Answer:
a) r(t) = 0.783t radians
b) h(t) = 30cos(0.783*t) feet
Step-by-step explanation:
The situation is depicted in the picture attached
<h3>(see picture)
</h3>
Since the angular speed is constant, to find an expression for the angle r(t) in radians we just cross-multiply using the fact that 1 min = 60 seconds
4.7 radians __________ 60 seconds
r(t) radians ____________ t seconds
The height h(t) after t seconds is given by
h(t) = 30cos(r(t)) ===>
h(t) = 30cos(0.783*t) feet
Answer:
2,520
Step-by-step explanation:
The number of possible arrangements of officers patrolling the streets is the combination of choosing 5 officers out of 10 (₁₀C₅). After choosing the patrolling officers, the number of arrangements for the officers working full time at the station is given by the combination of choosing 2 officers out of the 5 remaining (₅C₂). The remaining officers should be on reserve at the station (₃C₃). The total number of arrangements is:
There are 2,520 possible divisions.
Answer:
0.164 = 16.4% probability that at least one color will be missing from the 10 selected balls.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Determine the probability that at least one color will be missing from the 10 selected balls.
Red missing:
Each time, there are 55 + 25 = 80 non-red balls, out of 100. So, in each of the 10 trials, 80% = 0.8 probability of not picking a red ball. The probability that no red ball is picked is given by:
(0.8)^10 = 0.1074
White missing:
55 + 20 = 75 non-white balls, out of 100, in each trial. The probability that no white ball is picked is given by:
(0.75)^10 = 0.0563
Blue missing:
45 non-blue balls, out of 100. The probability that no blue ball is picked is given by:
(0.45)^10 = 0.0003
Total:
0.1074 + 0.0563 + 0.0003 = 0.164
0.164 = 16.4% probability that at least one color will be missing from the 10 selected balls.
Answer:
16.06
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