15.
Add "g" on both sides
Multiply 5 on both sides to get x by itself
x = 5(a + g)
x = 5a + 5g
18. a = 3n + 1
Subtract 1 on both sides
a - 1 = 3n
Divide 3 on both sides to get n by itself
= n
21. M = T - R
Add "R" on both sides to get "T" by itself
M + R = T
24. 5p + 9c = p
Subtract "5p" on both sides
9c = p - 5p
9c = -4p
Divide 9 on both sides to get "c" by itself
c = or c =
27. 4y + 3x = 5
Subtract "4y" on both sides
3x = 5 - 4y
Divide 3 on both sides to get "x" by itself
x =
x =
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.