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3 years ago

.222222222 as a fraction Please help

Mathematics

2 answers:

statuscvo [17]3 years ago

8 0

Answer:

222222222/1000000000

Step-by-step explanation:

baherus [9]3 years ago

8 0

Answer:

2/9

Step-by-step explanation:

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What's the probability of the compound event for. A bag contains 4 red, 8 blue, 6 yellow and 2 green marbles. Maria selects a ma

Nataly [62]

Given:

Number of red marbles = 4

Number of blue marbles = 8

Number of yellow marbles = 6

Number of green marbles = 2

To find:

The probability of getting a blue marble then a red marble, i.e., P(blue, red).

Solution:

Using the given information,

The total number of marbles = 4+8+6+2

= 20

Probability of getting a blue marble in first draw is

$P(Blue)=\dfrac{\text{Number of blue marbles}}{\text{Total number of marbles}}$

$P(Blue)=\dfrac{8}{20}$

$P(Blue)=\dfrac{2}{5}$

Maria selects a marble, puts it back and then selects a second marble. It means the total number of marbles remains the same.

$P(red)=\dfrac{\text{Number of red marbles}}{\text{Total number of marbles}}$

$P(red)=\dfrac{4}{20}$

$P(red)=\dfrac{1}{5}$

Now, the probability of getting a blue marble then a red marble is

$P(blue,red)=\dfrac{2}{5}\times \dfrac{1}{5}$

$P(blue,red)=\dfrac{2}{25}$

Therefore, the required probability P(blue, red) is $\dfrac{2}{25}$ .

5 0

2 years ago

4-It has been a bad day for the market, with 70% of securities losing value. You are evaluating a portfolio of 20 securities and

riadik2000 [5.3K]

Answer:

b) 0.0007

c) 0.4163

d) 0.2375

Step-by-step explanation:

We are given the following:

We treat securities lose value as a success.

P(Security lose value) = 70% = 0.7

Then the securities lose value follows a binomial distribution, where

$P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}$

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 20.

a) Assumptions

There are 20 independent trials.
Each trial have two possible outcome: security loose value or security does not lose value.
The probability for success of each trial is same, p = 0.7

b) P(all 20 securities lose value)

We have to evaluate:

$P(x = 20)\\= \binom{20}{0}(0.7)^0(1-0.7)^{20}\\= 0.0007$

0.0007 is the probability that all 20 securities lose value.

c) P(at least 15 of them lose value.)

$P(x \geq 15)\\= P(x=15) + P(x = 16) + P(x=17) + P(x=18) +P(x = 19) +P(x = 20)\\ \binom{20}{15}(0.7)^{15}(1-0.7)^{5} +...+ \binom{20}{20}(0.7)^{20}(1-0.7)^{0} \\=0.4163$

d) P(less than 5 of them gain value.)

P(gain value) = 1 - 0.7 = 0.3

$P(x < 5)\\= P(x=0) + P(x = 1) + P(x=2) + P(x=3) +P(x = 4)\\ \binom{20}{0}(0.3)^{0}(1-0.3)^{20} +...+ \binom{20}{4}(0.3)^{4}(1-0.3)^{16} \\=0.2375$

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3 years ago

Find the slope and the y intercept<br> Y=1/3x + 2

Andrej [43]

Answer:

m = 1/3, b = 2

Step-by-step explanation:

The equation is already written is slope-intercept form, y = m x + b.

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2 years ago

1. Identify each situation in which a quantity grows or decays by a constant percent rate per unit interval. A. The number of ca

zvonat [6]

Answer:

Step-by-step explanation:

1) For each situation to grow or decay by a constant percent rate, it must be exponential. Therefore, the correct examples are

A. The number of cars sold doubles every year. It is a 200% growth every year.

D. Each time you start a car engine the remaining engine life decreases by 0.0075%. A case of decay

E. The number of people creating cat videos increases by 15% percent every year.

F. Computer technology increases by a factor of 3 every five years.

2) this is a case of exponential decay. The expression for exponential decay is

y = b(1 - r)^t

y = final value

b = initial value

r = decay rate

t = time

Given that

r = 10% = 10/100 = 0.1

b = 50 kilograms

y = W kilograms

The relationship is

W = 50(1 - 0.1)^t

W = 50(0.9)^t

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2 years ago

Factor 8x^5+4x^2−12

Effectus [21]

D) because only 4 is the common factor in the equation.

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2 years ago

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