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erma4kov [3.2K]

2 years ago

5

From their house to their parents house, the Leightons have to drive 276 miles. if they have already driven 2/3 of the distance,

how far have they gone?

2 answers:

xxMikexx [17]2 years ago

8 0

184 miles is how much they have left.

geniusboy [140]2 years ago

5 0

They have traveled 184 miles

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one serving of cereal is 32 grams ella needs 18 servings of cereal for a soccer team breakfast she wants to buy enough cereal wi

Mumz [18]

You should buy 576 grams of cereal. I believe this is right because 32g x 18=576. But you might want me to work it different or something.

5 0

2 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

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

$1000 = 300e^{24r}$

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

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

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

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

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

$r = 0.05$

So

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

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

Solve each equation.<br> 7) 18 =-2+a<br> 8) -7= m - 12<br> 9) -8(7 + 7n)=-336<br> 10) -140=-7(-4+36)

lesya692 [45]

Answer:

7) a= 20

8) m= 5

9)n = 5

10) b = 8

Step-by-step explanation:

7) 18+2=-2+2+a

>> 20 = a >> a = 20

18 + 2 = 20 so that isolates the variable leaving a = 20

8) -7+12 = m -12+12

>>> 5 = m >> m = 5

-7 + 12 = 5 so that again isolates the variable leaving m = 5

9) <u>-8(7</u> + <u>7n</u>) = -336

>> -56+56 + -56n = -336+56

>>> -56n/-56 = -280/-56

>>>> n = 5

use distributive property, cancel out necessary numbers, isolate the variable. leaving n = 5.

10) -140 = <u>-7(-4 </u>+ <u>3b)</u>

>> -140 = 28 - 21b >> -140-28 = -21b +28-28 ( flipped the numbers)

>>> -168/-21 = -21b /-21

>>>> 8 = b >> b =8

Hope it helps!

5 0

2 years ago

Solve for r.<br> -13 = r/9 +8

love history [14]

R/9 = -21
Multiply by 9
r = -189

4 0

2 years ago

Read 2 more answers

During the summer, the population of spring lake is 30,155. During the winter, the population drops down to 13,876. How many peo

aleksley [76]

30,155-13,876=16,279
16,279 people spend on the summer months in spring lake.

3 0

3 years ago

Read 2 more answers