The probability that the first random choice will be a matho-file and not a -phobe is 18/23. The probability of the second one is 17/22, and for the third one it's 16/21. The probability of all 3 is 4,896/10,626 = (18x17x16)/(23x22x21). That's 46.1% (rounded).
Answer:
third option
Step-by-step explanation:
Given
x² + 4x - 4 = 0 ( add 4 to both sides )
x² + 4x = 4
Using the method of completing the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(2)x + 4 = 4 + 4, that is
(x + 2)² = 8 ( take the square root of both sides )
x + 2 = ± 
= ± 2
( subtract 2 from both sides )
x = - 2 ± 2
Answer: Choice A) 1990 to 1991
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Explanation:
Let's go through the answer choices one by one.
For choice A, we go from the year 1990 to 1991 which is a change of 1 year. The wage goes from 3.80 to 4.25 over this timespan, which is an increase of 4.25-3.80 = 0.45 dollars. Divide the change in wage (0.45 dollars) over the change in change in time (1 year) to get 0.45/1 = 0.45; this indicates that the wage increased by 0.45 dollars per year over the timespan 1990 to 1991
Now onto choice B. We have a wage increase of 3.80-3.35 = 0.45 over a course of 9 years (since 1990-1981 = 9) so 0.45/9 = 0.05 is the rate of wage growth, meaning that the wage bumps up by a nickel each year. So far choice A is the winner.
Moving onto choice C, we have a wage increase of 0.25 dollars (3.35-3.10 = 0.25) over an 1 year period (1981-1980 = 1) so the rate of change for this slice of time is 0.25/1 = 0.25 dollars per year. Choice A is still the winner.
Finally, for choice D, this is over a year as well (1980-1979 = 1) and the wage increases by 0.20 dollars (3.10-2.90 = 0.20) leading to a rate of change to be 0.20/1 = 0.20
So choice A has the largest rate of change which is the same as saying it has the largest rate of wage increase. This shows why choice A is the answer.
Answer:
If w represented the number of weeks he does his chores, the equations would be:
Miles: 120+10w
Simon:75+15w
