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lyudmila [28]
3 years ago
14

The sum of the numerator and the denominator of the certain fraction is equal to 4,140. When the fraction was reduced, the resul

t was 7 13 . What was the original fraction?
Mathematics
1 answer:
Sunny_sXe [5.5K]3 years ago
3 0

Answer:

1449/2691

Step-by-step explanation:

We must start from the fraction that is 7/13. Now, we know that it was simplified, with trial and error we can reach the result.

First, let's multiply both by 200:

7 * 200 = 1400

13 * 200 = 2600

1400 + 2600 = 4000

It means that we are missing 140, to reach the objective, that is, we are close, let's try 205 now:

7 * 205 = 1435

13 * 205 = 2665

1435 + 2665 = 4100

We get even closer, only 40 missing, let's try 207 below:

7 * 205 = 1449

13 * 205 = 2691

1449 + 2691 = 4140

We managed to get to the corresponding numbers, therefore the original fraction was 1449/2691

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Your friend tells you that if you let him keep 50 of your Pokemon cards for a month, he will give you 1 card extra when he retur
oksano4ka [1.4K]

Answer:

the answer depends on which type of interest we use:

  • simple interest rate = 24%
  • compound interest rate = 26.82%

Step-by-step explanation:

the interest rate paid for holding the cards one month 1/50 or 2%.

to convert 2% monthly interest rate to a simple annual rate:

monthly rate x 12 months = 2% x 12 = 24%

now to convert 2% monthly interest rate to an annual rate (using compound interest):

  • = (1 + r)ⁿ - 1
  • = (1 + 0.02)¹² - 1 = 1.2682 - 1 = 0.2682 or 26.82%

in compound interest, earned interest earns even more interest by itself besides the interest earned by the principal.

3 0
3 years ago
The South Coast Air Basin (Los Angeles, Orange, and San Bernardino counties) does not meet the air quality standards for carbon
Archy [21]

Answer:

0.2225 gr/mile

Step-by-step explanation:

Let's work out first the amount of CO sent out in 1990.

The population we estimated in 12.5 million people with a total of driven miles per year of about  

12.5 million*8,700 = 108,750 million miles.

With an CO emission factor of 0.9 g per mile, we would have a total of CO emitted rounding 0.9*180,750 = 97,875 million grams

Now, we must estimate the population for 2020.

Since we are assuming an exponential growth, the population in year t is given by a function

\bf P(t)= Ce^{kt}

where C and k are constants to be determined.

We can take 1980 as year 0. This way calculations are lighter. 1990 is year 10 and 2020 is year 20.

So P(0) = 10.3 and C=10.3

So far we have

\bf P(t)= 10.3e^{kt}

Given that P(10)=12.5

\bf 10.3e^{k*10}=12.5\rightarrow e^{10k}=\frac{12.5}{10.3}=1.21359\rightarrow \\10k=log(1.21359)\rightarrow k=0.01936

And the function that models the population growth is

\bf P(t)= 10.3e^{0.01936t}

We need P(20)

\bf P(20)= 10.3e^{0.01936*20}=10.3e^{0.38717}=15.17\;million

If the miles driven per person per year remains constant at 8700 mi/yr.person, then we have a total miles driven of

15.17*8,700=131,979 million miles, so the CO emitted would be 0.9*131,979=118,781.1 million grams.

The 30% of the CO sent out in 1990 is 0.3*97,875=29,362.5 million grams.

We must reduce 118,781.1 down to 29,362.5

Hence the new CO emission factor would be

29,362.5/131,979 = 0.2225 gr/mile

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3 years ago
Select the order pair(s) that are solutions to this system of inequalities:
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Use desmos.com and graph those inequalities. It is pretty easy.
6 0
3 years ago
Find the value of x.
BigorU [14]

Answer:

x=11 degrees

Step-by-step explanation:

45+4x+1=90

46+4x=90

4x=44

x=11

4 0
3 years ago
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4, 10, 4, 10. 10*4 gives area of 40. 10+10+4+4 gives 48 as shown in question
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3 years ago
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