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3 years ago

Select the pie chart that accurately represents Sabrina's variable expenses for the month of June.

Mathematics

1 answer:

masha68 [24]3 years ago

8 0

Answer:

BOTTOM RIGHT CHART, JUST TOOK THE TEST

Step-by-step explanation:

PLATO

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The Department of Agriculture is monitoring the spread of mice by placing 100 mice at the start of the project. The population,

uranmaximum [27]

Answer:

Step-by-step explanation:

Assuming that the differential equation is

$\frac{dP}{dt} = 0.04P\left(1-\frac{P}{500}\right)$ .

We need to solve it and obtain an expression for $P(t)$ in order to complete the exercise.

First of all, this is an example of the logistic equation, which has the general form

$\frac{dP}{dt} = kP\left(1-\frac{P}{K}\right)$ .

In order to make the calculation easier we are going to solve the general equation, and later substitute the values of the constants, notice that $k=0.04$ and $K=500$ and the initial condition $P(0)=100$ .

Notice that this equation is separable, then

$\frac{dP}{P(1-P/K)} = kdt$ .

Now, intagrating in both sides of the equation

$\int\frac{dP}{P(1-P/K)} = \int kdt = kt +C$ .

In order to calculate the integral in the left hand side we make a partial fraction decomposition:

$\frac{1}{P(1-P/K)} = \frac{1}{P} - \frac{1}{K-P}$ .

So,

$\int\frac{dP}{P(1-P/K)} = \ln|P| - \ln|K-P| = \ln\left| \frac{P}{K-P} \right| = -\ln\left| \frac{K-P}{P} \right|$ .

We have obtained that:

$-\ln\left| \frac{K-P}{P}\right| = kt +C$

which is equivalent to

$\ln\left| \frac{K-P}{P}\right|= -kt -C$

Taking exponentials in both hands:

$\left| \frac{K-P}{P}\right| = e^{-kt -C}$

Hence,

$\frac{K-P(t)}{P(t)} = Ae^{-kt}$ .

The next step is to substitute the given values in the statement of the problem:

$\frac{500-P(t)}{P(t)} = Ae^{-0.04t}$ .

We calculate the value of $A$ using the initial condition $P(0)=100$ , substituting $t=0$ :

$\frac{500-100}{100} = A}$ and $A=4$ .

So,

$\frac{500-P(t)}{P(t)} = 4e^{-0.04t}$ .

Finally, as we want the value of $t$ such that $P(t)=200$ , we substitute this last value into the above equation. Thus,

$\frac{500-200}{200} = 4e^{-0.04t}$ .

This is equivalent to $\frac{3}{8} = e^{-0.04t}$ . Taking logarithms we get $\ln\frac{3}{8} = -0.04t$ . Then,

$t = \frac{\ln\frac{3}{8}}{-0.04} \approx 24.520731325$ .

So, the population of rats will be 200 after 25 months.

6 0

3 years ago

I just need yall help ... {:

KonstantinChe [14]

Answer:C

Step-by-step explanation:

The answer is C because the minimum is 33 and the maximum is 51. The first quartile is 33. THE SECOND QUATILE IS 39 and the 3rd quartile is 47.

4 0

3 years ago

Read 2 more answers

30 points. Please help!!

yarga [219]

Answer:

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

Draw a picture to show the product of 4:7 x 3. Then write the product

Hoochie [10]

Answer:

¹²/₇

Step-by-step explanation:

Model ⁴/₇ × 3

Assume that you have three pies, each dived into seven slices.

There are only four slices remaining in each pie, that is, there is ⁴/₇ pie in each pie plate

The picture represents ⁴/₇ × 3.

Model the product

Now, transfer slices to get as many filled pie plates as possible.

Count the total slices.

You have 12 slices, and each slice represents ⅐ of a pie.

You have ¹²/₇ pie.

∴ ⁴/₇ × 3 = ¹²/₇

6 0

3 years ago

Solve for X, square root 2x = square root x+5

inessss [21]

X = 5
Move the variable then cells to like terms and simplify

4 0

3 years ago