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3 years ago

Please answer correctly !!!!!!!!!! Will mark brainliest !!!!!!!!!!!!

Mathematics

2 answers:

Drupady [299]3 years ago

5 0

Answer:

Step-by-step explanation:

f(6) = -6 this is the value when the x value is 6

g(5) = -5 this is the value when the x value is 5

4 * f(6) -6*g(5)

4*-6 - 6* -5

-24 + 30

uysha [10]3 years ago

4 0

Answer:

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adelina 88 [10]

Answer:

Step-by-step explanation:

x  0 , VCB ln(1 4x2 ) tương đương với

6 0

3 years ago

Practice B

Alona [7]

Answer:

Where did the writer go in holiday

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2 years ago

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

What is the difference between brackets and parentheses in math?

DaniilM [7]

There’s really not one !

3 0

2 years ago

Three potential employees took an aptitude test. Each person took a different version of the test. The scores are reported below

gavmur [86]

Answer:

Tobias did best on the aptitude test.

Step-by-step explanation:

The formula for calculating a z-score is is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.

For Emilio

Emilio got a score of 76; this version has a mean of 70.6 and a standard deviation of 9.

z = (x-μ)/σ

z = 76 - 70.6/9

z = 0.6

For Alissa

Alissa got a score of 298.8; this version has a mean of 282 and a standard deviation of 24.

z = (x-μ)/σ

z = 298.8 - 282/24

z = 0.7

For Tobias

Tobias got a score of 8.04; this version has a mean of 7.2 and a standard deviation of 0.4.

z = (x-μ)/σ

z = 8.04 - 7.2/0.4

z = 2.1

Looking at the calculated z score above, we can see that Tobias did better on his aptitude test because he had a higher z score compared to Emilio and Alissa.

8 0

3 years ago