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3 years ago

Write a multiplication sentence to describe each model

Mathematics

1 answer:

Delicious77 [7]3 years ago

4 0

No picture? I can help but I need you to explain more lol

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If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple ar

erma4kov [3.2K]

Answer:

$\frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{120}$

Step-by-step explanation:

Given

5 tuples implies that:

$n = 5$

$(h,i,j,k,m)$ implies that:

$r = 5$

Required

How many 5-tuples of integers $(h, i, j, k,m)$ are there such that $n\ge h\ge i\ge j\ge k\ge m\ge 1$

From the question, the order of the integers h, i, j, k and m does not matter. This implies that, we make use of combination to solve this problem.

Also considering that repetition is allowed: This implies that, a number can be repeated in more than 1 location

So, there are n + 4 items to make selection from

The selection becomes:

$^{n}C_r => ^{n + 4}C_5$

$^{n + 4}C_5 = \frac{(n+4)!}{(n+4-5)!5!}$

$^{n + 4}C_5 = \frac{(n+4)!}{(n-1)!5!}$

Expand the numerator

$^{n + 4}C_5 = \frac{(n+4)!(n+3)*(n+2)*(n+1)*n*(n-1)!}{(n-1)!5!}$

$^{n + 4}C_5 = \frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{5!}$

$^{n + 4}C_5 = \frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{5*4*3*2*1}$

$^{n + 4}C_5 = \frac{(n+4)*(n+3)*(n+2)*(n+1)*n}{120}$

<u><em>Solved</em></u>

6 0

3 years ago

Take a square sheet of paper 20 cm by 20 cm, cut identical squares from each corner, and fold up the flaps to make a box (withou

iris [78.8K]

The maximum possible volume of this type of box that can be made from a 20 cm by 20 cm square of paper is 512cm³.

<h3>How to calculate the volume?</h3>

From the information, when the side of 1cm are cut, this will become an open box. The volume will be:

= 18 × 18 × 1

= 324cm³

Also, when 2cm is cut, the volume will be:

= 16 × 16 × 2

= 512cm³

Learn more about volume on:

brainly.com/question/1972490

#SPJ1

3 0

2 years ago

The sum of two numbers is 39 and the difference is 3. What are the numbers?

frosja888 [35]

Answer: 21 & 18

Step-by-step explanation:

Sum of two numbers is 39

Difference is 3

Let the numbers be x & y

X+y=39........equation 1

X-y=3...........equation 2

X=3+y............equation 3

Substitute equation 3 into equation 1

(3+y)+y=39

3+y+y=39

3+2y=39

2y=39-3

2y=36

Y=36/2

Y=18

Substitute for y in equation 2

X-y=3

X-18=3

X=3+18

X=21

The two numbers are 21 & 18

8 0

4 years ago

16+ (-26) = -10<br> 9.-16+(-4)<br> - 16+(-4)=<br> 12<br> 3-(4)

Stels [109]

Answer:

The answer is -1.

Step-by-step explanation:

It is a little messy tho. I will assume that you want 3-(4)

6 0

4 years ago

Given AB intersects DE at point C. prove: DCB = ECA. What is the missing reason in step 5

kicyunya [14]

Answer: the answer is linear pair

Step-by-step explanation:

5 0

3 years ago