Let θ be an angle in standard position lying in Quadrant 1. If sin(θ)= 0.227, then find the value of sin(2π−θ). Hint: Use symmet
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Answer:
Option B and C are correct.
are the expression incorrect for slope
Step-by-step explanation:
Slope is defined as the change in the dependent variable relative to the change in the dependent variable
or the ratio of the horizontal changes to vertical changes between any two points on the graph of the line.
The vertical changes between any two points is rise
The horizontal changes between any two points is run.
Formula for slope is given by:
For any two points and
then slope is:
or we can write this as:
Δy =
Δx =
⇒
Therefore, the expression which are incorrect for slope are;
Answer:
And if we solve for a we got
And if we solve for a we got
So then the limits where 50% of the data lies are -47.05 and 50.35
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 variable of interest of a population, and for this case we know the distribution for X is given by:
Where and
For this case we want the limits for the 50% of the values.
So on the tails of the distribution we need the other 50% of the data, and on ach tail we need to have 25% since the distribution is symmetric.
Lower tail
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 0.25 of the area on the left and 0.75 of the area on the right it's z=-0.674. On this case P(Z<-0.674)=0.25 and P(z>-0.674)=0.75
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 25% of data from the top 75% is -47.05.
Upper tail
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 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25
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 75% of data from the top 25% is 50.35.
So then the limits where 50% of the data lies are -47.05 and 50.35
the diagonal of the triangle representa the lenght of the ladder and is 12 foot
as the Sen alpha = CO/H, OF THIS FORMULA , CO IS THE HICK OPPOSITE AND REPRESENT THE HEIGHT
CO = Sen alpha*H = Sin (60°)* 12 = 10,39 FOOT
