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svetoff [14.1K]
3 years ago
12

The numerator of a fraction is 15 less than twice its denominator. If the numerator is increased by 5 and the denominator is inc

reased by 7, the new fraction will be equal to 2/3. What is the original fraction?
Mathematics
1 answer:
denis-greek [22]3 years ago
7 0

Answer:

  7/11

Step-by-step explanation:

Let d represent the original denominator. Then the original numerator is ...

  2d-15

The new numerator is ...

  (2d-15) +5

and the new denominator is ...

  d+7

The ratio of these is 2/3, so we have ...

  \dfrac{2d-15+5}{d+7}=\dfrac{2}{3}\\\\3(2d-10)=2(d+7) \quad\text{cross multiply}\\\\4d=44 \quad\text{add 30-2d}\\\\d=11\\\\2d-15=2(11)-15=7

The original fraction is 7/11.

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When Isaac commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 44 minutes and a s
mario62 [17]

Answer:

[34,54]

Step-by-step explanation:

-The empirical rule states that the 95% of the sampled observations will fall within two standard deviations of the mean for a normally distributed population.

Where:

  • 68% is the first standard deviation
  • 95% is the second standard deviation about the mean
  • 99.7% is the 3rd standard deviation about the mean.

-Therefore. the middle 95% interval is calculated as:

CI=\mu+2\sigma\\\\=44\pm 2(5)\\\\=44\pm 10\\\\=[34,54]

Hence, the interval is [34,54]

5 0
3 years ago
Solve surface area please! Quick it’s due soon
just olya [345]

Answer:

SA = 470 m²

volume = 494 m³

Step-by-step explanation:

<u>Individual areas</u>

Back = 4 x 19 = 76 m²

Top = 5 x 19 = 95 m²

sloped side = 5 x 19 = 95 m²

base = 8 x 19 = 152 m²

end = (4 x 5) + 1/2(3 x 4) = 26 m²

Total SA = 76 + 95 + 95 + 152 + (2 x 26) = 470 m²

<u>Volume</u>

volume = (4 x 5 x 19) + 1/2(3 x 4 x 19) = 494 m³

5 0
2 years ago
55 mi / h = ____ ft / s <br> a. 8.7 <br> c. 80.7 <br> b. 26.9 <br> d. 806.7
Tcecarenko [31]
The answer is c. If the answer is wrong i am sorry
4 0
3 years ago
Question 18<br> Decrease £4600 by 20%
NISA [10]

Answer:

3680

Step-by-step explanation:

So, we would subtract. But, first we have to find the percent. But, we all use calculators so, it is 920. Saves us a lot of time.

4600 - 920 = 3680

Therefore your answer is 3680

Hope this helps!

4 0
3 years ago
Finish the sequence<br> 1,1,2,3,5,8,_,_,_
Papessa [141]
This is a Fibonacci sequence
1; 1
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8
next terms:
5 + 8= 13
8 +13 = 21
13 + 21 = 34


3 0
3 years ago
Read 2 more answers
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