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Lelu [443]
3 years ago
12

8. A home security system has a pad with 9 digits (1 to 9). Find the number of possible 5-digit pass codes:

Mathematics
1 answer:
nikdorinn [45]3 years ago
5 0

Answer:

a. 59049

b. 15120

Step-by-step explanation:

<u>a. If digits can be repeated:</u>

  • There are 9 possible numbers for each digit

That is:  possible 5-digit pass codes are 9×9×9×9×9=9^{5}=59049

<u>b. If digits cannot be repeated.</u>

There is

  • 9 possibility for the first digit,
  • 8 possibility for the second digit
  • 7 possibility for the third digit
  • 6 possibility for the fourth digit
  • 5 possibility for the fifth digit

That is:  possible 5-digit pass codes are 9×8×7×6×5=15120

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The recycling bin in the shape of a rectangular prism is 15.5 inches long, 8 inches wide and 7 inches high. The recycling bins n
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Answer:

694 cubic inches

Step-by-step explanation:

Dimension of prism

Length = 15.5 inches

width =  8 inches

height =  7 inches

Volume of regular prism is given  by area of base * height

area of base  = length * width ( as bin is rectangular)

area of base  = 15.5 * 8 square inches = 124 square inches

Volume of regular prism = area of base * height

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868 cubic inches is the full capacity of the recycling bin

it is given that recycling bins need to be emptied when it is 80% full

so we need to find the 80% capacity of recycling bin

80% capacity of recycling bin = 80/100 *  full capacity of the recycling bin

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694.4 cubic inches is the amount needed before the recycle bin is ready to empty .

But question says answer should in nearest cubic inch

hence answer is 694 cubic inches

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