Angle of elevation please help if you know .tysm

Angle Of Elevation Please Help If You Know .tysm

Answers

Answer 1

Answers:

Y = 176.0 feetX = 128.7 feet

Note: Your teacher may not want you to type "feet" into the answer boxes.

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Explanation:

The tree's shadow is 120 ft long, so it's the length of the horizontal side of the triangle. With regard to the reference angle (47 degrees), this 120 ft side is adjacent to the angle because it's as close as possible to the angle. That means the X is the opposite side of the reference angle.

The Y side is the longest side. It's the hypotenuse. The hypotenuse is always the longest side and always opposite the largest angle of a right triangle (so it's always opposite the 90 degree angle).

-------------

To find Y, we'll use the cosine rule

cos(angle) = adjacent/hypotenuse

cos(47) = 120/Y

Y*cos(47) = 120

Y = 120/cos(47)

Y = 175.9535 .... make sure your calc is in degree mode

Y = 176.0

When rounding to the nearest tenth, the second '5' will bump that 9 up to 10, which then carries over and why 175 bumps up to 176.

The distance from the tip of the tree to the tip of the shadow is roughly 176 feet.

-------------

We can use the tangent rule to find X

tan(angle) = opposite/adjacent

tan(47) = X/120

120*tan(47) = X

X = 120*tan(47)

X = 128.6842

X = 128.7

The tree is roughly 128.7 feet tall

This is somewhere between a 12 story and 13 story building assuming each story is 10 ft (since 12 stories = 12*10 = 120 ft, and 13 stories = 130 ft).


Related Questions

Is 12 16 20 a right triangle?

Answers

No, 12 16 20 is not a right triangle. In order to be a right triangle, one side must be the same as the square root of the sum of the squares of the other two sides. In this case, the hypotenuse (side 20) is not equal to the square root of 12^2 + 16^2 which is 20.

No, 12 16 20 is not a right triangle. To determine whether or not something is a right triangle, we need to use the Pythagorean Theorem. This theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is side 20, and the other two sides are 12 and 16. When we calculate the square root of 12^2 + 16^2, we get 20, which does not match the length of the hypotenuse. Therefore, 12 16 20 is not a right triangle.

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PLEASE HELP I AM DESPERATE!
Question is in the picture please help!!!

Answers

Answer:

  (a)  (5, 9)

Step-by-step explanation:

You want the solution to the system ...

x = 5y = 2x -1

Solution

The value of x is already given, so no work is required to find that.

The value of y is found by using that value of x in the equation for y:

  y = 2x -1

  y = 2·5 -1 = 10 -1 = 9

The solution is (x, y) = (5, 9).

the ratio of red to grern to blue sweets in a packet is 2:3:1. if there are 18 green sweets, how many blue sweets are there?? ​

Answers

If the ratio is 2:3:1

You are looking for y in x:18:y

To get from 2:3:1 you multiply by 3 so your new ratio would be

6:18:3 so there would be 3 blue sweets

Math

A 6. 0 kg bowling ball traveling at 2 m/s strikes a 1. 5 kg bowling pin. Describe and compare the forces that act on the bowling ball and the bowling pin

during the collision.

Answers

By using formula and solving, Force of impact (pin) = Change in momentum (pin) / Time of collision = 12 kg*m/s / t

What is collision?

A collision is an event in which two or more objects come into contact with each other. In physics, a collision is defined as a rapid and forceful interaction between two or more objects that causes a transfer of energy. Collisions can be elastic or inelastic, depending on whether or not the total kinetic energy of the objects is conserved.

What is force?

Force is a physical quantity that describes the interaction between two or more objects. It is a vector quantity, meaning it has both magnitude and direction. Forces can cause an object to accelerate, change its shape, or change its direction of motion. Forces can be categorized into different types, such as contact forces, which act when two objects are in contact, and non-contact forces, which act at a distance. Some examples of non-contact forces are gravitational force, electric force, and magnetic force.

To calculate the force of impact on the bowling ball and bowling pin during the collision, you can use the formula:

Force of Impact = Change in momentum / Time of collision

The change in momentum is given by the formula:

Change in momentum = Final momentum - Initial momentum

The initial momentum of the 6 kg bowling ball traveling at 2 m/s is:

Initial momentum (ball) = 6 kg * 2 m/s = 12 kg*m/s

The final momentum of the bowling ball can be calculated using the conservation of momentum principle, which states that the total momentum of the system remains constant before and after the collision. In this case, since the bowling pin is moving after the collision and the bowling ball is not, the final momentum of the bowling ball is zero.

Final momentum (ball) = 0

Change in momentum (ball) = Final momentum (ball) - Initial momentum (ball) = 0 - 12 kgm/s = -12 kgm/s

The force of impact on the bowling ball is:Force of impact (ball) = Change in momentum (ball) / Time of collision = -12 kg*m/s / t (t is the time of collision, assuming it's a short time)

Similarly, the initial momentum of the 1.5 kg bowling pin at rest is:

Initial momentum (pin) = 1.5 kg * 0 m/s = 0 kg*m/s

The final momentum of the bowling pin can be calculated using the conservation of momentum principle, which states that the total momentum of the system remains constant before and after the collision.

Final momentum (pin) = Initial momentum (ball) = 12 kg*m/s

Change in momentum (pin) = Final momentum (pin) - Initial momentum (pin) = 12 kgm/s - 0 kgm/s = 12 kg*m/s

The force of impact on the bowling pin is:

Force of impact (pin) = Change in momentum (pin) / Time of collision = 12 kg*m/s / t

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What is the x in 4x+20?

Answers

Answer:

the answer is 5 because if you divide it its your answer

Answer:

x=-5

Step-by-step explanation:

Set " 4x+20" equal to 0 (4x+20=0)

Do the opposite operation of 20 (in this case is subtraction) and subtract 20 from both sides (4x+20-20=0-20).

You'll be left with 4x=-20.

Divide both sides by 4 (4x/4=-20/4).

4 divided 4 equals x.

-20 divided by 4 equals -5.

x=-5.

Hope this was helpful.

HELP ASAP

The quadrilateral below is a trapezoid

Answers

Answer:

Step-by-step explanation:

9x+2+5x-4=180

14x-2=180

14x=80+2

x=182/14

x=13

angle B=5x-4

=5*13-4

=65-6

=61

Ricardo's town recently voted on a new education funding package. Of the voters who voted for the bill, 20% voted for it. What fraction of the voters voted in favor of the measure?

Enter the fraction in simplest form.

Answers

The fraction of the voters who voted in favor of the measure will be 1/5.

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Ricardo's town recently voted on a new education funding package. Of the voters who voted for the bill, 20% voted for it.

The fraction of the voters who voted in favor of the measure will be given as,

⇒ 20%

⇒ 20 / 100

⇒ 1 / 5

The fraction of the voters who voted in favor of the measure will be 1/5.

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8. Given DF bisects LEDF, find n and then find FG. The diagram is not drawn to scale.
2 points
Show your work to find FG
Show your work to find n

GIVING 20 POINTS!!

Answers

The measure of length of FG is 105 units.

What is bisection?

To determine the roots of a polynomial problem, utilise the bisection method. It splits and separates the interval in which the equation's root is located. The continuous functions intermediate theorem serves as the method's guiding premise.

From the given diagram, since Line DF bisects angle EDG, then -

EF = FG

Given the following parameters -

EF = 9n - 3

FG = 8n + 9

Equating both expressions -

9n - 3 = 8n + 9

9n - 8n = 9 + 3

n = 12

Get the measure of FG -

FG = 8n + 9

FG = 8(12) + 9

FG = 96 + 9

FG = 105

Hence, the line FG measures as 105 units.

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For every 150 dogs, there are 300 cats. write this ratio in simples form in all three ways.

Answers

Answer:

Step-by-step explanation:

150 : 300

In simplest form

1 : 2

In fraction form

1/2

In decimal form

0.5

Answer:

1:2 1/2 1÷2

Step-by-step explanation:

divide both of them by 150. You get 1:2, which can be converted to 1/2 and 1÷2

PLS HELP ASAP 50 POINTS!!!!
Triangle ABC is congruent to triangle PDF. Dude AC corresponds to what side in triangle PDF

Answers

Answer:

PF

Step-by-step explanation:

Since the triangles are congruent, meaning they are the same shape, we can just match the lines between the two triangles. In triangle ABC, the line AC is the hypotenuse of the triangle. So, we need to find the hypotenuse of the triangle PDF. Looking, we can see the hypotenuse of the triangle PDF is the line, or side, PF.

Hope this helped!

Math please help!!!!!!

Answers

Answer:

12?

Step-by-step explanation:

The scatter plot shows the number of strawbernes that have been picked on the farm during the month of February.


Part A Using computer software, a correlation coefficient of 0. 01 was calculated Based on the scatter plot, is that an accurate value for this data? Why or why not? (5 points)


Part B. Instead of comparing the number of strawberries picked and the day in February, write a scenario that would be a causal relationship for strawberries picked on the farm (5 points)

Answers

There is a relationship between the numbers of strawberries gathered and the amount of rainfall that can be found in a model (function).

What is a Scatter Plot?

A scatter plot with a trendline along which the data points are situated can be used to demonstrate the relationship between correlated variables.

Indicating a positive correlation is when the trendline slopes higher from left to right, while the opposite is true.

Part A:

The correlation coefficient of r = 0.1 is valid based on the provided scatter plot.

Part B:

The independent variable (the explanatory variable) is the cause of the dependent variable in a causal connection.

As a result, you need to identify a plausible factor that can influence the number of strawberries collected.

The week before harvest, I could picture how much it would rain.

Hence, There is a relationship between the number of strawberries gathered and the amount of rainfall that can be found in a model (function).

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g(x)=\sqrt{x} -5

what is the range and domain

Answers

Answer:

Function Domain and Range

g(x)=\sqrt{x} -5

what is the range and domain

To find the range of g(x), we can substitute a few values of x into the expression for g(x) to see what the output is. For example, when x = 0, g(x) = sqrt(0) - 5 = 0 - 5 = -5. When x = 1, g(x) = sqrt(1) - 5 = 1 - 5 = -4. When x = 2, g(x) = sqrt(2) - 5 = 1.4142 - 5 = -3.5858.

As we can see, the output of g(x) is always a negative number for any value of x in the domain. Therefore, the range of g(x) is the set of all negative real numbers, or (-infinity, 0).

So, the domain of g(x) is all real numbers x such that x >= 0, and the range of g(x) is all negative real numbers (-infinity, 0).

How do you find the height of an acute triangle?

Answers

The height of an acute triangle can be calculated using the Pythagorean Theorem. The formula for this theorem is a2 + b2 = c2, where a and b are the two legs of a right triangle and c is the hypotenuse.

To find the height of an acute triangle, we must first identify the two legs of the triangle. The length of the two legs can be determined by measuring the lengths of the three sides of the triangle. Once we have the lengths of the two legs, we can apply the Pythagorean Theorem to calculate the length of the hypotenuse.

Once the length of the hypotenuse is determined, we can use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle. This formula states that the square of the height of the triangle is equal to the square of the hypotenuse minus the square of the two legs. So, to find the height of an acute triangle, we first measure the lengths of the three sides, then use the Pythagorean Theorem to calculate the hypotenuse, and finally use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle.The height of an acute triangle can be calculated using the Pythagorean Theorem. The formula for this theorem is a2 + b2 = c2, where a and b are the two legs of a right triangle and c is the hypotenuse. To find the height of an acute triangle, we must first identify the two legs of the triangle. The length of the two legs can be determined by measuring the lengths of the three sides of the triangle. Once we have the lengths of the two legs, we can apply the Pythagorean Theorem to calculate the length of the hypotenuse.

Once the length of the hypotenuse is determined, we can use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle. This formula states that the square of the height of the triangle is equal to the square of the hypotenuse minus the square of the two legs. So, to find the height of an acute triangle, we first measure the lengths of the three sides, then use the Pythagorean Theorem to calculate the hypotenuse, and finally use the formula h2 = c2 - a2 - b2 to calculate the height of the triangle.

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Given square ABCD, what is the length of AD?

Answers

If you want me to answer the question I obviously need the measurements

1. What is the sum of the interior angles of a quadrilateral?​

Answers

Answer:

360 degrees

Step-by-step explanation:

Answer:

360°

Step-by-step explanation:

The sum of the interior angles of any quadrilateral is 360°

True or False: The point (0, 3) lies on the x-axis.

Answers

Answer:

false

Step-by-step explanation:

(x,y)

if the first cord is 0 its on y

is the second cord is 0 its on x

Answer: True

Since the x-coordinate being 0, the point lies on the y-axis. The y-coordinate =+3 being positive, the point lies on the +ve y-axis.

Step-by-step explanation: Hope this help :D

what is 37 and 4/8 rounded to the nearest whole number

Answers

Answer:

38

Step-by-step explanation:

Answer:

38

Step-by-step explanation:

What are the different types of algorithms?

Answers

Different types of algorithms are:

Brute Force algorithm Greedy algorithmRecursive algorithmBacktracking algorithm

What is Brute Force algorithm?

As a very general approach to problem solving and an algorithmic paradigm, brute-force search or exhaustive search—also referred to as generate and test—involves iteratively listing all potential candidates for the solution and determining whether each one satisfies the problem's statement.

A brute-force algorithm would count all integers from 1 to n and determine whether each one divides n without a remainder in order to find the divisors of a natural number n.

For the eight queens puzzle, a brute force method would look at all possible configurations of 8 pieces on the 64-square chessboard and determine whether each queen piece could engage in mutually exclusive attacks for each configuration.

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A football team consists of 20 each freshmen and sophomores, 15 juniors, and 10 seniors. Four players are selected at random to serve as captains. Find the probability that

Answers

On solving the provided question, we can say that Probability ( At least one of the students is a senior) = 0.4632 approx

What is probability?

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

P(All four players are senior) = 0.00033 approx

P(There is one each: freshman, sophomore, junior and senior) = 0.0944 approx.

P(There are 2 sophomores and 2 freshman) = 0.0568  approx

P( At least one of the students is a senior) = 0.4632 approx

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Complete each nuclear fission reaction. 235 92 u 1 0 n → 90 36 kr a 56 ba 3 1 0 n a: 239 94 pu 1 0 n → b c ba 91 38 sr 3 1 0 n b: c:

Answers

a: 235 92 U + 1 0 n → 90 36 Kr + 141 56 Ba + 3 1 0 n

b: 239 94 Pu + 1 0 n → 96 38 Sr + 143 55 Ba + 3 1 0 n

c: It is not possible to complete this nuclear fission reaction as it is not a valid input. There is no nuclide with the atomic number 94 and mass number 239.

What is nuclear fission?

Nuclear reactions are those that involve the nucleus of an atom. Nuclear fission involves the splitting of an atomic nucleus and the formation of two distinct atomic species.

Nuclear fission is a nuclear reaction in which the nucleus of an atom is split into two or more smaller nuclei, along with the release of a large amount of energy. In the first reaction, an atom of Uranium-235 (U-235) is hit by a neutron, which causes the nucleus to split into Krypton-90 (Kr-90) and Barium-141 (Ba-141) along with 3 neutrons. In the second reaction, an atom of Plutonium-239 (Pu-239) is hit by a neutron, which causes the nucleus to split into Strontium-96 (Sr-96) and Barium-143 (Ba-143) along with 3 neutrons.

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The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=1 and roots of multiplicity 1 at x=0 and x=-3. It goes through the point (5,256)

Answers

Answer:

P(x) = ([tex]\frac{2}{5}[/tex])x(x + 3)(x - 1)²

Step-by-step explanation:

Given - The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=1 and roots of multiplicity 1 at x=0 and x=-3. It goes through the point (5,256)

To find - Formula for P(x) ?

Proof -

Given that,

P(x) has a root of multiplicity 2 at x=1

So,

(x - 1)² is a factor.

Now,

Given that, there is roots of multiplicity 1 at x=0 and x=-3

So,

(x - 0) and ( x - (-3) are also factor

So,

P(x) can be written as

P(x) = Ax(x + 3)(x - 1)²           .........(1)

where A is a constant.

Now,

Given that, It goes through the point (5,256)

⇒At x = 5, P(x) = 256

So,

Put the values of x and P(x) in equation (1), we get

P(x) = Ax(x + 3)(x - 1)²

⇒256 = A(5)(5 + 3)(5 - 1)²

⇒256 = 5A(8)(4)²

⇒256 = 40A(16)

⇒256 = 640 A

⇒A = [tex]\frac{256}{640}[/tex] = [tex]\frac{2}{5}[/tex]

∴ we get

P(x) = ([tex]\frac{2}{5}[/tex])x(x + 3)(x - 1)²

Solve for h.

h/ 6 - 1 = 3 h =​

Answers

You should get photo math it’ll answer it for you and show you how

Let A, B and C represent distinct non-zero digits. Suppose x is the sum ofall possible 3-digit numbers formed by A, B and C without repetition.Consider the following statements1. The 4-digit least value of x is 1332.2. The 3-digit greatest value of x is 888.Which of the above statements islare correct?

Answers

Statement 1 is correct and Statement 2 is not correct.

As A, B and C represent distinct non-zero digits

For least value of x

Let A=1, B=2, C=3

The possible numbers that can be formed using 1,2,3 are 6 {using permutations}

123, 132, 213, 312, 231, 321

x is the sum of all possible 3-digit numbers formed by A, B and C without repetition so

x= 123+ 132+ 213+ 312+ 231+ 321

x=1332

So statement 1 is correct

statement 2 cannot be correct as least value of x is  4-digit so  greatest value of x cannot be a three digit number.

The 4-digit least value of x is 1332 so Statement 1 is correct and Statement cannot be correct.

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Hannah either walks or cycles to school. The probability that she walks to school is 0.75 If she walks, the probability that she is late is 0.6 If she cycles, the probability that she is late is 0.2 Work out the probability that on any one day Hannah will not be late for school. ​

Answers

If Hanna is walking there is a 0.4 chance of not being late. 0.75 x 0.4 = 0.3 probability of not being late.

If Hanna cycles there is a chance of 0.8 of not being late. 0.6 x 0.8 = 0.48.

0.48 + 0.3 = 0.78.

In other words, there is a 78% probability of her not being late.

What is the distance between the points (3,7) and (-2, 10)

Answers

Answer:

√34

Step-by-step explanation:

To find the distance between two points, you can use the distance formula, which is:

d = √[(x2 - x1)^2 + (y2 - y1)^2]

We can plug in the points (3, 7) and (-2, 10) to get:

d = √[(-2 - 3)^2 + (10 - 7)^2]

We can simplify.

d = √[(-5)^2 + (3)^2]

d = √(25 + 9)

d = √(34)

d =  √34

PLZZZ HELPPP ILL GIVE BRAINLIEST

Answers

Answer:

45

Step-by-step explanation:

when a = 6 , b =2

2a^2/ b^3 + b(2a+6)

=2(6)^2/ (2)^3 +(2)[2(6)+6)

=45

can someone help me plssss. ill give u extra points like 50

Answers

I think it’s B hope this helps:)

What is the value of -36 - (-40)
0-76
076
O 4
0-4

Answers

Answer:

4

Step-by-step explanation:

–36 – ( –40 )

Whenever there is sign of subtraction before the brackets, signs of the numbers inside the brackets get changed when we removed the brackets.

( – ) × ( – ) = ( + )

36 + 40

4

[tex] \therefore [/tex] 4 is the required answer.

Determine and state an equation of the line perpendicular to the line 5x-4y=10 and passing through the point (5,12)

Answers

The equation of the line perpendicular to the line 5x-4y=10 and passing through the point (5,12) is y = 4x/5 + 8.

What is a slope?

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

Given:

The line 5x-4y=10.

Simplifying,

y = (-5/4)x + 5/2

Comparing with the slope-intercept form,

y = mx + b,

where m is the slope and b is y-intercept.

The slope is = -5/4

The slope of the perpendicular line,

= negative reciprocal of the slope of the line where the line is perpendicular.

= 4/5

So, the line:

If a line passes through one point (x₁ ,y₁) and have slope m,

then the equation of line is

y - y₁ = m (x - x₁)

y - 12 = (4/5)(x-5)

y = 4x/5 + 8

Therefore, the equation of the line is y = 4x/5 + 8

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PLZ HELP ASAP!!A map of the United States showing which ethnic groups dominate each region. Asians have small pockets of dominance in Central and Eastern states; Blacks dominate southern states, Hispanics dominate Texas and sections of other southwest and western states. Whites dominate eastern and north central states. Native Americans dominate in the northern plains states, other western states, Oklahoma, and Alaska. Pacific islanders have pockets of dominance in the Midwest. Multiethnic dominates in the western states and Alaska.Data courtesy of the SSDAN (2000)Based on the above map, multiethnic citizens dominate which region of the United States?A.the NortheastB.the WestC.the SoutheastD.the MidwestPlease select the best answer from the choices providedABCD Which angles are alternate exterior angles?1. EFH and BCF2. EFH and DCA3. EFH and EFC4. EFH and BCA Eden has 300 pounds in his savings accounts. his bank offers him a fixed 5 percent simple interest rate per annum, for a period of 3 years? How much interest will he have earned after 3 years? How do you simplify 3 ratios? intuit our radio station is running a show in which the songs are ordered in a specific way the last word of the title of one song must match the first word Equations of Exponential FunctionsThe population, P, of six towns with time t in years are given by the following exponential equations:(i) P = 1000(1.08)t (ii) P = 600(1.12)t(iii) p = 2500(0.9)t (iv) P = 1200(1.185)t(v) P = 800(0.78)t (vi) 2000(0.99)tWhich town decreasing the fastest?a. ii c.iiib. v d. viPlease select the best answer from the choices provided At quickie car wash, The wash process as advertised to take less than six minutes. Consequently management has set a target average of 330 seconds for the wash process. Suppose the average range for a sample of seven cars is 10 seconds. Use the accompanying table to establish control limits for sample means in ranges for the car wash process. Which of the following is generally an opportunity cost of investment in human capital?a. future job securityb. increased earning potentialC. FORGONE PRESENT WAGESd. All of the abovee. None of the above Traditionally, how have people characterized Loch Ness and the creature that is saidto live in it? Are attitudes about Loch Ness and the creature any different today? Consciousness refers to a state of awareness or alertness in which the subject is cognizant of one's environment and self. Chris drew the following diagram of his park with a scale factor of 1 inch = 9 points7 feet. What is the area of the actual park?*11 inches7 inches Lacey runs a stable that boards a range of horses.brown 8black 9gray 3Considering this data, how many of the next 15 horses that come to board should you expect to be brown horses? In the sequence 9, 14, 19, 24, 29,.... Say we're using a to describe the terms. What is the value of the term below?149192924 What extra qualifications are required for a broker's application of a community association manager 2. Outer planets have these characteristics:A. Long orbits, made up of gas, have many moonsB. Long orbits, made up of gas, have few moonsC. Short orbits, made up of gas, have many moonsD. Long orbits, have a rocky crust, have many moons A 6-ft tall person is standing next to a tree. The tree is 15 feet tall and casts a shadow 5 feet long. How long is the shadow of the person? Now let's think about a balloon. We know the gas particles inside of the balloon are bumping against the sides. What keeps those gas particles from forcing the balloon to expand What was a result of the Pequot War and King Philips War?A:The Indians were totally wiped out.B:Very few colonists and Indians died.C:Many Indians and colonists died.D:Many Indians died, but no colonists were killed. A game has a deck of cards with 10 red cards and 4 blue cards. You randomly choose one card and without replacing it choose another card. What is the probability of choosing a red card and then a blue card? Who collects income tax that is payable to the federal government?Income tax that is payable to the federal government is collected by the .