Mary has her own business, a nail salon that she runs out of her home. She is the only nail technician but serves many clients in one day. The following tables provide information about time between arrivals and service time required for a manicure. Assume the only service offered is a manicure.

Time Between Arrivals

Probability

Random Numbers

10 min

.2

00-19

20 min

.3

20-69

30 min

.2

70-89

40 min

.3

90-99

Service Time

Probability

Random Numbers

10 min

.3

00-29

20 min

.4

30-69

30 min

.2

70-89

40 min

.1

90-99

Random Numbers

Customer

1

2

3

4

5

6

7

8

9

Arrivals

12

19

43

23

6

87

92

45

56

Services

12

45

65

78

22

43

58

98

1

The first random number generted for arrivals is used to tell us then the first customer arrives after the shop opens. the second random number generated for service is used to tell us how long the service took.

Answer the following questions using the charts above:

1) What time does the first customer arrive if the shop opens at 8 am?

2) What number customer will be the first to wait?

3) How long does the second customers appointment take?

Which is the graph of f(x) = (4)x? image for option 1 image for option 2 image for option 3 image for option 4

Cor d? ? me ? max recorded the heights of 500 male humans. he found that the heights were normally distributed around a mean of 177 centimeters. which statements about max’s data must be true? a) the median of max’s data is 250 b) more than half of the data points max recorded were 177 centimeters. c) a data point chosen at random is as likely to be above the mean as it is to be below the mean. d) every height within three standard deviations of the mean is equally likely to be chosen if a data point is selected at random.

In δabc shown below, ∠bac is congruent to ∠bca: triangle abc, where angles a and c are congruent given: base ∠bac and ∠acb are congruent. prove: δabc is an isosceles triangle. when completed (fill in the blanks), the following paragraph proves that line segment ab is congruent to line segment bc making δabc an isosceles triangle. (4 points) construct a perpendicular bisector from point b to line segment ac . label the point of intersection between this perpendicular bisector and line segment ac as point d: m∠bda and m∠bdc is 90° by the definition of a perpendicular bisector. ∠bda is congruent to ∠bdc by the definition of congruent angles. line segment ad is congruent to line segment dc by by the definition of a perpendicular bisector. δbad is congruent to δbcd by the line segment ab is congruent to line segment bc because consequently, δabc is isosceles by definition of an isosceles triangle. 1. corresponding parts of congruent triangles are congruent (cpctc) 2. the definition of a perpendicular bisector 1. the definition of a perpendicular bisector 2. the definition of congruent angles 1. the definition of congruent angles 2. the definition of a perpendicular bisector 1. angle-side-angle (asa) postulate 2. corresponding parts of congruent triangles are congruent (cpctc)