In a lumberjack competition, a contestant is blindfolded and then spun around 9 times. The contestant then immediately tries to hit a single point (the target) in the middle of a horizontal log with an axe (while still blindfolded). The contestant receives

15 points if their swing is within 3cm of the target.
10 points if their swing is between 3cm and 10cm of the target.
5 points if their swing is between 10cm and 20cm of the target
zero points if their swing is further away from the target (and someone may lose a finger!).

Let Y record the position of the hit, so that Y = y > 0 corresponds to missing the target point to the right by y cm and Y = - y < 0 corresponds to missing the target to the left by y cm. Assume that Y is normally distributed with mean mu = 0 and variance 100 cm^2. Find the expected number of points that the contestant wins.

Answers

Answer 1

Answer:

9.364 is the expected number of points.

we can approximate this to 10 points if we want a whole number

Step-by-step explanation:

We have these variables:

[0,5,10,15]

P(x= 0) = p(y>20)+p(y<-20) = 2p(y>20)

P(x=5) = p(-20<=y<=10)+p(10<=y<=20) = 2p(10<=y<=20)

P(x=10) = p(-10<=y<=-3)+p(3<=y<=10) = 2p(3<=y<=10)

P(x=15) = p(-3<=y<=3) = 2p(0<=y<=3)

Z = y/10

Therefore

P(x= 0) = 2(y>20)

= 2p(z>2) = 2(1-p<=2)

= 2(1-0.9772)

= 0.0456

P(x= 5)

= 2p(10<=y<=20)

= 2p(1<=z<=2)

= 2(0.9772-0.8413)

= 0.2718

P(x= 10)

= 2p(3<=y<=10)

= 2p(0.3<=z<=1)

= 2(0.8413-0.6179)

= 0.4468

P(x = 15)

= P(0.6179-0.3821)

= 0.2358

To get expected value of Y

0(0.0456)+5(0.2718)+10(0.4468)+15(0.2358)

= 1.359 + 4.468 + 3.537

= 9.364

E[Y] = 9.364


Related Questions

If 60 minutes equals one hour, which expression would you use to find the number of
hours in 240 minutes?

Answers

Answer is: 60x=240
240/60=40

If l=3, w= 3, and h= 5, what is the volume of this box​

Answers

Answer and Step-by-step explanation:

To find the volume, we multiply the length by the width by the height for a rectangular prism (aka the box).

length = l = 3

width = w = 3

height = h = 5

Now, we multiply each together.

3 × 3 × 5

9 × 5

45

The volume of the box is 45.

#teamtrees #PAW (Plant And Water)

Answer:

the volume of the box would be 45

Step-by-step explanation:

Simplify.
5a√2+3a√2


16a
8
8a

Answers

Answer:

8a[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Given

5a[tex]\sqrt{2}[/tex] + 3a[tex]\sqrt{2}[/tex] ← factor out [tex]\sqrt{2}[/tex] from each term

= [tex]\sqrt{2}[/tex] (5a + 3a)

= 8a[tex]\sqrt{2}[/tex]

the 30% discount on a $49 dollhouse​

Answers

Answer:

34.30

Step-by-step explanation:

$14.70 is 30% of $49 so

The total would be $34.30 after the discount

But the discount is %14.70

Can someone help me plzzzz with this math question!!!!!! “Buy one, get one free” special at T-Mobile for an iPhone 12. The cost is $1150. Calculate what you are actually paying for each item since you are getting two for one price. What is the sale price of each phone?

Answers

Answer:

$575

Step-by-step explanation

1150/2 = 575

Answer:

$1150

Step-by-step explanation:

because it is a buy one (for sale price), get one free

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Answers

Answer:

F = (-2,4); E = (-2,0); D = (2,0)

Step-by-step explanation:

F = 4 points from A, so by a scale factor of 2, it would be 2 times father away from A. The same thing applies for all of the other points; just find how much father A is from a point, then dilate that point by multiplying it by the scale factor, and settling the point closer or father from A.

I need help please.

Answers

Step-by-step explanation:

if I had to guess it's probably true

Using the same survey methodology: random sample of US residents between the ages of 18 to 75 who registered on the Crest website as a product, Crest wants to divide the research population into heterogeneous groups based on age and gender and then draw a random sample from each of the different groups. Based on this information, what type of sampling method would Crest use to conduct this survey

Answers

Answer:

Stratified sampling

Step-by-step explanation:

Samples may be classified as:

Convenient: Sample drawn from a conveniently available pool.

Random: Basically, put all the options into a hat and drawn some of them.

Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.

Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.

Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.

In this question:

Population divided into groups, and random samples are drawn from the groups. This is a mark of stratified sampling.

a solution set always include....

Answers

A solution is any value of a variable that makes the specified equation true. A solution set is the set of all variables that makes the equation true. ... If the two sides are equal, the equation is true and thus the value is a solution.

PLEASE HELP
x + 2/3 = 9/10

Answers

Answer:

The answer is x= 7/30

PLEASE I NEED HELP CLICK ON THIS IMAGE

Answers

Answer:

Mean: 10

Median: 10.5

Mode: none

Step-by-step explanation:

there is no mode, mean is 10 and median is 10.5

A clothing business finds there is a linear relationship between the number of shirts, n (in thousands) it can sell and the price, P, it can charge per shirt. In particular, historical data shows that 3 thousand shirts can be sold at a price of $69 each, and that 7 thousand shirts can be sold at a price of $61 each. Find the equation of the form P(n)

Answers

Answer:

The equation of the form P(n) is:

P(n)=-0.002n+75

Step-by-step explanation:

From the information provided, you have two points: (3000, 69) and (7000, 61). With this, you can find the slope using the following formula:

m=(p1-p2)/(n1-n2)

m=slope

p1=69

p2=61

n1=3000

n2=7000

m=(69-61)/(3000-7000)

m=8/-4000

m=-0.002

Now that you have the slope, you can find the the equation of the form P(n):

P(n)=-0.002(n-3000)+69

P(n)=-0.002n+6+69

P(n)=-0.002n+75

According to this, the answer is that the equation of the form P(n) is:

P(n)=-0.002n+75

What is mZ1?
820
660
1

Answers

Answer:

∠1 = 148°

Step-by-step explanation:

the triangle interior angles = 180°

the unknown interior angle = 180° - 82° - 66° = 32°

∠1 = 180° - 32° = 148°  because it is supplementary to 32°  (adds together to total 180°)

For the following right triangle, find the side length x.
12
5

Answers

Answer:

x = 13

Step-by-step explanation:

[tex]c^{2} = a^{2} + b^{2}[/tex]

[tex]c^{2} = 5^{2} + 12^{2}[/tex]

[tex]c ^{2} = 25 + 144[/tex]

[tex]c^{2} = 169[/tex]

[tex]\sqrt{c^2} = \sqrt{169}[/tex]

[tex]c = 13[/tex]

what is y=3x and y=2x+2 solution ??
( , )



PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
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Answers

Answer:

Try this: (2,6)

x=2, y=6

Step-by-step explanation:

Answer:

i belive it is (-2,-6)

An architect’s blueprint for a new house shows the kitchen being 7 inches wide. If the scale used to create the blueprint is 0.5 in. = 1 ft, what is the actual width of the kitchen?

Answers

You would do 7x0.5 which equals 3.5 ft :^)

What's all equivalent to 7/8

Answers

Answer:

0.875?

Step-by-step explanation:

I just did 7 divided by 8

Answer:

14/16

49/56

Step-by-step explanation:

I looked it up for you!!!

If 3 inches of rain fell in 5 hours, how much rain fell each hour? *

Answers

Answer:

Step-by-step explanation:

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Answers

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Step-by-step explanation: deltamath

Answer:

197735

Step-by-step explanation:

see attached image

(10y + 3) - (2y - 2)

Answers

Answer:

8y+5

Step-by-step explanation:

Explain why a variable's coefficient is 1 unless you see another number in front of it.

Answers

when you add variables you have to have something to add so instead of it being x^2 it would be x+x=2x

For adding variables we use the coefficient as 1 if there is no number infront of variable.

What is Expression?

An expression is combination of variables, numbers and operators.

A coefficient is a multiplicative factor in some term of a polynomial, a series, or an expression; it is usually a number, but may be any expression.

Let us consider a algebraic expression

ax+by+z=0

In the given expression a, b are coefficients of x and y respectively.

We use coefficient as one when there is no number before a variable because when we add variables there should be some number before varibales. So we consider 1 as coefficient for those variables which does not have any coefficient.

Hence, for adding variables we use the coefficient as 1 if there is no number infront of variable.

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https://brainly.com/question/14083225

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A principal wants to know if students at a particular high school are in favor of a new dress code at their school. The principal is not able to ask the opinion of every student at the school, so she needs to select an appropriate sample of the students to represent the high school. Select which sample of students the principal should choose. A Students randomly selected from a list of all students at the school. B Students sitting at randomly selected tables in the library. Students she selects from the hallway between classes. Students selected by the teachers.​

Answers

Answer:

student randomly selected from a list of all students at the school

Chupapi munyanyo uhhh zaddy

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Answers

That is basic algarethem that is your answer

Help help thank you

Answers

Meter is 0.5 and the fraction is I think 1/2

Two bags of flour have a total weight of 8 3/4 pounds. What could be their individual weight

Answers

Answer:

4 3/8 lbs.

..................

There are infinitely many possible values for the individual weights of the bags of flour that would add up to a total weight of 8(3/4) pounds.

What is an expression?

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The individual weights of the bags of flour must add up to a total weight of 8 3/4 pounds.

We can express 8 3/4 as an improper fraction by multiplying the whole number 8 by the denominator 4 and adding the numerator 3, giving us 35/4.

Therefore, we can set up an equation:

x + y = 8 3/4

where x is the weight of one bag of flour, and y is the weight of the other bag of flour.

We can simplify 8 3/4 to 35/4, so the equation becomes:

x + y = 35/4

We can solve for one variable in terms of the other:

x = 35/4 - y

Now we can substitute this expression for x into the original equation and solve for y:

x + y = 35/4

(35/4 - y) + y = 35/4

35/4 = 35/4

This equation is true for any value of y.

Therefore, there are infinitely many possible values for the individual weights of the bags of flour that would add up to a total weight of 8(3/4) pounds.

For example, one bag could weigh 4 pounds and the other could weigh 4 3/4 pounds, or one bag could weigh 3 pounds and the other could weigh 5 3/4 pounds, and so on.

Thus,

There are infinitely many possible values for the individual weights of the bags of flour that would add up to a total weight of 8(3/4) pounds.

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Come I need answers

Answers

67, 79, 81, 83, 83, 85, 87, 88, 89 then find the bumber in middle so answer is 83

Solve the proportion.
10
15
a
24
a = [?]

help please I will give you brainliest!!

Answers

Let's solve your equation step-by-step.

10/a=15/24

Step 1: Cross-multiply.


10/a=15/24


(10)*(24)=15*a


240=15a


Step 2: Flip the equation.


15a=240


Step 3: Divide both sides by 15.

15a / 15 = 240/15

a=16

an oil company bores a hole 80m deep estimate the cost of boring if the cost is £30 for drilling the first meter with an increase in cost of £2 per meter for each succeeding meter​

Answers

Answer: £188

Step-by-step explanation:

Given

The depth of the hole is 80 m

For the first meter, it is £30

After that, it is £2 per meter

after a meter, it is 79 m more

The total cost is C

[tex]\Rightarrow C=30+2\times 79\\\Rightarrow C=30+158=188[/tex]

Helppppppppppp I have 3 minutes

Answers

Answer:

It definitely is linear, and it is a straight line

Step-by-step explanation:

Try using desmos, it may help

Answer:

A) it is linear and it is a straight line

Step-by-step explanation:

it is a linear equation. It will be straight

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Sine divided by Cosine is equal to Tangent. True or false?

Answers

Answer:

True

Step-by-step explanation:

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