A sphere with a radius of 3 cm has the same volume as a cone with a radius of 6 cm. What is the height of the cone?!
2 answers:
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Answer:
2.625 cups or 21 ounces
Step-by-step explanation:
Ava needs 3/4 cup of blue paint for every 1 cup of white paint. So, the ratio is 0.75 : 1.
She has 28 ounces of white paint. But, you have to convert ounces to cups.
1 cup = 8 ounces
28 ounces ÷ 8 ounces/cup = 3.5 cups
Now set up a ratio.
X (how much blue paint is needed) is over 3.5 cups (the amount of white paint she has)
Cross multiply and divide.
x = 0.75 × 3.5
x = 2.625 cups
To convert to ounces, multiply by 8.
2.625 cups × 8 ounces = 21 ounces
Therefore, Ava needs 2.625 cups or 21 ounces of blue paint.
Hope that helps.
Answer:
a) 68.26% probability that a student scores between 350 and 550
b) A score of 638(or higher).
c) The 60th percentile of test scores is 475.3.
d) The middle 30% of the test scores is between 411.5 and 488.5.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
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:
a. What is the probability that a student scores between 350 and 550?
This is the pvalue of Z when X = 550 subtracted by the pvalue of Z when X = 350. So
X = 550
has a pvalue of 0.8413
X = 350
has a pvalue of 0.1587
0.8413 - 0.1587 = 0.6826
68.26% probability that a student scores between 350 and 550
b. If the upper 3% scholarship, what score must a student receive to get a scholarship?
100 - 3 = 97th percentile, which is X when Z has a pvalue of 0.97. So it is X when Z = 1.88
A score of 638(or higher).
c. Find the 60th percentile of the test scores.
X when Z has a pvalue of 0.60. So it is X when Z = 0.253
The 60th percentile of test scores is 475.3.
d. Find the middle 30% of the test scores.
50 - (30/2) = 35th percentile
50 + (30/2) = 65th percentile.
35th percentile:
X when Z has a pvalue of 0.35. So X when Z = -0.385.
65th percentile:
X when Z has a pvalue of 0.35. So X when Z = 0.385.
The middle 30% of the test scores is between 411.5 and 488.5.