To get from the post office to the library, Sindy walked due north and then due east. The distance Sindy walked east is 20 meter
s more than the distance she walked north. If Sindy were able to walk directly from the post office to the library in a straight line, she would have walked 150 meters. Suppose x represents the distance Sindy walked north. Which equation can be used to find x?
x^2 (x 20)^2=150^2
202=x^2-150^2
x (x 20)=150
x^2 (x 150)^2=20^2
x^2 (x 20)^2=150^2
202=x^2-150^2
x (x 20)=150
x^2 (x 150)^2=20^2
2 answers:
Answer:
x² + (x + 20)² = 150²
Step-by-step explanation:
Sindy walked x meters in north and then x+20 meters toward east. If Sindy were able to walk directly from the post office to the library directly in a straight line, the distance she would have walked 150 meters.
Thus Sindy forms a right angle triangle as in the figure attached.
From Pythagoras theorem
x² + (x + 20)² = 150²
This is the equation we can use to find x.
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Answer:
And if we solve for a we got
So the value of height that separates the bottom 16% of data from the top 84% is 2.6024 years
The answer rounded would be 2.6 years approximately
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the shelf life of a population, and for this case we know the distribution for X is given by:
Where and
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.16 of the area on the left and 0.84 of the area on the right it's z=-0.994. On this case P(Z<-0.994)=0.16 and P(z>-0.994)=0.84
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 16% of data from the top 84% is 2.6024 years
The answer rounded would be 2.6 years approximately