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3 years ago

Which fraction is between 0.6 and 0.7

2 answers:

7 0

If you write .6 and .7 as fractions you get 6/10 and 7/10. If you double those you get 12/20 and 14/20, so one potential fraction between the two could be 13/20.

vova2212 [387]3 years ago

4 0

0.5? i think i know 0.6 is 3/5 hope this helps

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Problems 2.21, 2.22, 2.23

RoseWind [281]

Statements can be proved by contrapositive, contradiction or by induction.

2.21 and 2.23 are proved by contrapositive
2.22 is proved by induction

2.21: If $n^3$ is even, then n is even (By contrapositive)

The contrapositive of the above statement is that:

If n is odd, then $n^3$ is odd

Represent the value of n as:

$n = 2k + 1$ , where $k \ge 0$

Take the cube of both sides

$n^3 = (2k + 1)^3$

Expand

$n^3 = 8k^3 + 6k^2 + 6k + 1$

Group

$n^3 =[ 8k^3 + 6k^2 + 6k] + 1$

Factor out 2

$n^3 =2[4k^3 + 3k^2 + 3k] + 1$

Assume w is an integer; where:

$w =4k^3 + 3k^2 + 3k$

So, we have:

$n^3 =2w + 1$

The constant term (i.e. 1) means that $n^3$ is odd.

Hence, the statement has been proved by contrapositive.

i.e. If n is odd, then $n^3$ is odd

2.22 $3n + 4$ is even, if and only if n is even

We have: $3n + 4$

Assume that: $n = 2k + 2$ for $k \ge 0$

So, we have:

$3n + 4 = 3(2k + 2) + 4$

Open bracket

$3n + 4 = 6k + 6 + 4$

$3n + 4 = 6k + 10$

Factorize

$3n + 4 = 2(3k + 5)$

The factor of 2 means that $3n + 4$ is even.

Hence, $3n + 4$ is even, if and only if n is even

2.22: $s \ne -1$ and $t \ne -1$ , then $s + t + st \ne -1$

To do this, we prove by contrapositive.

The contrapositive of the above statement is:

If $s = -1$ and $t=-1$ , then $s + t + st = -1$

We have:

$s + t + st = -1$

Substitute the values of s and t in: $s + t + st = -1$

$-1 -1 -1 \times -1 = -1$

$-1 -1 + 1 = -1$

$-1 = -1$

Hence, by contrapositive:

If $s = -1$ and $t=-1$ , then $s + t + st = -1$

Read more about proofs at:

brainly.com/question/19643658

7 0

3 years ago

Vicky is renting an apartment.In addition to the first month’s rent, the landlord requires him to pay half of a month's rent as

Slav-nsk [51]

Answer:

$2000

Step-by-step explanation:

Let the monthly rent be x.

Then we have:

x + 0.5x + 0.4x = 3800
1.9x = 3800
x = 3800/1.9
x = 2000

Monthly rent is $2000

7 0

3 years ago

Read 2 more answers

Hewo can anyone help

Tasya [4]

Answer:

Hewo can anyone help

Step-by-step explanation:

I would go with the last option,it looks like it makes sense.

Hope that helped,I have snap if you need anything else :)

3 0

3 years ago

Kim makes a bar graph to record votes for the choice of a class pet.Each grid line represents 4 votes.Fish got 10 votes.The bar

rosijanka [135]

Answer: they got 40 votes

Step-by-step explanation:

because 10+10+10+10 eqauls 40 yw friend follow me on tiktok @tayleerosee

8 0

3 years ago

If 3 times a square of an integer is added to 1 times the integer, the result is 2

jarptica [38.1K]

Let unknown integer be n.

So then your sentence would translate to 3n² + n = 2.

If you need to solve for n then we can move 2 to left side by subtract both sides by 2:

3n² + n - 2 = 0

Now you can factor:

3n² + 3n -2n - 2 = 0

3n( n + 1 ) - 2( n + 1 ) = 0

( 3n - 2 )( n + 1 ) = 0

3n - 2 = 0 OR n + 1 = 0

3n = 2 OR n = -1

n = 2/3 OR n = -1

Final answer: n = 2/3 OR n = -1

6 0

3 years ago