Q1 (a) As part of an investigation into levels of overtime working, a company decides to tabulate the number of orders received weekly and compare this with the total weekly overtime worked to give the following Week
1
2
3
4
5
6
7
8
9
10

Orders received
83
22
107
55
48
92
135
32
67
122

Total overtime
38
9
42
18
11
30
48
10
29
51

Using the method of least squares obtain the regression equation of total overtime on orders received and predict the level of total overtime necessary for 100 orders (7 marks)
(b) As a result of tests of 20,000 electric bulbs manufactured by a company it was found that lifetime of the bulbs are normally distributed with an average life of 2040 hours and standard deviation of60 hours. On the basis of the information, estimate the number of bulbs expected to burn for;
(i) More than 2150 hours
(ii) Less than 1960 hours​

Given: ad¯¯¯¯¯ is an altitude. prove: ab2+ac2=cb2 right triangle a b c with right angle a. point d lies on side b c and segment a d is drawn. angle a d c is a right angle. drag and drop a reason into each box to correctly complete the two-column proof. statement reason ad¯¯¯¯¯ is an altitude, and ∠bac is a right angle. given ∠adb and ∠adc are right angles. definition of altitude ∠bac≅∠bda ? ∠bac≅∠adc ? ∠b≅∠b ? ∠c≅∠c reflexive property of congruence △abc∼△dba ? △abc∼△dac aa similarity postulate abbd=cbab ? ab2=(cb)(bd) cross multiply and simplify. acdc=cbac polygon similarity postulate ac2=(cb)(dc) cross multiply and simplify. ab2+ac2=ab2+(cb)(dc) addition property of equality ab2+ac2=(cb)(bd)+(cb)(dc) substitution property of equality ab2+ac2=(cb)(bd+dc) ? bd+dc=cb segment addition postulate ab2+ac2=cb2 substitution property of equality

Which expression is a perfect cube? a. x8 b. y24 c. m28 d. x64

Match the one-to-one functions with the graphs of their inverse functions.