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3 years ago

2. (10.03)

Mathematics

1 answer:

faust18 [17]3 years ago

3 0

This question is incomplete because it was not written properly

Complete Question

A teacher gave his class two quizzes. 80% of the class passed the first quiz, but only 60% of the class passed both quizzes. What percent of those who passed the first one passed the second quiz? (2 points)

a) 20%

b) 40%

c) 60%

d) 75%

Answer:

d) 75%

Step-by-step explanation:

We would be solving this question using conditional probability.

Let us represent the percentage of those who passed the first quiz as A = 80%

and

Those who passed the first quiz as B = unknown

Those who passed the first and second quiz as A and B = 60%

The formula for conditional probability is given as

P(B|A) = P(A and B) / P(A)

Where,

P(B|A) = the percent of those who passed the first one passed the second

Hence,

P(B|A) = 60/80

= 0.75

In percent form, 0.75 × 100 = 75%

Therefore, from the calculations above, 75% of those who passed the first quiz to also passed the second quiz.

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4 years ago

A carpenter wants to cut a board 16 1/2 feet in length into 1 7/8 feet pieces. How many pieces can be cut from the board? The ca

yawa3891 [41]

<h3>Answer:</h3>

8 pieces
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<h3>Explanation:</h3>

a) Let n represent the number of 1 7/8 ft pieces. Then we have ...

... 16 1/2 ft = n × (1 7/8 ft)

We can find n by dividing this equation by 1 7/8.

... (16 1/2)/(1 7/8) = n = (132/8)/(15/8) = 132/15

... n = 8 12/15 = 8 4/5

The integer number of pieces that can be cut is 8 pieces.

b) The length of the left-over piece is 4/5 of the full length of a piece, so is ...

... (4/5) × (15/8 ft) = 12/8 ft

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Comment on arithmetic with fractions

This problem is easier if you convert the mixed numbers to improper fractions. This is done by expressing the integer as a number of fractional parts, then adding the fraction part of the mixed number:

... a + b/c = (a×c/c) + b/c = (ac +b)/c

Division with fractions is taught a couple of different ways. One way you can do it is to "invert and multiply". That is, you multiply the numerator fraction by the reciprocal of the denominator fraction:

... (a/b)/(c/d) = (a/b)×(d/c)

Another way you can do the division is to express each of the numerator and denominator fractions over the same denominator. Then the quotient is the ratio of numerators.

... (a/c)/(b/c) = a/b

This is the method we used here. Effectively, we converted 16 1/2 to 16 4/8 then to (16×8 +4)/8 = 132/8. Then the numerator and denominator fractions both had denominators of 8, so (132/8)/(15/8) = 132/15. This fraction can be reduced by removing a factor of 3 from numerator and denominator to give ...

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3 years ago

Which score indicates the highest relative position? I. A score of 2.6 on a test with X = 5.0 and s = 1.6 II. A score of 650 on

Zanzabum

Answer:

A score of 2.6 on a test with $\bar X$ = 5.0 and s = 1.6 and A score of 48 on a test with $\bar X$ = 57 and s = 6 indicate the highest relative position.

Step-by-step explanation:

We are given the following:

I. A score of 2.6 on a test with $\bar X$ = 5.0 and s = 1.6

II. A score of 650 on a test with $\bar X$ = 800 and s = 200

III. A score of 48 on a test with $\bar X$ = 57 and s = 6

And we have to find that which score indicates the highest relative position.

For finding in which score indicates the highest relative position, we will find the z score for each of the score on a test because the higher the z score, it indicates the highest relative position.

The z-score probability distribution is given by;

Z = $\frac{X-\bar X}{s}$ ~ N(0,1)

where, $\bar X$ = mean score

s = standard deviation

X = each score on a test

The z-score of First condition is calculated as;

Since we are given that a score of 2.6 on a test with $\bar X$ = 5.0 and s = 1.6,

So, z-score = $\frac{2.6-5}{1.6}$ = -1.5 {where $\bar X = 5.0$ and s = 1.6 }

The z-score of Second condition is calculated as;

Since we are given that a score of 650 on a test with $\bar X$ = 800 and s = 200,

So, z-score = $\frac{650-800}{200}$ = -0.75 {where $\bar X = 800$ and s = 200 }

The z-score of Third condition is calculated as;

Since we are given that a score of 48 on a test with $\bar X$ = 57 and s = 6,

So, z-score = $\frac{48-57}{6}$ = -1.5 {where $\bar X = 57$ and s = 6 }

AS we can clearly see that the z score of First and third condition are equally likely higher as compared to Second condition so it can be stated that A score of 2.6 on a test with $\bar X$ = 5.0 and s = 1.6 and A score of 48 on a test with $\bar X$ = 57 and s = 6 indicate the highest relative position.

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4 years ago