Use the graph of f(x) to graph y= f(x+1)-2

Sal and her three friends plan to bowl one or two games each. Each game costs $2.50 each. Identify the independent and dependent

tino4ka555 [31]

So the dependent is the number of games because it's not definite they dont know for sure. so the domain always involves money!!! always! the range wiyld be the numbers they migh play like 8-10 so 4 to 8 is the range value. so determining off of that the indepedent variable would be the total cost becuase it wont change so your answer is C hope this helped have a good day!!!

3 0

2 years ago

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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

A triangle with angle measures of 45 45 and 90 is

kiruha [24]

Answer:

A right triangle

Step-by-step explanation:

The answer is a right triangle because it has a right angle. A right angle is 90 degrees

6 0

2 years ago

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Simplify. Write each answer in scientific notation

Greeley [361]

Answer:

5*10^1

Step-by-step explanation:

7 0

3 years ago

Plot a point on the coordinate plane to represent each of the ratio values in the table.

SOVA2 [1]

Answer:

Dot 1. y = 3, x = 1

Dot 2. y = 6, x = 2

Dot 3. y = 12, x = 4

Dot 4. y = 18, x = 6

Step-by-step explanation:

Distance(m) = y

Time(s) = x

Therefore whatever is traveling at that speed is getting faster (A Perpetual Energy Producing Bullet) since at first it goes a = 3 Distance(m) and then duplicates its distance and Time traveled which makes sence. Then it does the same thing again! (∑²ᵇ⁽¹⁾) This is the mathematical equation that changes it. It basically means it takes a sum of the last number than multiplies it by itself to the power of (2ᵇ) and then to the power of 1 to finish off the equation. (∑²ᵇ⁽¹⁾) = ( (u x 2) x2) + c) = Infinite power looping then taking breaks in between to take a variable that was 2 last of itself and add that to the sum of the entire equation!

c = (u x 2)!

Hope this helps!

<u><em>Also can I have brainliest...</em></u>

7 0

3 years ago

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