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3 years ago

The consecutive odd integers have a sum of 36. find the integers

Mathematics

2 answers:

svet-max [94.6K]3 years ago

5 0

<h3>Answer: 17 and 19</h3>

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Work Shown:

x = some integer

2x = even integer

2x+1 = odd integer

(2x+1)+2 = 2x+3 = odd integer just after 2x+1

The integers 2x+1 and 2x+3 add to 36

(2x+1)+(2x+3) = 36

2x+2x+1+3 = 36

4x+4 = 36

4x+4-4 = 36-4 ... subtract 4 from both sides

4x = 32

4x/4 = 32/4 .... divide both sides by 4

x = 8

With x = 8, we can say

2x+1 = 2*8+1 = 17 is the first odd integer

2x+3 = 2*8+3 = 19 is the next odd integer

17+19 = 36, so the answer is confirmed

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A non-algebraic way to get the answer is to divide 36 in half to get 18

Then try odd integers around 18, so 19+21 = 40 but thats too high

then maybe try 15+17 = 32, thats too low

17+19 = 36 is right on the money

DanielleElmas [232]3 years ago

4 0

how many consecutive odd integers are there, or else I can't help you

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<h3>Further explanation</h3>

The probability of an event is defined as the possibility of an event occurring against sample space.

$\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }$

<h2>Permutation ( Arrangement )</h2>

Permutation is the number of ways to arrange objects.

$\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }$

<h2>Combination ( Selection )</h2>

Combination is the number of ways to select objects.

$\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }$

Let us tackle the problem.

This problem is similar to Pascal Triangle.

The Lord can move to the right or up in one way only.

We can put "1" in each box on the bottom and left to represent 1 possible movement.

To get the possibility of movement to another box, we will add the possibility of movement to the left, right, and diagonal squares as shown in Figure 1.

This process is repeated for the next box as shown in Figure 2.

Finally, after this process is repeated until the top right box, we get the results as shown in Figure 3.

There are 48639 ways for a lord to move from the bottom left to top right corner of the 8 by 8 chessboard.

<h3>Learn more</h3>

Different Birthdays : brainly.com/question/7567074
Dependent or Independent Events : brainly.com/question/12029535
Mutually exclusive : brainly.com/question/3464581

<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Probability

Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation

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