The probability that Aaron will win the drawing is 0.083. What is the probability that he will not win?
2 answers:
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The opposite of the number 0 that is -0 on the number line will be equal to 0 itself.
A number line may be defined as a scale consisting of numbers labelled from 0 to 9 which are used to plot or mark different points for various entities. Number line extends from 0 to 9 in the positive side that is usually taken as right-hand side and it extends from 0 to -9 in the negative side that is usually taken as the left-hand side. The numbers on the right-hand side of number line have their opposites on the left-hand side. The opposite of a number x is taken as -x. For example, the opposite of 4 is taken as -4 and 4 lies on right-hand side whereas -4 lies on left-hand side. 0 lies on the center of number line and is taken as the main point. It is neither positive nor negative so the opposite of 0 is 0. The figure of number line is attached.
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Answer:
- $20,000 at 8.5%
- $10,000 at 10%
Step-by-step explanation:
There are a number of ways to solve mixture problems like this. Some are simple enough you can almost write down the answer. One I like uses a diagram to help you find the ratios of the components of the mix. You can do the same thing with a formula (without the diagram).
The basic idea is that you compute a ratio between two differences. The numerator is the difference between the average interest rate and the lower interest rate. Here, the average interest rate is 2700/30,000 = 0.09 = 9%. Then the numerator is 9% -8.5% = 0.5%
The denominator is the difference between the two interest rates of the investments: 10% -8.5% = 1.5%. And the ratio of these two values is ...
0.5%/1.5% = 1/3
This is the fraction of the total investment that was invested at the higher interest rate:
(1/3)×$30,000 = $10,000 . . . . was invested at 10%
Then the remaining amount, $20,000, was invested at 8.5%.
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If you would prefer an equation, you can let x represent the amount invested at the higher rate. (That is the most convenient assignment of variables, as it keeps all of the numbers positive.) Then (30,000 -x) is the amount invested at the lower rate. The total amount of interest is ...
10%(x) +8.5%(30,000 -x) = 2700
x(10% -8.5%) = 2700 -8.5%(30000) . . . . . subtract 8.5%(30,000)
x = (2700 -8.5%(30,000))/(10% -8.5%) . . . . divide by the coefficient of x
We have purposely left the expression unevaluated so that you can compare it to the math we described above. If you factor out 30,000 from the numerator of this fraction, you see the ratio that we described in words:
This tells us $10,000 was invested at 10%, and $20,000 was invested at 8.5%.
Answer:
Option C
Step-by-step explanation:
See attached the graphical solution
