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3 years ago

Tiff's Treats two-thirds of a glass of juice which fraction is equivalent to 2/3

1 answer:

4 0

2/3 is equal to 4/6 because if you have the numerater and denominator both multiply 2 it would be equal.
2×2 4
____ = ____
3×2 6

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Need ASAP please help me

aniked [119]

Multiply both sides:

(2x + 2)(x + 3)

= 2x^2 + 6x + 2x + 6

= 2x^2 + 8x + 6

<h2>Answer: (1) 2x^2 + 8x + 6</h2>

4 0

3 years ago

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

3 years ago

Look at the pattern below.

valentinak56 [21]

You could do 33, 36, 39, 42

5 0

3 years ago

Negative 48 plus 31 -3-5-7-4

nexus9112 [7]

The answer to your question is -36

3 0

3 years ago

Read 2 more answers

Simplify (-5i)+(5-1)+6

Liono4ka [1.6K]

Hi there

-5i + 5-1 + 6

= -5i + 11- 1

= 5i + 10

That's the answer :0

I hope that's help... Do you have any question ?

5 0

3 years ago