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4 years ago

PLEASE HELP ME!!!!!! DUE TOMORROW!!!!!!!

Mathematics

1 answer:

gayaneshka [121]4 years ago

8 0

Answer:

Step-by-step explanation:

Initial number occurs when x = 0

so its 9(2)^0

= 9*1

= 9 answer

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Eight identical slips of paper, each containing one number from one to eight, inclusive, are mixed up inside a bag. Subset A of

DochEvi [55]

Answer: The correct option is (C) A = {1, 2, 3, 4, 5, 7, 8}.

Step-by-step explanation: Given that eight identical slips of paper, each containing one number from one to eight, inclusive, are mixed up inside a bag.

The sample space, S will be

S = {1, 2, 3, 4, 5, 6, 7, 8}.

Subset A of the sample space represents the complement of the event in which the number 6 is drawn from the bag.

Let, 'B' represents the event in which the number 6 is drawn from the bag.

So, B = {6}.

Since 'A' is the complement of 'B', so the set 'A' will contain those element of the sample space 'S' that are not in the set 'B'.

Therefore,

A = B' = {1, 2, 3, 4, 5, 7, 8}

⇒ A = {1, 2, 3, 4, 5, 7, 8}.

Thus, (C) is the correct option.

7 0

3 years ago

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Which statement is true? I am giving a lot of points away for this so please provide the correct answer and an explanation.

ikadub [295]

Answer:

the second option from the top

7 0

3 years ago

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Why is 6 1/2 equal to the square root of 6

Aleksandr-060686 [28]

Because It Can Be Simplified Many Ways

4 0

4 years ago

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Math graph equation. (Picture.)

vladimir1956 [14]

Answer:

y = -2x + 3 is the required equation

Step-by-step explanation:

From the graph we will get two ordered pairs

If we see that When x=0 then y=3 and when x = 1 then y=1

Now from this we can find the slope of the Graph

So slope of graph = (y2 - y1) / (x2-x1)

=(1-3) / (1-0)

=-2

Slope = m = -2

Now the equation is

y = mx + b

We have to find the value of b

as we have two ordered pairs we can take any of it to find the value of b because line passes through those points

taking (0,3) as a point

y= mx + b

put values

3 = -2*(0) + b

b=3

Now the equation of the line in this form is

y = mx + b

which is

y = -2x + 3

5 0

3 years ago

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 $s + t + st = -1$