Answer:
p² -16pq + 36q²
Step-by-step explanation:
Given
(- p + 6q)²
= (- p + 6q)(-
p + 6q)
Each term in the second factor is multiplied by each term in the first factor, that is
- p(-
p + 6q) + 6q(-
p + 6q)
= p² - 8pq - 8pq + 36q² ← collect like terms
= p² - 16pq + 36q²
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
your question is incomplete, here you can find the complete question below:
An angles vertex is located at (0,0) and the initial ray of the angle points in the 3 oclock direction. Let theta represent the varying radian measure of the angle.
a. if the terminal ray of the angle passes through the point(3.38,2.32), whta is the slope of the terminal ray of the angle?
b. if the terminal ray of the angle passes through the point(1.49,3.82), whta is the slope of the terminal ray of the angle?
c. if the terminal ray of the angle passes through the point(1.1,3.95), what is the slope of the terminal ray of the angle?
Answer:
a. 1.45
b. 2.56
c. 3.59
Step-by-step explanation:
As we know that formula to find the slope is change in y-coordinates divided by change in x-coordinates.
It is given that initial point is (x1,y1)=(0,0)
Part(a)
initial point is (x1,y1)=(0,0)
terminal point is (x2,y2)=(3.38,2.32)
so the slope of the terminal ray is
Part(b)
initial point is (x1,y1)=(0,0)
terminal point is (x2,y2)=(1.49,3.82)
so the slope of the terminal ray is
Part(c)
initial point is (x1,y1)=(0,0)
terminal point is (x2,y2)=(1.1,3.95)
so the slope of the terminal ray is