Erin received the following scores on her past four spelling test

N is a positive integer

Murrr4er [49]

Part (1)

n is some positive integer. Let's say for now that n is even. So n = 2k, for some integer k

This means n-1 = 2k-1 is odd since subtracting 1 from an even number leads to an odd number.

Now multiply n with n-1 to get

n(n-1) = 2k(2k-1) = 2m

where m = k(2k-1) is an integer

The result 2m is even showing that n(n-1) is even

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Let's say that n is odd this time. That means n = 2k+1 for some integer k

And also n-1 = 2k+1-1 = 2k showing n-1 is even

Now multiply n and n-1

n(n-1) = (2k+1)(2k) = 2k(2k+1) = 2m

where m = k(2k+1) is an integer

We've shown that n(n-1) is even here as well.

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So overall, n(n-1) is even regardless if n is even or if n is odd.

Either n or n-1 will be even. If you multiply an even number with any number, the result will be even.

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Part (2)

n is some positive integer

2n is always even since 2 is a factor of 2n

2n+1 is always odd because we're adding 1 to an even number. The sequence of integers goes even,odd,even,odd, etc and it does this forever.

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Another way to see how 2n+1 is odd is to divide 2n+1 over 2 and you'll find that we get (2n+1)/2 = 2n/2+1/2 = n+0.5

The 0.5 at the end is not an integer, so there's no way that (2n+1)/2 is an integer; therefore 2n+1 is odd.

6 0

3 years ago

Before a new video game is released, it is tested by a number of volunteer gamers. During testing, the experimental probability

sesenic [268]

Answer:

2000 players will complete the game with a perfect score.

Step-by-step explanation:

The testing phase tells us that $\frac{1}{500}$ is the probability that a person will finish with a perfect score.

This means 1 out of 500 people will be able to finish with perfect score.

Now,

the game is given to 1,000,000 (1 million) people and how much do we expect to finish with perfect score?? Simple! It would be $\frac{1}{500}$ the of 1 million!

We do the calculation shown below:

$\frac{1}{500}*1,000,000=2000$

So, 2000 players will complete the game with a perfect score.

3 0

4 years ago

Read 2 more answers

The following data summarizes results from 945 pedestrian deaths that were caused by accidents. If one of the pedestrian deaths

VikaD [51]

Answer:

37.67% probability that the pedestrian was intoxicated or the driver was intoxicated.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question:

945 accidents.

In 64 of them, the pedestian was intoxicated.

In 292 of them, the driver was intoxicated.

Probability that the pedestrian was intoxicated or the driver was intoxicated.

(64+292)/945 = 0.3767

37.67% probability that the pedestrian was intoxicated or the driver was intoxicated.

6 0

3 years ago

Maya and Mabel are inspecting an 80:1 scale floor plan of their new house. The dimensions of the living room on the scaled floor

AveGali [126]

Answer:

208 ⅓ ft²

Step-by-step explanation:

1⅞ = 15/8 inches ÷ 12

= 5/32 feet on map

Actual = 5/32 × 80

= 25/2 feet

2½ = 5/2 inches ÷ 12

= 5/24 feet on map

Actual = 5/24 × 80 = 50/3

Actual area:

25/2 × 50/3

= 625/3 ft²

= 208 ⅓ ft²

4 0

3 years ago

X + y + 5) and (2x – 2y – 3)

Aleonysh [2.5K]

Step-by-step explanation:

Since your question is incomplete, I have given you two different options based on your incomplete question.

Hope you understand this.

HAVE A GOOD DAY!

4 0

3 years ago