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svetoff [14.1K]

1 year ago

7

Students are measuring various objects around the classroom. A pencil measures 8 ⅜ inches while a pair of scissors measures 5 ½

inches. How much longer is the pencil than the pair of scissors?

1 answer:

Maslowich1 year ago

5 0

The pencil is longer than the pair of scissors by $2\frac{7}{8}$ inches.

A pencil measures $8\frac{3}{8}$ inches.

A pair of scissors measures $5\frac{1}{2}$ inches.

We need to find the difference between the measures of a pencil and the scissors.

We see that the pencil measure is greater than the pair of scissors.

<h3>What is a mix fraction?</h3>

A fraction is a part of a whole number. It has two parts - numerator and denominator.

Example: If you cut a cake into three slices each slice is 1/3.

Where 1 = numerator and 3 = denominator.

Four types of fractions:

Unit fraction - when the numerator is 1.

Proper fraction - When the numerator is less than the denominator.

Improper fraction - When the numerator is greater than the denominator.

Mixed fraction - When the fraction contains a whole number with a proper fraction.

Example: $3\frac{1}{3}$

The given measure of the pen and the pair of scissors is in mix fraction.

The pencil measure is longer than the pair of scissors measure so,

We will subtract the measure of the pair of scissors from the measure of the pen.

We have,

= $8\frac{3}{8} - 5\frac{1}{2}$

We can write the mix fraction into an improper fraction.

We multiply the denominator with the whole number and add this product with the numerator to get our numerator of the improper fraction. The denominator will remain the same as the mix fraction in the improper fraction.

So,

$8\frac{3}{8}=\frac{(8\times8)+3}{8}=\frac{64 + 3}{8} = \frac{67}{8}\\ 5\frac{1}{2} =\frac{(5\times2)+1}{2}= \frac{(10+1)}{2} = \frac{11}{2}$

= 67/8 - 11/2

= (67-44) / 8

= 23 / 8

Writing in mix fraction.

= $2\frac{7}{8}$

Thus the pencil is longer than the pair of scissors by $2\frac{7}{8}$ inches.

Learn more about mix fraction here:

brainly.com/question/13881046

#SPJ1

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3 years ago

The probability that your call to a service line is answered in less than 30 seconds is 0.85. Assume that your calls are indepen

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Answer:

a) 0.1720

b) 0.8298

c) 19

Step-by-step explanation:

For each call, there are only two possible outcomes. Either they are answered in less than 30 seconds. Or they are not. The probabilities for each call are independent. 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.

In this problem we have that:

$p = 0.85$

(a) If you call 12 times, what is the probability that exactly 9 of your calls are answered within 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X = 9)$ when $n = 12$ .

So

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

$P(X = 9) = C_{12,9}.(0.85)^{9}.(0.15)^{3} = 0.1720$

(b) If you call 20 times, what is the probability that at least 16 calls are answered in less than 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X \geq 16)$ when $n = 20$

So

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)$

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

$P(X = 16) = C_{20,16}.(0.85)^{16}.(0.15)^{4} = 0.1821$

$P(X = 17) = C_{20,17}.(0.85)^{17}.(0.15)^{3} = 0.2428$

$P(X = 18) = C_{20,18}.(0.85)^{18}.(0.15)^{2} = 0.2293$

$P(X = 19) = C_{20,19}.(0.85)^{19}.(0.15)^{1} = 0.1368$

$P(X = 20) = C_{20,20}.(0.85)^{20}.(0.15)^{0} = 0.0388$

So

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.1821 + 0.2428 + 0.2293 + 0.1368 + 0.0388 = 0.8298$

(c) If you call 22 times, what is the mean number of calls that are answered in less than 30 seconds? Round your answer to the nearest integer.

The expected value of the binomial distribution is:

$E(X) = np$

In this question, we have $n = 22$

So

$E(X) = 22*0.85 = 18.7$

The nearest integer to 18.7 is 19.

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3 years ago

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tia_tia [17]

Answer:

Step-by-step explanation:

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Blue = 3

Green = 5

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Third Marble = 4/12 = 1/3

Result

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P(3 Red) = 1/7 * 5/13

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3 years ago

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IceJOKER [234]

Answer:

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Step-by-step explanation:

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3 years ago