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Anettt [7]
2 years ago
6

What are the odds of rolling a 5 on a standard number cube? A. 1/5 B. 1/6 C. 5/6 D. 4/5

Mathematics
1 answer:
Maslowich2 years ago
8 0
B. 1/6. This is because there are six possible answers but only one favorable outcome(rolling a 5) so it’s a 1 in 6 chance
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Prove that 2n^3 + 3n^2 + n is divisible by 6 for every integer n > 1 by mathematical induction. (7 marks)
notka56 [123]

Answer:

The answer is True

Step-by-step explanation:

A <em>mathematical induction</em> consists in only 2 steps:  

<u>First step</u>: Show the proposition is true for the first one valid integer number.

<u>Second step</u>: Show that if any one is true then the next one is true  

Finally, if first step and second step are true, then the complete proposition is true.

So, given 2*n^3+3*n^2+n

First step: using and replacing n=2 (the first valid integer number >1)

2*(2)^3 +3*(2)^2+2=30

\frac{30}{6} =5

As the result is an integer number, so the first step is true.

Second step: using any next number, n+1, let it replace

2*(n+1)^3+3*(n+1)^2+(n+1)\\2*(n^3+3*n^2+3*n+1)+3*(n^2+2*n+1)^2+(n+1)\\2*n^3+6*n^2+6*n+2+3*n^2+6*n+3+n+1\\(2*n^3+3*n^2+n)+(6*n^2+12*n+6)

As the First step is true, we know that

2*n^3+3*n^2+n=6*k,

So let it replace in the previous expression

6*k+6*(n^2+2*n+1)\\6*[k+(n^2+2*n+1)]

Finally

\frac{6*[k+(n^2+2*n+1)]}{6} =k+(n^2+2*n+1)

where the last expression is an integer number

So the second step is true, and the complete proposition is True

5 0
2 years ago
The number of point a baketball team cored ha 3,4, and 5 a factor. What i the leat number of point the team could have cored
Inga [223]

The least number of point the team could have scored is the LCM of the factors given = 60.

Factor 1 = 3

Factor 2 = 4

Factor 3 = 5

therefore, LCM  

= 4 * 5 * 3   [because they don't have any factors in common]

= 60

The positive integers that can divide a number evenly are referred to as factors. Let's say we multiply two numbers to produce a result. The product's factors are the number that is multiplied.

Each number has a self-referential element. There are several examples of factors in everyday life, such putting candies in a box, arranging numbers in a certain pattern, giving chocolates to kids, etc. We must apply the multiplication or division method in order to determine a number's factors.

To learn more about LCM

brainly.com/question/20739723

#SPJ4

6 0
1 year ago
1. Jonathan can run 12 laps in 15 minutes, how long would it take him to run 4 laps?
lakkis [162]

Answer:

1.2

Step-by-step explanation:

4 0
2 years ago
Nina's car exponentially depreciates at a rate of 7% per year. If Nina bought the car when it was six year old for $12,000 what
Maksim231197 [3]
<span>$18,547.42, hope it works!

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7 0
3 years ago
I really need help, this is probability and statistics, if anyone else is taking this class, please help, it is a unit test stud
Vikki [24]

Answer:

id like to help but the picture is really blurry so im afraid that i cant. but i know there are others who can!

Step-by-step explanation:

i hope this helps you!

3 0
2 years ago
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