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4 years ago

A and B are two events.

Mathematics

1 answer:

svlad2 [7]4 years ago

5 0

Answer:

A and B are not independent events because P(A|B)≠P(A)

is the correct answer.

Step-by-step explanation:

If A and B are independent then we must have

P(AB) = P(A) P(B) and also

P(A/B) = P(A)

We are given that

A and B are two events.

Let P(A)=0.5 , P(B)=0.25 , and P(A and B)=0.15 .

P(A/B) = P(AB)/P(B) = 0.15/0.5 = 0.3

i.e. P(A/B) is not equal P(A)

Similarly P(B/A) = P(AB)/P(A) = 0.15/0.25 = 0.6 not equal to P(B)

Hence A and B are not independent.

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OLEGan [10]

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3 years ago

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Pat made a total of 48 pottery plates and cups. if she made twice as many plates as cups, how many plates did she make?

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If C stands for cups, solve for C

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3 years ago

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The 2010 General Social Survey reported a sample where about 48% of US residents thought marijuana should be made legal. If we w

Sati [7]

Answer:

The sample size is $n = 600$

Step-by-step explanation:

From the question we are told that

The sample proportion is $\r p = 0.48$

The margin of error is $MOE = 0.04$

Given that the confidence level is 95% the level of significance is mathematically represented as

$\alpha = 100 - 95$

$\alpha = 5 \%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table , the values is

$Z_{\frac{\alpha }{2} } = 1.96$

The reason we are obtaining critical value of $\frac{\alpha }{2}$ instead of $\alpha$ is because

$\alpha$ represents the area under the normal curve where the confidence level interval ( $1-\alpha$ ) did not cover which include both the left and right tail while

$\frac{\alpha }{2}$ is just the area of one tail which what we required to calculate the margin of error

Generally the margin of error is mathematically represented as

$MOE = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\r p(1- \r p )}{n} }$

substituting values

$0.04= 1.96* \sqrt{ \frac{0.48(1- 0.48 )}{n} }$

$0.02041 = \sqrt{ \frac{0.48(52 )}{n} }$

$0.02041 = \sqrt{ \frac{ 0.2496}{n} }$

$0.02041^2 = \frac{ 0.2496}{n}$

$0.0004166 = \frac{ 0.2496}{n}$

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3 years ago

PLEASE HELP ASAP!!!

barxatty [35]

Answers:

<u>24000 dollars</u> invested at 4%
<u>18000 dollars</u> was invested at 7%

======================================================

Work Shown:

x = amount invested at 4%

If she invests x dollars at 4%, then the rest (42000-x) must be invested at the other rate of 7%

She earns 0.04x dollars from that first account and 0.07(42000-x) dollars from the second account

This means we have

0.04x+0.07(42000-x)

0.04x+0.07*42000-0.07x

0.04x+2940-0.07x

-0.03x+2940

This represents the total amount of money earned after 1 year.

We're told the amount earned in interest is $2220, so we can say,

-0.03x+2940 = 2220

-0.03x = 2220-2940

-0.03x = -720

x = -720/(-0.03)

x = 24000 dollars is the amount invested at 4%

42000-x = 42000-24000 = 18000 dollars was invested at 7%

----------------------

As a check, we can see that

18000+24000 = 42000

and also

0.04x = 0.04*24000 = 960 earned from the first account

0.07*18000 = 1260 earned from the second account

1260+960 = 2220 is the total interest earned from both accounts combined

This confirms our answers.

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3 years ago

Simplify ( I dont have a calculator-.-)

notsponge [240]

The answer is 2 4/9.

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