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3 years ago

Suppose P(A) = 0.9, P(B) = 0.3, and P(B|A) = 0.2. What is P(A|B) ?

Mathematics

1 answer:

Elenna [48]3 years ago

6 0

By definition of conditional probability,

$P(B\mid A)=\dfrac{P(B\cap A)}{P(A)}\implies P(B\cap A)=0.2\cdot0.9=0.18$

Similarly,

$P(A\mid B)=\dfrac{P(A\cap B)}{P(B)}=\dfrac{0.18}{0.3}=0.6$

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Identify rational numbers and intergers from the following

Nina [5.8K]

Answer:

Rational: all

Integers: 4, -36, -6

Step-by-step explanation:

A rational number is a number that can be written as a fraction of integers.

All numbers shown are rational numbers.

The integers are all positive and negative whole numbers and zero.

The integers are: 4, -36, -6

6 0

2 years ago

A Web music store offers two versions of a popular song. The size of the standard version is 2.9 megabytes (MB). The size of the

Lady bird [3.3K]

Write the equations: $2.9s+4.7h=6076
 \\ h= 4s$
Substitute for h: $2.9s+4.7(4s)=6076$
Solve for s: $2.9s+4.7(4s)=6076 \\ 2.9s+18.8s=6076 \\ 21.7s=6076 \\ s=280$
There were 280 downloads of the standard version. There were 1120 downloads of the high-quality version.

5 0

2 years ago

Robert gets a loan from his bank.

Goryan [66]

Answer:

£10,200

Step-by-step explanation:

Simple interest = principal × rate × time

Principal = £6000

Rate = 7% = 0.07

Time = 10 years

Simple interest = principal × rate × time

= £6000 × 0.07 × 10

= £4,200

Total = simple interest + principal

= £4,200 + £6,000

= £10,200

He would have to pay back a total of £10,200 in 10 years

5 0

2 years ago

Please help mee, (30 points will give brainliest!!!)

Vadim26 [7]

Answer:

-4

-0.5, 12.25

x = -0.5

Step-by-step explanation:

The x intercepts are the values of x when y = 0 ie the roots of the equation
$-x^2 -x +12 = 0$

$x^2 + x - 12 = 0$

We can re-write the above as:
(x+4) (x-3) = 0
This gives the two roots as x = -4 and x = +3. Leftmost (smallest) root is -4 and rightmost(largest) root is +3

y intercept is when x = 0. Plugging into the original equation, y value at x = 0 is 12

Vertex x value is given by the formula -b/2a where a is the coefficient of x^2 and b the coefficient of x

Here a = -1, b= -1 so vertex x value = - (-1)/(-1).2 = - 1/2 = -0.5

Plugging this value of x into the original function gives the vertex y value
$y = - (0.5^{2}) - (-0.5) + 12\\= -0.25 + 0.5 + 12 = 12.25$

The line of symmetry is the vertical line corresponding to the vertex x value so line of symmetry is at x = -0.5

The graph of the quadratic function shows these values

3 0

2 years ago

A fast food restaurant executive wishes to know how many fast food meals adults eat each week. They want to construct a 98% conf

adelina 88 [10]

Answer:

$n=(\frac{2.326(1.1)}{0.07})^2 =1336.006 \approx 1337$

So the answer for this case would be n=1337 rounded up to the nearest integer

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=1.1$ represent the population standard deviation

n represent the sample size

Solution to the problem

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =0.07 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 98% of confidence interval now can be founded using the normal distribution. And in excel we can use this formula to find it:"=-NORM.INV(0.01;0;1)", and we got $z_{\alpha/2}=2.326$ , replacing into formula (b) we got:

$n=(\frac{2.326(1.1)}{0.07})^2 =1336.006 \approx 1337$

So the answer for this case would be n=1337 rounded up to the nearest integer

3 0

3 years ago