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3 years ago

In how many ways can ann, bob, chuck, don and ed be seated in a row such that ann and bob are not seated next to each other?

1 answer:

7 0

The 5 people can seat in a row in 5! ways
But we need to exclude the ways that ann and bob are seated next to each other which is = 4! * 2!

So, the number of ways can ann, bob, chuck, don and ed be seated in a row such that ann and bob are not seated next to each other = 5! - 4! * 2! = 72

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Another solution:

If ann seated in one of the ends, the number of ways = 3*2

If ann didn't seat in one of the ends , the number of ways = 2*3

So, the total number of ways that can ann, bob be seated = 3*2 + 2*3 = 12

The remaining persons can seat with a number of ways = 3! = 6
So, the total ways that the five persons can seat = 12*6 = 72

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The average national SAT score is 1119. If we assume a bell-shaped distribution and a standard deviation equal to 206, what perc

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Solution: We are given:

$\mu=1119, \sigma =206$

a. what percentage of scores will fall between 501 and 1737?

In order to find the percentage of scores that fall between 501 and 1737, we use the z score formula first:

When x = 501, we have:

$z=\frac{x-\mu}{\sigma}$

$=\frac{501-1119}{206}=-3$

When x = 1737, we have:

$z=\frac{x-\mu}{\sigma}$

$=\frac{1737-1119}{206}=3$

Therefore, we have to find $P(-3\leq z \leq 3)$ .

From the empirical rule of normal distribution 99.7% of data falls within 3 standard deviation's from mean.

Therefore, 99.7% of scores will fall between 501 and 1737.

b. what percentage of scores will fall between 707 and 1531?

In order to find the percentage of scores that fall between 707 and 1531, we use the z score formula first:

When x = 707, we have:

$z=\frac{x-\mu}{\sigma}$

$=\frac{707-1119}{206}=-2$

When x = 1531, we have:

$z=\frac{x-\mu}{\sigma}$

$=\frac{1531-1119}{206}=2$

Therefore, we have to find $P(-2\leq z \leq 2)$ .

From the empirical rule of normal distribution 95% of data falls within 2 standard deviation's from mean.

Therefore, 95% of scores will fall between 707 and 1531.

c. what percentage of scores will fall between 931 and 1325?

In order to find the percentage of scores that fall between 931 and 1325, we use the z score formula first:

When x = 931, we have:

$z=\frac{x-\mu}{\sigma}$

$=\frac{931-1119}{206}=-1$

When x = 1325, we have:

$z=\frac{x-\mu}{\sigma}$

$=\frac{1325-1119}{206}=1$

Therefore, we have to find $P(-1\leq z \leq 1)$ .

From the empirical rule of normal distribution 68% of data falls within 1 standard deviation's from mean.

Therefore, 95% of scores will fall between 707 and 1531.

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3 years ago

Simplify the expression 4.2v - 5 - 6.5v

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The simplified version of this is -2.3v-5

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3 years ago

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A bag contains three black balls and five white balls. Paul picks a ball at random from the bag and replaces it back in the bag

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Answer:

Step-by-step explanation:

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3 years ago

Juan just took a 40 question math test. He scored 75%. How many questions did he get correct

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Answer:

Step-by-step explanation:

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3 years ago

Which statement describes the behavior of the function f(x)=3x/4-x?

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Answer:

The graph approaches –3 as x approaches infinity. Option a is correct.

Step-by-step explanation:

The given function is

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$\lim_{x\rightarrow \infty}f(x)=\lim_{x\rightarrow \infty}\frac{3x}{4-x}$

Taking x common from the denominator.

$\lim_{x\rightarrow \infty}f(x)=\lim_{x\rightarrow \infty}\frac{3x}{x(\frac{4}{x}-1)}$

Cancel out common factor x.

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Apply limits.

$\lim_{x\rightarrow \infty}f(x)=\frac{3}{\frac{4}{\infty}-1}$

$\lim_{x\rightarrow \infty}f(x)=\frac{3}{0-1}$

$\lim_{x\rightarrow \infty}f(x)=-3$

Therefore the graph approaches –3 as x approaches infinity.

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