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2 years ago

What are three consecutive integers whose product is 480 more than their sum?

Mathematics

1 answer:

Natali [406]2 years ago

4 0

Answer:

The three numbers are 7 8 and 9

Step-by-step explanation:

Givens

Let the first number be n - 1
Let the second number be n
Let the third number = n + 1

Equation

(n - 1)(n)(n + 1) - (n-1 + n + n+1) = 480

Solution

Multiply (n - 1) and (n + 1) = (n - 1)*(n + 1) = n^2 - 1

Multiply the second integer by the result of the first and third: n (n^2 - 1)

Add the three integers together: (x - 1) + (n - 1) + n = 3n Combine these 2 steps

n(n^2 - 1) - 3n = 480 Remove the brackets

n^3 - n - 3n = 480

n^3 - 4n = 480

n^3 - 4n - 480 = 0

Graph

The graph shows that the intercept point is n =8. This is the only way I can see to solve this cubic. There are no other real roots.

Answer

n - 1 = 7

n = 8

n + 1 = 9

Check

Product 7*8*9 = 504

Sum = 7 + 8 + 9 = 24

504 - 24 = 480 Which checks.

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3. The adult men of the Dinaric Alps have the highest average height of all regions. The

ahrayia [7]

Using the normal distribution, it is found that:

3 - a) The 40th percentile of the height of Dinaric Alps distribution for men is of 72.2 inches.

3 - b) The minimum height of man in the Dinaric Alps that would place him in the top 10% of all heights is of 76.84 inches.

4 - a) The 25th percentile for the math scores was of 71.6 inches.

4 - b) The 75th percentile for the math scores was of 78.4 inches.

<h3>Normal Probability Distribution </h3>

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

It measures how many standard deviations the measure is from the mean.

After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

Question 3:

The mean is of 73 inches, hence $\mu = 73$ .

The standard deviation is of 3 inches, hence $\sigma = 3$ .

Item a:

The 40th percentile is X when Z has a p-value of 0.4, so X when Z = -0.253.

$Z = \frac{X - \mu}{\sigma}$

$-0.253 = \frac{X - 73}{3}$

$X - 73 = -0.253(3)$

$X = 72.2$

The 40th percentile of the height of Dinaric Alps distribution for men is of 72.2 inches.

Item b:

The minimum height is the 100 - 10 = 90th percentile is X when Z has a p-value of 0.9, so X when Z = 1.28.

$Z = \frac{X - \mu}{\sigma}$

$1.28 = \frac{X - 73}{3}$

$X - 73 = 1.28(3)$

$X = 76.84$

The minimum height of man in the Dinaric Alps that would place him in the top 10% of all heights is of 76.84 inches.

Question 4:

The mean score is of 75, hence $\mu = 75$ .

The standard deviation is of 5, hence $\sigma = 5$ .

Item a:

The 25th percentile is X when Z has a p-value of 0.25, so X when Z = -0.675.

$Z = \frac{X - \mu}{\sigma}$

$-0.675 = \frac{X - 75}{5}$

$X - 75 = -0.675(5)$

$X = 71.6$

The 25th percentile for the math scores was of 71.6 inches.

Item b:

The 75th percentile is X when Z has a p-value of 0.25, so X when Z = 0.675.

$Z = \frac{X - \mu}{\sigma}$

$0.675 = \frac{X - 75}{5}$

$X - 75 = 0.675(5)$

$X = 78.4$

The 75th percentile for the math scores was of 78.4 inches.

To learn more about the normal distribution, you can take a look at brainly.com/question/24663213

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Natali5045456 [20]

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Yakvenalex [24]

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snow_lady [41]

Answer:

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Step-by-step explanation:

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