What is the least number of transformations performed to create similar rectangle k' from rectangle k?
a. 1; rotation about the origin
b. 2; rotation about the origin, dilation
c. 3; rotation about the origin, translation, dilation
d. 4; reflection across y-axis, dilation, translation, rotation about origin
(not b.)

C.3; rotation about the origin, translation, dilation

Step-by-step explanation:

The first obvious step is to rotate it 270° counterclockwise [90° clockwise], next you translate it, then you dilate [long and wide].

I hope this helps you out alot, and as always, I am joyous to assist anyone at any time.

(a) 0.24

(b) 0.76

Step-by-step explanation:

We are given that let Y be the number of homes with a dust mite level that exceeds 2 mg/g. The probability distribution for Y=y is shown below ;

     y                 P(y)

     0                 0.09

     1                  0.30

     2                 0.37

     3                 0.20

    4                  0.04

(a) Probability that three or four of the homes in the sample have a dust mite level that exceeds 2 µg/g = P(y = 3) + P(y = 4)

                                           = 0.20 + 0.04 = 0.24 .

(b) Probability that fewer than three homes in the sample have a dust mite level that exceeds 2 µg/g = P(y = 0) + P(y = 1) + P(y = 2)

                                           = 0.09 + 0.30 + 0.37 = 0.76 .