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2 years ago

5

The tank for a car15 gallon. The gasoline gauge shows the tank is 1/8 full. How much gas is still in the tank

1 answer:

slamgirl [31]2 years ago

5 0

30=5x divide both sides by 5 x=6 gal

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Kate paid $27 for a dress that was on sale at 10% off. What was the original price for this dress?

Art [367]

Answer:

$30

Step-by-step explanation:

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3 years ago

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What is the midpoint of the segment shown below?

Bogdan [553]

C. 5/2, 3 this is the answer

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3 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

What is HL???<br><br> HL=__<br><br> Image Below

Advocard [28]

Consider a trapezoid GJKF with:

GH=JH (hypothesis)

FL=KL (hypothesis)

so HL is the median of trapezoid GJKF

so: HL=1/2(2.5+1.2)=1.85

4 0

2 years ago

It’s only one question plz help (DON’T GUESS NO LINKS) please I will do anything there is a part two I’m struggling and this is

pshichka [43]

Answer:

For question 1 it's B

For question 2 it's C

Step-by-step explanation:

<u>For question 1, you have to apply the "Triangle Inequality Theorem"</u>

A+B > C

B+C > A

A+C > B

Let's say that A=22, B=17, C= 14

22+17 > 14 True

17+14 > 22 True

22+14 > 17 True

Therefore, the answer is B

<u>For question 2, you apply the rule of the sum of the triangles which is 180°</u>

70+70+? = 180

140+? = 180

? = 40

Therefore, it's C

8 0

3 years ago