The foci and the vertices of the hyperbola are labeled.

Which equation represents the hyperbola?

(x + 2)2

64

(y + 4)? -

36

-22-20-18-16-14-12 10 -

2

4

6

8

10 12 14 16

18

x

(-12-4)

(-10-4)

1 (6-4)

(8,-4).

© (x+2? . (+ 4) = 1

. (x - 2) - (y )? = 1

(x+2. (V-42=1

An automated water dispenser fills packets with one liter of water on average, with a standard deviation of 5 milliliter. the manual says that after a year of operation the dispenser should be tested to see if it needs recalibration. a year later a number of filled packets are set aside and measured separately. it is found that the average packet now contains about 0.995 liters. does the dispenser need calibration? explain your answer.

The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips. (a) what is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips, inclusive? (b) what is the probability that a randomly selected bag contains fewer than 1125 chocolate chips? (c) what proportion of bags contains more than 1225 chocolate chips? (d) what is the percentile rank of a bag that contains 1425 chocolate chips?

What are the equivalent ratios for 24/2= /3= /5.5=108/ = /15