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3 years ago

Prove that (n+5)^2 - (n+3)^2 is a multiple of 4 for all positive integer values of n.

Mathematics

1 answer:

Drupady [299]3 years ago

3 0

Answer:

(n+5)² - (n+3)² =

= (n² + 10n + 25) - (n² + 6n + 9)

= n² + 10n + 25 - n² - 6n - 9

= 4n + 16

= 4(n + 4) ⋮ 4

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4 years ago

Fiona needs to choose a five-character password with a combination of three letters and the even numbers 0, 2, 4, 6, or 8.

katen-ka-za [31]

The total outcomes of creating a password is 20

<h3>How to determine the total outcomes creating different passwords with the given characters and numbers?</h3>

The given parameters are

Letters = 3

Digits = 5 digits i.e 0, 2, 4, 6, or 8.

From the question, the digits and the letters cannot be repeated.

So, we have:

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2 years ago

A consumer advocate wants to collect a sample of jelly jars and measure the actual weight of the product in the container. He ne

Ivahew [28]

Answer:

n=3.8416≅4

So Minimum Sample Size is 4

Step-by-step explanation:

In order to find the minimum sample size, the formula we use will be:

$n= \frac{Z^2*S^2}{E^2}$

Where:

n is sample size

Z is the distribution

S is the standard deviation

E is the Margin of error

S=3 ,E=3

For Z:

Alpha=1-0.95=0.05

Alpha/2=0.025=2.5%

From Cumulative Standard Distribution Table:

Z at Alpha/2 = 1.960

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3 years ago

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VMariaS [17]

Answer:

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Step-by-step explanation:

We need to find the value of x if the polygons in each pair are similar.

As they are similar, the ratio of their sides are equal.

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So,

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So, the value of x is equal to 9.

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3 years ago

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Sunny_sXe [5.5K]

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3 years ago