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victus00 [196]
3 years ago
13

A 20,000 gallon tank is 3/4full. If the drain valve on this tank allows 2.5 gallons of water to be drained per minute, about how

many hours will it take to drain the tank?
Mathematics
1 answer:
patriot [66]3 years ago
6 0

Answer:

100 Hours

Step-by-step explanation:

since the tank has 15,000 gallons of water. it drains at a rate of 150 gallons per hour so 15,000 divided by 150 equals 100

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. A population of rabbits oscillates 25 above and below an average of 129 during the year, hitting the lowest value in January (
Burka [1]

Answer:

Because we know that here we have an oscillation, we can model this with a sine or cosine function.

P = A*cos(k*t) + M

where:

k is the frequency

A is the amplitude

M is the midline

We know that at t = 0, we have the lowest population.

We know that the mean is 129, so this is the midline.

We know that the population oscillates 25 above and below this midline,

And we know that for t = 0 we have the lowest population, so:

P = A*cos(k*0) + 129 = 129 - 25

P = A + 129 = 129 - 25

A = -25

So, for now, our equation is

P = -25*cos(k*t) + 129

Because this is a yearly period, we should expect to see the same thing for t = 12 (because there are 12 months in one year).

And remember that the period of a cosine function is 2*pi

Then:

k*12 = 2*pi

k = (2*pi)/12 = pi/6

Finally, the equation is:

P = -25*cos(t*pi/6) + 129

Now we want to find the lowest population was in April instead:

if January is t = 0, then:

February is t = 2

March is t = 3

April is t = 4

Then we would have that the minimum is at t = 4

If we want to still use a cosine equation, we need to use a phase p, such that now our equation is:

P = -25*cos(k*t + p) + 129

Such that:

cos(k*4 + p) = 1

Then:

k*4 + p = 0

p =  -k*4

So our equation now is:

P = -25*cos(k*t  - 4*k) + 129

And for the periodicity, after 12 months, in t = 4 + 12 = 16, we should have the same population.

Then, also remembering that the period of the cosine function is 2*pi:

k*12 - 4*k = 2*pi

k*8 = 2*pi

k = 2*pi/8 = pi/4

And remember that we got:

p = -4*k = -4*(pi/4) = -pi

Then the equation for the population in this case is:

P = -25*cos( t*pi/4 - pi) + 129

7 0
2 years ago
Maya dropped her keys down a storm drain. Her hand was 1 meter above the ground when she dropped them. The keys fell 10 meters t
Ganezh [65]
A because 1-10 would be -9 and she was a meter above so positive but they descended 10 meters no negitve
3 0
3 years ago
Read 2 more answers
Sarah bought a lawnmower for $320. She signed up for the buy now pay later plan at the store with the following conditions: $100
marishachu [46]
Cost of the lawnmower bought by Sarah = $320
Amount of down payment made by Sarah = $100
Amount paid by Sarah in 12 months = (12 * 25) dollars
                                                          = 300 dollars
Total amount paid by Sarah = (300 + 100) dollars
                                             = 400 dollars
Excess amount paid as interest by Sarah = (400 - 320) dollars
                                                                   = 80 dollars
Actual yearly rate of interest paid by Sarah = (80/320) * 100 percent
                                                                     = 25 percent
So 25% yearly interest was paid by Sarah. The correct option is option "C".
4 0
3 years ago
Find the 91st term of the arithmetic sequence 28, 8, –12, ...<br><br> Anybody know the answer?
tankabanditka [31]

Answer:

-1772

Step-by-step explanation:

The nth term of an arithmetic sequence is expressed as;

Tn = a+(n-1)d

a is the first term

n is the number of terms

d is the common difference

From the sequence

a = 28

d = 8-28 = -12-8 = -20

n =91(since we are looking for the 91st term)

Substrate

T91 = 28+(91-1)(-20)

T91 = 28+90(-20)

T91 = 28-1800

T91 = -1772

Hence the 91st term is -1772

6 0
3 years ago
The time spent watching a movie. Discrete or Continuous?
jeka94

Answer:

The durations of movies in minutes can only take on integer values from 0 to 60. Therefore, it is a discrete data.

5 0
2 years ago
Read 2 more answers
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