(Geometry Question) A sledding run is 300 yards long with a vertical drop of 27.6 yards. Find the angle of depression of the run
1 answer:
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Answer:
Option C and E are correct.
The sequences which are arithmetic:
18, 5.5, -7, -19.5, -32,....
16, 32, 48, 64, 80
Step-by-step explanation:
Arithmetic sequence states that a sequence in which a common difference between each consecutive term is constant.
Common difference(d) = for every natural number n.
Option A:
-5, 5, -5, 5, -5, .....
5-(-5) = 5+5 = 10 ,
-5 -5 = -10 .....
Since, the common difference for the given sequence is not constant.
Option B:
96, 48, 24, 12, 6
48 -96 = -48
24-48 = -24 ....
Common difference for the given sequence is not constant.
Option C:
18, 5.5, -7, -19.5, -32,....
5.5-18 = -12.5
-7 -5.5 = -12.5 ....
∴Common difference for the sequence is constant.
Option D:
-1, -3, -9, -27, -81 ,....
-3 -(-1) = -3+1 = -2
-9-(-3) = -9+3 = -6 ....
∴Common difference for the sequence is not constant.
Option E:
16, 32, 48, 64, 80
32-16 = 16
48 - 32 = 16 and so on...
∴Common difference for the sequence is constant.
Therefore, the sequences which are arithmetic are:
18, 5.5, -7, -19.5, -32,....
16, 32, 48, 64, 80
Answer:
0.3085 = 30.85% probability that the mean years of experience from the sample of 4 is greater than 3.5 years.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation
Distribution of years of experience:
Mean 3, so
Standard deviation 2, so
Sample of 4:
What is the probability that the mean years of experience from the sample of 4 is greater than 3.5?
1 subtracted by the pvalue of Z when X = 3.5. So
By the Central Limit Theorem
has a pvalue of 0.6915
1 - 0.6915 = 0.3085
0.3085 = 30.85% probability that the mean years of experience from the sample of 4 is greater than 3.5 years.