G if v lies in the first quadrant and makes an angle π/3 with the positive x-axis and |v| = 8, find v in component form.
1 answer:
First, illustrate the problem into a diagram like the one shown in the attached picture. The component vectors are shown in red (y-component) and blue (x-component). Since this is a right triangle, let's apply the trigonometric functions of sine and cos.
y-component, vy:
sin (π/3) = vy/8
vy = 6.928
x-component, vx:
cos (π/3) = vx/8
vx = 4
y-component, vy:
sin (π/3) = vy/8
vy = 6.928
x-component, vx:
cos (π/3) = vx/8
vx = 4
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Answer:
At least 8.96 hours of sleep to be in the top 1%.
Step-by-step explanation:
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.
In this question, we have that:
How many hours of sleep to be on the top 1%?
The top 1% is the 100 - 1 = 99th percentile, which is X when Z has a pvalue of 0.99. So X when Z = 2.327. Then
At least 8.96 hours of sleep to be in the top 1%.