The probabilities of event E are: Option A: P(E) = 23/36, Option B: P(E) = 1/5, Option D: P(E) = 29/48
The probability of an event can be calculated from the odds in favor of the event, using the following formula:
Probability of E occurring = Odds in favor of E / (Odds in favor of E + Odds against E)
Here, the odds in favor of E are given as
6:30, 29:19, and 23:13, respectively.
To use these odds to compute the probability of event E, we first need to convert them to fractions.
6:30 = 6/(6+30)
= 6/36
= 1/5
29:19 = 29/(29+19)
= 29/48
23:1 = 23/(23+13)
= 23/36
Using these fractions, we can now calculate the probability of E as:
P(E) = Odds in favor of E / (Odds in favor of E + Odds against E)
For each of the given odds, the corresponding probability is:
P(E) = 1/5 / (1/5 + 4/5)
= 1/5 / 1
= 1/5
P(E) = 29/48 / (29/48 + 19/48)
= 29/48 / 48/48
= 29/48
P(E) = 23/36 / (23/36 + 13/36)
= 23/36 / 36/36
= 23/36
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1.Find the period of the following functions. a) f(t) = (7 cos t)² b) f(t) = cos (2φt²/m)
Period of the functions: The period of the function f(t) = (7 cos t)² is given by 2π/b where b is the period of cos t.The period of the function f(t) = cos (2φt²/m) is given by T = √(4πm/φ). The period of the function f(t) = (7 cos t)² is given by 2π/b where b is the period of cos t.
We know that cos (t) is periodic and has a period of 2π.∴ b = 2π∴ The period of the function f(t) =
(7 cos t)² = 2π/b = 2π/2π = 1.
The period of the function f(t) = cos (2φt²/m) is given by T = √(4πm/φ) Hence, the period of the function f(t) =
cos (2φt²/m) is √(4πm/φ).
The function f(t) = (7 cos t)² is a trigonometric function and it is periodic. The period of the function is given by 2π/b where b is the period of cos t. As cos (t) is periodic and has a period of 2π, the period of the function f(t) = (7 cos t)² is 2π/2π = 1. Hence, the period of the function f(t) = (7 cos t)² is 1.The function f(t) = cos (2φt²/m) is also a trigonometric function and is periodic. The period of this function is given by T = √(4πm/φ). Therefore, the period of the function f(t) = cos (2φt²/m) is √(4πm/φ).
The period of the function f(t) = (7 cos t)² is 1, and the period of the function f(t) = cos (2φt²/m) is √(4πm/φ).
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Jeff has 32,400 pairs of sunglasses. He wants to distribute them evenly among X people, where X is
a positive integer between 10 and 180, inclusive. For how many X is this possible?
Answer:
To distribute 32,400 pairs of sunglasses evenly among X people, we need to find the positive integer values of X that divide 32,400 without any remainder.
To determine the values of X for which this is possible, we can iterate through the positive integers from 10 to 180 and check if 32,400 is divisible by each integer.
Let's calculate:
Number of possible values for X = 0
For each value of X from 10 to 180, we check if 32,400 is divisible by X using the modulo operator (%):
for X = 10:
32,400 % 10 = 0 (divisible)
for X = 11:
32,400 % 11 = 9 (not divisible)
for X = 12:
32,400 % 12 = 0 (divisible)
...
for X = 180:
32,400 % 180 = 0 (divisible)
We continue this process for all values of X from 10 to 180. If the remainder is 0, it means that 32,400 is divisible by X.
In this case, the number of possible values for X is the count of the integers from 10 to 180 where 32,400 is divisible without a remainder.
After performing the calculations, we find that 32,400 is divisible by the following values of X: 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 64, 72, 75, 80, 90, 96, 100, 108, 120, 128, 135, 144, 150, 160, 180.
Therefore, there are 33 possible values for X between 10 and 180 (inclusive) for which it is possible to distribute 32,400 pairs of sunglasses evenly.
Hope it helps!