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Natasha2012 [34]
3 years ago
15

4. Determine whether the statement is true or false. Prove the statement directly from the definition if it is true, and give a

counterexample if it is false. The average of two odd integers is odd.
Mathematics
1 answer:
natta225 [31]3 years ago
3 0

Answer:

The statement is false.

Step-by-step explanation:

Let a and b represent two odd integers.

The average (A) is defined by:

A=\frac{a+b}{2}

In order to prove the statement, you have to show that it's true for all odd integers. But, to disprove it, you just have to find a counterexample where the statement is false.

Notice that it is easier to try to find a counterexample.

For example, a=3 and b=5

A= \frac{3+5}{2} = \frac{8}{2} = 4

The result of the average is even, therefore the statement is false.

The previous calculation is a counterexample.

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cassidy loves black and yellow jelly beans she noticed when she was counting them that she had 7 less than three times as many b
Dmitriy789 [7]
Most of the information's are already given in the question. It is important to understand the language of the problem for solving the problem. Once the language is understood, then solving the problem is easy.
Let us assume the number of black jelly beans = x
Number of yellow jelly beans = y
Then from the question we can get to a equation.
3x - 7 = y
We also know from the question that
x + y = 225
x + 3x -7 = 225
4x = 225 + 7
4x = 232
x = 232/4
   = 58
So Cassidy has 58 black jelly beans out of the total of 225 jelly beans
4 0
2 years ago
Can somebody prove this mathmatical induction?
Flauer [41]

Answer:

See explanation

Step-by-step explanation:

1 step:

n=1, then

\sum \limits_{j=1}^1 2^j=2^1=2\\ \\2(2^1-1)=2(2-1)=2\cdot 1=2

So, for j=1 this statement is true

2 step:

Assume that for n=k the following statement is true

\sum \limits_{j=1}^k2^j=2(2^k-1)

3 step:

Check for n=k+1 whether the statement

\sum \limits_{j=1}^{k+1}2^j=2(2^{k+1}-1)

is true.

Start with the left side:

\sum \limits _{j=1}^{k+1}2^j=\sum \limits _{j=1}^k2^j+2^{k+1}\ \ (\ast)

According to the 2nd step,

\sum \limits_{j=1}^k2^j=2(2^k-1)

Substitute it into the \ast

\sum \limits _{j=1}^{k+1}2^j=\sum \limits _{j=1}^k2^j+2^{k+1}=2(2^k-1)+2^{k+1}=2^{k+1}-2+2^{k+1}=2\cdot 2^{k+1}-2=2^{k+2}-2=2(2^{k+1}-1)

So, you have proved the initial statement

4 0
3 years ago
Write the equation of a line in slope intercept form that has a slope of -½ and contains (4, –5)
evablogger [386]

Answer:

Step-by-step explanation:

y + 5 = -1/2(x - 4)

y + 5 = -1/2x + 2

y = -1/2x - 3

6 0
3 years ago
Juan earns $18 per hour. He receives time and a half for overtime. Last week he worked 50 hours. What was Juan’s gross pay last
larisa [96]

Answer:

$900

Step-by-step explanation:

18 x 50 = 900

69.25 i belive for taxes

3 0
2 years ago
im rushing and have like 20 more things so if someone could actually help me right answers, please. T~T
igomit [66]
1. a. 0=0, 4x=4x, -18=-18
b. 3
2.a. 0=-2, 2= 0
b. 2
7 0
2 years ago
Read 2 more answers
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