Simplify (3x^2y^3)^3

a cooler contains 50 bottles; 30 bottles of water, which 8 are lemon flavored and 20 bottles of tea, of which 5 are lemon flavor

xenn [34]

Answer:

The required probability is $\dfrac{13}{50}$

Step-by-step explanation:

Total number of bottles = 50

Total number of water bottles = 30

Total number of lemon flavored water bottles = 8

Total number of tea bottles = 20

Total number of lemon flavored tea bottles = 5

Probability of selecting a lemon flavored water bottle = Probability of selecting a water bottle $\times$ Probability of selecting a lemon bottle out of water bottles.

Probability of selecting a lemon flavored tea bottle = Probability of selecting a tea bottle $\times$ Probability of selecting a lemon bottle out of tea bottles.

Formula for probability of an event E can be observed as:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

Probability of selecting a water bottle:

$\dfrac{30}{50} = \dfrac{3}{5}$

Probability of selecting a lemon flavored bottle from water bottle:

$\dfrac{8}{30}$

Probability of selecting a lemon flavored water bottle = P(A)

$\dfrac{3}{5} \times \dfrac{8}{30} = \dfrac{4}{25}$

Probability of selecting a tea bottle:

$\dfrac{20}{50} = \dfrac{2}{5}$

Probability of selecting a lemon flavored bottle from tea bottle:

$\dfrac{5}{20} = \dfrac{1}{4}$

Probability of selecting a lemon flavored tea bottle = P(B)

$\dfrac{2}{5} \times \dfrac{1}{4} = \dfrac{1}{10}$

The required probability is:

P(A) + P(B):

$\dfrac{4}{25} + \dfrac{1}{10}\\\Rightarrow \dfrac{8+5}{50}\\\Rightarrow \dfrac{13}{50}$

8 0

3 years ago

Which of the following is NOT a lifestyle factor that affects physical fitness?

jolli1 [7]

Answer:

option D clothing

Step-by-step explanation:

Physical fitness is defined as the ability of one to carry out his task without fatigue. This includes muscle strength, flexibility, body composition, cardio respiratory endurance.

Hence we find that clothing has nothing to do with the above things in any way.

Work burns calories and related to physical fitness similarly chores and exercise also

So option D clothing is right answer.

4 0

3 years ago

Read 2 more answers

What is the value of x?

qaws [65]

Answer:

5

Step-by-step explanation:

6x+12 = 9x-3

3x = 15

x= 5

3 0

3 years ago

Currently 1 United States dollar equals 19.25 Mexican pesos. If you exchanged 725 Mexican pesos for US dollars, what amount woul

Irina18 [472]

Answer:

The value of 725 Mexican pesos is equals to 37.66 US dollars

Step-by-step explanation:

Given as :

The value of 1 US dollar equals to 19.25 Mexican pesos

The total amount of Mexican pesos = 725

Now,

∵ 19.25 Mexican pesos equals to 1 US dollars

∴ 725 Mexican pesos equals to $\frac{725}{19.25}$ = 37.66 US dollars

Hence The value of 725 Mexican pesos is equals to 37.66 US dollars Answer

5 0

3 years ago

Gallup conducted a survey from April 1 to 25, 2010, to determine the congressional vote preference of the American voters.15 The

Lisa [10]

Answer:

p ( x > 2746 ) = p ( z > - 1.4552 )

= 1 - 0.072806

= 0.9272

This shows that there is > 92% of a republican candidate winning the election hence I will advice Gallup to declare the Republican candidate winner

Step-by-step explanation:

Given data:

51% of male voters preferred a Republican candidate

sample size = 5490

To win the vote one needs ≈ 2746 votes

In order to advice Gallup appropriately lets consider this as a binomial distribution

n = 5490

p = 0.51

q = 1 - 0.51 = 0.49

Hence $n_{p}$ > 5 while $n_{q}$ < 5

we will consider it as a normal distribution

From the question :

number of male voters who prefer republican candidate ( mean ) ( u )

= 0.51 * 5490 = 2799.9

std = $\sqrt{npq}$ = $\sqrt{5490 * 0.51 *0.49}$ = 37.0399 ---- ( 1 )

determine the Z-score = (x - u ) / std ---- ( 2 )

x = 2746 , u = 2799.9 , std = 37.0399

hence Z - score = - 1.4552

hence

p ( x > 2746 ) = p ( z > - 1.4552 )

= 1 - 0.072806

= 0.9272

This shows that there is > 92% of a republican candidate winning the election hence I will advice Gallup to declare the Republican candidate winner

7 0

2 years ago