Answer:
1/41416353 probability of all five numbers and the mega number matching the winning numbers
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, the order of the numbers is not important. So we use the combinations formula to solve this question.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
Probability of the five numbers matching:
Desired outcomes: 1 -> the matching numbers
Total outcomes: 5 from a set of 47. So
Probability:
Probability of the mega number matching:
1 from a set of 27. So
Probability of both matching:
Independent events, so we multiply the probabilities:
1/41416353 probability of all five numbers and the mega number matching the winning numbers
Five squared with the little two and 2 because 5 Times 10 is 50 and five is prime so then from 10 and you get five and two and both five and two are prime
Problem 1
<h3>Answer: False</h3>
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Explanation:
The notation (f o g)(x) means f( g(x) ). Here g(x) is the inner function.
So,
f(x) = x+1
f( g(x) ) = g(x) + 1 .... replace every x with g(x)
f( g(x) ) = 6x+1 ... plug in g(x) = 6x
(f o g)(x) = 6x+1
Now let's flip things around
g(x) = 6x
g( f(x) ) = 6*( f(x) ) .... replace every x with f(x)
g( f(x) ) = 6(x+1) .... plug in f(x) = x+1
g( f(x) ) = 6x+6
(g o f)(x) = 6x+6
This shows that (f o g)(x) = (g o f)(x) is a false equation for the given f(x) and g(x) functions.
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Problem 2
<h3>Answer: True</h3>
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Explanation:
Let's say that g(x) produced a number that wasn't in the domain of f(x). This would mean that f( g(x) ) would be undefined.
For example, let
f(x) = 1/(x+2)
g(x) = -2
The g(x) function will always produce the output -2 regardless of what the input x is. Feeding that -2 output into f(x) leads to 1/(x+2) = 1/(-2+2) = 1/0 which is undefined.
So it's important that the outputs of g(x) line up with the domain of f(x). Outputs of g(x) must be valid inputs of f(x).
One is 3pi/2 - 2pi = -pi/2
also -7pi/2
Answer:
441
Step-by-step explanation:
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