Using proportions, it is found that the estimate of the the per capita consumption from 2011 was of 29.25 gallons.
<h3>What is a proportion?</h3>
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The amount in 2012 was a increase of 5.3% from 2011, that is, 105.3% = 1.053 of x, and the consumption per capita was of 30.8 gallons, hence:
1.053x = 30.8
x = 30.8/1.053
x = 29.25 gallons.
More can be learned about proportions at brainly.com/question/24372153
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Let's convert the problem into Arithmetic progression:
It would be: 5, 9, 13, ....
Here, a = 5, d = 9 - 5 = 4
We know, S(n) = n/2 [ 2a + (n-1)d ]
Substitute the known values,
434 = n/2 [ 2(5) + (n - 1)4 ]
434 * 2 = n [ 10 + 4n - 4 ]
868 = 10n + 4n² - 4n
= 4n² + 6n - 868 = 0
d = b² - 4ac
d = 6² - 4(4)(-868)
d = 36+13888
d = 13924
Now, roots = -b +- √d / 2a
= (-6 + √13924) / 2(4) OR (-6 - √13924) / 2(4)
= (-6 + 118) / 8 OR (-6 - 118) / 8
= 112/8 OR -124/8
= 14 OR -15.5
As number of sticks can't be in negative/decimal or fraction form, -15.5 would be fully rejected.
In short, Your Answer would be 14 [ Remaining root ]
Hope this helps!
Answer: p=8,−1
Step-by-step explanation:
p^2-7p--8=0
(p-8)(p+1)=0
p=8,−1
Either 175.25 ( 175.2 + 0.1/2) or 175.15 ( 175.2 - 0.1/2) ----------> Range. 175.15 < weight < 175.25
Answer: the number of boats that are in the marina is 105.
Step-by-step explanation:
Let x represent the number of boats that are in the marina.
Two-thirds of the boats in the marina are white. It means that the number of white boats in the marina is
2/3 × x = 2x/3
The remaining number of boats will be
x - 2x/3 = x/3
4/7 of the remaining boats are blue. It means that the number of boats that are blue is
4/7 × x/3 = 4x/21
The number of boats left would be
x/3 - 4x/21 = 3x/21
If there are 15 red boats, it means that
3x/21 = 15
3x = 21 × 15 = 315
x = 315/3
x = 105
