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Vadim26 [7]
3 years ago
7

Logan paid 2.16 dollars for 3 lollipops. Each lollipop cost c cents. Create an equation and solve to find the cost of one lollip

op. Hint convert dollars to cents to begin
Mathematics
2 answers:
Nutka1998 [239]3 years ago
4 0
We can set up the equation as follows:
3c = 2.16, and dividing by 3 on both sides, we get:
c = 0.72.
Each lollipop cost 72 cents.
---
Hope this helps!
==jding713==
natulia [17]3 years ago
4 0
2.16/3 = .72

Each lollipop was .72 cents
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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
4 years ago
Helpppppppppppppppppppppppppppppppppppp
Vadim26 [7]

Answer:

m = - 1

Step-by-step explanation:

9m + 13 = 4

subtract 13 from both sides

9m = 4 - 13

9m = - 9

divide both sides by 9

m = - 1  (negative 1)

5 0
3 years ago
Amanda has a car loan for 12,000 She is paying 3% interest for 6 years. How much will she pay in interest for the 6 years
NNADVOKAT [17]
She should get
12000 \times 3\% \times 6
... I hope it's right ?:)
5 0
4 years ago
Dr. Potter provides vaccinations against polio and measles. Each polio vaccination consists of 444 doses, and each measles vacci
nataly862011 [7]

Answer:

37 polio vaccinations and 23 measles vaccination.

Step-by-step explanation:

Let the number of polio vaccination given=x

Let the number of measles vaccination given=y

Dr. Potter gave a total of 60 vaccinations

x+y=60

Since each polio vaccination consists of 4 doses, and each measles vaccination consists of 2 doses. A total of 184 doses was given out.

4x+2y=184

To find the values of x and y, we solve the two equations simultaneously.

x+y=60             (1)

4x+2y=184        (2)

From (1), x=60-y

Substitute x=60-y into equation 2.

4x+2y=184

4(60-y)+2y=184

240-4y+2y=184

240-184=4y-2y

56=2y

Divode both sides by 2

y=23

Recall earlier that x=60-y

x=60-23=37

Dr Potter gave 37 polio vaccinations and 23 measles vaccination.

6 0
3 years ago
What is the sum of an 8-term geometric series if the first term is -11, the last term is 859,375, and the common ratio is -5?
NikAS [45]
Formula of the sum of the 1st nth term in a Geometric Progression:


Sum = a₁(1-rⁿ)/(1-r), where a₁ = 1st term, r = common ratio and n= rank nth of term (r≠1)

Sum = (-11)[1-(-5⁸)] /[(1-(-5)]

Sum = (-11)(1- 390625)/(6)


SUM = 716,144
3 0
3 years ago
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