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taurus [48]
3 years ago
5

A student guesses on every question of a​ multiple-choice test that has 9 ​questions, each with 3 possible answers. what is the

probability that the student will get at least 7 of the questions​ right
Mathematics
1 answer:
Ber [7]3 years ago
3 0
This is a binomial related problem. In this case,

P(correct) = p = 1/3
P(wrong) = q = 1-p = 1-1/3 = 2/3

The general formula for binomial is;
Summation [nCk(p)^k(q)^(n-k)]

Where
n = 9
k = 7,8,9

Substituting;
P(7≤X≤9) = [9C7(1/3)^7(2/3)^2]+[9C8(1/3)^8(2/3)^1]+[9C9(1/3)^9(2/3)^0] = [16/2187]+[2/2187]+[1/19683]=163/19683 ≈ 0.00828

Therefore, the  probability of getting atleast 7 question right is 0.00828.
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3 years ago
1. Find the zeros of the function.
Mama L [17]
1. f(x) = 9x² + 6x - 8
f(x) = (3x - 2)(3x + 4)
When  (3x - 2) = 0, then x = 2/3
When (3x + 4) = 0, then x = -4/3

Answer: The zeros are two divided by three and negative four divided by three.

2. f(x) = 9x³ - 45x² + 36x
  f(x) = 9x(x² - 5x + 4)
        = 9x(x - 1)(x - 4)
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  When (x-1) = 0, then x = 1
  When (x-4) = 0, then x = 4

 Answer: 0, 1 and 4

3. f(x) = 4(x+7)²(x-7)³
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 Answer: 7, multiplicity 2; -7 multiplicity 3

4. The zeros of f(x) are √5, -√5, -7
 The factors of f(x) are (x-√5)(x+√5)(x+7)
 Note that (x-√5)(x+√5) = x² - (√5)² = x² - 5
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Answer: f(x) = x³ + 7x² - 5x - 35

5. Expand (2x + 4)³
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 (2x + 4)³ = 1(2x)³(4)⁰ + 3(2x)²(4)¹ + 3(2x)¹(4)² + 1(2x)⁰(4)³
                = 8x³ + 48x² + 96x + 64

 Answer: 8x³ + 48x² + 96x + 64
3 0
3 years ago
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