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matrenka [14]
3 years ago
14

Given that events A and B are mutually exclusive, i.e., A?B = ? and P(A?B) =0, and that P(A)=0.7 and P(B)=0.2, find P(A or B).

Mathematics
1 answer:
arsen [322]3 years ago
8 0

Answer:

P(A or B)= P(A \cup  B) = 0.9

Step-by-step explanation:

given ,      P(A)=0.7    P(B)=0.2

                   P(A or B) = P(A \cup  B) =0

since it is mutually exclusive event ,  P(A and B)= P(A \cap B) =P(A?B) = 0

           P(A \cup  B) = P(A) + P(B) - P(A\cap B)

            P(A \cup  B) = 0.7 + 0.2 - 0

            P(A \cup  B) = 0.9

   

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Answer:

a) Statistic.

b) The population proportion is expected to be between 0.29 and 0.31 with a 94% degree of confidence.

Step-by-step explanation:

a) The proportion of 30% is a statistic, as it is a value that summarizes data only from the sample taken in the study from USA Today. Other samples may yield different proportions.

b) We can use the statistic to estimate a confidence interval for the parameter of the population.

The standard error for the proportion is calculated as:

\sigma_p=\sqrt{\dfrac{p(1-p)}{N}}=\sqrt{\dfrac{0.3\cdot 0.7}{7335}}=\sqrt{2.83\cdot10^5}= 0.00535

The margin of error is 0.01. We can use this value to determine the level of confidence that represents.

The formula for the margin of error is:

E=z\cdot \sigma_p=0.01\\\\z\cdot 0.0535=0.01\\\\z=1.87

This z-value, according to the the standard normal distribution, corresponds to a confidence interval of 94%.

The interval for this margin of error is:

p-E\leq \pi \leq p+E\\\\0.30-0.01\leq \pi \leq 0.30+0.01\\\\0.29\leq \pi \leq 0.31

Then, we can conclude that the population proportion is expected to be between 0.29 and 0.31 with a 94% degree of confidence.

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a manufacturer of spiral notebooks randomly checked a box of 500 notebooks and found that 8 had defects. If the manufacturer pro
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Tina decided to build a pen for her new puppy. She decided the length of the pen would be 7 feet and the width would be 4 2/3 fe
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Answer:

The perimeter of the object is 23.\overline3 feet.

Step-by-step explanation:

The perimeter of an object is solved with the formula:

\bullet \ \ \ 2l + 2w = p,

where <em>p</em> is the perimeter of the object, <em>l</em> is the length of the object, and <em>w</em> is the width of the object.

Therefore, we want to define the values we have been given:

  • 7 feet - length (<em>l </em>)
  • 4 2/3 feet - width (<em>w </em>)

We can use these and supply them into the equation to solve for p.

\displaystyle 2(7) + 2(4\frac{2}{3})=p\\\\14 + \frac{20}{3} = p\\\\p = \frac{70}{3}

Therefore, the perimeter of the object is \displaystyle \frac{70}{3} or 23.\overline{3} feet.

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A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by th
Mashutka [201]

Here is the full question

A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of second.

Equation:

y=-16x^2+153x+98

Answer:

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Step-by-step explanation:

Given equation :

y=-16x^2+153x+98 shown the expression of a quadratic equation

Let y =0

∴

0 = -16x^2+153x+98

where;

a=-16\\b=153\\c=98

Using the quadratic formula:

x=\frac{-b\±\sqrt{b^2-4ac}}{2a}

replacing it with our values; we have:

x=\frac{-153\±\sqrt{153^2-4(-16)(98)}}{2(-16)}

x=\frac{-153\ + \sqrt{153^2-4(-16)(98)}}{2(-16)}    OR     x=\frac{-153\ - \sqrt{153^2-4(-16)(98)}}{2(-16)}

x_1=10.17   OR     x_2=-0.60

Hence, we go by the positive value since,  is the time that the rocket will hit the ground.

x= 10.17

x = ≅ 10.2 seconds

Therefore, the rocket will hit the ground,  to the nearest 100th of second.  = 10.2 seconds

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