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bearhunter [10]
3 years ago
8

Alan sells electronics, earning a base wage of $320 for one week, and a commission equal to 5% of his sales. he needs to earn at

least $600 each week to cover his expenses. set up and solve an inequality to determine what Alans sales can be in order to ensure his expenses are covered.
Mathematics
1 answer:
aksik [14]3 years ago
5 0

Answer:

  • 320 +0.05s ≥ 600
  • sales ≥ $5600

Step-by-step explanation:

For sales of 's', Alan's earnings will be ...

  320 +0.05s

He wants that to be at least 600, so the inequality is ...

  320 +0.05s ≥ 600

__

Its solution is found by subtracting 320 and dividing by 0.05.

  0.05s ≥ 280

  s ≥ 5600

Alan's weekly sales must be at least $5600 for his earnings to cover his expenses.

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5/8

Step-by-step explanation:

You need to convert to a simplified fraction by placing the numbers to the right of the decimal over 1000. Then reduce the fraction.

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If a positive integer is equal to the following product: 25b3c425b3c4, where b and c are distinct prime numbers greater than 2,
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Answer: 64 distinct even factors

Step-by-step explanation:

let the 2 distinct numbers be b and c and the integer is expected to be 25b3c425b3c4

since b, c > 2 and prime numbers,

potential options include 3, 5, and 7

hence the likelihoods are (b = 3, c = 5), (b = 5, c = 3), (b = 3, c = 7), (b = 7, c = 3), (b = 5, c = 7), (b = 7, c = 5)

Possibility 1 (b = 3, c = 5)

integer is now 253354253354

the distinct even factors = 2, 202, 262, 1934, 19802, 26462, 195334, 253354, 2000002, 2594062, 19148534, 25588754, 262000262, 1934001934, 2508457954, 253354253354

number of distinct even factors = 16

Possibility 2 (b = 5, c = 3)

integer is now 255334255334

the distinct even factors = 2, 86, 202, 5938, 8686, 19802, 253354, 599738, 851486, 2000002, 25788734, 58792138, 25588754, 86000086, 2528061934, 1934001934, 5938005938, 253354253354

number of distinct even factors = 18

Possibility 3 (b = 3, c = 7)

integer is now 253374253374

the distinct even factors = 2, 6, 22, 66, 202, 242, 606, 698, 726, 2094, 2222, 6666, 7678, 19802, 23034, 24442, 59406, 70498, 73326, 84458, 211494, 217822, 253374, 653466, 775478, 2000002, 2326434, 2396042, 6000006, 6910898, 7188126, 8530258, 20732694, 22000022, 25590774, 66000066, 76019878, 228059634, 242000242, 698000698, 726000726, 836218658, 2094002094, 2508655974, 7678007678, 23034023034, 84458084458,253354253354

number of distinct even factors = 48

Possibility 4 (b = 7, c = 3)

integer is now 257334257334

the distinct even factors = 2, 6, 14, 22, 42, 66, 154, 202, 462, 606, 1114, 1414, 2222, 3342, 4242, 6666, 7798, 12254, 15554, 19802, 23394, 36762, 46662, 59406, 85778, 112514, 138614, 217822, 257334, 337542, 415842, 653466, 787598, 1237654, 1524754, 2000002, 2362794, 3712962, 4574262, 6000006, 8663578, 11029714, 14000014, 22000022, 25990734, 33089142, 42000042, 66000066, 77207998, 121326854, 154000154, 231623994, 363980562, 462000462, 849287978, 1114001114, 2547863934, 3342003342, 7798007798, 12254012254, 23394023394, 36762036762, 85778085778, 257334257334

number of distinct even factors = 64

Possibility 5 (b = 5, c = 7)

integer is now 255374255374

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number of distinct even factors = 64

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