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vladimir1956 [14]
3 years ago
7

Which fractions are greater than -2/9 ?Choose exactly two answers that are correct. A. -7/12 B. -1/15 C. -1/3 D. -1/9

Mathematics
1 answer:
galina1969 [7]3 years ago
3 0
In case you want the working out -
You will want to put all these fractions over the same denominator, the lowest common multiple is 180
-2/9
180/9 = 20
20 x -2 = -40/180

A
-7/12
180/12 = 15
15 x -7 = -105/180

B -1/15
180/15 = 12
12 x -1 = -12/180

C -1/3
180/3 = 60
60 x -1 = -60/180

D
-1/9
180/9 = 20
20 x -1 = -20/180

-105 < -60 < -40 < -20 < -12

   A   <  C  <   x   <  D   <  B

B and D
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3 years ago
A multiple-choice examination has 15 questions, each with five answers, only one of which is correct. Suppose that one of the st
Alex

Answer:

0.0111% probability that he answers at least 10 questions correctly

Step-by-step explanation:

For each question, there are only two outcomes. Either it is answered correctly, or it is not. The probability of a question being answered correctly is independent from other questions. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

A multiple-choice examination has 15 questions, each with five answers, only one of which is correct.

This means that n = 15, p = \frac{1}{5} = 0.2

What is the probability that he answers at least 10 questions correctly?

P(X \geq 10) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 10) = C_{15,10}.(0.2)^{10}.(0.8)^{5} = 0.0001

P(X = 11) = C_{15,11}.(0.2)^{11}.(0.8)^{4} = 0.000011

P(X = 12) = C_{15,12}.(0.2)^{12}.(0.8)^{3} \cong 0

P(X = 13) = C_{15,13}.(0.2)^{13}.(0.8)^{2} \cong 0

P(X = 14) = C_{15,14}.(0.2)^{14}.(0.8)^{1} \cong 0

P(X = 15) = C_{15,15}.(0.2)^{15}.(0.8)^{0} \cong 0

P(X \geq 10) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) = 0.0001 + 0.000011 = 0.000111

0.0111% probability that he answers at least 10 questions correctly

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Answer:

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m + 18 + 23 = 71

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