Answer:
Population after 16 year = 927 people (Approx.)
Step-by-step explanation:
Given:
Decrease rate = 10% per year
Current population = 5,000
Find:
Population after 16 year
Computation:
A = P[1-r]ⁿ
A = 5,000[1-0.1]¹⁶
A = 5,000[0.9]¹⁶
A = 5,000[0.1853]
A = 926.51
Population after 16 year = 927 people (Approx.)
Answer:
when x>2 (x= 3)
f(x) = -(x-2)² +1
when x = 3
f(3) = -(3-2)²+1
f(3) = -(-1)²+1
f(3) = -1+1
f(3) = 0
taking lesser value of x
makes f(x) increase
and when x>1
(x=2)
Now let's take x = 2
f(2) = -(2-2)²+1
f(2)= -(0)²+1
f(2)= 0+1 = 1
Therefore the values of x that makes f(x) = -(x-2)²+1 to increase are are (x>2 and x>1)
9514 1404 393
Answer:
- 100 pounds Earl Grey
- 300 pounds Orange Pekoe
Step-by-step explanation:
Let x represent the number of pounds of Earl Gray tea in the mix. Then the total cost of the mix is ...
6x +4(400-x)=4.50(400)
2x +1600 = 1800 . . . . . . . simplify
2x = 200 . . . . . . . . . . . subtract 1600
x = 100 . . . . . . . . . . . divide by 2. Pounds of Earl Grey
(400 -x) = 300 . . . . . Pounds of Orange Pekoe
The blend should have 100 pounds of Earl Grey and 300 pounds of Orange Pekoe.
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<em>Additional comment</em>
It is easy to show that the relationship between the quantities of high-cost (H) and low-cost (L) items in the mix (M) is ...
fraction of mix that is H is (M -L)/(H -L)
Here, we have H=6, L=4, M=4.5, so the fraction of the mix that is Earl Grey is ...
(4.5 -4)/(6 -4) = 0.5/2 = 0.25
There are 400 pounds of mix, so 0.25(400) = 100 pounds is Earl Grey.
The solution above is essentially 2-step, so using this relation doesn't necessarily save any steps. It just makes it possible to solve the problem in your head.
Answer:
5x + 4($1.5) = $12.25
Step-by-step explanation:
Since we know that the paper is $1.50 per package and she bought 4 packages of paper, then she spent a total of $6 on the paper. Which leaves ($12.25-$6) $6.25 that she spent on buying 5 pencils. Now the cost per pencil can be derived by dividing $6.25/5, which is $1.25. Each pencil is $1.25.
The equation that can be used is the following where the cost per pencil is represented by x:
5x + 4($1.5) = $12.25
Answer:
y=-x
Step-by-step explanation:
The easiest one to use would be y=-x because it is parallel to the given line and goes through the stated point.
