8. A home security system has a pad with 9 digits (1 to 9). Find the number of possible 5-digit pass codes:
1 answer:
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==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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Answer:
The cars are 10702ft apart
Step-by-step explanation:
Height of the plane from the high way = 5150ft
Considering Triangle ABD, we will be using SOHCAHTOA
Tan = Opposite/ Adjacent
Tan 54° = Y/5150
Y = 5150*tan54°
Y = 7088 ft
Considering Triangle ADC, Tan = Opposite/ Adjacent is also applicable
Tan 34° = X/5150
X = 5150*tan 54°
X = 3614ft
The distance between the two cars = (X+Y)
= 7088 + 3614
= 10702ft
