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2 years ago

Divide using a common factor of 3 to find an equivalent fraction for

Mathematics

2 answers:

Maurinko [17]2 years ago

6 0

Three sixths cause your have to torment

kupik [55]2 years ago

4 0

Answer:

3/4 is equivalent to 9/12,

Step-by-step explanation:

So we know that 3/4 is equivalent to 9/12, because 3×12=36 and 4×9=36. A simple way to look at how to check for equivalent fractions is to do what is called “cross-multiply”, which means multiple the numerator of one fraction by the denominator of the other fraction.

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During optimal conditions, the rate of change of the population of a certain organism is proportional to the population at time

Lana71 [14]

Answer:

The population is of 500 after 10.22 hours.

Step-by-step explanation:

The rate of change of the population of a certain organism is proportional to the population at time t, in hours.

This means that the population can be modeled by the following differential equation:

$\frac{dP}{dt} = Pr$

In which r is the growth rate.

Solving by separation of variables, then integrating both sides, we have that:

$\frac{dP}{P} = r dt$

$\int \frac{dP}{P} = \int r dt$

$\ln{P} = rt + K$

Applying the exponential to both sides:

$P(t) = Ke^{rt}$

In which K is the initial population.

At time t = 0 hours, the population is 300.

This means that K = 300. So

$P(t) = 300e^{rt}$

At time t = 24 hours, the population is 1000.

This means that P(24) = 1000. We use this to find the growth rate. So

$P(t) = 300e^{rt}$

$1000 = 300e^{24r}$

$e^{24r} = \frac{1000}{300}$

$e^{24r} = \frac{10}{3}$

$\ln{e^{24r}} = \ln{\frac{10}{3}}$

$24r = \ln{\frac{10}{3}}$

$r = \frac{\ln{\frac{10}{3}}}{24}$

$r = 0.05$

$P(t) = 300e^{0.05t}$

At what time t is the population 500?

This is t for which P(t) = 500. So

$P(t) = 300e^{0.05t}$

$500 = 300e^{0.05t}$

$e^{0.05t} = \frac{500}{300}$

$e^{0.05t} = \frac{5}{3}$

$\ln{e^{0.05t}} = \ln{\frac{5}{3}}$

$0.05t = \ln{\frac{5}{3}}$

$t = \frac{\ln{\frac{5}{3}}}{0.05}$

$t = 10.22$

The population is of 500 after 10.22 hours.

7 0

2 years ago

Identify the y-intercept for the line 4x – 2y = 4

stellarik [79]

Answer: (0,-2)

Step-by-step explanation: uhdehdwhehehhH

6 0

2 years ago

I WILL GIVE BRAINLIEST

vazorg [7]

Graph a... you go down on the y axis 3, and then using the rise over run method, you go up 3, over 4

3 0

2 years ago

Read 2 more answers

The bases of the trapezoid are 6 and 10. The height is 4. Find the area.

ollegr [7]

Answer

b. 32 sq. unit

Step-by-step Explanation

The area of the trapezoid is given by

$A = \frac{1}{2} (b_{1} + b_{2}) \times h$

We substitute the given values into the formula to obtain;

$A = \frac{1}{2}(10 + 6) \times 4$

Simplify

$A = \frac{1}{2} (16) \times 4$

$A = 16 \times 2$
Hence the area is

$A = 36 \: sq \: units$

6 0

3 years ago

What's 2|-9| - |-2|?

UNO [17]

Answer:

Step-by-step explanation:

First, simplify by finding the absolute values:

2|-9| - |-2|

2(9) - (2)

Then, simplify this by multiplying 2 and 9:

18 - 2

= 16

So, the answer is 16

3 0

2 years ago