A ferris wheel with a diameter of 214 feet was built in a city. The top of the wheel stands 223 feet above the ground. Find h if θ = 150°, 240°, and 315°. Round your answers to the nearest whole number.

The diagram in the attached image is a model of the wheel.

A Ferris Wheel With A Diameter Of 214 Feet Was Built In A City. The Top Of The Wheel Stands 223 Feet

Answers

Answer 1

The height at 150°, 240°, and 315° will be 208.66 feet, 169.5 feet, and 40.34 feet, respectively.

What is a vector?

The quantity which has magnitude, direction and follows the law of vector addition is called a vector.

A Ferris wheel with a diameter of 214 feet was built in a city.

The top of the wheel stands 223 feet above the ground.

Then the radius will be

r = 214 / 2

r = 107 feet

The distance between the ground and bottom of the Ferris wheel will be

d = 223 – 214

d = 9 feet

Then the height will be given as

h = r(1 – cos θ) + h

h = 107(1 – cos θ) + 9

At θ = 150°, then the height will be

h = 107(1 – cos 150°) + 9

h = 208.66 feet

At θ = 240°, then the height will be

h = 107(1 – cos 240°) + 9

h = 169.5 feet

At θ = 315°, then the height will be

h = 107(1 – cos 315°) + 9

h = 40.34 feet

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Related Questions

Factorize:
a⁴-a³+2a²​

Answers

[tex] {a}^{4} \: - \: {a}^{3} \: + \: {2a}^{2} [/tex]

Factor the expression with the common factor that is "a²".

[tex] \boxed{ \bold{ {a}^{2} \: \times \: ( {a}^{2} \: - \: a \: + \: 2)}}[/tex]

MissSpanish

Answer:

a²​(a²​-a+2)

Step-by-step explanation:

Solution Given:

a⁴-a³+2a²​

first taking common a²​

we get

a²​(a²​-a+2) which is a required answer.

Kylie borrowed a book from a library. The library charged a fixed rental for the book and a late fee for every day the book was overdue. The expression below shows the charges Kylie paid for the book when she returned it x days after the
due date:
2 +0.25x
What does the constant term of the expression represent?
The late fee for the book
The fixed rental for the book
The number of books borrowed
The number of days the book was overdue

Answers

Answer:

B - fixed rental for the book.

Since for everyday the book is late the fee is 0.25 multiplied by X, X is the days the book is not returned.

Thus, the constant would be 2, 2 is the constant whereby the rental for the book regardless of other variables.

What is the value of StartFraction 6 Over x EndFraction + 2x2, when x = 3?

Answers

D. 20
(6/X) + 2x^2 =
(6/3) + 2(3^2) =
2 + 2(9) =
2 + 18=
20

Answer:

D) 20

Step-by-step explanation:

Hope It Helps!!!

PLEASE HELP ME, I BEG OF YOU TO HAVE MERCY ON MY POOR SOUL
1. Calculate the slope of the trend line. (Choose two points on the line and find vertical change over horizontal change.)

2. Using the slope and y-intercept, write the equation of the trend line (y = mx + b).

3. Choose a "calories from fat" value that is not in your collected data set and that is at least 10 fat calories away from any collected value. Use the equation calculated in step to predict the number of fat grams in an item having that number of fat calories. Be sure to show your work.

4. Search for an item in a fast food menu having the same number of fat calories as the one you chose above. (If you cannot find the exact value, get as close as you can.) Compare the calculated value from step VI to this actual value. Explain why (or why not) you would have expected your prediction (calculated value) to be close to the actual value.

Answers

The regression line is y = 10x + 300, and the value of calories is 90 and when x = 14 the value of y = 440 from the regression line, but the actual value is 330.

What is the line of best fit?

A mathematical notion called the line of the best fit connects points spread throughout a graph.

It's a kind of linear regression that uses scatter data to figure out the best way to define the dot's relationship.

From the data given, we can write the slope and y-intercept form:

y = mx + b

here, m = 10 and b = 300

y = 10x + 300

The number of fat grams in an item has that number of fat calories.

As we have the regression line:

y = 10x + 300

Put x = 1 in the regression line:

y = 10(1) + 300

y = 310 calories

For x = 14

y = 10(14) + 300 = 440

But the actual value from the graph is 330.

Thus, the regression line is y = 10x + 300, and the value of calories is 90 and when x = 14 the value of y = 440 from the regression line, but the actual value is 330.

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EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE I NEED HELP

Answers

Answer:

B.

Step-by-step explanation:

It is the only one that is not a fraction or a decimal that terminates or repeats.

tôi là người Việt Nam ai giúp giải bài này nha bài 2 ạ

Answers

-3-x+5=x^2-x-2

-3+5=x^2-2

2=x²-2
-x^2=-4
x^2=4
x=+2 or -2
Answer:
x (1)=-2
x(2)=2

Write the equation of the line that passes through (5, 6) and (8, 4) in slope-intercept form.

Answers

Answer:

Step-by-step explanation:

Equation of the line in slope- intercept form:

       [tex]\sf \boxed{\bf y = mx +b}[/tex]

Here, m is the slope and b is the y-intercept

  Find the slope with the given two points.

   [tex]\sf \boxed{slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

             [tex]\sf =\dfrac{4-6}{8-5}\\\\=\dfrac{-2}{3}[/tex]

Slope = -2/3 and choose any one the given points.

Substitute m = -2/3  and (5,6)  in the above equation and find 'b'

      [tex]\sf 6 =\dfrac{-2}{3}*5+b\\\\6 =\dfrac{-10}{3}+b\\\\6+\dfrac{10}{3}=b\\\\\dfrac{6*3}{1*3}+\dfrac{10}{3}=b\\\\\dfrac{18}{3}+\dfrac{10}{3}=b\\\\\boxed{b=\dfrac{28}{3}}[/tex]

Equation of the line:

            [tex]y = \dfrac{-2}{3}x + \dfrac{28}{3}[/tex]

Where would 1.84 be on a number line?

Answers

Answer:

It is located to the right of the 0 on the line,

Step-by-step explanation:

the numbers are increasing going from left to right. 1.84 is located 1.84 from 0.

On a number line (which we will presume to be whole integers), 1.84 would be located definitely to the right of 0 because it is a positive decimal. In terms of full numbers, however, 1.84 would be located between integers 1 and 2, and it would be skewed closer to 2. Why? Well, 1.50 is representative of what would be considered halfway between 1 and 2. Because 1.84 is greater than 1.50, we know that 1.84 will be closer to 2 than it will be to 1. In terms of a widespread number line, between integers 1 - 10, 1.84 would be near the beginning, or further left side, of the number line because it is more than 1 but less than 2.

Your final answer: As far as a general number line, 1.84 will be located between 1 and 2, where it is skewed right more toward 2 than 1.

Add2√3+√5 and√3 -3√5​

Answers

Answer:

[tex] \sqrt[2]{3} + \sqrt{5} = \sqrt[2]{8} [/tex]

[tex] \sqrt{3 } - \sqrt[3]{5} = \sqrt[3]{2} [/tex]


A ship is carrying gold bars and silver bars in the ratio 13:17. The ship's load
weighs 600 kg in total. If each bar weighs 5 kg, how many gold bars is the
ship carrying

Answers

Using proportions, considering the weight of each bar and the ratio, it is found that the ship is carrying 52 gold bars.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Each bar weighs 5 kg, and the total weight is of 600 kg, hence the number of bars is given by:

n = 600/5 = 120.

The proportion of gold bars is given by:

p = 13/(13 + 17) = 13/30

Hence, out of 120 bars, the number of gold bars is given by:

nG = 120 x 13/30 = 4 x 13 = 52.

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What is one of the solutions to the following system of equations?
x² + y² = 25
y - 3x = -5

Answers

Answer:

x = 0 y = -5

x = 3 y = 4

Step-by-step explanation:

x² + y² = 25

y - 3x = -5

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

y = 3x-5

x² + y² = 25

x² + (3x-5)² = 25

(3x-5)(3x-5) = 9x² -15x -15x + 25

x² + 9x² -15x -15x + 25 = 25

x² + 9x² -15x -15x = 0

x² + 9x² - 30x = 0

10x² - 30x = 0

x(10x-30)=0

x = 0

10x-30=0

x = 3

y - 3x = -5

y - 3(0) = -5

y = -5

y - 3(3) = -5

y - 9 = -5

y = 4

Answer:

(4,3) and (0,-5) are both solutions where we have (x,y).

Step-by-step explanation:

Here are simplified steps:

https://www.symbolab.com/solver/matrix-calculator/x%5E%7B2%7D%2By%5E%7B2%7D%3D25%3B%20y-3x%3D-5?or=input

Symbolab is an excellent tool for just most math.

3. The elevation of a hilltop is 250 feet above sea level. The
hill slopes gradually to a valley that is 100 feet below sea
level. The hilltop and the valley are 28,000 feet apart. What
is the average rate of change in elevation from the hilltop tot
the valley?

Answers

Answer:

0.00893 feet elevation per 1 foot distance.

Step-by-step explanation:

The hill reaches an elevation of 250 ft (above sea level) over the course of 28,000 feet.  The average rate of change would be (250 ft)/(28,000 ft), or 0.00893 feet elevation/1 foot distance.

((0.00893 (feet up/foot distance))*(28,000 feet distance) = 250 feet  up (elevation).

A, B C, or D because i’m not sure

Answers

Answer:

C

Step-by-step explanation:

SAS axiom

SAS axiom

SAS axiomSAS axiom

SAS axiom

Photo attached

A. -2
B. -1
C. 1/-2
D. 1/2

Answers

Step-by-step explanation:

(X1,Y1) = (-2,2)

(X2,Y2) = (0,1)

• Find slope.

m = (Y2 - Y1)/(X2 - X1)

m = (1 - 2)/(0 - (-2))

m = -1/2

The answer is C.

A car travels a distance of 300 miles along a straight road from point A to point B. The car maintains a speed of 30 miles pr
hour (mph) during the first 150 miles and a speed of 50 mph during the remaining 150 miles. What is the average speed of
car for the whole trip?
O20.0 mph
37.5 mph
40.0 mph
O45.0 mph
O80.0 mph
Click Save and Submit to save and submit. Click Save All Answers to save all answers.

Answers

Answer:

Definition: The average speed over the course of mobion can be calculated using the formula Total Distance Traveled Average Speed = Time of Travel A car fravels a distance of 300 miles along a straight road from point A to point B. The car maintains a speed of 30 miles per hour (mph) during the first 150 miles and a speed of 50 mph during the remaining 150 miles. What is the average speed of the car for the whole trip? 20.0 mph 37.5 mph 40.0 mph 45.0 mph 80.0 mph QUESTION 13 Wriat is the height h, of the equilateral triangle shown below? Aak Sareend Sabmit ro save and submit. Click Save AlAnseers to save all ansuers Save

Average speed of the whole trip is equals to 37.5 mph.

What is average speed?

" Average speed is defined as the ratio of the total distance travelled to the total time taken."

Formula used

Average speed = [tex]\frac{Total distance travelled }{Total time taken}[/tex]

According to the question,

Total distance travelled = 300miles

Speed for first 150 miles = 30 miles per hour

For,  30  miles = 1hour

    ⇒150 miles = 5 hours

Speed for remaining 150 miles = 50 miles per hour

For,  50  miles = 1hour

    ⇒150 miles = 3 hours

Substitute the value in the formula to get average speed,

Average speed = [tex]\frac{300miles}{(5 + 3)hours}[/tex]

                          [tex]=\frac{300}{8}\\ \\= 37.5 miles per hour[/tex]

Hence, average speed of the whole trip is equals to 37.5 mph.

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A circle with the equation (x + 6)2 + (y + 3)2 = 16 is reflected over the line x = 2.

What is the equation of the image?

( x + 10) 2 + ( y + 3) 2 = 16
( x - 10) 2 + ( y + 3) 2 = 16
( x + 6) 2 + ( y + 7) 2 = 16
( x + 6) 2 + ( y - 7) 2 = 16

Answers

Answer: [tex](x-10)^{2}+(y+3)^{2}=16[/tex]

Step-by-step explanation:

We know the center of the original circle is (-6, -3). After reflecting this over the line x=2, the new center is now (10, -3).

Thus, the equation of the circle is [tex](x-10)^{2}+(y+3)^{2}=16[/tex].

Help ASAP, with a explanation :)

Answers

C is due north I think not sure

PLS HELP IF POSSIBLE ASAP

Answers

The value of y if x is equal to 5 is 75 and the value of y when x = 7 is 8/7

Direct and inverse variation

Variations shows the relationship between variables.

4) If y varies directly as x², hence;

y = kx²

27 = 9k
k = 3

In order to determine y if x = 5

y = 3(5*5)
Y = 75

Hence the value of y if x is equal to 5 is 75

5) If y varies inversely as x, hence;

y = k/x
k = xy
k = 16(1/2)

k = 8

If x = 7, the value of y will be;

y = 8/7

Hence the value of y when x = 7 is 8/7

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ΔXYZ was reflected over a vertical line, then dilated by a scale factor of One-half, resulting in ΔX'Y'Z'. Which must be true of the two triangles? Select three options.

Answers

The options that are true of the triangles include:

∆XYZ ~∆X'Y'Z'AngleXZY ≅ AngleY'Z'X'XZ = 2X'Z'

The complete question is given below:-

ΔXYZ was reflected over a vertical line, then dilated by a scale factor of One-half, resulting in ΔX'Y'Z'. Which must be true of the two triangles? Select three options.

△XYZ ~ △X'Y'Z'AngleXZY ≅ AngleY'Z'X'YX ≅ Y'X'XZ = 2X'Z'mAngleYXZ = 2mAngleY'X'Z'

What is translation?

The process of changing the location of the image on the coordinate system will be known as the translation.

It should be noted that triangle XYZ is reflected over a vertical line. Then, it's dilated by 1/2 to form XYZ.

This implies that the triangles are similar, the angles are congruent and the side length of XYZ is twice that of X'Z.

Therefore the options that are true of the triangles include:

∆XYZ ~∆X'Y'Z'AngleXZY ≅ AngleY'Z'X'XZ = 2X'Z'

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+
Carla babysits and tutors to make extra money. She babysits for $5 an hour and tutors for $10 an hour.
She can only work at most 15 hours a week. She wants to go on a trip with her friend and needs to
make $95 dollars this week to cover the cost of the trip. Write a system of inequalities to represent this
situation.

Answers

The system of inequalities to represent this situation will be x + y ≤ 15 and 5x + 10y ≤ 95.

What is the linear system?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Carla babysits and tutors to make extra money.

She babysits for $5 an hour and tutors for $10 an hour.

She can only work at most 15 hours a week.

Likewise, she wants to go on a trip with her friend and needs to make 95 dollars this week to cover the cost of the trip.

Then the system of inequalities to represent this situation will be

Let x be the number of babysits hours and y be the number of tutor's hours.

     x + y ≤ 15

5x + 10y ≤ 95

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Mr.krabs sold a total of 29 krabby patties and krabby shakes. krabby patties cost $3 each while krabby shakes cost $2 each and he made a total of $70 . how many krabby patties and krabby shakes did mr.krabs sell?

Answers

Answer:

s = 12 and p = 17

Step-by-step explanation:

→ Set up 2 simultaneous equations

p + s = 29

3s + 2p = 70

→ Rearrange the first equation for p as the subject

p = 29 - s

→ Substitute into 2nd equation

3s + 58 - 2s = 70

→ Solve

s = 12

→ Substitute into first equation

p + 12 = 29

→ Solve

p = 17

find y in terms with z. help me please :)​

Answers

Answer:

y = 5z

Step-by-step explanation:

added in the picture

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow y = 5z [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[ let the point at which line segments SV and RT intersects be O ]

[tex]\qquad \tt \rightarrow \: \angle ROV + \angle ROS = 180° [/tex]

[ linear pair ]

[tex]\qquad \tt \rightarrow \: \angle ROV = 180 - \angle ROS[/tex]

[tex]\qquad \tt \rightarrow \: \angle ROV = 180 -2y[/tex]

____________________________________

[tex]\qquad \tt \rightarrow \: \angle SVU = \angle ROV + \angle TRV[/tex]

[ Exterior angle = sum of opposite interior angles ]

[tex]\qquad \tt \rightarrow \: \angle SVU = 180 - 2y + y[/tex]

[tex]\qquad \tt \rightarrow \: \angle SVU = 180 - y [/tex]

( let it be equation 1 )

____________________________________

[tex]\qquad \tt \rightarrow \: \angle SVU + \angle SUV + \angle VSU = 180°[/tex]

[ Sum of angles of Triangle ]

[tex]\qquad \tt \rightarrow \: \angle SVU + 4z + z = 180°[/tex]

[tex]\qquad \tt \rightarrow \: \angle SVU + 5z = 180°[/tex]

[tex]\qquad \tt \rightarrow \: \angle SVU = 180° - 5z[/tex]

( let it be equation 2 )

____________________________________

By comparing both equations :

[tex]\qquad \tt \rightarrow \: \angle SVU = 180 - y = 180 - 5z[/tex]

[tex]\qquad \tt \rightarrow \: 180 - y = 180 - 5z[/tex]

( Add 180° on both sides )

[tex]\qquad \tt \rightarrow \: 180 - y + 180 = 180 - 5z + 180[/tex]

[tex]\qquad \tt \rightarrow \: - y = - 5z[/tex]

[tex]\qquad \tt \rightarrow \: y = 5z[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Find the values of a and b if 5+3√3/7+4√3 = a + √3b

Answers

The values of a and b are :

[tex]a = \sqrt{3} \\ \\ •\sqrt{3} b = - 1 \\ \\ b = \frac{ - 1}{ \sqrt{3} }. [/tex]

The surface area of the cone below is about 151.58 inches squared. The radius of the base is 4 inches. What is the slant height? Use 3.14 for Pi. Round your answer to the nearest whole number.

Answers

The slant height of the given cone will be 12.06 inches.

What is slant height?

The measurement from the base to the peak along the "center" of a lateral face of an object, such as a cone, is its slant height.

Given that:-

The surface area of the cone below is about 151.58 inches squared. The radius of the base is 4 inches.

The slant height will be calculated as:-

Surface area = π r l

151.58 = π x 4 x l

l = 151.58 / ( π x 4 )

l = 12.06 inches.

Therefore slant height of the given cone will be 12.06 inches.

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the equation for the circle shown below is x2 + y2 = 64 What is the length of the circles radius

Answers

Answer:

radius = 8

Step-by-step explanation:

the equation of a circle centred at the origin is

x² + y² = r² ( r is the radius )

x² + y² = 64 ← is in this form

with r = [tex]\sqrt{64}[/tex] = 8

Who wants to solve a question.

Answers

Answer:

Step-by-step explanation:

5(p-3)

the 3 lbs she uses are being subtracted and then is being multiplied per lb


Alexa needs 20.5 pints of blueberries to
jam. She picked 7.75 pints on Friday and
pints on Saturday. How many more pints
she need to pick?

Answers

Answer:

Your question does not make much sense but that was only because you were missing one variable which was 4.25 which was what you picked up on Saturday. but anyways you just add 7.75 and 4.25 and you'd end up with 12 so she has 12 pints of the blueberries she needs and to find out the remanding you just subtract from the 20.5 but its better to look at it like 20.50 because that's what it is and then you subtract 12 from 20.50 and you are left with 8.50.

Your answer is 8.5

HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
write and solve a proportion to complete the statement. Round to the nearest hundredth if necessary.
1. 6km ≈ ?mi
2. 2.5 L≈ ?gal
3. 90lb ≈ ?kg
pls help

Answers

1. 6 km ≈ 3.73 mi

2. 2.5 L ≈ .66 gal

3. 90 lb ≈ 40.82 kg

y = x2 − 2x − 19
y + 4x = 5

Answers

Answer:

(x=4, y=-11) (x=-6, y=29)

Step-by-step explanation:

The solution is in the picture above...

In 2010, your company paid overtime wages or hired temporary help during 32 weeks of the year. Overtime was paid for 26 weeks and temporary help was hired for 15 weeks. If at year’s end an auditor
checks your accounting records and randomly selects one week to check the company’s payroll, what is the probability that the auditor will select a week in which you paid overtime wages and hired
temporary help?

Answers

The probability that the auditor will select a week in which you paid overtime wages and hired is 0.28

In 2010, your company paid overtime wages or hired temporary help during 32 weeks of the year. Overtime was paid for 26 weeks and temporary help was hired for 15 weeks.

What is probablitity?


Probability, can be define as the ratio of favorable outcomes to the n number of total events.

Here, p(a) = Overtime was paid for 26 weeks = 26/32= 0.81
       p(b) =  temporary help was hired for 15 weeks = 0.46
Required probability = P(a) + P(b) - 1
                                  =   0.81 + 0.46 -1
                                  =   0.28

The the required probability that the auditor will select a week in which you paid overtime wages and hired is 0.28

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Write a two paragraph analysis in which you: Write 5-10 sentences in each paragraph Paragraph one: Give general information about the new time period Paragraph two: Provide an overview of how your story would be different within the new time period Use topic sentences in your paragraph. Use correct grammar, punctuation, and spelling. Write using the third person point of view. (This is what i have so far, yeah i know its bad) Whilst investigating the death of a local assassin, a brave student called Kurisu uncovers a legend about a supernaturally-cursed, golden kunai circulating throughout New York. As soon as anyone uses the kunai, he or she has exactly 8 weeks left to live. The doomed few appear to be ordinary people during day to day life, but when photographed, they look distorted. A marked person feels like a burning fire to touch. Kurisu gets hold of the kunai, refusing to believe the superstition. A collage of images flash into his mind: a bloody mask balancing on a assassin's face, an old newspaper headline about a gang accident, a hooded man ranting about bodys and a drinking well located in a hidden location in the woods. When Kurisu notices his arms have fire-like properties, he realizes that the curse of the golden kunai is true and calls in his friend, a nurse called Alex, to help. Alex examines the kunai and willingly submits herself to the curse. She finds that the same visions flash before her eyes. She finds the bloody mask balancing on an assassin's face particularly chilling. She joins the queue for a supernatural death. Kurisu and Alex pursue a quest to uncover the meaning of the visions, starting with a search for the hooded man. A few years later, Kurisu walked over to the window and reflected on his dark surroundings. He had survived the curse and was now living in the forest next to the well. He had figured his friend Alex burned up in flames as he didnt see her make it to drink from the well in time. Then he saw something in the distance, or rather someone. It was the figure of Alex. Kurisu gulped. He was not prepared for Alex. As Kurisu stepped outside and Alex came closer, he could see the easy glint in her eye. "I am here because I want you dead," Alex bellowed, in a giving tone. You left me to die out there she showed him a burn across her arms. This is what that curse did to me She slammed her fist against Kurisu's chest, with the force of 10 bulls. "But it made me stronger, Kurisu." Kurisu looked back, even more shocked and still holding the gold kunai. "Alex, I don't want to hurt you," he replied. They looked at each other with mixed feelings. While classical music played in the background, two angry and confused people were standing in the rain. Kurisu regarded Alex's skinny limbs and burnt body. He held out his hand. "Let's not fight," he whispered, gently. "Hmph," pondered Alex. "Please?" begged Kurisu I never meant to hurt you. He showed her that he had a scar across his face from the golden blade. Alex looked concerned, her body glistening in the morning rain like a bloody knife. Then Kurisu led Alex inside for a nice glass of lemonade. THE END What is the difference when estimating? been having this question for a while and this app wont help If the line segment joining the points A(4, 5) and B(4, 5) is divided by the point P such that AP/PB = 2/5. find the co-ordinates of P. 2.4. My father drops me at school. in passive voice simple present On Earth, a scale shows that you weigh 490 N. What is your mass?A 50 kgB 100 kgc) 75 kgD 22 kg How do i graph those Given a sand box with dimensions of 4 feet, 6 feet and 2 feet. What is the maximumamount of sand it can hold? What compromises were brokered to deal with this issue of slavery?