When ever you have percentages, it should be helpful to bear in mind you can express them as multipliers. In this case, it will be helpful.
So, if we let:
a = test score
b = target score
then, using the information given:
a = 1.1b + 1
a = 1.15b - 3
and we get simultaneous equations.
'1.1' and '1.15' are the multipliers that I got using the percentages. Multiplying a value by 1.1 is the equivalent of increasing the value by 10%. If you multiplied it by 0.1 (which is the same as dividing by 10), you would get just 10% of the value.
Back to the simultaneous equations, we can just solve them now:
There are a number of ways to do this but I will use my preferred method:
Rearrange to express in terms of b:
a = 1.1b + 1
then b = (a - 1)/1.1
a = 1.15b - 3
then b = (a + 3)/1.15
Since they are both equal to b, they are of the same value so we can set them equal to each other and solve for a:
(a - 1)/1.1 = (a + 3)/1.15
1.15 * (a - 1) = 1.1 * (a + 3)
1.15a - 1.15 = 1.1a + 3.3
0.05a = 4.45
a = 89
Answer:4
Step-by-step explanation:
1 plus 6
9514 1404 393
Answer:
3. x = 10
4. a = 8
Step-by-step explanation:
A reasonably simple rule to remember for secants outside the circle or chords inside the circle: <em>the product of the lengths from the point of intersection of the lines to the points of intersection of the circle is the same for each line</em>.
When the external line is tangent to the circle, the two points of intersection of the line with the circle are the same: the point of tangency. Effectively, this means the length is squared.
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3. For line QP, the product is 3(3+5) = 24.
For line QR, the product is 2(2+x). The rule above says these are equal:
24 = 2(2+x)
12 = 2+x . . . . . divide by 2
10 = x . . . . . . . subtract 2
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4. For line BC, the product is (a)(a) = a^2.
For line GC, the product is 4(12+4) = 64. The rule above says these are equal:
a^2 = 64
a = √64 . . . . take the square root
a = 8
FV value of the amount using future value annuity will be:
FV=P[(1+r)^n-1]/r
FV=2460[(1+0.01175)^18-1]/(0.01175)
FV=48,992.23
The present value of this amount will be:
PV=pe^(-rt)
PV=48992.23e^(-0.0235*9)
PV=39,652.81
