The figure is formed by a rectangle and a square. Find the area of the shaded part of the figure.

What is the inverse of the function??

Firlakuza [10]

$$\begin{matrix}
y=ln(x+3)\\
e^y=x+3\\
e^y-3=x\\
swap ~x~and~y\\
 \huge\underline{y=e^x-3}}
 \end{matrix}$
$

To get the inverse of any function f(x) [ just make sure that it passes the horizontal line test] follow the steps:

- Solve for x, i.e separate x in one side and the other terms in the other side, included f(x).

- Swap x and f(x).

- The result is the inverse of the original function $f^{-1}(x)$ .

-------------------------

Apply that on your function
$$\begin{matrix}
y=ln(x+3)\\
e^y=x+3\\
e^y-3=x\\
swap ~x~and~y\\
 \huge\underline{y=e^x-3}}
 \end{matrix}$
$

5 0

3 years ago

We are studying the proportion of cities that have private garbage collector. We want a maximum error of 0.10 and a 95% confiden

True [87]

Answer:

The minimum number of cities we need to contact is 96.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence interval $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

Z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

95% confidence interval

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

In this problem, we have that:

$p = 0.5, M = 0.1$

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.1 = 1.96*\sqrt{\frac{0.5*0.5}{n}}$

$0.1\sqrt{n} = 0.98$

$\sqrt{n} = 9.8$

$(\sqrt{n})^{2} = (9.8)^{2}$

$n = 96$

The minimum number of cities we need to contact is 96.

8 0

3 years ago

In a study of 30 high school students, researchers found a high correlation, 0.93, between amount of exercise and weight lost. W

zloy xaker [14]

Answer:

Option A is true

The researchers proved that exercise causes weight loss only for high school students.

Step-by-step explanation:

We are told that the researchers found a high correlation, 0.93, between amount of exercise and weight lost.

Now, looking at each of the options;

- A is True because due to the high correlation, the research proves that exercise causes weight loss but only for high school students.

- B is not true because we are told the correlation is very high at 0.93. Thus, it is untrue that there is no proven causation.

-C is not true because there's no where that the researchers have completely proved that exercise causes weight loss generally. It is only peculiar to the high school students studied.

-D is not true because the 93% is just a correlation and not a percentage of those who lost weight

8 0

3 years ago

A research team is testing a product that will minimize wrinkles among women. Volunteers in the age group of 40 to 45 are includ

artcher [175]

There are mistakes in the answer options attached. These are the correct ones.

a. The group that received the bottle of solution is the control group.

b. The group that received the bottle of solution that did not contain the ingredients that are meant to lessen wrinkles is the control group.

c. Both the groups are control groups.

d. Neither group is an control group.

Answer:

B. The group that received the bottle of solution that did not contain the ingredients that are meant to lessen wrinkles is the control group

Step-by-step explanation:

In an experiment of this type, the control group is the group that does not contain the treatment. So in this group The effect of the treatment unknown unlike the experimental group which gets the treatment that the researcher is trying to find it's effect.

I. Conclusion, the group that got bottles that did not contain Ingredients for wrinkles lessening is the control group.

4 0

3 years ago

Tony is saving money to purchase a new TV that costs $276.99. He has $135 in his savings account already. If he earns $8.50 per

Natasha2012 [34]

Answer:

I believe that Tony will have to work 16 or 17 hours to have enough money to buy the TV

Step-by-step explanation:

$276.99 - 135 = $141.99

$8.50 x 8 = $68

$8.50 x 16 = $136

$8.50 x 17 = $144.50

$8.50 x 33 = $280.50

$136 < $141.99 $144.50 > $141.99

$8.50 x 16 or $8.50 x 17

Check to see if the numbers are correct.

If they are you will have to make a choice.

I hope this helped. ☺

6 0

2 years ago