If f(3) = 24, what is f-1 (24)?

1/x-4 + 1/x+3 = x-6/ x^2-x-12

STALIN [3.7K]

There is no solution

7 0

3 years ago

How many two digit number divisible by 4

MAVERICK [17]

Answer:

the total is 22 two digit number which are divisible by 4

4 0

2 years ago

The number of bacteria in a certain culture doubled every hour. If there were 30 bacteria present in the culture initially, how

vichka [17]

Answer:

The number of bacteria after $8th$ will be $3840$

Step-by-step explanation:

Given the initially 30 bacteria present in the culture.

Also, the number of bacteria got doubled every hour.

So, using the equation

$A=A_0r^{n-1}$

Where $A$ is number of bacteria after $n$ hours.

$A_0$ is bacteria present initially.

$r$ is the common ration, in our problem it is given that bacteria doubles every hour. So, $r=2$

And $n$ is the number of hours. In our problem we need amount of bacteria at the end of $8th$ hours. So, $n=8$

Plugging values in the formula we get,

$A=30(2)^{8-1}\\A=30\times 2^7\\A=30\times 128\\A=3840$

So, number of bacteria after $8th$ will be $3840$

3 0

3 years ago

With a height of 68 in, Nelson was the shortest president of a particular club in the past century. The club presidents of the

Ivahew [28]

Answer:

a. The positive difference between Nelson's height and the population mean is: $\\ \lvert 68-70.7 \rvert = \lvert 70.7-68 \rvert\;in = 2.7\;in$ .

b. The difference found in part (a) is 1.174 standard deviations from the mean (without taking into account if the height is above or below the mean).

c. Nelson's z-score: $\\ z = -1.1739 \approx -1.174$ (Nelson's height is below the population's mean 1.174 standard deviations units).

d. Nelson's height is usual since $\\ -2 < -1.174 < 2$ .

Step-by-step explanation:

The key concept to answer this question is the z-score. A z-score "tells us" the distance from the population's mean of a raw score in standard deviation units. A positive value for a z-score indicates that the raw score is above the population mean, whereas a negative value tells us that the raw score is below the population mean. The formula to obtain this z-score is as follows:

$\\ z = \frac{x - \mu}{\sigma}$ [1]

Where

$\\ z$ is the z-score.

$\\ \mu$ is the population mean.

$\\ \sigma$ is the population standard deviation.

From the question, we have that:

Nelson's height is 68 in. In this case, the raw score is 68 in $\\ x = 68$ in.
$\\ \mu = 70.7$ in.
$\\ \sigma = 2.3$ in.

With all this information, we are ready to answer the next questions:

a. What is the positive difference between Nelson's height and the mean?

The positive difference between Nelson's height and the population mean is (taking the absolute value for this difference):

$\\ \lvert 68-70.7 \rvert = \lvert 70.7-68 \rvert\;in = 2.7\;in$ .

That is, the positive difference is 2.7 in.

b. How many standard deviations is that [the difference found in part (a)]?

To find how many standard deviations is that, we need to divide that difference by the population standard deviation. That is:

$\\ \frac{2.7\;in}{2.3\;in} \approx 1.1739 \approx 1.174$

In words, the difference found in part (a) is 1.174 standard deviations from the mean. Notice that we are not taking into account here if the raw score, x, is below or above the mean.

c. Convert Nelson's height to a z score.

Using formula [1], we have

$\\ z = \frac{x - \mu}{\sigma}$

$\\ z = \frac{68\;in - 70.7\;in}{2.3\;in}$

$\\ z = \frac{-2.7\;in}{2.3\;in}$

$\\ z = -1.1739 \approx -1.174$

This z-score "tells us" that Nelson's height is 1.174 standard deviations below the population mean (notice the negative symbol in the above result), i.e., Nelson's height is below the mean for heights in the club presidents of the past century 1.174 standard deviations units.

d. If we consider "usual" heights to be those that convert to z scores between minus2 and 2, is Nelson's height usual or unusual?

Carefully looking at Nelson's height, we notice that it is between those z-scores, because:

$\\ -2 < z_{Nelson} < 2$

$\\ -2 < -1.174 < 2$

Then, Nelson's height is usual according to that statement.

7 0

3 years ago

Calculate the average rate of change for the function f(x) = −x4 + 4x3 − 2x2 + x + 1, from x = 0 to x = 1.

Alekssandra [29.7K]

Really
just calculate the slope
slope is (y2-y1)/(x2-x1)

for x=0, y=1
for x=1, y=3

slope=(y1-y1)/(x-x1)=(3-1)/(1-0)=2/1=2

answer is 2

3 0

3 years ago