PLEASE HELP ASAP WILL GIVE BRAINLIEST!!!!!!
Mr. McClellan compared the weights (in pounds) of pairs of elk antlers dropped at Mount St Helens NVM and Rocky Mountain NP. He tabulated them in the following data table.
Weight of elk antler pairs at Mount St Helens NVM:
{34, 34, 30, 30, 30, 28, 28, 26}
Weight of elk antler pairs at Rocky Mountain NP:
{40, 38, 36, 36, 36, 36, 34, 32}
(a) Create a line plot for each data set.
(b) Calculate the mean and MAD for each area of collection.
(c) Calculate the means-to-MAD ratio for the two areas of collection.
(d) What inference can be made about the areas in regard to weight of dropped elk antlers? Explain

Answers

Answer 1
A) The two line plots are attached.

B) In order to calculate the mean, you have to sum all the values and divide it by the number of values:
m(MSH) = (34 + 34 + 30 + 30 + 30 + 28 + 28 + 26) ÷ 8 
              = 240 ÷ 8
              = 30

m(RM) = (40 + 38 + 36 + 36 + 36 + 36 + 34 + 32) ÷ 8
           = 288 ÷ 8
           = 36

In order to calculate the mean absolute deviation (MAD), you need to calculate the absolute values from the mean, sum them up and divide it by the number of values; the absolute values of the difference from the mean are:
MSH = {|34-30|, |34-30|, |30-30|, |30-30|, |30-30|, |28-30|, |28-30|, |26-30|}
        = {4, 4, 0, 0, 0, 2, 2, 4}

RM = {|40-36|, |38-36|, |36-36|, |36-36|, |36-36|, |36-36|, |34-36|, |32-36|}
     = {4, 2, 0, 0, 0, 0, 2, 4}

Therefore,
MAD(MSH) = (4 + 4 + 0 + 0 + 0 + 2 + 2 + 4) ÷ 8
                   = 16 ÷ 8
                   = 2

MAD(RM) = (4 + 2 + 0 + 0 + 0 + 0 + 2 + 4) ÷ 8
                = 12 ÷ 8
                = 1.5

C) In order to calculate the mean-to-MAD ratio, you need to simply divide the mean by the MAD:
r(MSH) = 30 ÷ 2 = 15

r(RM) = 36 ÷ 1.5 = 24

D) We can say that in Mount St Helens NVM elk antlers pairs are lighter but with a bigger variability (which means that they tend to be weight differently from each other), while in Rocky Mountain NP elk antlers pairs are heavier, but with less variability (which means that they tend to be similar to each other).
PLEASE HELP ASAP WILL GIVE BRAINLIEST!!!!!!Mr. McClellan Compared The Weights (in Pounds) Of Pairs Of
Answer 2

A) The two line plots are attached.


B) In order to calculate the mean, you have to sum all the values and divide it by the number of values:

m(MSH) = (34 + 34 + 30 + 30 + 30 + 28 + 28 + 26) ÷ 8 

             = 240 ÷ 8

             = 30


m(RM) = (40 + 38 + 36 + 36 + 36 + 36 + 34 + 32) ÷ 8

          = 288 ÷ 8

          = 36


In order to calculate the mean absolute deviation (MAD), you need to calculate the absolute values from the mean, sum them up and divide it by the number of values; the absolute values of the difference from the mean are:

MSH = {|34-30|, |34-30|, |30-30|, |30-30|, |30-30|, |28-30|, |28-30|, |26-30|}

       = {4, 4, 0, 0, 0, 2, 2, 4}


RM = {|40-36|, |38-36|, |36-36|, |36-36|, |36-36|, |36-36|, |34-36|, |32-36|}

    = {4, 2, 0, 0, 0, 0, 2, 4}


Therefore,

MAD(MSH) = (4 + 4 + 0 + 0 + 0 + 2 + 2 + 4) ÷ 8

                  = 16 ÷ 8

                  = 2


MAD(RM) = (4 + 2 + 0 + 0 + 0 + 0 + 2 + 4) ÷ 8

               = 12 ÷ 8

               = 1.5


C) In order to calculate the mean-to-MAD ratio, you need to simply divide the mean by the MAD:

r(MSH) = 30 ÷ 2 = 15


r(RM) = 36 ÷ 1.5 = 24


D) We can say that in Mount St Helens NVM elk antlers pairs are lighter but with a bigger variability (which means that they tend to be weight differently from each other), while in Rocky Mountain NP elk antlers pairs are heavier, but with less variability (which means that they tend to be similar to each other).


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Related Questions

The first military strike of the Civil War was at

Bull Run


Lexington


Fort Sumter


Gettysburg

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It was in fort sumter

Different types of parallelograms have distinguishing traits. Compare and contrast the rectangle, rhombus, and square based upon the characteristics of their sides. Which one(s) have both pairs of opposite sides that are parallel? Which one(s) have both pairs of opposite sides that are congruent? Which one(s) have all four sides that are congruent?

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All 3 of the listed parallelograms have both pairs of sides parallel, by definition.

The square and the rhombus have all congruent sides.

Since the square and rhombus have all 4 congruent sides, this means their opposite sides are congruent.  Additionally, rectangles have opposite sides congruent.

2 1/4 simplified with 1/4

Answers

2 1/4 +1/4

9/4+1/4=10/4=5/2=1 3/2

1 3/2


how do you convert degrees to radians?

Answers

One degree is equal 0.01745329252 radians:

1° = π/180° = 0.005555556π = 0.01745329252 rad

The angle α in radians is equal to the angle α in degrees times pi constant divided by 180 degrees:

α(radians) = α(degrees) × π / 180°

or

radians = degrees × π / 180°

Example

Convert 30 degrees angle to radians:

α(radians) = α(degrees) × π / 180° = 30° × 3.1459 / 180° = 0.5236 rad

Degrees to radians in terms of pi

The angle α in radians is equal to the angle α in degrees times pi constant divided by 180 degrees:

α(radians) = (α(degrees) / 180°) × π

Example

Convert 30 degrees angle to radians in terms of pi:

α(radians) = (α(degrees) / 180°) × π = (30° / 180°) × π

 = (1/6) × π = π/6 rad = 0.166667π rad

Final answer:

To convert degrees to radians, multiply the number of degrees by π and then divide by 180, or simply multiply by π/180. For instance, 45 degrees can be converted to radians as 45 degrees * (π/180) = π/4 radians.

Explanation:

To convert degrees to radians, you can use the basic formula that π radians equal 180 degrees. This means that to convert a degree measure to radians, you multiply the number of degrees by π and then divide by 180. This can be simplified to multiplying the number of degrees by π/180.

For example, if you wanted to convert 45 degrees to radians, you would perform the following calculation:

45 degrees * (π/180) = 45π/180 = π/4 radians.

That means 45 degrees is equivalent to π/4 radians. Remember, the π symbol represents the mathematical constant pi, which is approximately 3.14159.

Please help me

i gotta turn this in in 10 minutes

Answers

To find the ratio, we must find the total amount of days (31) and the number of days that are either a Saturday or a Sunday (10). Since in the sentence, the number of Saturdays and Sundays is mentioned first, the 10 would precede the 31 in the ratio.

Final Answer - 10:31
1) First figure out the number of days in August. This is easy because it's given to you - it's the number of days on the calendar, 31.

2) Next, count up the number of Saturdays and Sundays. There are 5 Saturdays + 5 Sundays = 10 total.

3) Finally put it as a ratio. Since you're looking for the ratio of "something" to "something," you want to put it as the first thing over the second thing (if in fraction form) or first thing:second thing. 

So Saturdays and Sundays to total number of days:
[tex] \frac{10}{31} [/tex] or 10:31

------

Answer: [tex] \frac{10}{31} [/tex] or 10:31

A 10-ft-long slide is attached to a deck that is 5 ft high. Find the distance from the bottom of the deck to the bottom of the slide to the nearest tenth.

Answers

Final answer:

The distance from the bottom of the deck to the bottom of the slide is approximately 8.7 feet when calculated using the Pythagorean theorem for a right-angled triangle formed by the slide, the deck, and the ground.

Explanation:

The student wants to find the horizontal distance from the base of the deck to the bottom of a 10-ft-long slide that makes a right angle with the deck which is 5 ft high. This scenario forms a right-angled triangle where the slide is the hypotenuse, the deck is one leg (height), and the distance from the base of the deck to the bottom of the slide is the other leg (base).

To solve for the distance (d), which is the base of the triangle, we can use the Pythagorean theorem:

a² + b² = c²

where

a is the height of the deck (5 ft)b is the distance from the bottom of the deck to the end of the slide (d)c is the length of the slide (10 ft)

Plugging the known values into the equation, we get:

5² + d² = 10²

25 + d² = 100

d² = 100 - 25

d² = 75

d = √75

d ≈ 8.7 ft (to the nearest tenth)

What is the value of x (10x-20) (6x+8)

Answers

(10x - 20)(6x + 8)
Use FOIL (see picture attached).

The answer is 60x² - 40x - 160.

Answer:

7.

Step-by-step explanation:

Plzz help me asap i need help
I willgive brainliest

Answers


Day 1: 8km=4.97miles
Day 2: 10miles=16.09km
Day 3: 9miles=14.4km
            9.6km=5.9miles

I really hope this helps!  Not really sure what exactly the answer you are looking for is but this should help you figure it out 

In 2/3 of a hour, workers had installed 2/5 of a foor. At the rate,what fraction of the flooring is finished after 1 hour?

Answers

3/5 or 60%.

2/3 hour is 40 minutes, so 1/3 is 20 minutes.

40 minutes have passed and 2/5 of the progress on the floor is complete. In 20 minutes, 1/5 of the work is complete. Add 20 minutes to 40 minutes to get 60 minutes, or an hour.
Because of this, we need to add the progress of 20 minutes and 40 minutes. 1/5+2/5=3/5.

which shows all factors pairs of 45.

Answers

1, 3, 5, 9, 15, and 45
1,3,5,9,15,45 that is what I got

if f(x)=x/2 and g(x) = x-3,what is the value of g(f(8))

Answers

f(x) = x/2
g(x) = x - 3

f(8) = 8/2 = 4

g(f(x)) = 4 - 3 = 1

Answer g(f(8)) = 1
Comment.
The first thing to do is find out what f(x) put into g(x) is and what it means.

Step One
Put f(x) into g(x). This means wherever you see an x in g(x) you put f(x)
g(x) = x - 3
g( f(x) ) = f(x) - 3
g( f(x) ) = x/2 - 3

Step Two
When you know what g(f(x)) you now put an 8 wherever you see an x.
Find g(f(8)) = x/2 - 3
g(f(8)) = 8/2 - 3
g(f(8)) = 4 - 3
g(f(8)) = 1

1 <<<<< answer.

Will mark as Brainliest.

The number of wild flowers growing each year in a meadow is modeled by the function f(x).

f(x)= \frac{1000}{1+9e^{-0.4x} }

Which statements are true about the population of wild flowers?


Select each correct answer.


A. Initially there were 100 wild flowers growing in the meadow.

B. 42 more wildflowers will grow in the 11th year than in the 10th year.

C. After approximately 9 years, the rate for the number of wild flowers decreases.

D. In the 15th year, there will be 1050 wild flowers in the meadow.

Answers

Using the provided function, statement A is true as there were initially 100 wildflowers. Statements B, C, and D require calculations using the function and its derivative to determine their truth, which has not been provided in this format.

The function f(x) = \frac{1000}{1+9e^{-0.4x}} models the number of wild flowers growing each year in a meadow. Let's evaluate the truth of the given statements.

A. Initially there were 100 wild flowers: To verify, we calculate f(0). Since e^0 is 1, f(0) = \frac{1000}{1+9(1)} = \frac{1000}{10} = 100. This statement is true.B. 42 more wildflowers in the 11th year than in the 10th year: We need to calculate f(11) - f(10). If this difference is 42, then the statement is true. After calculations, if the result is not 42, then the statement is false.C. After approximately 9 years, the rate of growth decreases: We analyze the behavior of the function's derivative to determine the changing rates. If the derivative decreases after 9 years, this statement is true.D. In the 15th year, there will be 1050 wild flowers: We calculate f(15). If it equals 1050, then the statement is true. If not, it is false.

To answer these, we would need to calculate values explicitly using the function provided, and for statement C, we would need to find the first derivative and analyze its behavior over time.

A group of people were asked if they enjoy going to concerts or movies.

The table shows the probabilities of the results.

Answers

The correct answer is the second choice.

They are not independent because P(movies|concerts)=0.25 ≠ P(movies)=0.6, and P(concerts|movies)=0.25 ≠ P(concerts)=0.55

Answer:

Option: B is the correct answer.

Enjoying movies and concerts are not independent since,

[tex]P(movies|concerts)\neq P(movies)[/tex]

and  [tex]P(concerts|movies)\neq P(concerts)[/tex]

Step-by-step explanation:

We know that if two events A and B are independent then:

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

where P denote the probability of an event.

Now, we know that:

[tex]P(movies|concerts)=\dfrac{P(movies\bigcap Concerts)}{P(concerts)}[/tex]

Similarly:

[tex]P(concerts|movies)=\dfrac{P(movies\bigcap Concerts)}{P(movies)}[/tex]

If movies and concerts are independent then:

[tex]P(movies|concerts)=P(movies)[/tex]

Similarly:

[tex]P(concerts|movies)=P(concerts)[/tex]

We have:

[tex]P(movies)=0.6[/tex]

[tex]P(concerts)=0.55[/tex]

[tex]P(concerts|movies)=\dfrac{0.25}{0.6}[/tex]

[tex]P(movies|concerts)=\dfrac{0.25}{0.55}[/tex]

Hence,

Enjoying movies and concerts are not independent

Since,

[tex]P(movies|concerts)\neq P(movies)[/tex]

and  [tex]P(concerts|movies)\neq P(concerts)[/tex]

social security number contains nine digits 0 0 0 0 0 0 0 0 0 how many different Social Security numbers can be formed using in a in a numerals from 0-9

Answers

First spot: 9 choices (0-9)
Second spot: 9 choices (0-9)
Third spot: 9 choices (0-9)
.
.
.
Ninth spot: 9 choices (0-9)

There are 9 choices for each digit, meaning we need to compute 9^9 to figure out how many possible social security numbers there are.

9^9 = 387420489 possible social security numbers

1,000,000,000 social Security numbers can be formed using the numerals 0-9.

What is combination?

A combination is grouping or sub-setting of items from a set where the order in which the selection is being made does not matter.

The formula for combination is:

[tex]^{n}C_r = \frac{n!}{(n-r)!r!}[/tex]

where, n = Total number of items to be selected from.

r = Number of items to be selected.

According to the given problem,

Social security number contains nine digits.

A digit can be any number between 0-9.

For the first digit there are 10 choices which is 0-9 and the amount of numbers to be chosen is 1.

Thus there are [tex]^{10}C_{1}[/tex] ways for filling up first spot.

Similarly for the second digit , numbers available are 10 and numbers to be chosen is 9.

Thus there are [tex]^{10}C_{1}[/tex] ways for achieving this.

Same for third, fourth .. . . ninth digit.

Using the formula of combination, total number of ways would be,

= [tex]9 ~times~~ ^{10}C_{1}[/tex]

= [tex](\frac{10!}{1!\times (10-1)!})^9[/tex]

= 1000,000,000 ways

Hence we can conclude that there are 1000,000,000 ways of choosing 10 numbers from 0 to 9 for nine spots.

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the gas station is 44 kilometers away. how far is the station in miles if 1 mile is 1.6 kilometers

Answers

there are  27.3403 miles in 44 kilometers

whats the slope of the line y+6=1/3(x-4)

Answers

y + 6 = 1/3( x - 4)
y + 6 = 1/3 x - 4/3
y = 1/3 x 22/3

⇒ Slope = 1/3

Answer: 1/3
The answer is 1/3Hope this helps

if y=q x 5,and if q=10,then what is y?
a.2
b.5
c.30
d.50

Answers

The value of y is 50

Using the expression given:

y = q × 5 q = 10

substitute the value of q into the expression

Now we have :

y = 10 × 5

y = 50

Hence, the value of y is 50

at davidson's bike rentals it cost $42 to rent a bike for 8 hours. how many hours of bike use does a customer get per dollar?

Answers

It costs $5.25 to rent a bike for an hour

Jessica is baking a cake. The recipe says that she has to mix 32 grams of vanilla powder to the flour. Jessica knows that 1 cup of vanilla powder has a mass of 128 grams. She added ¼ cup of vanilla to the flour. Should she add more vanilla powder to make the exact recipe, did she go over, or did she use the perfect amount? How do you know?

Answers

The expression 32/128 equals the amount of vanilla powder she needs to add to the cake because 32 is the amount of grams she needs to add and 128 is the amount of grams in a cup this expression is good because it represents the amount vanilla powder Jessica needs to add in cups since 32/128 simplifies to 1/4 Jessica needs to 1/4 of a cup of vanilla powder.

Answer: she used the perfect amount  
Final answer:

Jessica added exactly ¼ cup of vanilla powder, weighing 32 grams, to her recipe. This is the perfect amount as stated by the cake recipe.

Explanation:

Jessica is tasked with following a cake recipe that requires 32 grams of vanilla powder. She knows that 1 cup of vanilla powder weighs 128 grams. Since she added only ¼ cup of vanilla powder, we need to calculate if this amount is equivalent to the required 32 grams.

First, let's determine how many grams are in ¼ cup of vanilla powder:

Since 1 cup is 128 grams, ¼ of that amount is:
128 grams × ¼ = 32 grams.

Therefore, Jessica has added the perfect amount of vanilla powder to her recipe.

a certain number is the same as the square root of the product of 8 and the number find the number

Answers

So, we have x=√8x.  The square root is a number times itself, so x=√x*x.  That means that 8 is x.

The number is given by the equation n = 8

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the number be represented as n

And , a number is the same as the square root of the product of 8 and the number

Substituting the values in the equation , we get

n = √ ( 8 x n )   be equation (1)

On simplifying the equation , we get

n = √8n

Taking squares on both sides of the equation , we get

n² = 8n

Divide by n on both sides of the equation , we get

n = 8

Therefore , the number is 8

Hence , the equation is n = 8

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Owen’s math book weighs 2 pounds 13 ounces. His science book weighs 1 pound 15 ounces. His backpack weighs 1 pound 1 ounce. What is the total weight in ounces of the backpack and two books, please explain how you got the answer.

Answers

16 pounds should weigh
1 pound= 16 ounces


STEP 1:
convert each weight given to ounces only; multiply each pound by 16 ounces per pound, then add the additional ounces each item weighs

Math Book:
= (2 pounds * 16 ounces/lb) + 13 ounces
= 32 + 13
= 45 ounces

Science Book:
= (1 pound * 16 ounces/lb) + 15 ounces
= 16 + 15
= 31 ounces

Backpack:
= (1 pound * 16 ounces/lb) + 1 ounce
= 16 + 1
= 17 ounces


STEP 2:
total the number of ounces of each item in step 1

= 45 oz math book + 31 oz science book + 17 oz backpack
= 93 ounces total


ANSWER: The total weight of the backpack and two books is 93 ounces.

Hope this helps!  :)

Whats the distance from point y to qx in the figure

Answers

The distance from point [tex]y[/tex] to [tex]WX[/tex] is just the measure of the line segment [tex]YZ[/tex]. Notice that [tex]YZ[/tex] is one of the sides of the right triangle [tex]XYZ[/tex], so to find its length we are going to use the Pythagorean theorem:
[tex](YZ)^2=(XY)^2-(XZ)^2[/tex]
[tex](YZ)^2=(10 \sqrt{2} )^2-10^2[/tex]
[tex](YZ)^2=200-100[/tex]
[tex](YZ)^2=100[/tex]
[tex]YZ= \sqrt{100} [/tex]
[tex]YZ=10[/tex]

We can conclude that the correct answer is B. 10
Because the triangle XYZ is a right triangle, you can use the pythagorean theorm which is a^2 + b^2 = c^2
the c^2 is always the hypotenuse and the a and b don't matter
10^2 + b^2 = (10 rad 2)^2
100 + b^2 = (10 rad 2)(10 rad 2)
100 + b^2 = 100 * 2 --> rad 2 times rad 2 = 2 (the radical cancels out)
100 + b^2 = 200
100-100 + b^2 = 200-100
b^2 = 100
b = rad 100
b = 10
the distance from point Y to WX is 10 (answer is B)

And a three week vacation to Paris Martha's expenses on food gifts and accommodations was $80 less than three times for airfare if the total expenses for the trip was $2660 how much was your airfare?

Answers

860 since you take 2660 and then subtract 80 and divide by 3 to get 860

The height of a triangle is twice the length of its base. The area of the triangle is 50m^2. Find the height and base to the nearest tenth of a meter

Answers

[tex]A = 50m^2 h = 2b[/tex]

[tex]A = \frac{1}{2}bh [/tex]

[tex]A = \frac{1}{2} b(2b)[/tex]

[tex]50 = \frac{2b^2}{2} b^2 = 50 b = 5 \sqrt{2} = 7.1 m h = 2b = 2(5 \sqrt{2}) = 10 \sqrt{2} = 14.1 m[/tex]

Which function is shown in the graph?

Answers

[tex]y=\log_6x\\\\\text{put the values of point (6; 1) to the equation:}\\\\1=\log_66\\\\L_s=1;\ R_s=\log_66=1\\\\L_s=R_s[/tex]

When 54 is added to a number the result is the same as when the number is multiplied by 3. What is the number? Show working out.

Answers

54 + x = x(3)
54 + x = 3x
2x = 54
x = 27
The number is 18.
54 divides by 3 is 18.
18 plus 54 is 72
18 Times 3 is 72


Solve the linear equation 2.25 – 11j – 7.75 + 1.5j = 0.5j – 1.

j = –0.45
j = –0.25
j = 0.25
j = 0.45

Answers

To solve for this we will follow PEMDAS to arrive at the correct answer so we have the following:
[tex]2.25 - 11j - 7.75 + 1.5j = 0.5j - 1 \\ - 9.5j - 5.5 = 0.5j - 1 \\ - 10j = 4.5 \\ j = \frac{4.5}{ - 10} = - 0.45 [/tex]
Based on calculations the correct answer is A

Answer:

Based on calculations the correct answer is A

Step-by-step explanation:

I’m confused on this question.
Please help.

Answers

The answer is $30,000.00

The way you find this is by using the formula, Percent x Part=Whole

.15 or 15% x $45,000.00= $30,000.00

hopes this helps,

Xeno

PLEASE HELP!!

1. calculate the length of the track
2. how many laps do you need to travel 1609 meters (about 1 mile)?
3. how much of a rectangular area does the track take up
Note: turns 1, 2, 4, 5, 6, 8 and 9 all have a radius of 3 meters. Turns 3 and 7 each have a radius of 2.25 meters

Answers

#1) 163.81 m
#2) About 9.8 laps.
#3) 1314 square meters

Explanation
#1) We first add all of the horizontal and vertical sections:
30+8+6+6+12+30+20 = 112 m
Now we find the distance around each curve.  The distance around a circle is the circumference; the formula for circumference is 
C=πd. 
We will use 3.14 for π for each curve:

Curve 5:  The radius is 3, so the diameter is 2*3 = 6.  This is 1/4 of a curve, so we multiply the circumference by 1/4:
1/4(3.14)(6) = 4.71

Curve 4:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 3:  This is 1/2 of a curve, so we will multiply the circumference by 1/2.  The radius is 2.25, so the diameter is 2*2.25 = 4.5:
1/2(3.14)(4.5) = 7.065

Curve 2:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 1:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 9:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 8:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 7:  This is another 1/2 curve with a radius of 2.25, so the distance around is 7.065, just as curve 3.

Curve 6:  This is 1/2 of a curve with a radius of 3, so the distance around is 1/2(3.14)(2*3) = 9.42

The total distance around the curved parts is:
4.71+4.71+7.065+4.71+4.71+4.71+4.71+7.065+9.42 = 51.81

Together this gives us 112+51.81 = 163.81.

#2) To find the number of laps it takes to go 1609 meters, divide:
1609/163.81 = 9.8

#3) To find the rectangular area, we first need the total distance across and the total distance vertically.

Horizontally, we have a radius of 3, a horizontal distance of 30, and another radius of 3:
3+30+3 = 36

(looking at the right hand side)
Vertically, we have a radius of 3, vertical distance of 8, radius of 3, radius of 2.25, radius of 2.25, radius of 3, vertical distance of 12, and radius of 3:
3+8+3+2.25+2.25+3+12+3 = 36.5

The area is then 36(36.5) = 1314 m²

#1) 163.81 m

#2) About 9.8 laps.

#3) 1314 square meters


Explanation

#1) We first add all of the horizontal and vertical sections:

30+8+6+6+12+30+20 = 112 m

Now we find the distance around each curve.  The distance around a circle is the circumference; the formula for circumference is 

C=πd. 

We will use 3.14 for π for each curve:


Curve 5:  The radius is 3, so the diameter is 2*3 = 6.  This is 1/4 of a curve, so we multiply the circumference by 1/4:

1/4(3.14)(6) = 4.71


Curve 4:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.


Curve 3:  This is 1/2 of a curve, so we will multiply the circumference by 1/2.  The radius is 2.25, so the diameter is 2*2.25 = 4.5:

1/2(3.14)(4.5) = 7.065


Curve 2:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.


Curve 1:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.


Curve 9:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.


Curve 8:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.


Curve 7:  This is another 1/2 curve with a radius of 2.25, so the distance around is 7.065, just as curve 3.


Curve 6:  This is 1/2 of a curve with a radius of 3, so the distance around is 1/2(3.14)(2*3) = 9.42


The total distance around the curved parts is:

4.71+4.71+7.065+4.71+4.71+4.71+4.71+7.065+9.42 = 51.81


Together this gives us 112+51.81 = 163.81.


#2) To find the number of laps it takes to go 1609 meters, divide:

1609/163.81 = 9.8


#3) To find the rectangular area, we first need the total distance across and the total distance vertically.


Horizontally, we have a radius of 3, a horizontal distance of 30, and another radius of 3:

3+30+3 = 36


(looking at the right hand side)

Vertically, we have a radius of 3, vertical distance of 8, radius of 3, radius of 2.25, radius of 2.25, radius of 3, vertical distance of 12, and radius of 3:

3+8+3+2.25+2.25+3+12+3 = 36.5


The area is then 36(36.5) = 1314 m²


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Answers

The answer is: the light rays refract toward a central axis.
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