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2 years ago

One third of a birds eggs hatched. If 2 eggs hatched, how many eggs did the bird lay?

Mathematics

2 answers:

solniwko [45]2 years ago

5 0

He laid 6 eggs and 2 hatched

Maurinko [17]2 years ago

4 0

6 total eggs were laid. simple fraction.

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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

2 years ago

Shirley is decorating the gym for a party, she has 4 rolls of blue streamer and 7 rolls of green streamer. if each roll of blue

Radda [10]

You do 4 times 95 and you get 380 plus 7 times 84 and that's 588 and 380+588=968 feet.

3 0

2 years ago

It's possible to build a triangle with side lengths of 3.3, and 9 A. True B. False

mario62 [17]

True it is possible to built a triangle with 3.3 and 9. Two long we sides would be 9 and the bottom side would be 3

4 0

2 years ago

Anna has 7 baskets and some flowers. she has 5 fewer baskets than flowers. how many flowers does anna have

MrRa [10]

Answer:

2 flowers

Step-by-step explanation:

if she has 7 baskets and 5 fewer baskets than flowers

you get the equation 7-5 which is 2

8 0

2 years ago

How to simplify -6k +7k 12r -8 -12 n -10 +9n -3 -4x-10x -r -10r

Semmy [17]

Answer:

Solve by adding or subtracting like terms. (Ex. 2k + 4k = 6k; 9 + 7 = 16)

- 6k + 7k = 1k = k

(7 - 6 = 1)

12r - 8 - 12 = 12r - 20

(8 + 12 = 20 but sign is negative) 12r will stay the same because there are no terms with a letter r.

n - 10 + 9n - 3 = 9n + n - 10 - 3 = 10n - 10 - 3 = 10n - 13

(n = 1 so 9 + 1 = 10; 10 + 3 = 13 but negative sign)

- 4x - 10x = 14x

(10 + 4 = 14)

- r - 10r = 11r

(r = 1 so 10 + 1 = 11)

6 0

2 years ago