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Pie
2 years ago
12

ILL GIVE BRAINLIEST! PLEASE HELP I DONT UNDERSTAND!

Mathematics
1 answer:
blsea [12.9K]2 years ago
7 0

Answer:

S₁₅ = 645

Step-by-step explanation:

The sum to n terms of an arithmetic sequence is

S_{n} = \frac{n}{2} [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Using the nth term formula a_{n} = 5n + 3 , then

a₁ = 5(1) + 3 = 5 + 3 = 8

a₂ = 5(2) + 3 = 10 + 3 = 13 , then

d = a₂ - a₁ = 13 - 8 = 5

Thus

S₁₅ = \frac{15}{2} [ (2 × 8) + (14 × 5) ]

     = 7.5( 16 + 70)

     = 7.5 × 86

     = 645

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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
<img src="https://tex.z-dn.net/?f=%20%7B2x%7D%5E%7B2%7D%20%20-%205x%20%2B%203" id="TexFormula1" title=" {2x}^{2} - 5x + 3" alt=
alexdok [17]
There’s the link to this answer
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3 years ago
Twenty students in Class A and 20 students in Class B were asked how many hours they took to prepare for an exam. The data sets
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3 0
3 years ago
Read 2 more answers
1. What is( - 1/2 + 2)<br>2. 4( 1/2+5/4) + (-5)<br>(please answer, I will mark brainliest)<br>:)​
Ulleksa [173]

1)

\longrightarrow (-\dfrac{1}{2} +2)

\longrightarrow (-\dfrac{1}{2} +\dfrac{4}{2} )

\longrightarrow \dfrac{-1+4}{2}

\longrightarrow \dfrac{3}{2}

\sf \bold{\longrightarrow 1\dfrac{1}{2}}         (final answer)

2)

\longrightarrow \sf 4(\dfrac{1}{2} +\dfrac{5}{4} ) + (-5)

\longrightarrow \sf 4(\dfrac{2}{4} +\dfrac{5}{4} ) + (-5)

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4 0
2 years ago
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aalyn [17]

Answer:

A = 24 cm^2

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A = 1/2 bh

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A = 24 cm^2

4 0
2 years ago
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