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natka813 [3]
3 years ago
7

Find the rate in the following problem. What percent of 371 is 120?

Mathematics
1 answer:
statuscvo [17]3 years ago
4 0
To get the solution, we are looking for, we need to point out what we know.

1. We assume, that the number 120 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 100% equals 120, so we can write it down as 100%=120.
4. We know, that x% equals 371 of the output value, so we can write it down as x%=371.
5. Now we have two simple equations:
1) 100%=120
2) x%=371
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
100%/x%=120/371
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 371 is what percent of 120

100%/x%=120/371
(100/x)*x=(120/371)*x - we multiply both sides of the equation by x
100=0.323450134771*x - we divide both sides of the equation by (0.323450134771) to get x
100/0.323450134771=x
309.166666667=x
x=309.166666667

now we have:
371 is 309.166666667% of 120
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A bacteria culture starts with 12,000 bacteria and the number doubles every 50 minutes.
Vlada [557]

Answer:

a)  y=12000(2)^{\frac{t}{50}}

b)  Approx. 27,569 bacteria

c)  About 103 minutes

Step-by-step explanation:

a)

This will follow exponential modelling with form of equation shown below:

y=Ab^{\frac{t}{n}}

Where

A is the initial amount (here, 12000)

b is the growth factor (double, so growth factor is "2")

n is the number of minutes in which it doubles, so n = 50

Substituting, we get our formula:

y=Ab^{\frac{t}{n}}\\y=12000(2)^{\frac{t}{50}}

b)

To get number of bacteria after 1 hour, we have to plug in the time into "t" of the formula we wrote earlier.

Remember, t is in minutes, so

1 hour = 60 minutes

t = 60

Substituting, we get:

y=12000(2)^{\frac{t}{50}}\\y=12000(2)^{\frac{60}{50}}\\y=12000(2)^{\frac{6}{5}}\\y=27,568.76

The number of bacteria after 1 hour would approximate be <u>27,569 bacteria</u>

<u></u>

c)

To get TIME to go to 50,000 bacteria, we will substitute 50,000 into "y" of the equation and solve the equation using natural logarithms to get t. Shown below:

y=12000(2)^{\frac{t}{50}}\\50,000=12,000(2)^{\frac{t}{50}}\\4.17=2^{\frac{t}{50}}\\Ln(4.17)=Ln(2^{\frac{t}{50}})\\Ln(4.17)=\frac{t}{50}*Ln(2)\\\frac{t}{50}=\frac{Ln(4.17)}{Ln(2)}\\\frac{t}{50}=2.06\\t=103

After about 103 minutes, there will be 50,000 bacteria

4 0
3 years ago
What is the ratio of 120%
Helga [31]

Answer:

5: 6

Step-by-step explanation:

becuase it was basically 100:120 but divide it by 20 and thats  how you get 5;6

7 0
3 years ago
By using the table in the handbook, the present value of $12,000 for six years compounded at 6 percent semiannually is
denis23 [38]
Take a look at the attachment to see the solution.
A = future value
P = principal (P = 12,000)
r = interest rate (r=6)
n = time periods (n=12)

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3 years ago
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mina [271]
314 feet of fencing
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Jaiden's pen pal from Mexico said that he lives 3.3 kilometers from school. Jaiden knows
marissa [1.9K]

Answer:

2 miles

Step-by-step explanation:

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To get your approximate answer, multiply 3.3 (kilometers) by 0.62 (miles).

You get 2.046 if you multiply it by 0.62 like the question says to do.

3 0
3 years ago
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