2/3x = 27 please help

Which of the following expressions “ the sum of n and the sum of n and 6 ?

faltersainse [42]

what do u mean by that

3 0

3 years ago

The rate of growth of profit (in millions) from an invention is approximated by Upper P prime (x )equals x e Superscript negati

Alecsey [184]

Answer:

The function is $P(x) = \frac{1}{2} e^{-x^2} +0.016$

Step-by-step explanation:

From the question we are told that

The rate of growth is $P'(x) = xe^{x} - x^2$

The total profit is $P(2) =$ $25,000

The time taken to make the profit is $x = 2 \ years$

From the question

$P'(x) = xe^{-x^2}$ is the rate of growth

Now here x represent the time taken

Now the total profit is mathematically represented as

$P(x) = \int\limits {P'(x)} \, = \int\limits {xe^{-x^2}} \,$

So using substitution method

We have that

$u = - x^2$

$du = 2xdx$

So

$p(x) = \int\limits {\frac{1}{2} e^{-u}} \, du$

$p(x) = {\frac{1}{2} [ e^{-u}} +c ]$

$p(x) = {\frac{1}{2} e^{-x^2}} + \frac{1}{2} c$ recall $u = - x^2$ and let $\frac{1}{2} c = Z$

At x = 2 years

$P(x) =$ $25,000

So

Since the profit rate is in million

$P(x) =$ $25,000 = $\frac{25000}{1000000} =$ $0.025 millon dollars

So

$0.025 = {\frac{1}{2} e^{-2^2}} + Z$

=> $Z = 0.025 - {\frac{1}{2} e^{-2^2}}$

$Z = 0.016$

So the profit function becomes

$P(x) = \frac{1}{2} e^{-x^2} +0.016$

5 0

3 years ago

The wildlife department has been feeding a special food to rainbow trout fingerlings in a pond. based on a large number of obser

Liono4ka [1.6K]

The normal distribution curve for the problem is shown below

We need to standardise the value X=405.5 by using the formula

$z-score= \frac{X-Mean}{Standard Deviation}$
$z-score= \frac{405.5-402.7}{8.8} =0.32$

We now need to find the probability of z=0.32 by reading the z-table

Note that z-table would give the reading to the left of z-score, so if your aim is to work out the area to the right of a z-score, then you'd need to do:

$P(Z\ \textgreater \ z)=1 - P(Z\ \textless \ z)$

from the z-table, the reading $P(Z\ \textless \ 0.32)$ gives 0.6255

hence,
$P(Z\ \textgreater \ 0.32)=1-0.6255=0.3475$

The probability that the mean weight for a sample of 40 trout exceeds 405.5 gram is 0.3475 = 34.75%

7 0

3 years ago

Noralie is making a necklace using a total of 48 beads. All of the beads will be either blue or yellow. She plans to use 1/3 as

Morgarella [4.7K]

Since there are a total of 48 beads and each bead will either be blue or yellow, in order to find out how many of each colour bead she will use, do the following:

Divide 48 by 3 to get 16 yellow beads.

Now that you know how many yellow beads there are, just subtract that from 48:
48 - 16 = 32

Therefore, she will use 16 yellow beads and 32 blue beads.

5 0

3 years ago

The point (4,-5) is rotated 90° clockwise

V125BC [204]

Answer:

5,4

Step-by-step explanation:

here is the rule (4,-5) rotate 90 clockwise = (5,4)

4,-5 will put you in the 4 quadrant rotate it 90 clock wise Put you in the first quadrant

6 0

3 years ago