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1. In a quadrilateral OABC, D is the midpoint of BC and E is the point on AD such

that AE : ED = 2 : 1. Given that OA = a, OB = b and OC = c, express OD and

OE in terms of a, b and c.

**Question 5**

The number of items rejected daily by a manufacturer because of defects for the last 30 days are:

20, 21, 8, 17, 22, 19, 18, 19, 14, 17, 11, 6, 21, 25, 4, 19, 9, 12, 16, 16, 10, 28, 24, 6, 21, 20, 25, 5, 17, 8

a) Construct a stem-and-leaf display. What can conclude based on the display? *(7 marks)*

b) Calculate the mean, median, and mode of the data. *(6 marks)*

c) Based on the answers in (b), make a conclusion about the skewness of the data. *(3 marks)*

A fast-food chain decided to carry out an experiment to assess the influence of advertising expenditure on sales. Different relative changes in advertising expenditure, compared to the previous year, were made in eight regions of the country, and resulting changes in sales levels were observed the accompanying table shows the results.

Increase in advertising expenditure (%)

0

5

15

20

25

30

35

40

Increase in sales (%)

5

10

18

25

35

50

60

65

Brian and Jennifer are planning to get married at the end of the year. They read that certain diets are healthier for specific blood types and hope that they both have the same blood type. Unfortunately, neither Brian nor Jennifer can remember their blood type.

Suppose a recent study shows that 25% of adults have blood type A, 28% of adults have blood type B, 34% of adults have blood type AB, and 13% of adults have blood type O. The tree diagram shows the possible outcomes for Brian and Jennifer along with their associated probabilities.

What is the probability that Brian and Jennifer share the same blood type? Give your answer as a decimal, precise to at least two decimal places.

This Venn diagram shows the makeup of attendees at a college social event sponsored by the French Club. The event is open to all students. There are 20 students at the party who are fluent in French. There are 35 students at the party who are fluent in English. There are 115 students at the party.

Use the Venn diagram and given information to find the probability that a student selected at random is fluent in both French and English. Assume the chance of being selected is the same for each student. Express your answer as a percentage rounded to one decimal place