Answer:
a)
b) 
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".
Part a
Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:
Where
and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability like this:
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
Part b
For this case we select a sample size of n =32. Since the distribution for X is normal then the distribution for the sample mean
is given by:
And the new z score would be:



Answer: (A) The image of JKL after a 90° counterclockwise about the origin is shown in figure 1. (B) The image of JKL after a reflection across the y-axis is shown in figure 2.
Explanation:
(A)
From the given figure it is noticed that the coordinate points are J(-4,1), K(-4,-2) and L(-3,-1).
If a shape rotate 90 degree counterclockwise about the origin, then,




Therefore, the vertex of imare are J'(-1,-4), K'(2,-4) and L'(1,-3). The graph is shown in figure (1).
(B)
If a figure reflect across the y-axis then,




Therefore, the vertex of imare are J''(4,1), K''(2,-4) and L''(3,-1). The graph is shown in figure (2).
Answer: The inverse is f^-1 (x) = x - 11
Answer:
113.04
Step-by-step explanation:
Answer:
A) 3/4
Step-by-step explanation:
Given: Both circle A and circle B have a central angle measuring 50°.
The area of circle A's sector is 36π cm2.
The area of circle B's sector is 64π cm2.
We know, area of the circle= 
lets assume the radius of circle A be "
" and radius of circle B be "
"
As given, Area of circle A and B´s sector is 36π and 64π repectively.
Now, writing ratio of area of circle A and B, to find the ratio of radius.
⇒
Cancelling out the common factor
⇒ 
⇒ 
Taking square on both side.
Remember; √a²= a
⇒ 
⇒ 
⇒
Hence, ratio of the radius of circle A to the radius of circle B is 3:4 or 3/4.