Given that events A and B are independent with P(A)=0.85 and P(B) = 0.3,determine the value of P(A|B), rounding to the nearest thousandth, if necessary.

Answers

Answer 1

The Solution.

Given that

[tex]\begin{gathered} P(A)=0.85 \\ P(B)=0.3 \end{gathered}[/tex]

The conditional probability P(A/B) is given as

[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]

But for independent events, we have that

[tex]P(A\cap B)=P(A)\times P(B)[/tex]

Hence, it follows that

[tex]\begin{gathered} P(A|B)=\frac{P(A)\times P(B)}{P(B)}=P(A)=0.85\approx0.850 \\ \text{though the nearest thousandth is not necessary.} \end{gathered}[/tex]

Therefore, the correct answer is 0.85 ( 0.850 if you consider it necessary)


Related Questions

Justin places a bet on the giants to win the superbowl. the odds are 2:3. a) Are the giants expected to win? why or why not?b) Find P(Giants win)=

Answers

To convert the odds to a probability, we can divide the odds by one plus the odds.

then, in this case we have the following:

[tex]\begin{gathered} \text{odds:} \\ 2\colon3=\frac{2}{3} \\ \Rightarrow1+\frac{2}{3}=\frac{5}{3} \end{gathered}[/tex]

then, we have that the probability is:

[tex]\frac{\frac{2}{3}}{\frac{5}{3}}=\frac{2\cdot3}{5\cdot3}=\frac{2}{5}[/tex]

thus, the probability that the Giants will win the superbowl is 2/5=0.4=40%

As we can see, we cannot expect for sure that the giants will win

If 3 dogs eat 4 pounds of food per day, how many dogs eat 15 pounds of food?

Answers

11 dogs will eat 15 pounds of food.

According to the question,

We have the following information:

3 dogs eat 4 pounds.

We have to find how many dogs will eat 15 pounds.

We have the following expression:

4 pounds = 3 dogs

We can treat dog as a non-living object or a product.

So, we can find the parts devoted to 1 pound:

1 pound = 3/4

Now, we have to find the same for 15 pounds:

15 pounds = (3/4)*15

15 pounds = 11.25

Now, note that the number of dogs can not be in points. So, we will round it off to form a whole number.

So, 15 pounds = 11 dogs

Hence, 15 pounds of food is enough for 11 dogs.

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13. The model represents an equation. 1 1 1 1 À AC X DOOD D0000 solue.) What value of x makes the equation true? 15.

Answers

Answer:

The equation is true when x = 2.25

Explanation:

On the left side of the equation, there are 3 triangles with value -x and 10 triangles with value 1. So, the expression for the left side of the equation is:

3*(-x) + 10*(1)

-3x + 10

For the right side, we have 5 triangles with value x and 8 triangles with value -1. So, the expression for the right side is:

5*x + 8*(-1)

5x - 8

Now, we can write the equation as:

-3x + 10 = 5x - 8

So, solving for x, we get:

-3x + 10 + 3x = 5x - 8 + 3x

10 = 8x - 8

10 + 8 = 8x - 8 + 8

18 = 8x

18/8 = x

2.25 = x

Therefore, the equation is true when x is equal to 2.25

Inverse & Composition of Functions
1. Find the inverse of f(x) = x² + 2

Answers

Answer: √x−2,−√x−2

Step-by-step explanation:

What is the completely simplified form of the expression 2(1 - 3x) - (5x + 1)?

A) -11x + 1
B) -8x + 1
C) -11x + 3
D) -8x + 3

Answers

Answer:

A

Step-by-step explanation:

2(1-3x)-(5x+1)

=2-6x-5x-1

=1-6x-5x

=1-11x/-11x+1

Find the value of x in the diagram. ΔPQR ~ ΔSTU

Answers

X is 12.5 by using cross multiplication.

Find the volume of the cone, use 3 for π

Answers

Given:

Cone with diameter of 14 ft, and height of 4 ft.

First, determine the radius of the cone, by dividing the diameter by 2.

[tex]\begin{gathered} r=\frac{d}{2} \\ r=\frac{14\text{ ft}}{2} \\ r=7\text{ ft} \end{gathered}[/tex]

Now that we have the radius, substitute π = 3, r = 7 ft, and h = 4 ft to the formula of the volume of the cone.

[tex]\begin{gathered} V=\frac{\pi r^2h}{3} \\ V=\frac{(3)(7\text{ ft})^2(4\text{ ft})}{3} \\ V=\frac{3(49\text{ ft}^2)(4\text{ ft})}{3} \\ V=\frac{588\text{ ft}^3}{3} \\ V=196\text{ ft}^3 \\ \\ \text{Therefore, the volume of the cone is }196\text{ ft}^3. \end{gathered}[/tex]

URGENT!!!!!!!!!
Thank you to whoever solves it right!

Answers

Answer:

D

Step-by-step explanation:

The plane was at 24,000+ feet above the ground and then it ROSE (indicating an addition of feet to the original) 7,00+ feet.

Hope that helps

The amount of vinegar that melody used for a recipe can be written as a whole number which could be the amount of vinegar that Melody used?A. -3.75 tspB. 1.5 tspC. 2 1/3 tspD. 12/3

Answers

Given:

The amount of vinegar that melody used for a recipe can be written as a whole number.

So, we will check the options to find which one represents a whole number

The whole number does not contain numbers after the decimal point and also the denominator will be 1

So, the answer is option D) 12/3 = 4

HELP ASAP I NEED ANSWER NOWW IT'S MISSING PLEASE HELP 50 POINTS

Answers

Answer:Let r be the number of rides and g be the number of games.

2.50g + 4.00r = 52.50

r = 2g

Step-by-step explanation:

Answer:

lol no

Step-by-step explanation:

Can you please explain? I have the other options also.

Answers

Given

[tex]f(x)=\frac{1}{3}\lvert x+4\rvert-4[/tex]

The graph

A rectangular room is 4 meters longer than it is wide, and its perimeter is 24 meters. Find the dimension of the room.The length is : meters and the width is meters.

Answers

We are given the following information

Perimeter of the rectangular room = 24 meters

The rectangular room is 4 meters longer than it is wide.

Let L be the length and W be the width of the rectangular room.

[tex]L=4+W[/tex]

The perimeter of a rectangular shape is given by

[tex]P=2(L+W)[/tex]

Substitute P = 24 and L = 4 + W into the above equation

[tex]\begin{gathered} P=2(L+W) \\ 24=2(4+W+W) \\ 24=2(4+2W) \\ 24=8+4W \\ 24-8=4W \\ 16=4W \\ \frac{16}{4}=W \\ W=4\;m \end{gathered}[/tex]

So, the width of the rectangular room is 4 meters.

[tex]\begin{gathered} L=4+W \\ L=4+4 \\ L=8\;m \end{gathered}[/tex]

So, the length of the rectangular room is 8 meters.

Length = 8 meters

Width = 4 meters

Example Problem:

Suppose that perimeter is 1055 meters.

The length is 45 meters longer than the width of the rectangle.

[tex]L=45+W[/tex]

Now, substitute P = 1055 and L = 45 + W into the equation for the perimeter of the rectangle.

[tex]\begin{gathered} P=2(L+W) \\ 1055=2(45+W+W) \\ 1055=2(45+2W) \\ 1055=90+4W \\ 1055-90=4W \\ 965=4W \\ W=\frac{965}{4} \\ W=241.25\;m \end{gathered}[/tex]

So, the width of the rectangle is 241.25 meters.

[tex]\begin{gathered} L=45+W \\ L=45+241.25 \\ L=286.25\;m \end{gathered}[/tex]

So, the length of the rectangle is 286.25 meters

45.6 divided by 0.03

Answers

Answer:

1,520

Step-by-step explanation:

2) A toy store is having a sale on puzzles. For each puzzle, Naomi buys she
gets 75% off of a second puzzle. The original price of each puzzle is
$16.50. Naomi bought 4 puzzles. How much did she spend?

Answers

Naomi bought 4 puzzles and she spend total $21.91

What is percentage?

The Latin word "per centum," which means "by the hundred," is where the word "percentage" originally came from. With 100 as the denominator, percentages are fractions. To put it another way, it's the relationship between a component and a whole in which the value of the whole is always assumed to be 100.

Given that : A toy store is having a sale on puzzles. For each puzzle, Naomi buys she gets 75% off of a second puzzle. The original price of each puzzle is $16.50. Naomi bought 4 puzzles

Naomi first puzzle price is $16.50

she get 75% off on as second puzzle

=[tex]16.50(\frac{75}{100} )[/tex]

=12.375

=16.50 - 12.375

= 4.125

So , second puzzle price is 4.124

=[tex]4.125(\frac{75}{100} )[/tex]

=3.09

= 4.125 - 3.09

=1.03

So , third puzzle price is 1.03

=[tex]1.03(\frac{75}{100} )[/tex]

=0.7725

=0.2575

So ,fourth puzzle price is 16.50+4.124+1.03+ 0.2575

=21.91

Total naomi spend 0.2575

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A cylinder with a radius of 1 yd and a height of 2 yd

Answers

The volume is 6.28 yard

Pls help me with this ill give brainlist

Answers

What’s the question?

following points would fall on the line produced by the point-slope form equation y - 3 = 1/2(x - 7) when graphed

Answers

Points which would fall on the line produced by the point-slope form equation y - 3=1/2(x - 7) when graphed are as follow:

c. (1,0)

d. (3, 1)

As given,

Equation of given line

y - 3=1/2(x - 7)

Points which would fall on the line produced by the point-slope form:

a.(0,1)

x=0

y-3=1/2(0-7)

⇒ y=-1/2

b.(1,-1)

x=1

y-3=1/2(1-7)

⇒y=0

c.(1,0)

x=1

y-3=1/2(1-7)

⇒y=0

Required point

d.(3,1)

x=3

y-3=1/2(3-7)

⇒y=1

Required point

Therefore, points which would fall on line produced by the point-slope form equation y - 3 = 1/2(x - 7) when graphed are as follow:

c. (1,0)

d. (3, 1)

The complete question is :

Which of the following points would fall on the line produced by the point-slope form equation y - 3 = 1/2(x - 7) when graphed?

a. (0,1)      b. ( 1,-1)       c. (1,0)       d. (3,1)

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determine the domain of each function yx-3x=3y-1

Answers

Domain of the given function yx-3x=3y-1 is ( -∞,3) ∪ (3,∞), {x|x [tex]\neq[/tex] 3}.

What is a domain?

The dependent variable and the independent variable are the two types of variables used to define a function.

The domain of a function is a set of all possible values of x which is an independent variable. For example The domains of function f(x)=x² can be all real numbers.

Despite x=0, the domain of g(x)=1/x can contain any real number.

The input values to a function are referred to as domains, while the output values are referred to as the range. The data flow is as follows:

Domain → Function → Range

We are aware that the value of x is the function's domain. Therefore, the domain is ( -∞,3) ∪ (3,∞), {x|x [tex]\neq[/tex] 3} for the provided function.

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Hello! I need some help with this homework question, please? The question is posted in the image below. Q11

Answers

A one-to-one function means that there are no two elements in the domain of the function that corresponds to the same element in the range,

Mathematically since

[tex]\begin{gathered} x\text{ is the input or the domain, then} \\ f(x)\text{ is the output} \end{gathered}[/tex]

A one-to-one follows that

[tex]\text{if }x_1\text{ and }x_2\text{ are two different inputs of a function }f,\text{ then }f(x_1)\neq f(x_2)[/tex]

Tina has two bags of counters. Bag A has 5 red and 3 blue. Bag B has 4 red and 5 blue. Work out the probability that tina takes two blue counters in fraction.

Answers

Tina has two bags of counters. Bag A has 5 red and 3 blue. Bag B has 4 red and 5 blue. The probability that tina takes two blue counters in fraction is 15/72

What is the probability?

Given parameters:

Bag A= 5 red + 3 blue

Bag B = 4 red + 5 blue

Hence,

Total counters in bag A = 5 +3 = 8

Total counters in bag B = 4 + 5 = 9

Now let determine the probability that she takes two blue counters

Probability =  3 /8 × 5 /9

Probability = 15 / 72

Therefore 15 / 72 is the probability that two blue was taken.

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find the ratio of the boxes and the circles there are 7 boxes and 10 circles

Answers

The ratio of boxes to the circles is 7: 10

Tickets of a program at college cost $4 for general admission or $3 with a student ID. If 181 people paid to see a performance and$616 was collected, how many of each type of ticket were sold?In a program at college tickets ?were sold for general admission and?tickets were sold with a student ID.

Answers

Tickets were sold for a program at a college .It cost $4 for general admission or $3 with a student ID.

Let

number of people that used student ID = x

number of people that used the general admission cost = y

[tex]x\text{ + y = 181}[/tex][tex]3x\text{ + 4y = 616}[/tex][tex]\begin{gathered} x+y\text{ = 181} \\ 3x+4y=616 \\ x=181-y \\ 3(181-y)+4y\text{ = 616} \\ 543-3y+4y=616 \\ y=616-543 \\ y=73 \\ x+73=181 \\ x=181-73 \\ x=108 \end{gathered}[/tex]

108 used the student ID ticket while 73 used the general admission ticket .

Christine gets $71 for working the weekend. She buys $53 in clothes and then
makes another $45 babysitting. How much does she have now?

Answers

Answer:

63 i think!

Step-by-step explanation:

71-53 is 18. 18+45 is 63!

Im so so so sorry if im wrong, have a nice day friend!: )

It’s 71-53=18
18 +45=63 dollar left



4. What is the value of x such that 5x + 2a > 2x-a?
a. x < -a
b. x > -a
C. x < a
d. x > a

Answers

Answer:

D: x > a

Step-by-step explanation:

We have 5x - 2a > 2x-a

We can rewrite this equation by subtracting 2x on both sides, which gives:

5x - 2x -2a > 2x - 2x - a,

so 3x - 2a > a

We now add 2a on both sides, which gives:

3x -2a + 2a > a + 2a, so 3x > 3a

We nog divide both sides by 3, which gives:

3x/3 > 3a/3, so x>a

The correct answer is D

The proportion of a population with a characteristic of interest is p = 0.37. What is the standard deviation of the sampling distribution when the sample size is 1,600?

Answers

The standard deviation (SD) of a sample proportion obtained when the sample size is 1,600 is equal to 0.0121.

What is a sample proportion?

A sample proportion can be defined as the proportion of individuals in a sample that have a specified characteristic or trait.

Mathematically, sample proportion can be calculated by using this formula:

[tex]\hat{p} = \frac{x}{n}[/tex]

Where:

x represent the number of individuals with a specified characteristic.n represent the total number of individuals in a sample.

In Mathematics, the standard deviation (SD) of a sample proportion obtained when the sample size is 1,600 can be calculated by using this formula:

Standard deviation (SD) = √(p(1 - p)/n)

Substituting the given parameters into the formula, we have;

Standard deviation (SD) = √(0.37(1 - 0.37)/1,600)

Standard deviation (SD) = √(0.37(0.63)/1,600)

Standard deviation (SD) = √(0.2331)/1,600)

Standard deviation (SD) = √0.0001457

Standard deviation (SD) = 0.0121.

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Plllsss help answer the question in the picture below!!!!!

Answers

The proportion of the generated values that fall inside the range of each histogram bar is used to compute the vertical scale. The standard deviation is an indicator of how much the values in the data set typically deviate from the mean.

What is the difference between standard deviation and histogram?

It always displays the median and the middle 50% of the data. For data displayed in histograms, a similar spread measurement is helpful. The term for it is the standard deviation. The standard deviation is an indicator of how much the values in the data set typically deviate from the mean.

The proportion of the generated values that fall inside the range of each histogram bar is used to compute the vertical scale. The sum of the bar heights is therefore one. Only discrete variables (right), where the histogram heights now total to unity, are suitable for relative frequency analysis.

A measurement of how far points deviate from the mean is the standard deviation. The first histogram includes fewer points that are close to the mean and more points that are distant from the mean (scores of 0, 1, 9, and 10). (scores of 4, 5 and 6). As a result, its standard deviation will be higher.

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all the odd numbers from 51 to 5001 are written what is the total number of digits used

Answers

Answer:

9404 digits

Step-by-step explanation:

The numbers written:

51, 53, 55, 57, 59, . . . 97, 99 [5*5=25 numbers; 50 digits]

101, 103, 105, . . . 997, 999 [9*50=450 numbers; 1350 digits]

1001, 1003, 1005, . . . 4997, 4999, 5001 [40*50+1=2001 numbers; 8004 digits]

Total:

50 + 1350 + 8004 = 9404 digits

Bill owns land but has no access to water so he has to pay for well water from Jim.
Jim charges him $8 per month plus $0.80 per gallon.
During any given summer month, his water bill costs between $48 and $72.
Write and solve a compound inequality to determine how much water Bill is using.

Answers

Answer is above. Bhchyg

Martin eats 3/8 of a pizza. Felix eats 2/5of a pizza of
same size. Who eats more pizza? How much more pizza
does he eat?

Answers

find the least common demnator

two trains travel at a constant speed. Train a travels 1400 miles in 5 hours and train b travels 2100 miles in 7 hours. Which train travels faster?

Answers

Train b

Explanation: 1400 divided by 5 times by 7= 1960 miles
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