, write equivalent ratios that represent the situation and solve. 12. Angela pays $120 for 4 piano lessons. How much does she pa
1 answer:
Answer:
She pays $240 for 8 lessons.
Step-by-step explanation:
We need to set up equivalent ratios so we can cross-multiply and solve for x, the amount Angela pays for 8 lessons. Make sure to have both the costs in the numerator, and the number of lessons in the denominator. If you mix it up, this won't work.
Cross-multiply:
120*8 = 4x
Solve for x:
960 = 4x
960/4 = x
<u>x = $240</u>
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Answer:
a) 20.16; b) 20.49 and 21.51
Step-by-step explanation:
We use z scores for each of these. The formula for a z score is
.
For part a, we want the 20th percentile; this means we want 20% of the data to be lower than this. We find the value in the cells of the z table that are the closest to 0.20 as we can get; this is 0.2005, which corresponds with a z score of -0.84.
Using this, 21 as the mean and 1 as the standard deviation,
-0.84 = (X-21)/1
-0.84 = X-21
Add 21 to each side:
-0.84+21 = X-21+21
20.16 = X
For part b, we want the middle 39%. This means we want 39/2 = 19.5% above the mean and 19.5% below the mean; this means we want
50-19.5 = 30.5% = 0.305 and
50+19.5 = 69.5% = 0.695.
Looking these values up in the cells of the z table, we find those exact values; 0.305 corresponds with z = -0.51 and 0.695 corresponds with z = 0.51:
-0.51 = (X-21)/1
-0.51 = X-21
Add 21 to each side:
-0.51+21 = X-21+21
20.49 = X
0.51 = (X-21)/1
0.51 = X-21
Add 21 to each side:
0.51+21 = X-21+21
21.51 = X