A farmer has an orchard that covers an area of 40 acres. He grows apples on 25 acres, peaches on 7 acres
nectarines on 5 acres, and plums on 3 acres. The fruit trees are equally distributed within the orchard. A wees
chosen at random. Rounded to the nearest tenth of a percent, what is the theoretical probably that the trees
within the acres of apple trees?
25.0
37.5%
62.5%
75.4%

Answers

Answer 1

Answer:

Option-C=> 62.5%

Step-by-step explanation:

Given that the area where apple is grown: 25 acres

Total area of cultivation:40 acres

Percentage ={ (Area where apple is grown / Total area of cultivation) ×100

=>(25/40)×100

=>(25/4)×10

=>62.5%

∴The percentage of the trees are within the orchard area is : 62.5%

MARK AS BRAINLIEST

Answer 2

The theoretical probability of selecting a tree within the acres of apple trees is 62.5%.

To find the probability of selecting a tree within the acres of apple trees, we need to consider the proportion of apple trees to the total number of trees in the orchard.

The total area of the orchard is 40 acres, and the area dedicated to apple trees is 25 acres. Since the trees are equally distributed within the orchard, the proportion of apple trees to the total number of trees is:

[tex]\[ \text{Proportion of apple trees} = \frac{\text{Area of apple trees}}{\text{Total area of orchard}} \][/tex]

[tex]\[ \text{Proportion of apple trees} = \frac{25}{40} = 0.625 \][/tex]

To convert this proportion to a percentage, we multiply by 100:

[tex]\[ \text{Probability} = 0.625 \times 100\% = 62.5\% \][/tex]

Rounded to the nearest tenth of a percent, the theoretical probability of selecting a tree within the acres of apple trees is 62.5%. Therefore, the correct answer is: 62.5%


Related Questions

The weight, in grams, of eight different kiwis was used to create the box plot shown above. Which of the sets of numbers below matches the given box plot?
A.
Weights of Kiwis: 68, 73, 75, 75, 76, 76, 78, 80

B.
Weights of Kiwis: 68, 70, 75, 75, 75, 76, 77, 80

C.
Weights of Kiwis: 68, 72, 75, 75, 76, 76, 77, 80

D.
Weights of Kiwis: 68, 70, 72, 75, 75, 76, 78, 80

Answers

Answer:

Step-by-step explanation:

The answer is d because 75 is the medain of the kiwi fruit

The answer is 75 because it explain it

y = 2×2square+ 4× - 2 value

Answers

Answer:

y=2(2x+3)

Step-by-step explanation:

y=2*2^2+4x-2

y=8+4x-2

y=4x+6

y=2(2x+3)

What is 3a2 + a2 added to a + 6?


Answers

The addition of 3a^2 + a^2 to a + 6 gives 3a^2 + a^2 + a +6.

What is addition?

The addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

We have to find when 3a^2 + a^2 added to a + 6.

3a^2 + a^2 + a +6

This cannot be added further because they do not have any like terms.

Since those terms are not like terms, their coefficient won't be add and the expression we've got right now, is its simplest form and cannot be reduced more.

Those terms which have same variables raised with same power are like terms.

For example, 5t^3 and 6t^3 are like terms since variable is same, and it is raised to same power 3.

Thus, the addition of 3a^2 + a^2 to a + 6 gives 3a^2 + a^2+ a +6

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[tex]4a^2 + a + 6[/tex] is the final expression represents the sum of the given terms.

To add the expressions 3a2 + a2 to a + 6, follow these steps:

Identify and group the like terms:3a2 + a2 for the squared termsa for the linear term6 for the constant termCombine the like terms:3a2 + a2 = 4a2Write down the final expression after addition:4a2 + a + 6

Thus, the result of adding the given expressions is[tex]4a^2 + a + 6.[/tex]

The radius of a dog's collar

should be at least 0.5 inch larger than

the radius of the dog's neck. A dog collar

adjusts to a circumference of 10 to

14 inches. Should the collar be worn

by a dog with a neck circumference of

12.5 inches? Explain.

Answers

Answer:

No. The collar should not be worn by this dog.

Step-by-step explanation:

Please kindly go through the attached files for more explanation.

Final answer:

the collar is too small for the dog.

Explanation:

To answer whether the dog collar should be worn by a dog with a neck circumference of 12.5 inches, we must consider the information given: the dog's collar adjusts between a circumference of 10 and 14 inches and it should be at least 0.5 inch larger than the dog's neck circumference.

First, we calculate the radius of the dog's neck using the formula for circumference: C = 2πr. For a neck circumference of 12.5 inches, the radius (r) would be:

C = 2πr
12.5 = 2πr
r = 12.5 / (2π)
r ≈ 1.9875 inches

Now, to ensure comfort, the collar's radius should be at least 0.5 inch greater than the dog's neck radius. Adding 0.5 inch to the dog's neck radius gives us:

1.9875 inches + 0.5 inch = 2.4875 inches

Which means the collar's circumference should be at least:

C = 2πr
C ≈ 2π(2.4875)
C ≈ 15.63 inches

Given that the collar adjusts to a maximum of 14 inches, this would be too small for a dog with a neck radius as calculated. Therefore, the collar should not be worn by a dog with a neck circumference of 12.5 inches, as it would not accommodate the extra 0.5 inch needed for comfort.

Which is true about the domains and ranges of the functions f(x) = 1/8 (x) and g(x) = 8(x) ?

Answers

Answer:

both have a domain and range of all real numbers

Step-by-step explanation:

the figure is the net for a rectangular prism. what is the surface area of the rectangular prism represented by the net? enter your answer in the box.

Answers

Answer:

544

Step-by-step explanation:

someone help please!!

Answers

9) 3/10
10) 0
11) 2/5
12) 4/5

Answer:

9. 0.3

10. 0.0

11. 0.4

12. 0.3

Step-by-step explanation:

I am not 100% sure about this, but this is what I could come up with.

Given: mlln

What is the value of x?

Answers

Answer:

x = 8°

Step-by-step explanation:

m II n

Alternate interior angles are equal.

6x - 2 = 46

6x = 46 +2

6x = 48

x = 48/6

x = 8

Answer:

8

Step-by-step explanation:

When you have a line intersecting parallel lines, the opposite interior angles are always the same.

46 + 2 = 48

48 / 6 = 8

what is Pythagorean theorem

Answers

A^2+B^2=C^2, this formula is used to find the length of a hypotenuse only if the triangle is a right triangle (has a 90 degree angle)

Answer:

Pythagorean theorem - theorem that states that the sum of the squares of the two legs is equal to the square of the hypotenuse in a right triangle

Suppose a bag contains 5 balls numbered 1 through 5. In how many way scan you select 5 balls from the bag if there is no replacement after selection?

Answers

Answer:

5

Step-by-step explanation:

We are being asked in how many ways an enumerated ball can be removed without any type of replacement, therefore it would be a combination without repetition:

nCr = n! / r! * (n-r)!

n, total number of balls, 5

r, specific number of balls, 1

5C1 = 5! / (1! * 4!) = 5

Therefore there are 5 ways to do the above.

Is u = - 1/2 a solution of 8u - 1 = 6u

Answers

Answer:

-1/2 is not a solution

Step-by-step explanation:

8u-1 = 6u

Subtract 8u from each side

8u-1 -8u = 6u-8u

-1 = -2u

Divide each side by -2

-1 /-2 = -2u/-2

1/2 = u

Answer:

No, u = - 1/2 is not a solution of 8u - 1 = 6u

Step-by-step explanation:

[tex]8u - 1 = 6u \\ 8u - 6u = 1 \\ 2u = 1 \\ \\ u = \frac{1}{2} [/tex]

here we get u = +1/2

HELPPP, please:) super easy

Answers

Answer:

6.8

Step-by-step explanation:

Answer:

Just by approximating without a calculator, you would know it under the sqrt of 49, so it should be less than 7 and greater than 6 (sqrt of 36)

With a calculator and rounding, you will find that the answer is 6.8.

What is the approximate circumference of the globe?
Part of the North Carolina Museum of Natural Sciences
is a model of a three-story globe. Assuming the globe
represents a full sphere, the volume of the sphere would
be approximately 57,166 cubic feet.
z feet

Answers

Answer:

70

Step-by-step explanation:


IN UNIT TEST!
Rectangle PQRS is rotated 90° counterclockwise about the origin.

On a coordinate plane, rectangle P Q R S has points (2, 3), (5, 3), (5, 1), (2, 1).

What are the coordinates of point Q’?
Q’( –3, 5)
Q’(3, –5)
Q’(5, –3)
Q’(–5, –3)

Answers

Answer:

(-3, 5)

Step-by-step explanation:

im assuming the orginal point q is (5, 3)

Based on the given scenario above, the coordinates of point Q  is known to be (-3, 5).

What is the points about?

Note that if a point P(x, y) is rotated 90° counterclockwise around the origin, one has to flip x and y and reverse the sign of y.

So, The rule to rotate a point P(x, y)  after a rotation 90° counterclockwise around the origin is said to be:

P(x, y) = P'(-y, x)

In this question, rectangle PQRS is rotated 90° counterclockwise about the origin.

The rectangle is said to have the coordinates:

P(2, 3)

Q(5, 3)

R(5, 1)

S(2, 1)

Therefore we look for the coordinates of the point Q’.

By using the rule to rotate a point P(x, y)  after a rotation 90° counterclockwise around the origin, then:

P(x, y) = P'(-y, x)

Therefore, coordinates of the point Q’ will be:

Q(5, 3)  = Q'(-3, 5)

Therefore, the coordinates of point Q' is:  Q'(-3, 5)

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Cait purchases a $20 item at a store. She uses a coupon to receive a 15% discount, and she pays a 6% sales tax on

the item. She calculates the total cost, in dollars, of the item using the expression shown.

en este

personen

in om

die pan en

Cait's Expression

(1.15)(1.06)(20)

A. Describe the error in the expression Cait used for her calculation.

B. Show or explain how you would calculate the total cost of Cait's purchase.

Type your answers in the space provided.

Answers

Answer:

A. Cait treated the discount as an increase

B.  (20) (1.06) (0.85)

Step-by-step explanation:

Hi, Cait treated the discount as an increase.

Cait multiplied the price (20) by the tax percentage (increase) 1.06  

Since the sale tax increase is 6% and it is added to the price we have to express it in decimal form (6/100=0.06) and add it to 1.

20 (1 +0.06) = 20 (1.06)

The coupon discount is subtracted to the price. So, the correct form is:

15/100= 0.15

20 (1-0.15) = 20 (0.85)  

Instead of this, Cait expressed the percent discount as a percent increase .

20 (1+0.15) = 20 (1.15)

The correct form is (20) (1.06) (0.85)

Please help me solve this question

Answers

Answer:

x=12

Step-by-step explanation:

The shapes are similar, so their corresponding sides will be proportionate

Use the bases and the right most sides to create the proportion

14/56=3/x

Cross multiply

14*x=56*3

14x=168

Divide both sides by 14

x=12

Answer:

missing side is x =12

Step-by-step explanation:

[tex]given \: that \: two \: figures \: are \: similar \\ correspondung \: sides \: are \: proportional \\ let \: us \: take \: any \: two \: sides \: \\ including \: the \: value \: of \: x \\ \frac{10}{40} = \frac{3}{x} \\ \frac{1}{4} = \frac{3}{x} \\ x = 3 \times 4 \\ x = 12[/tex]

HAVE A NICE DAY!

THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.





The image shows parallel lines cut by a transversal. The expressions represent unknown angle measurements. What is the value of x?
A)5 B)7 C)9 D)11

Answers

Answer: C

because

it is

Answer:

Step-by-step explanation:

the answer is B cause a Supplementary angles sum is 180°. So, set the angles equal to 180° and solve for x.

11x + 8 + 12x + 11 = 180

23x + 19 = 180

23x = 161

x = 7

(SAT Prep) In the figure, what is the length of BC?
A. 25
B. 15
C. 18
D. 22

Answers

Answer:

I got 18 as my answer

Step-by-step explanation:

I made a triangle with the right side by dropping a vertical. Lets call the point straight down from C, E

Then I found the angle of D

sin θ = 5/13

θ = sin-¹(5/13)

θ≅22.619°

Then I found length of DE by

cosθ (remember we know what theta is) = X/13

12cosθ = X

X = 12

The length of DE is 12.

Since AD is 30, and the left side has two right angles we can do

AD - DE to find BC.

30-12 is 18

The length of BC is C. 18.

What is Pythagoras Theorem?

Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.

Given is a trapezoid.

First draw a perpendicular line from C to the segment AD.

Mark the intersecting point of line and AD by P.

We know that,

CP = BA = 5

Using Pythagoras theorem,

PD = √(13² - 5²) = √(169 - 25) = √144 = 12

Now, AP + PD = AD

AP = AD - PD

     = 30 - 12

     = 18

Now, BC = AP = 18.

Hence the length of BC is 18.

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what is -10(-7x-7)-4(-8x-9)

Answers

Answer:

The answer is -202

The answer of this question is , -788 !

2/7 converted to percentage

Answers

Look at the attached picture

Hope it will help u...:)

Answer:

Step-by-step explanation:

[tex]\frac{2}{7}*100=\frac{200}{7}\\\\=28.5714\\[/tex]

= 28.57% or

≈ 29%

Which equation is used to find the experimental probability of an event?


Answers

Tbh ik for a fact that that answer is ?b

What’s the slope of this question

Answers

Answer:

i believe its 1.5

Step-by-step explanation:

its -4.5 crossing over the y-axis then 3 across divide that and get 1.5

A sphere has a volume of 32/3 pie cubic units what is the radius of the sphere

Answers

Answer:

radius=2

Step-by-step explanation:

volume= 4/3 pi r^3

32/3pi=4/3r^3

divide out 4/3

8pi=r^3

cube root

r=2

Work out the surface area of a
cuboid 3cm by 3cm by 4cm?

Answers

Answer: 14 cm

Step-by-step explanation:

Answer:

It was 36 cm3

Step-by-step explanation:

3cm x 3 cm x 4 cm

=36 cm3

True or false 0.20 is equivalent to 2/100

Answers

Answer:

0.02 is equivalent to 2/100

therefore it is false

if i can have brainliest that would be great

Final answer:

The statement that 0.20 is equivalent to 2/100 is false. The correct equivalent fraction of 0.20 is 20/100, which simplifies to 1/5.

Explanation:

The question asks whether 0.20 is equivalent to 2/100. This is false. The decimal 0.20 is equivalent to 20/100, which simplifies to 1/5 when you divide the numerator and the denominator by the greatest common divisor, which is 20 in this case. To convert a decimal to a fraction, place the decimal number over its place value. Since there are two digits to the right of the decimal point in 0.20, you would put 20 over 100, which reduces to 1/5. On the other hand, 2/100 cannot be simplified further and remains as is. Thus, 0.20 is not equivalent to 2/100; it is actually ten times larger.

To make a profit, stores mark up the prices on the items they sell. A sports store buys skateboards from a supplier for s dollars. What is the retail price for skateboards that the manager buys for $35 and $56 after a 42% markup ? Which expressions represent the markup of the skateboard, where s is the original cost of the skateboard

Answers

Answer:

The retail price for the $35 skateboard = $49.70

The retail price for the $56 skateboard = $79.20

Step-by-step explanation:

Please kindly check the attached files for detalils

Which of the following is a linear function?

y = 3x^2
y = 1 over 3x
y = x^3 + 5
2 over 3x = y − 1

Answers

Answer:

y= 1 over 3x

Step-by-step explanation:

I thought it was 2 over 3x but it was wrong so it has to be y= 1 over 3x

HELPPPPPPPPP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
IF THEY ARE CORRECT ANSWERS I WILL MARK BRAINLIEST
2.094 2.702 which is greater than
2.75 2.6 which is greater than
8.235 8.1 which is greater than
21.337 21.31 which is greater than

Answers

Answer:

1- is 2.702

2- is 2.75

3- 8.235

4- 21.337

Step-by-step explanation:

Final answer:

The question involves comparing decimal numbers. The larger numbers for the pairs given are 2.702, 2.75, 8.235 and 21.337 respectively. The rule for comparing decimals is to start from the left and compare digits in the same position.

Explanation:

The question asks to identify which of the two numbers for each pair is larger. It's clear this involves a basic understanding of comparing decimals, which is a key skill in mathematics.

Between 2.094 and 2.702, 2.702 is greater.Between 2.75 and 2.6, 2.75 is greater.Between 8.235 and 8.1, 8.235 is greater.

  Between 21.337 and 21.31, 21.337 is greater.  

The rule for comparing decimals is to start from the left and compare digits in the same position. This way, you can identify which number is larger or smaller.

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Solve for an angle in right triangles help

Answers

Answer:

26.39

Step-by-step explanation:

[tex] \sin(B) = \frac{AC}{AB} = \frac{4}{9} [/tex]

[tex]B = {sin}^{ - 1} = \frac{4}{9} [/tex]

[tex] = 26.387[/tex]

[tex] = 26.39[/tex]

Answer: 26.39 degrees

Step-by-step explanation: sin ^-1= 4/9

26.3877

Anderson’s Nursery was choosing between two different greenhouses.

2 greenhouses have a rectangular prism base with a length of 12 meters, width of 12 meters, and height of 10 meters.

Greenhouse 1 has a square pyramid top with a base of 12 meters by 12 meters and height of 8 meters.

Greenhouse 2 has a triangular prism top. The triangular sides have a base of 12 meters and height of 8 meters. The prism has a height of 12 meters.


Which statements are true about the greenhouses? Select two options.

The space inside greenhouse 1 can be found using the equation V = 12 (12) (10) + one-half (12) (12) (8).

The space inside greenhouse 1 can be found using the equation V = 12 (12) (10) + one-third (12) (12) (8).

The space inside greenhouse 2 can be found using the equation V = 12 (12) (10) + one-half (12) (12) (8).

The space inside greenhouse 2 can be found using the equation V = 12 (12) (10) + one-third (12) (12) (8).

The space inside greenhouse 1 is 192 meters cubed greater than the space inside greenhouse 2.

Answers

Answer:

B and C

Step-by-step explanation:

Hope this helps!

Doing this question now! :)

Applying the appropriate volume formula for the square pyramid and prism, the statements that are true are: B and E.

What is the Volume of Square Pyramid?

Volume = 1/3(a²)h

What is the Volume of a Triangular Prism?

Volume = 1/2(a)(b)(h)

What is the Volume of a Rectangular Prism?

Volume = lbh

Space inside Greenhouse 1 = volume of rectangular prism + volume of square pyramid = lbh + 1/3(a²)h

= (12)(12)(10)  + 1/3(12)(12)8

= 1,824 m³

Space inside Greenhouse 2 = volume of rectangular prism + volume of triangular prism = lbh + 1/2(a)(b)(h)

= (12)(12)(10) + 1/2(12)(8)(12)

= 2,016 m³

Space inside Greenhouse 2 - Greenhouse 1 = 192 m³

The true statements are B and E.

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The Shirt Works sells a large variety of tee shirts and sweatshirts. Steve Hooper, the owner, is thinking of expanding his sales by hiring high school students, on a commission basis, to sell sweatshirts bearing the name and mascot of the local high school.These sweatshirts would have to be ordered from the manufacturer six weeks in advance, and they could not be returned because of the unique printing required. The sweatshirts would cost Hooper $17.00 each with a minimum order of 320 sweatshirts. Any additional sweatshirts would have to be ordered in increments of 50.Since Hoopers plan would not require any additional facilities, the only costs associated with the project would be the costs of the sweatshirts and the costs of the sales commissions. The selling price of the sweatshirts would be $34.00 each. Hooper would pay the students a commission of $8.00 for each shirt sold.1. To make the project worthwhile, Hooper would require a $5,850 profit for the first three months of the venture. What level of unit sales and dollar sales would be required to reach this target net operating income? (Round your intermediate calculations to 2 decimal places.) Sales level in units sweatshirts Sales level in dollars what do you mean by DEFCON ? Use a trigonometric ratio to find the value of x. Round your answer to the nearesttenth. HELPPP MEEEE I showed picture up there plsssss help I need it in your own words not copy and pasted from other answersThe male resplendent quetzal bird has evolved to have tail feathers that are approximately 60 cm long. The female quetzal has short tail feathers. Using the quetzal as your example, describe how the mechanism of natural selection may have led to the evolution of the male quetzals extraordinarily long tail feathers. Using the expectations hypothesis theory for the term structure of interest rates, determine the expected return for securities with maturities of two, three, and four years based on the following data. (Input your answers as a percent rounded to 2 decimal places.) Interest Rate 1-year T-bill at beginning of year 1 4 % 1-year T-bill at beginning of year 2 5 % 1-year T-bill at beginning of year 3 9 % 1-year T-bill at beginning of year 4 11 % A cyclist rode at constant speed of 23 mph for 4 hours. Then, she decreased her rate of speed to 16 mph for 5 hours. How far did the cyclist ride in 9 hours? Assume the role of one noted Personality Theorist Carl Rogers. Carl (you) is going to write a letter to a client in response to this situation:Someone has come to you expressing a number of problems: the person's marriage is a mess, they hate their job, they cannot complete work on time, they feel overwhelmed and cranky much of the time, and even their dog doesn't like them much of the time. While working from the Humanistic (client centered) perspective, you will need to inform your fictional "client" what you believe the client can do about the problems the client is having. Using Rogerian theory, how might you tell them to set things to right again? After you have completed adequate research on Rogers, and how he envisioned both problems and solutions, write a letter your fictional client. Your letter should display clear evidence (such as textbook terms) that you understand what the theorist considers a healthy, well-adjusted personality, and how to help someone build one. No direct quotes of the textbook or other source is permitted. what happens when the amplitude of a sound wave changes? Dakota corporation 15-year bonds have an equilibrium rate of return of 9 percent. for all securities, the inflation risk premium is 1.60 percent and the real risk-free rate is 3.30 percent. the security's liquidity risk premium is 1.05 percent and maturity risk premium is 1.65 percent. the security has no special covenants. calculate the bond's default risk premium. Elite Couture, a high-end fashion goods store has to decide on the quantity of Luella Bartley handbags to sell during the Christmas season. The unit cost of the handbag is $28.50 and the handbag sells for $150. All handbags remaining unsold at the end of the season are purchased by a discounter for $20 each. Further, there is a significant 40% inventory holding cost incurred for each unsold bag. Demand for bags is distributed normally with mean 150 and standard deviation 20. How many bags should be purchased to maximize expected profit? a)150 b)155 c)160 d)165 e)170 f)175 g)180 Can someone please help Who went to the play with Abraham Lincoln and Mary Todd Lincoln James cut out four parallelograms, the dimensions of which are shown below. Parallelogram 1 length: 12 in. width: 15 in. diagonal: 20 in. Parallelogram 2 length: 16 in. width: 30 in. diagonal: 34 in. Parallelogram 3 length: 20 in. width: 21 in. diagonal: 29 in. Parallelogram 4 length: 18 in. width: 20 in. diagonal: 26 in. James put the parallelograms together so one vertex from each paper exists on a point, as shown in the circle. 4 parallelograms are put together so that one vertex from each paper exists on a point. Which statement explains whether or not the parallelgrams can be put together so each occupies one-quarter of the area of the circle without overlapping any other pieces? Check all that apply. The quadrilaterals can be placed such that each occupies one-quarter of the circle. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 1 do not form right angles. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 2 do not form right angles. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 3 do not form right angles. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 4 do not form right angles. In STU, u = 23 inches, T=158 and U=17. Find the length of t, to the nearest 10th of an inch. Listen to the question given in the audio. Record your response using a complete Spanish sentence. which sentence makes a logical comparison?We thought Kelly's office was most colorful than any office.We thought Kelly's office was more colorful than any other office.We thought Kelly's office was more colorful than any office.We thought Kelly's office was most colorful than any other office. A carpenter bought a piece of wood that was 4.9 centimeters long. Then he sawed 4.1 centimeters off the end. How long is the piece of wood now? The incoming infrared radiation from the Sun as it travels towards Earth is _____. mostly reflected back out into space mostly absorbed and transmitted toward Earth's surface equally absorbed and reflected completely blocked and reflected by the upper atmosphere Which group invaded the most territory through out Europe