The total cost, $C, of manufacturing n batches of biscuit boxes is given by the formula C = an + b, where a and b are constants. When 200 batches of biscuit boxes are manufactured, the total cost is $55 000.
When 500 batches of biscuit boxes are manufactured, the total cost is $62 500.
(i) Find the value of a and of b.
(ii) Calculate the total cost of manufacturing 420 batches of biscuit boxes.
(iii) Find the number of batches of biscuit boxes manufactured if the total cost is $70 000.
(iv) Draw the graph of C against n. Is C directly proportional to n? Use your graph to explain your answer.

Find the slope of the line passing through a pair of points

Acompany charges $0.10 for each letter engraved. bobby plans to spend no more than $5.00 on the engraving on a jewelry box. write and solve an inequality to find the maximum number of letters he can have engraved.

Aresearch study is studying the effects of a new drug for osteoporosis alzheimer's disease (ad) for women above the age of 65 years. a group of individuals with osteoporosis is randomized into two groups. one group is treated conventionally, and the second group is treated with the new medication. assessments are made at 3, 6, 12, 36, and 48 months. the conventionally treated group is assessed for ad using a serum blood test, and the treatment group is assessed for ad using a pet radiotracer that binds to beta-amyloid plaques. in comparing these 2 trial arms, the authors of the study may encounter which type of bias? a. selection bias on the risk of developing b. measurement bias c. confounding bias d. recall bias e. lead-time bias