Answer:
(g o f)(x) = (not simplified)
Step-by-step explanation:
(g o f)(x) = g(f(x))
g(x) = f(x) =
g(f(-5)) = g( =
=
g(-170) = =
Simplify the following expression (8x + 5y) - ( 2x -3y)
2 answers:
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Answer:
<u>Step-by-step explanation:</u>
greater than 3 means the sum is either 4, 5, or 6.
There are 15 permutations that meet the criteria:
(1, 3), (1, 4), (1, 5), (1,6)
(2, 2), (2, 3), (2, 4), (2, 5), (2,6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3,6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4,6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5,6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6,6)
There are 6²= 36 total permutations for 2 dice.
Answer: There are 4 male goats.
Step-by-step explanation:
We know that n of the 10 goats are male.
The probability that in a random selection, the selected goat is a male, is equal to the quotient between the number of male goats (n) and the total number of goats (10)
The probability is;
p = n/10
Now the total number of goats is 9, and the number of male goats is n -1
then the probability of selecting a male goat again is:
q = (n-1)/9
The joint probability (the probability that the two selected goats are male) is equal to the product of the individual probabilities, this is
P = p*q = (n/10)*((n-1)/9)
And we know that this probability is equal to 2/15
Then we have:
(n/10)*((n-1)/9) = 2/15
(n*(n-1))/90 = 2/15
n*(n-1) = 90*2/15 = 12
n^2 - n = 12
n^2 - n - 12 = 0
This is a quadratic equation, we can find the solutions if we use Bhaskara's formula:
For an equation:
a*x^2 + b*x + c = 0
The two solutions are given by:
For our case, the solutions will be:
The two solutions are:
n = (1 - 7)/2 = -3 (this solution does not make sense, we can not have a negative number of goats)
The other solution is:
n = (1 + 7)/2 = 4
This solution does make sense, this means that we have 4 male goats.