is used to increase the randomness of the sampling technique.

For this experiment, nicotine patches, antidepressants and bupropion are used to help people quit smoking.

It is explained that the the rate at which the participants quit smoking is recorded and at the end, a sample mean is obtained.

The difference in sample means of both groups is then obtained by solving

(Rate of quit smoking for the treatment group) - (Rate of quit smoking for the placebo group)

This difference was obtained to be positive 0.8%. It is evident that this figure represents a higher success rate for the treatment group than the placebo group, but the improvement was less than 1%. (0.8%).

All the other options are either incorrect or not clearly stated in the description ofthe experiment.

- In this experiment, the placebo group had a higher success rate than the nicotine group by 0.8%.

This is obviously not true, it is the reverse of the true statement.

- Nicotine patches will produce a slightly higher success rate when compared to a placebo, but the difference is not statistically significant.

This started with a true statement bit it ended with a statement we cannot confirm because we don't know the sample size for either of the groups involved in the experiment. So, it isn't totally true.

- Nicotine patches and the antidepressant bupropion work equally well on "quit smoking" rates.

They don't have an equal rate of working. The nicotine slightly works better as stated in the question.

Hope this Helps!!!

5 0

3 years ago