What is the LCM of 30 and 35?
1 answer:
Answer: 210
Explanation: To find the least common multiple for the integers 30 and 35, we start by making a factor tree for each of our integers.
So 30 is 10 · 3 and 10 is 5 · 2.
35 is 7 · 5.
Notice that our 5's match up as factors of each of our integers.
When finding the least common multiple, we simply multiply all of our factors together but since the 5's match up,
we only multiply by a 5 once.
So our least common multiple or LCM is
5 · the 2 that doesn't match up · the 3 that
doesn't match up · the 7 that doesn't match up.
So we have 5 · 2 · 3 · 7 or 210.
Work is shown below.
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Answer:
The numerical limits for a B grade are 81 and 89, that is, a score between 81 and 89 gets a B grade.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Scores on the test are normally distributed with a mean of 79.7 and a standard deviation of 8.4.
This means that
B: Scores below the top 13% and above the bottom 56%
So between the 56th percentile and the 100 - 13 = 87th percentile.
56th percentile:
X when Z has a p-value of 0.56, so X when Z = 0.15. Then
87th percentile:
X when Z has a p-value of 0.87, so X when Z = 1.13.
The numerical limits for a B grade are 81 and 89, that is, a score between 81 and 89 gets a B grade.
