14. (a). The cost C of manning household is partly constant and partly varies as the number of people n, in the house. For 8 people, the cost is ¢70,000 and for 10 people, the coast is $90,000, find i. An expression for C in terms of n ii. The weekly cost for 12 people​

C = 10000n - 10000 ;

$110,000

Step-by-step explanation:

Given :

Cost = C

C partly varies as n ; C α n ; C = k1 * n = k1n

C partly constant = k2

Hence,

C = k1n + k2

For n = 8 ; C = 70000

For n = 10 ; C = 90000

8k1 + k2 = 70000 - - - - - (1)

10k1 + k2 = 90000 - - - - (2)

Subtract 1 from 2

8k1 - 10k1 = 70000 - 90000

-2k1 = - 20000

k1 = 10000

Put k1 = 10000 in (1)

8(10000) + k2 = 70000

80000 + k2 = 70000

k2 = 70000 - 80000

k2 = - 10000

The expression :

C = 10000n - 10000

Weekly cost for 12 people :

n = 12

C = 10000(12) - 10000

C = 120000 - 10000

C = $110,000

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: