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Orlov [11]
3 years ago
9

HELP QUICK PLEASE!

Mathematics
1 answer:
olchik [2.2K]3 years ago
3 0

Answer:

Step-by-step explanation:

Side - side - side. In fact the two triangles have the side CD in common

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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
sleet_krkn [62]

This question is incomplete, the complete question is;

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 are written in increasing order but are not necessarily distinct.

In other words, how many 5-tuples of integers  ( h, i , j , m ), are there with  n ≥ h ≥ i ≥ j ≥ k ≥ m ≥ 1 ?

Answer:

the number of 5-tuples of integers from 1 through n that can be formed is [ n( n+1 ) ( n+2 ) ( n+3 ) ( n+4 ) ] / 120

Step-by-step explanation:

Given the data in the question;

Any quintuple ( h, i , j , m ), with n ≥ h ≥ i ≥ j ≥ k ≥ m ≥ 1

this can be represented as a string of ( n-1 ) vertical bars and 5 crosses.

So the positions of the crosses will indicate which 5 integers from 1 to n are indicated in the n-tuple'

Hence, the number of such quintuple is the same as the number of strings of ( n-1 ) vertical bars and 5 crosses such as;

\left[\begin{array}{ccccc}5&+&n&-&1\\&&5\\\end{array}\right] = \left[\begin{array}{ccc}n&+&4\\&5&\\\end{array}\right]

= [( n + 4 )! ] / [ 5!( n + 4 - 5 )! ]

= [( n + 4 )!] / [ 5!( n-1 )! ]

= [ n( n+1 ) ( n+2 ) ( n+3 ) ( n+4 ) ] / 120

Therefore, the number of 5-tuples of integers from 1 through n that can be formed is [ n( n+1 ) ( n+2 ) ( n+3 ) ( n+4 ) ] / 120

4 0
3 years ago
Write an equation for a line in slope-intercept form that is parallel to y=−2x+5 and passing through the point (3,−10)
STALIN [3.7K]

Answer: y=-2x-4

Step-by-step explanation:

y=-2x+b

-10=-2(3)+b

-10=-6+b

-4=b

5 0
3 years ago
Read 2 more answers
How do you solve what is 30% of $240
DerKrebs [107]
The Answer would be x=72. Why? Because \frac{x}{240} =  \frac{30}{100}.   Fraction  \frac{30}{100} is your %.  You Cross multiply 240 * 30 = 100x
240 time 30 = 7200. you want x to  be alone so you do 7200 divided by 100 equaling 72. So you get x=72. 
6 0
3 years ago
Marty ate 1/4 of his pizza and Luis ate 1/3 of his pizza. Marty ate more pizza than Luis. Is that possible?
Nataly_w [17]
Of course.

You can only say for sure that 1/4 of a whole thing is less than 1/3 of a whole thing
if the whole things are equal size.

If Marty's pizza was 1/3 bigger than Luis' pizza, then they both ate the same amount.
If Marty's was MORE than 1/3 bigger than Luis', then Marty ate more pizza.
8 0
3 years ago
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Dana wants to make two types of dog treats. She has 10 cups of peanut butter and 12 cups of flour. Her dog bone treat recipe use
strojnjashka [21]
Let x represent the number of trays of dog bone treats made and y represent number of trays of oatmeal dog treats made.
4 0
3 years ago
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