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ira [324]
3 years ago
10

I have 10 goats, n of which are male. I need to choose 2 of them to make a casserole.

Mathematics
1 answer:
snow_tiger [21]3 years ago
5 0

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:

x = \frac{-b +- \sqrt{b^2 - 4*a*c} }{2*a}

For our case, the solutions will be:

n = \frac{1 +- \sqrt{(-1)^2 - 4*1*(-12)} }{2*1 } = \frac{1+- 7}{2}

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.

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3 years ago
What is -2m^2-2mn+8-10m+10n+mn+4n^2-5n simplify to
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15) A, B, C, D, E and F are towns situated as follows. * A is 30 km east of D * C is 20 km east of E * F is 10 km west of B * D
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Answer:

Option D: 20km South

Step-by-step explanation:

Lets say A = (0, 0)

  • Finding B:

A is 30km East of D which makes D = (-30, 0)

D is 10km South of F which makes F = (-30, 10)

F is 10km West of B which makes B = (-20, 10)

  • Finding E:

A is 10km North of C which makes C = (0, -10)

C is 20km East of E which makes E = (-20, -10)

  • Finding the answer:

Find distance from B = (-20, 10) to E = (-20, -10)

     1. Cancel equivalent values:

x of B = (-20) and x of E = (-20)

Remove x from equation.

     2. Solve for answer:

B = 10 and E = (-10)

Find the difference: (-10) - 10 = (-20)

Conclusion:

South translates to negative on a graph making the answer 20km South

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Step-by-step explanation:

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