Consider a coin that a head is twice more likely to occur than a tail. Find the variance of number of heads when the coin is tossed three times.

Answers

Answer 1

Answer:

0.667

Step-by-step explanation:

Given that :

Head is twice more likely to occur than a tail.

P(head) = p(H) = 2/3

P(tail) = p(T) = 1/3

If coin is tossed 3 times :

P(H = 0) :

1st toss = tail ;2nd toss = tail ; 3rd toss =. Tail

(1/3) * (1/3) * (1/3) = 1 / 27

P(H= 1)

HTT, THT, TTH

(2/3 * 1/3 * 1/3) + (1/3 * 2/3 * 1/3) + (1/3 * 1/3 *2/3)

= 2/27 + 2 /27 + 2/27

= 6/27 = 2/9

P(H=2)

HHT, HTH, THH

(2/3 * 2/3 * 1/3) + (2/3 * 1/3 * 2/3) + (1/3 * 2/3 * 2/3)

= 4/27 + 4/27 + 4/27

= 12 / 27

= 4 /9

P(H = 3)

HHH

(2/3 * 2/3 * 2/3)

= 8 / 27

X ___ 0 ___ 1 ____ 2 ____ 3

P(x) _ 1/27 _ 2/9 __ 4/9 __ 8/27

E(X) = (0 * (1/27)) + (1 * (2/9)) + (2 * (4/9)) + (3 * (8/27)) = 2

E(X) = 2

Var(X) = Σx²p(x) - E(X)²

= (0^2 * (1/27)) + (1^2 * (2/9)) + (2^2 * (4/9)) + (3^2 * (8/27)) - 2^2

= 4.667 - 4

= 0.667

Hence, Var(x) = 0.667


Related Questions

Equa
Problem 1
3z - 4 = 52 - 12

Answers

Answer:

z=44/3

Step-by-step

Subtract the numbers 52-12=40

3z-4=40

Add 4 to both sides

3z-4+4=40+4

SImplify

3z=44

Divide both sides by 3

3z/3 = 44/3

z=44/3 or decimal form= 14.66

$1,400 principal earning 6%, compounded semi-annually, after 10 years

Answers

Answer: $2528.56  is the answer because if you do the problem you should get something like this

A=P(1+r/n)^nt

Plug in the values:

P=1400, r=6/100=0.6,

n=2 and t=10

A=1400(1+.06/2)^2(10)

A=$2528.56

Hope it helped

Yours,

Nathaniel

Step-by-step explanation:


A submarine started at the
surface of the water and was moving underwater at
22 feet per minute toward the ocean floor. The submarine traveled at this rate
for 75 minutes before coming to rest on the ocean floor. Which of the following
integers represent the depth of the ocean floor in feet?

Answers

Answer:

1650

Step-by-step explanation:

75x22+1650

Please help I’ll number 12!

Answers

Answer: y = -3/4x - 0.75

Step-by-step explanation:

The slope needs to be negative so that it's perpendicular to

y = 3/4x - 1

The equation then looks like this

y = -3/4x

We can get an exact y intercept number by using the cordinates

Lets input cordinates (3,-3)

-3 = -3/4(3)

-3 = -2.25 - 75 ( I inferenced )

-3 = -3

now that we got the y intercept lets put it all together

y = -3/4x - 0.75

In Oscar's grade, 70 students are enrolled in health and 30 students are not. What
percentage of the students in the school are enrolled in health?
Write your answer using a percent sign (%).

Answers

Answer:

70%

Step-by-step explanation:

Step 1:

70 + 30 = 100          Add

Step 2:

Total of 100 Students

Step 3:

70/100             Divide

Answer:

70%

Hope This Helps :)

Answer:

70% of the students are enrolled in health class.

Step-by-step explanation:

We are given that there are 70 students enrolled in health and that 30 are not. Therefore, we need to determine the total number of students in Oscar's grade.

[tex]70 + 30 = 100[/tex]

Oscar has 100 students in his grade. If 70 of those students are enrolled in health, we can divide those students by the total number of students and convert our fraction to a decimal and then a percentage.

[tex]\displaystyle\frac{70}{100} = \frac{7}{10} = 0.7\\\\0.7 \times 100 = 70\%[/tex]

Therefore, 70% of the students are enrolled in health class.

How many lines of symmetry does this figure have?
[Note: The black ball is part of the figure.]
A) 0
B) 1
C) 5
D) 10

Answers

Answer:

The answer is B) 1

Step-by-step explanation:

balls

which statements are true select all that apply. Extra points!!! ​

Answers

1 is false
2 is true
3. is false
4. is true


1 & 3 are false
2 & 4 are true

Why is it important to read division problems carefully before giving the answer

Answers

Answer:

Because, like with any problem, it is possible to make mistakes. With division, if you place a number in the wrong order or forget to remove a negative sign, the answer will obviously be wrong.

Step-by-step explanation:

A certain brand of coffee comes in two sizes. An 11.3-ounce package costs $2.88. A 27.8-ounce package costs $6.48.
Find the unit price for each size. Then state which size is the better buy based on the unit price.
Round your answers to the nearest cent.

Answers

Answer:

unit price for 11.3-ounce package = $0.25

unit price for 27.8-ounce package =  $0.23

27.8-ounce package is the better buy

Step-by-step explanation:

An 11.3-ounce package costs $2.88. A 27.8-ounce package costs $6.48.

a) 11.3-ounce package

11.3 ounces = $2.88

1 ounce = $2.88 ÷ 11.3

1 ounce = $0.25

b) 27.8-ounce package

27.8 ounces = $6.48

1 ounce = $6.48 ÷ 27.8

1 ounce = $0.23

$0.25 > $0.23

the product of 0.43 and 5.024 is greater than 0.43 and less than 5.024 true or false

Answers

Answer: True

Step-by-step explanation:

First find the product of 0.43 and 5.024 so see if it is greater than 0.43.

 0.43 * 5.024 = 2.16032  

2.16032 is indeed greater than 0.43  ,  2.16032 > 0.43

And 0.43 is indeed less than 5.024 , 0.43 < 5.024  

Meaning that this state is true.

Answer:

True

Step-by-step explanation:

Product refers to multiplication, the question is telling us to multiply 0.43 and 5.024 so lets do that

0.43 * 5.024 = 2.16032

Now we have to figure out if this fits the criteria. It must be larger than 0.43 but smaller then 5.024

...

...

...

That checks out.

True

Brainliest is much appreciated!

∠1 and ∠2 are a linear pair. If the m∠2 = 33°, find the m∠1.

Answers

Answer:

157 degrees

Step-by-step explanation:

A linear pair is 180 degrees.

180-33 = 157

Answer:

m∠1 = 147°

Step-by-step explanation:

Since both angles are a linear pair, they both add up to 180°. This means that if m∠2 = 33°, then m∠1 would be 180°-33° which is 147°.

180°-33°=147°

An ant starts walking along a parabola, y(x)=x^2 starting from the point where x=3 He walks until a point where x=3+a where a is a positive number. What is the y-coordinate of the point that he is at now?
plz no bs answers

Answers

Answer:

the y co-ordinate > 9

Step-by-step explanation:

I just graphed y = x^2 found the point where the x - axis was 3, found that the y co-ordinate was 9 and if you were to add any positive number the y co-ordinate would only get larger!

Hope this helps!

How do you divide decimals 10.305 divided by2.5?

Answers

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

[tex]10.305 \div 2.5 = [/tex]

[tex]10.305 \div \frac{10}{4} = \\ [/tex]

[tex]10.305 \times \frac{4}{10} = \\ [/tex]

[tex] \frac{10.305 \times 4}{10} = \\ [/tex]

[tex] \frac{41.220}{10} = \\ [/tex]

[tex]4.1220[/tex]

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

The sum of two real numbers is 8 and their product is 14. What is the sum of their reciprocals?

Answers

Answer:

Step-by-step explanation:Let our two numbers be  a  and  b . Then we can see that  a+b=8  and  ab=15 . Now consider

(a+b)3=a3+3a2b+3ab2+b3  by the binomial expansion. Now we have all the information to solve this, observe since  a+b=8  and  ab=15 . We have

(8)3=a3+3ab(a)+3ab(b)+b3  

a3+b3+3ab(a)+3ab(b)=83  

a3+b3+3ab(a+b)=83  

a3+b3=83−3ab(a+b)  

a3+b3=83−3(15)(8)=512−360=152  

You can also observe that  3  and  5  fulfill those conditions so, then  33+53=27+125=152 . Which is our result.

Find the percent as a fraction. Simplify if possible.

33 1/3%

Answers

Answer:

The answer would be 100/3

Step-by-step explanation:

Answer: 33 1/3% as a fraction is 1/3. It cannot be simplified. Hope this helps!

what is the value of 4/5(8+7)-2/3(8+7)​

Answers

Answer:

The answer is 2.

Hope this helps and if you could mark this as brainliest. Thanks!

How much simple interest would x dollars earn in 13 months at a rate of r percent?​

Answers

16 im adding this for yes reasons

A cardboard tube used for storing posters has the shape of a cylinder. It is 100 centimeters long and has a diameter of 8 canimeters. What is the volume of the tube

Answers

Answer:

[tex]Volume = 5028.6cm^3[/tex]

Step-by-step explanation:

Given

[tex]Height = 10cm[/tex]

[tex]Diameter = 8cm[/tex]

Required

Determine the volume

The volume of a cylinder is calculated as thus:

[tex]Volume = \pi r^2h[/tex]

Where [tex]r = radius[/tex]

[tex]r = \frac{1}{2} * Diameter[/tex]

[tex]r = \frac{1}{2} * 8cm[/tex]

[tex]r = 4cm[/tex]

[tex]h = 100cm[/tex]

Take

[tex]\pi = \frac{22}{7}[/tex], so we have

[tex]Volume = \pi r^2h[/tex]

[tex]Volume = \frac{22}{7} * 4^2 * 100[/tex]

[tex]Volume = \frac{22}{7} * 16 * 100[/tex]

[tex]Volume = \frac{22 * 16 * 100}{7}[/tex]

[tex]Volume = \frac{35200}{7}[/tex]

[tex]Volume = 5028.6cm^3[/tex]

What is 2 1/2 feet to inches?

Actual question:
1 foot=12 inches
2 1/2 feet= blank inches


IREADY!!
thanks :)

Answers

Answer: 30 inches

Explanation: since there is 2 feet you do 12x2. This gives you 24. Then since there is a half foot and a half foot is equal to 6 inches you add that to your 2 feet (24 inches) to get 2 1/2 feet or 30 inches. Hope this helps have a nice day!!!

Anthony is laying concrete for a driveway. The driveway is to be 24 feet long by 11 feet wide by 8 inches deep. Answer parts (a) through (c)

(a) Determine the volume of concrete needed in cubic feet.

(b) If 1 cubic yard = 27 cubic feet, how many cubic yards of concrete are needed?

(c) If the concrete costs $36 per cubic yard, what is the cost of the concrete? Concrete must be purchased in whole cubic yards​

Answers

Answer:

a) The volume of concrete needed in cubic feet is 2,112. b) The number of cubic yards of concrete needed in cubic yards is about 79. c) The cost of the concrete using cubic yards is $2,844.

Step-by-step explanation:

a) The formula of the volume is l*w*d. 24 * 11 * 8 = 264 * 8 = 2,112.

b) The way to find this is that you take 2,112 and divide it by 27. Since the answer is 78.2 repeating, you round it up to 79 so it will fill up all of the concrete.

c) Since you need 79 cubic yards of concrete, you do 79 multiplied by $36 to get the total cost of $2,844.


What is a proportional relationship?

Answers

Answer:

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality

Step-by-step explanation:

How do you do this question?

Answers

Answer:

-1

Step-by-step explanation:

dy/dt = y² − 1 = (y + 1) (y − 1)

At t = 0, y = 0, and dy/dt = -1.  Therefore, y is initially decreasing.

As y decreases, dy/dt increases.  When y = -1, dy/dt = 0 and changes signs from negative to positive.

As y increases above -1, dy/dt again becomes negative.  So y continues to approach -1 as t approaches infinity.

A wave is traveling with a speed of 500 m/sec and has a wavelength of 10 m. Determine its frequency.

Answers

Answer:

I'm gonna get more people here

Answer:

50 hz  yw pplz

Step-by-step explanation:

Will the solution to the following equation be positive or negative? b ÷ -2 = 5 positive negative

Answers

Answer:

I think that it is negative

Step-by-step explanation:

In △BCD, H is the centroid. If HF=6 find BF.

Answers

Answer:

18

Step-by-step explanation:

The centroid of a triangle is located ⅓ of the distance from each side to the opposite vertex

So HF=⅓BF

So BF=3xHF=3x6=18

Parallel to the line y=-3x + 5 passes through (-4,5)

Answers

Answer:

The equation of line that is Parallel to the line y=-3x + 5 passes through (-4,5) is: y = -3x-7

Step-by-step explanation:

Given equation of line is:

[tex]y = -3x+5[/tex]

General form of slope-intercept equation of line is:

[tex]y=mx+b[/tex]

Comparing both we get

m = -3

The slope of two parallel line sis equal.

Let m1 be the slope of line parallel to given line, then

m1 = -3

Putting in general form

[tex]y = -3x+b[/tex]

Putting (-4,5) in equation

[tex]5 = -3(-4) +b\\5 = 12+b\\b = 5-12\\b = -7[/tex]

Putting in the general form, we get

[tex]y = -3x-7[/tex]

Hence,

The equation of line that is Parallel to the line y=-3x + 5 passes through (-4,5) is: y = -3x-7

what ratio is equavelent to 5:4

Answers

Answer:

the two equivalent ratios of 4 : 5 are 8 : 10 and 12 : 15.

Step-by-step explanation:

the two equivalent ratios of 4 : 5 are 8 : 10 and 12 : 15.

Solve: |x - 4| = 0
Help if can

Answers

Answer:

answer is x=4 I'm pretty sure

Step-by-step explanation:

I used a calculator

Answer:

x=4

Step-by-step explanation:

If you plug 4 in, 4-4=0 and the absolute value will not change anything.

how do I know how many extraneous solutions there is

Answers

Answer:

how do u know how many extraneous solutions there is?

Step-by-step explanation:

To find whether your solutions are extraneous or not, you need to plug each of them back in to your given equation and see if they work. It's a very annoying process sometimes, but if employed properly can save you much grief on tests or quizzes.

Answer: To find whether your solutions are extraneous or not, you need to plug each of them back in to your given equation and see if they work. It's a very annoying process sometimes, but if employed properly can save you much grief on tests or quizzes

Step-by-step explanation:

Please can I have brainliest I need one more to rank up

what is order of operations for 20-5x2+6

Answers

Answer:

multiply, add, then subtract so your answer should be 4

Step-by-step explanation:

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

(please excuse my dear aunt sally)

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