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3 years ago

0.111111.... a rational or irrational number

1 answer:

8 0

0.111111… is a rational number because it can be represented as a fraction: 1/9
It is simply a non-terminating/repeating decimal

I hope this helps :)

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3(x+1) + 1 + 2x = 2(2x + 2) + x

WARRIOR [948]

0 = 0
The input is an identity: it is true for all values

3 0

3 years ago

Suppose that 4 fair coins are tossed. Let Equals The event that exactly 2 coins show tails and Equal The event that at least 2 c

faust18 [17]

Answer:

a) P ( E | F ) = 0.54545

b) P ( E | F' ) = 0

Step-by-step explanation:

Given:

- 4 Coins are tossed

- Event E exactly 2 coins shows tail

- Event F at-least two coins show tail

Find:

- Find P ( E | F )

- Find P ( E | F prime )

Solution:

- The probability of head H and tail T = 0.5, and all events are independent

So,

P ( Exactly 2 T ) = ( TTHH ) + ( THHT ) + ( THTH ) + ( HTTH ) + ( HHTT) + ( HTHT) = 6*(1/2)^4 = 0.375

P ( At-least 2 T ) = P ( Exactly 2 T ) + P ( Exactly 3 T ) + P ( Exactly 4 T) = 0.375 + ( HTTT) + (THTT) + (TTHT) + (TTTH) + ( TTTT)

= 0.375 + 5*(1/2)^4 = 0.375 + 0.3125 = 0.6875

- The probabilities for each events are:

P ( E ) = 0.375

P ( F ) = 0.6875

- The Probability to get exactly two tails given that at-least 2 tails were achieved:

P ( E | F ) = P ( E & F ) / P ( F )

P ( E | F ) = 0.375 / 0.6875

P ( E | F ) = 0.54545

- The Probability to get exactly two tails given that less than 2 tails were achieved:

P ( E | F' ) = P ( E & F' ) / P ( F )

P ( E | F' ) = 0 / 0.6875

P ( E | F' ) = 0

6 0

3 years ago

If equation one is mutiplied by 2 and then the equations are added the result is 2x+y=3 X-2y=-1

zloy xaker [14]

Question:

2x + y = 3, x - 2y = –1.

If equation one is multiplied by 2 and then the equations are added, the result is _____.

(A) 3x = 2

(B) 3x = 5

Answer:

Option C:

5x = 5

Solution:

Given equations are

2x + y = 3 – – – – (1)

x – 2y = –1 – – – – (2)

Let us first multiply equation (1) by 2, we get

(1) × 2 ⇒ 4x + 2y = 6 – – – – (3)

Now, add equation (3) to equation (2).

⇒ x – 2y + 4x + 2y = –1 + 6

Combine like terms together.

⇒ x + 4x – 2y + 2y = –1 + 6

⇒ 5x = 5

So, if equation one is multiplied by 2 and then the equations are added, the result is 5x = 5.

8 0

4 years ago

Which graph shows the solution set of ?

NNADVOKAT [17]

Answer:

The questions should be on the top of each question as they come.

Step-by-step explanation:

8 0

3 years ago

It turns out that (0.125)^3 can be written as 2^a for some integer a. Find a.

Ann [662]

Answer:

$a=-9$

Step-by-step explanation:

We begin with $(0.125)^3$

First, we can convert this decimal into a fraction

$(\frac{1}{8} )^3$

Now, we can simplify the denominator of the fraction

$(\frac{1}{2^{3} } )^3$

Next, we can remove the fraction by rewriting the fraction with a negative power.

$(2^{-3} )^3$

Lastly, we can remove the parenthesis by multiplying the powers together.

$2^{-9}$

This means that $a=-9$

4 0

3 years ago

0.111111.... a rational or irrational number​

0.111111.... a rational or irrational number