The tables below show running hours of three printers that produce greeting cards and the total number of greeting cards produced over three weeks.

number of hours machine is running

printer a
printer b
printer c
week 1
40
50
45
week 2
45
50
40
week 3
55
30
60

total cards produced
week 1
7,950
week 2
7,800
week 3
9,600

printer b uses $15 in ink every hour. what is the ink cost for each card coming from printer b?

$0.2456 / card in ink for printer B

Step-by-step explanation:

The formatting of the data tables isn't great in your question and it's hard to be sure of which numbers go where.

Since the question is about printer B, we'll assume the number of hours for printer B is 50 for week1, 50 for week2 and 3 for week3.

The numbers don't make much sense overall, but let's work with them.

We'll first calculate the ratio of hours worked by printer B with the overall hours all the printers worked, over the 3 weeks:

Printer A : 140 hours

Printer B : 130 hours

Printer C: 145 hours

Total 415 hours total, for the 3 printers.

Ratio of Printer B: 130 / 415 = 31.325%

Total of cards produced:

7,950 + 7,800 + 9,600 = 25,350 cards over 3 weeks.

We'll assume the productivity per hour is the same for all printers, since no indication otherwise.  So, the portion of those 25K cards of printer B should be the same as the ratio of the hours worked:

25,340 * 31.325% = 7941 cards (rounded to the nearest unit)

Since we know printer B ran for 130 hours, and it costs $15/hour in ink, we have:

130 hours * 15$/hour = $1,950 in ink.

Now, we divide by the number of cards:

$1,950 / 7941 cards = $0.2456 / card in ink for printer B

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form