There are slips of paper that are numbered from 1 to 15 in a hat. What is the theoretical probability that a slip of paper that
2 answers:
Answer:
the theoretical probability that a slip of paper that is chosen will be an even number is 0.466
Step-by-step explanation:
if we are going to choose a slip of paper with an specific condition, the theoretical probability could be calculated as a division between the total number of posibles choices and the number of choices that satisfy an specific condition.
In this case, there 15 posibles choices because we have 15 numbered slips of papers. from these 15 slips, 7 are numbered with an even number. This even numbers are: 2, 4, 6, 8, 10, 12 and 14.
Finally the theoretical probability is:
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Answer:
(c) 0
Step-by-step explanation:
Each of the terms in the expression represents a different transformation of a different trig function. Expressing those as the same trig function can make it easier to find the sum.
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We can start with the identity ...
cos(x) = sin(x +π/2)
Substituting the argument of the cosine function in the given expression, we have ...
cos(π/2 -θ) = sin((π/2 -θ) +π/2) = sin(π -θ) = -sin(θ -π)
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The first term, sin(π +θ), is a left-shift of the sine function by 1/2 cycle, so can be written ...
sin(π +θ) = -sin(θ)
The second term is the opposite of a right-shift of the sine function by 1/2 cycle, so can be written ...
cos(π/2 -θ) = -sin(θ -π) = sin(θ)
Then the sum of terms is ...
sin(π +θ) +cos(π/2 -θ) = -sin(θ) +sin(θ) = 0
The sum of the two terms is identically zero.
