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2 years ago

Which is a good comparison of the estimated sum and the actual sum of 7 7/8 + 2 11/12?

Mathematics

2 answers:

aleksley [76]2 years ago

5 0

Answer:27.20833333

Step-by-step explanation: all you do is add them up and pick b or a for the answers

Amanda [17]2 years ago

3 0

Answer:

*thinking*

you would assume that it is 11 the actual is 10 19/24

Wich is not quite 11

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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

I 3) At 10:30 am, a submarine was 43 feet below the ocean surface. By 10:45 am, it was 271 feet below the surface. How much did

Aleks [24]

Answer: 228 Feet

Step-by-step explanation: 271 feet - 43 feet = 228 feet descended.

3 0

3 years ago

The diagram shows two sets of vectors that result in a single vector. What are the first two steps for finding the magnitude of

Nookie1986 [14]

C. Find the sum of the two horizontal in the summer for two vertical vectors.

5 0

3 years ago

the width of the rectangle is 5 inches less than it's length, and the area is 84 square inches. what are the length and width of

inysia [295]

W= l - 5 where w = width and l = length

area = 84 = l*w = l(l-5)

l(l-5) = 84
l^2 - 5l - 84 = 0
(l - 12)(l + 7) = 0
l = 12

length = 12 and width = 7

7 0

3 years ago

What is the width of a rectangle with an area of 5/8in2 and a length of 10inches

Aneli [31]

Area = length * width
5/8 = 10 * width
width = (5/8) / 10
width = 1 / 16
width = 0.0625 inches

6 0

3 years ago