Answer: 
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Reason:
Plot the points (0,0) and (r,s). You can place (r,s) anywhere you want.
Connect the two points mentioned and form a right triangle such that the segment from (0,0) to (r,s) is the hypotenuse of said right triangle.
The horizontal leg has a length of r-0 = r units, while the vertical leg will be 's' units.
Check out the diagram below.
We then apply the pythagorean theorem to say 
where h is the hypotenuse. Solving for h gets us 
. We only focus on the positive square root since a negative hypotenuse makes no sense.
Since we made the hypotenuse the segment with endpoints (r,s) and (0,0), this means the hypotenuse length and the distance are the same thing.
Therefore, the distance from (r,s) to (0,0) is 
As an alternative, you can use the distance formula to get the same answer. The distance formula is effectively the pythagorean theorem phrased a different way.
Answer:
(15,595, 16,805)
Step-by-step explanation:
We have to:
m = 16.2, sd = 3.75, n = 150
m is the mean, sd is the standard deviation and n is the sample size.
the degree of freedom would be:
n - 1 = 150 - 1 = 149
df = 149
at 95% confidence level the t is:
alpha = 1 - 95% = 1 - 0.95 = 0.05
alpha / 2 = 0.05 / 2 = 0.025
now well for t alpha / 2 (0.025) and df (149) = t = 1,976
the margin of error = E = t * sd / (n ^ (1/2))
replacing:
E = 1,976 * 3.75 / (150 ^ (1/2))
E = 0.605
The 95% confidence interval estimate of the popilation mean is:
m - E <u <m + E
16.2 - 0.605 <u <16.2 + 0.605
15,595 <u <16,805
(15,595, 16,805)
Answer:
0.4
Step-by-step explanation:
Given:-
- The uniform distribution parameters are as follows:
a = $10,000 b = $15,000
Find:-
Suppose you bid $12,000. What is the probability that your bid will be accepted?
Solution:-
- We will denote a random variable X that defines the bid placed being accepted. The variable X follows a uniform distribution with parameters [a,b].
X ~ U(10,000 , 15,000)
- The probability of $12,000 bid being accepted can be determined by the cdf function of the uniform distribution, while the pmf is as follows:
Pmf = 1 / ( b - a )
Pmf = 1 / ( 15,000 - 10,000 )
Pmf = 1 / ( 5,000 )
Multiply the two numbers
206x20=4120
Points:
Quadrant I: (+, +)
Quadrant II: (-, +)
Quadrant III: (-, -)
Quadrant IV: (+, -)
Thus the point (5,4) is found in Quadrant I.
