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geniusboy [140]
3 years ago
8

Mrs. Rodriquez has 24 students in her class. Ten of the students are boys. Jeff claims that the ratio of boys to girls in this c

lass must be 5:12. What is Jeff’s error and how can he correct it?
Jeff found the ratio of the number of boys to the total number of students. He needed to first find that there are 14 girls to get a ratio of 10:14 or 5:7.Jeff found the ratio of the number of boys to the total number of students. He needed to first find that there are 14 girls. The ratio would be 14:10 or 7:5.Jeff did not write the ratio in the correct order. He should have written it as 24:10.Jeff did not write the ratio in the correct order. He should have written it as 12:5.
Mathematics
2 answers:
Ahat [919]3 years ago
8 0

Answer:

The correct option A.

Step-by-step explanation:

Total numbers of students = 24.

Number of boys = 10

Number of girls = 24 - 10 = 14

Jeff claims that the ratio of boys to girls in this class must be 5:12.

The ratio of the number of boys to the total number of students is

\frac{boys}{students}=\frac{10}{24}=\frac{5}{12}=5:12

Therefore Jeff found the ratio of the number of boys to the total number of students.

The ratio of boys to girls in this class is

\frac{boys}{girls}=\frac{10}{14}=\frac{5}{7}=5:7

Therefore the ratio of boys to girls in this class is 5:7.

Option A is correct.

dezoksy [38]3 years ago
4 0
The ratio is 10:14 or 5:7 which is the ratio of boys to girls!
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For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains
AnnZ [28]

Answer:

a) There is a 9% probability that a drought lasts exactly 3 intervals.

There is an 85.5% probability that a drought lasts at most 3 intervals.

b)There is a 14.5% probability that the length of a drought exceeds its mean value by at least one standard deviation

Step-by-step explanation:

The geometric distribution is the number of failures expected before you get a success in a series of Bernoulli trials.

It has the following probability density formula:

f(x) = (1-p)^{x}p

In which p is the probability of a success.

The mean of the geometric distribution is given by the following formula:

\mu = \frac{1-p}{p}

The standard deviation of the geometric distribution is given by the following formula:

\sigma = \sqrt{\frac{1-p}{p^{2}}

In this problem, we have that:

p = 0.383

So

\mu = \frac{1-p}{p} = \frac{1-0.383}{0.383} = 1.61

\sigma = \sqrt{\frac{1-p}{p^{2}}} = \sqrt{\frac{1-0.383}{(0.383)^{2}}} = 2.05

(a) What is the probability that a drought lasts exactly 3 intervals?

This is f(3)

f(x) = (1-p)^{x}p

f(3) = (1-0.383)^{3}*(0.383)

f(3) = 0.09

There is a 9% probability that a drought lasts exactly 3 intervals.

At most 3 intervals?

This is P = f(0) + f(1) + f(2) + f(3)

f(x) = (1-p)^{x}p

f(0) = (1-0.383)^{0}*(0.383) = 0.383

f(1) = (1-0.383)^{1}*(0.383) = 0.236

f(2) = (1-0.383)^{2}*(0.383) = 0.146

Previously in this exercise, we found that f(3) = 0.09

So

P = f(0) + f(1) + f(2) + f(3) = 0.383 + 0.236 + 0.146 + 0.09 = 0.855

There is an 85.5% probability that a drought lasts at most 3 intervals.

(b) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?

This is P(X \geq \mu+\sigma) = P(X \geq 1.61 + 2.05) = P(X \geq 3.66) = P(X \geq 4).

We are working with discrete data, so 3.66 is rounded up to 4.

Either a drought lasts at least four months, or it lasts at most thee. In a), we found that the probability that it lasts at most 3 months is 0.855. The sum of these probabilities is decimal 1. So:

P(X \leq 3) + P(X \geq 4) = 1

0.855 + P(X \geq 4) = 1

P(X \geq 4) = 0.145

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Please find the complete question in the attached file.

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