Answer:
Ralph's current age is 18.
Step-by-step explanation:
Let r and s represent the current ages of Ralph and Sara respectively. Our task here is to determine r, Ralph's age now.
If Ralph is 3 times as old as Sara now, then r = 3s.
Six years from now, Ralph's age will be r + 6 and Sara's will be s + 6. Ralph will be only twice as old as Sara will be then. This can be represented algebraically as
r + 6 = 2(s + 6).
We now have the following system of linear equations to solve:
r + 6 = 2s + 12, or r - 2s = 6, and r = 3s (found earlier, see above).
r - 2s = 6
r = 3s
Substituting 3s for r in r - 2s = 6, we get 3s = 2s + 6, or s = 6. Sara is 6 years old now, meaning that Ralph is 3(6 years), or 18 years old.
Ralph's current age is 18.
Answer:
16.7 percent decrease.
Step-by-step explanation:
Difference in value = 150,000 - 180,000
= -30,000
As a percent this = (-30,000 / 180,000) * 100
= -0.1667 * 100
= -16.67
So 8x+4+4x+8=15x-9
Combine like terms.
12x+12=15x-9
Add 9 to both sides.
12x+21=15x
Subtract 12 from both sides.
21=3x
Divide both sides by 3.
x=7
Now plug in 7 for x in 8x+4.
8(7)+4
56+4
=60
Answer:
The z-score for a data value of 121 is -2.29.
Step-by-step explanation:
In a set with mean 
and standard deviation 
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
Find the z-score for a data value of 121.
This is Z when X = 121. So
The z-score for a data value of 121 is -2.29.
