Simplify: 6a^2-2c+2a^3-2c^3

Andrej [43]

4a5+28+6b7-30
4a5+6b7-2<—- this is a to the power of 5 , b to the power of 7
(Is that 5a or a to the power of 5 )
20a+28+42b-30
20a+42b-2<—— this is 5a , 7b

4 0

3 years ago

Someone help please:

frozen [14]

Answer:

The sharing cone holds about 9 times more popcorn than the skinny cone.

Step-by-step explanation:

Cone volume:

$V = \frac{\pi r^{2}h}{3}$

r is the radius and h is the inches.

Skinny-size cone:

Radius is r, height h. So

$V_{sk} = \frac{\pi r^{2}h}{3}$

Sharing size:

Radius is now 3r. So

$V_{sh} = \frac{\pi (3r)^{2}h}{3} = \frac{9\pi r^{2}h}{3} = 3\pi r^{2}h$

How many times more popcorn?

$r = \frac{V_{sh}}{V_{sk}} = \frac{3\pi r^{2}h}{\frac{\pi r^{2}h}{3}} = \frac{3*3\pi r^{2}h}{\pi r^{2}h} = 9$

The sharing cone holds about 9 times more popcorn than the skinny cone.

6 0

3 years ago

If ƒ(x) = 2x, then ƒ -1(x) =<br><br> -2x<br> ½x<br> x - 2

kap26 [50]

Answer: second option

Step-by-step explanation:

To find the inverse function of the given function f(x):

$f(x)=2x$

You need to:

Substitute $f(x)=y$ into the function:

$y=2x$

Now, you need to solve for "x", to do this, you must divide both sides of the function by 2:

$\frac{y}{2}=\frac{2x}{2}\\\\\frac{y}{2}=x$

Now, replace "x" with "y" and replace "y" with "x":

$\frac{x}{2}=y$

Therefore, substituting $y=f^{-1}(x)$ you get:

$f^{-1}(x)=\frac{x}{2}$ or $f^{-1}(x)=\frac{1}{2}x$

7 0

3 years ago

Suppose the average price of gasoline for a city in the United States follows a continuous uniform distribution with a lower bou

Novay_Z [31]

Answer:

$P(X$

And we can use the cumulative distribution function given by:

$F(x) = \frac{x-a}{b-a} , a \leq X \leq b$

And for this case we can write the probability like this:

$P(X$

And then the final answer for this case would be $\frac{2}{3}=0.667$

Step-by-step explanation:

For this case we define our random variable X "price of gasoline for a city in the USA" and we know the distribution is given by:

$X \sim Unif (a=3.5, b=3.8)$

And for this case the density function is given by:

$f(x) = \frac{x}{b-a}= \frac{x}{3.8-3.5}=, 3.5 \leq X \leq 3.8$

And we want to calculate the following probability:

$P(X$

And we can use the cumulative distribution function given by:

$F(x) = \frac{x-a}{b-a} , a \leq X \leq b$

And for this case we can write the probability like this:

$P(X$

And then the final answer for this case would be $\frac{2}{3}=0.667$

5 0

3 years ago

In a given year, the average annual salary of a NFL football player was $189,000 with a standard deviation of $20,500. If a samp

nika2105 [10]

Answer:

15.15% probability that the sample mean will be $192,000 or more.

Step-by-step explanation:

To solve this problem, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$