Some people think that the Spaceship Earth geosphere at Epcot in Disney World in Orlando, Florida, resembles a golf ball. The building is a sphere measuring 165 feet in diameter. A typical golf ball has a diameter of approximately 1.5 inches.

d. What is the ratio of the volumes of Spaceship Earth to a golf ball?

Answers

Answer 1

The ratio of the volumes of the Spaceship Earth to a golf ball = 1926949795 : 1

We need to find the volumes of the Spaceship Earth and a golf ball.

Spaceship Earth

Radius, R = 165/2 ft = 82.5 ft

Volume of the Spaceship Earth = [tex]\frac{4\pi R^3}{3}[/tex] = (4 x 3.14 x 561515.625)/3

                                                    = 2350878.75 cubic ft.

A golf ball

Radius = 1.5/2 inches = 0.75 inches

1 ft = 12 inches

So 0.75 inches = 0.75/12 = 0.0625 ft.

So radius, r = 0.0625 ft

Volume of a golf ball =  [tex]\frac{4\pi r^3}{3}[/tex] = (4 x 3.14 x [tex]0.0625^3[/tex])/3

                                   = 0.00122 cubic ft.

Ratio of the volumes of Spaceship Earth to a golf ball

                    = 2350878.75:0.00122

                    = 1926949795 : 1

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Related Questions


Write each logarithmic expression as a single logarithm. 7 log p + 2log q

Answers

The given lograthimic expression 7log p + 2logq can be written as log(p^7q^2).

According to the given question.

We have a lograthimic expression.

7log p + 2logq

As we know that, a logarithmic expression is an expression that involves the logarithm of an expression containing a variable.

Also according to the product  and power rule we know that

log(mn) = logm + logn

log(x^y) = ylogx

Therefore, the given lograthimic expression 7log p + 2logq can be written as

7log p + 2logq

= log p^7 + log q^2

= log(p^7q^2)

Hence, the given lograthimic expression 7log p + 2logq can be written as log(p^7q^2) as log(p^7q^2).

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Find the coordinates of the midpoint of a segment with the given endpoints. A(2,14), C(0,5)

Answers

The coordinates of the midpoint of a segment with the given endpoints will be (1, 9.5).

What is the mid-point of the line segment?

Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).

Then the coordinate of the mid-point of the line segment is given as,

(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

The endpoints are A(2, 14) and C(0, 5).

Then the coordinates of the midpoint of a segment with the given endpoints will be

(x, y) = [(2 + 0) / 2, (14 + 5) / 2]

(x, y) = (2/2, 19/2)

(x, y) = (1, 9.5)

The coordinates of the midpoint of a segment with the given endpoints will be (1, 9.5).

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The sum of two numbers is thirty one. The first is five less than the second. Find the numbers

Answers

13+18=31 and I need at least

Answer:

Step-by-step explanation:

First Number : x - 5

Second Number : x

x + ( x - 5) = 31

     2x - 5 = 31

            2x = 31 + 5

           2x/2 = 36/2

               x = 18

Then plugin x= 18 into First numer X - 5

   x - 5

  18 - 5 = 13

18 + 13 = 31

so .....

First Number is 13

Second number is 18

Write an explicit and a recursive formula for each sequence. -5,-3.5,-2,-0.5,1, . . . . . .

Answers

The formula for an arithmetic series  -5,-3.5,-2,-0.5,1, is An = A1 + (n-1)d

What is arithmetic series ?

See the pattern

-5-(-3.5)= -1.5

-3.5-(-2)= -1.5

The formula for an arithmetic series  -5,-3.5,-2,-0.5,1, is  An = A1 + (n-1)d

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.

Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.

An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.

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HELP ASP WILL GET SHOW UR WORK!! BRAINILEsT AND 10 points

Answers

Answer:

x=4

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:


2x-2=6


Okay, first we need to create the inverse of this equation.

The inverse of subtraction is addition.
2(x)-2=6


2x = 6+2

Now, we solve the right-hand side.

2x = 8

Then, divide both sides by the greatest common factor.

We get x by itself.

2x = 8
/2     /2
x = 4


What is the vertex of y=|x|-5 ?
a. (5,0)
b. (-5,0)
c. (0,5)
d. (0,-5)

Answers

Answer: The answer is D

Step-by-step explanation:

A certain species of fish costs $3.49 each. You can spend at most $45: How many of this type of fish can you buy for your aquarium?​

Answers

3.29f ≤ 45
3.29f/3.29 ≤ 45/3.29
f ≤ 13.68

Since we can't buy 0.68 of a fish and our number must be less than 13.68, we can buy 13 fish.

which equation describes a line of symmetry for the figure shown? y=0 y=-x y =x x=0

Answers

Answer:

The last option:  x = 0

Step-by-step explanation:

The line of symmetry for a figure is a straight line that divides the figure into two congruent figures

The vertical line passing along the y axis is the line of symmetry and since it passes through all y values where x = 0, the equation is x = 0

y=X
y=0 and x=0 so wouldnt y=x

PLs help me pls help

Answers

The missing values from area model will be  48, 240.

Describe Area Model.

An area model is a rectangular diagram or model used in mathematics for problems involving multiplication and division, where the length and breadth of the rectangle are determined by the factors, quotient, and divisor.

Write the enlarged form of each component first. Next, sketch your model. To get the area of each smaller rectangle, multiply next. To determine the entire area, add those items last.

The area model will be -

                    60                        6

8                   480                      48

40                2400                    240

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Use the following information to complete parts I, II, and III.




Part I: Use scientific notation to estimate the number of hours in one year.

Part II: Use scientific notation to calculate the exact number of hours in one year.

Part III: In two or more complete sentences, compare your answers to parts I and II. In your comparison, discuss similarities and differences in your answers.

Answers

I) There are 8.76* 10³ hours in 1 year.

II) The exact number of hours in one year is 8.76582*10³ hours.

What is scientific notation?

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

Given:

1 hour=3600 seconds

1 year = 31556952 seconds.

Now,

I)  Use scientific notation to estimate the number of hours in one year.

1 day = 24 hours

1 year = 365 days

So, number of hours in one year is given by,

=24*365

=8760

=8.76* 10³

So, there are 8.76* 10³ hours in 1 year.

II) 1 year = 31556952 seconds.

1 hour = 3600 seconds

In one year the number of hour is given by,

=31556952/3600

=8765.82

=8.76582*10³

So, the exact number of hours in one year is 8.76582*10³ hours.

III)

The exact numbers of hours using 365 days is 8760 which is written as  in scientific notation but using the given data we get  hours.

Comparing these answers the first one has only 3 significant figures and the second answer has six significant figures.

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Given the formula for an exponential function, is it possible to determine whether the function grows or decays exponentially just by looking at the formula?

Answers

yes, actually it is possible. The mathematical expression f(x)=exp or ex denotes the exponential function.

What is meant exponential function?

The mathematical expression f(x)=exp or ex denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras. When the input variable x appears as an exponent in the formula f(x) = axe, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x.

One of the key mathematical operations is the exponential function (though it would have to admit that the linear function ranks even higher in importance). We allow the exponent to be the independent variable to create an exponential function. The formula f(x)=2x is a straightforward example.

Hence, yes, actually it is possible.

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Use a coordinate grid to write a coordinate proof of the following statement.
If the vertices of a triangle are A(0,0), B(2 a, b) , and C(4 a, 0) , then the triangle is isosceles.
c. Use the Distance Formula to write an expression for B C .

Answers

Distance between the points A and B are equal to distance between points B and C.

So, The given triangle is isosceles.

And, . By using distance formula we have to write an expression for BC as,

⇒ [tex]D_{BC} = \sqrt{4a^2+b^2}[/tex]

Here,

The vertices of a triangle are A (0, 0), B (2a, b) and C (4a, 0)

We have to check the triangle is isosceles.

And, Write an expression for BC.

What is Isosceles triangle?

When two sides of a triangle are equal then the triangle is said to be isosceles triangle.

Now,

The vertices of a triangle are A (0, 0), B (2a, b) and C (4a, 0)

We have to check the triangle is isosceles.

For this we use distance formula and prove that the two sides of triangle are equal.

Distance between the points A (0, 0) and B (2a, b) is;

[tex]D_{AB} = \sqrt{(2a-0)^2 + (b-0)^2} = \sqrt{4a^2+b^2}[/tex]

And, Distance between the points B (2a, b) and C (4a, 0) is;

[tex]D_{BC} = \sqrt{(4a-2a)^2 + (0-b)^2} = \sqrt{4a^2+b^2}[/tex]

Hence, Distance between the points A and B are equal to distance between points B and C.

So, The given triangle is isosceles.

c. By using distance formula we have to write an expression for BC as,

⇒ [tex]D_{BC} = \sqrt{(4a-2a)^2 + (0-b)^2} = \sqrt{4a^2+b^2}[/tex]

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Recycled​ CDs, Incorporated, offers a choice of 5 used CDs for ​$29​, with each additional CD costing ​$. Write a cost function for purchasing 5 or more CDs. What will the cost of buying CDs​ be? Let x represent the number of CDs over 5.

Answers

The cost function will be of the form f(x) = x + 29.

What is a  function ?

A function have a set of dependent variable for the given or specified independent variable.

According to the given question Recycled​ CDs, Incorporated, offers a choice of 5 used CDs for ​29 dollars with each additional CD costing a dollar.

We have to write a function for purchasing 5 or more CDs where x represents the no. of CDs over 5.

Let f(x) represents the cost of CDs.

∴ f(x) = x + 29.

Here the constant 29 dollars represents the cost of 5 CDs and x represents no. of CD's over 5.Put x = 0 and the cost for 5 CDs will be 29 and for any more value of x we will get our desire result.

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Theresa purchased 10 rakes and 15 shovels for $595. brett purchased 8 rakes and 20 shovels for $676. assume the rakes are all priced the same, and all shovels are priced the same.

Answers

The price of a rake and a shovel is $22 and $25 respectively.

Let's assume the price of a rake is x and the cost of a shovel is y.

Now, Theresa purchased 10 rakes and 15 shovels for $595.

10x + 15y = $595                                                                      -------------------(1)

Taking 5 common out from each side of the equation,

5( 2x + 3y) = 5( 119)

2x + 3y = 119                                                                             ------------------(2)

Brett purchased 8 rakes and 20 shovels for $676.

8x + 20y = $676                                                                       ------------------(3)

Multiply equation (2) by 4 and subtract from equation (3),

8x + 20y - ( 8x + 12y ) = 676 - 476

8x + 20y - 8x - 12y = 200

8y = 200

y = $25

Therefore,

10x + 15y = 595

10x + 15(25) = 595

10x + 375 = 595

10x = 595 - 375

10x = 220

x = $22

Hence, the price of a rake and shovel is $22 and $25 respectively.

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This question has three parts.
Bruce deposited a certain amount of money in a simple interest bearing savings account.
He neither deposited nor withdrew any money from his account for 4 years.
He kept track of the money in his account by making a graph as shown.

Part A:
What was Bruce’s principle (initial amount deposited)

Part B:
How much interest did Bruce earn after 1 year?

Part C:
What was the interest rate that Bruce’s savings account was earning

Answers

Bruce's principle is $140.

The interest that Bruce earned is $9.80

The interest rate that Bruce savings account is 7%.

What is the simple interest?

Simple interest is the interest that that is earned a certain amount over a period of time given a principal and the number of years.

Simple interest = amount deposited x time x interest rate.

A graph can be described as a pictorial representation of data. A graph has a y-axis and the x-axis. The y-intercept is a point where the graph touches the y-axis. The y-intercept represents the initial amount that is deposited. The principle is $140.

The slope of the graph represents the rate at which the amount invested increases in value.

Interest Bruce earned after 1 year : change in the slope

149.80 - 140 = $9.80

Interest rate = Interest / (principle x time)

9.80 / (140 x 1) = 0.07 = 7%

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Set both given equations equal to zero, then combine them into one standard form equation. x + 6 = 0 and y - 3 = 4 x + 6 = 0 → y - 3 = 4 → Combined equation

Answers

The standard form of the given equation is; x + (-y) = -5

How to write a linear combined equation in standard form?

We are given the equations;

x + 6 = 0  -----(1)

y - 3 = 4   -----(2)

Add 4 to both sides of equation 2 to get;

y - 3 + 4 = 0

y + 1 = 0    -----(3)

Put y + 1 for 0 in eq 1 to get;

x + 6 = y + 1

The standard form of an equation is expressed in the form;

Ax + By = C

Thus;

x + 6 = y + 1 can be rewritten as;

x + (-y) = 1 - 6

x + (-y) = -5

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You thought the balance in your checking account was $68. When your bank statement arrived, you realized that you forgot to record a check. The bank statement listed your balance as $26. What was the amount of the check that you forgot to record?

Answers

The amount of the check you forgot to record is $42!!! hope this helps:)


Find the distance between each pair of points. Round to the nearest tenth. X(5,4) and Y(2,1)

Answers

The distance between X(5,4) and Y(2,1) is 4.24 rounded to the nearest tenth.

How to find the distance between two points?

Let's consider we have two points (x₁, y₁) and (x₂, y₂) the distance between these two points is given by the formula;

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

The distance between two points (x₁, y₁) and (x₂, y₂)  is given by ;

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

So,

Distance between X(5,4) and Y(2,1)

[tex]d = \sqrt {\left( {5 - 2 } \right)^2 + \left( {4 - 1 } \right)^2 }[/tex]

d = √18 = 4.242640687

Roud to nearest tenth ⇒ 4.24 units.

Hence "The distance between X(5,4) and Y(2,1) is 4.24 rounded to the nearest tenth".

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Use the table below to find the cumulative frequency of the class "less then 30.5?"

Answers

I’m pretty sure it would be 12 correct me if I’m wrong

solve the equation

3(n+11)-5n = -2(n-12)+9

Answers

Answer:

infinite number of solutions

Step-by-step explanation:

3(n + 11) - 5n = - 2(n - 12) + 9 ← distribute parenthesis on both sides

3n + 33 - 5n = - 2n + 24 + 9 , that is

- 2n + 33 = - 2n + 33

since the expressions on both sides are the same then any value of n will make the equation true.

thus the equation has an infinite number of solutions

Answer:

Any real value. Infinite no. of solutions.

Step-by-step explanation:

Let's open the bracket first. Multiply the term outside the bracket with each term inside the bracket.

[tex]\Rightarrow[/tex] 3(n+11)-5n = -2(n-12)+9

[tex]\Rightarrow[/tex] 3n + 33 - 5n = -2n + 24 + 9

Now simplify the n terms on both sides

[tex]\Rightarrow[/tex] -2n + 33 = -2n + 33

Here both LHS and RHS are same. And the terms gets canceled. Any real value of n satisfy the above equation.

If there are ten marbles in a bag (those marbles being two yellow, three pink, and five blue) and two are randomly drawn, what is the probability of drawing two yellow marbles if the first one isn't put back before the second draw? please help T^T

Answers

Answer:

the answer is 2 upon 10 ndnznnznznzjzjzj

Workers in an office of 90 staff were asked their favourite type of take-away.
The results are summarised in the table.

Take-away Frequency Angle
Pizza 29
a
Curry 9
b
Fish & chips 24
c
Kebab 16
d
Other 12
e


How many degrees represent 1 person?

Answers

Each angle to draw a pie chart a, b, c, d, and e will be 116°, 36°, 96°, 64°, and 48°, respectively.

What is an angle?

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Workers in an office of 90 staff were asked their favorite type of takeaway. The results are summarised in the table.

Take-away             Frequency            Angle

   Pizza                         29                       a

   Curry                          9                        b

Fish & chips                 24                        c

  Kebab                        16                        d

   Other                         12                       e

The angles on the pie chart are calculated by multiplying the table by 4. Then the angles will be

∠a = 4 x 29 = 116°

∠b = 4 x 9 = 36°

∠c = 4 x 24 = 96°

∠d = 4 x 16 = 64°

∠e = 4 x 12 = 48°

Each angle to draw a pie chart a, b, c, d, and e will be 116°, 36°, 96°, 64°, and 48°, respectively.

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If A, B, and D are collinear and D bisects A and B. The Length of AD=2x-2 and the Length of DB=x+4.
Find the value of x. ​

Answers

The value of x if D bisects A and B is 6

How to determine the value of x?

The given parameters are

D bisects A and B.

Length AD = 2x - 2

Length DB = x + 4

This means that

AD =DB

So, we have

2x - 2= x + 4

Evaluate the like terms

x = 6

Hence, the value of x if D bisects A and B is 6


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Your aunt bought a new car. After three months of car payments she owed a total®
of $22,275 to the bank for the car loan. After 12 months, she owed $18,900 to
the bank for the car loan. What was her average payment rate on the principal of
the car loan during this time?

Answers

The principal of the car loan is $23,400, the interest rate of the car loan is 1.60% and the monthly payment is $375.

Given that, balance after 3 months = 22,275 and balance after 12 months = 18,900.

What is the average payment rate?

Average payment rate means, for any date of determination, the sum of the monthly payment rates for the prior three monthly periods divided by three.

Now, the difference of payment = 22,275 - 18,900

= $3,375

The difference of time = 12 - 3 = 9 months

So, the payment per month = 3,375 / 9

= $375 per month.

Now, 375 x 12 = $4,500

Principal amount = 4,500 + 18,900

= 23,400

Rate = 375 / 23400 × 100

= 0.016 × 100 = 1.60%

Therefore, the principal of the car loan is $23,400, the interest rate of the car loan is 1.60% and the monthly payment is $375.

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Complete the proofs on a seperate sheet of paper!

Answers

The proof is completed and showed that < 2 ≅ < 3 as required.

How to show that < 2 ≅ < 3

Given data

<1 and <2 are linear pair

<1 + <3 = 180 degrees

required to proof <2 ≅ <3

linear pair implies mathematically that the sum of the two angles are 180 degrees, hence we have:

< 1 + < 2 = 180 degrees    equation 1

also given that,

< 1 + < 3 = 180 degrees    equation 1

equating equation 1 and equation 2 gives

< 1 + < 2 = < 1 + < 3

< 2 = < 3

Hence the required proof

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What is the y -value of the focus of the parabola?

Answers

Answer:

8136366271773737i228882ywhw

Can someone please help answer the questions I posted 11 hours ago, I'll give 5 stars!!

Answers

What question???????
Can you post it again ?


Find the distance from the line to the given point.
x=4,(-2,5)

Answers

The distance from the line x=4 to the given point (-2,5) is 6 units .

Distance formula from line to point :

The distance from the line ax+by+c=0 to the point (u,v) is given by the formula

[tex]distance=\frac{|au+bv+c|}{\sqrt{a^{2} +b^{2} } }[/tex]

In the given question

the equation of the line is [tex]x=4[/tex]

taking all the terms to Left side we get

[tex]x-4=0[/tex]

[tex]1.x+0.y-4=0[/tex]

given the points (-2,5)

From above values we the values as a=1 , b=0 , c=-4 , u=-2 , v=5 .

Substituting the values in the distance formula we get

[tex]d=\frac{|1*(-2)+0*(5)-4|}{\sqrt{1^{2} +0^{2} } }[/tex]

[tex]=\frac{|-2+0-4|}{1} \\ \\ =|-6|\\ \\ =6[/tex]

Therefore , the distance from the line x=4 to the given point (-2,5) is 6 units.

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bonjour pouvez-vous m’aidez avec se devoir svp?

Lors des soldes, Rami, qui accompagne sa mère et s'ennuie un peu, compare trois étiquettes pour passer le temps:

n°1-valeurs: 120 €
soldé: 105 €

n°2-Robe rouge: 45 euros
soldé: -30%

n°3-soldes: 25 € - 12,50 €

1. Quel est le plus fort pourcentage de remise?
2. Est-ce que la plus forte remise en euros est la plus forte en pourcentage?

merci d’avance

Answers

Answer:

Step-by-step explanation:

g(t) = t^2 + 4t
h(t) = 2t
Find (g/t) (-6)

Answers

The value of h(g(t))(-6) is 24.

What is function?

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences.

An example of this would be y=x².

If you put in anything for x, you get one output for y. We would say that y is a function of x since x is the input value.

Given:

g(t) = t² + 4t

h(t) = 2t

h(g(t))

=h( t² + 4t)

=2( t² + 4t)

And, h(g(t)) (-6)

=2( (-6)² + 4(-6))

=2(36-24)

=2*12

=24

Hence, the value of the function is 24.

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Cameron+and+his+friend+john+bought+a+used+circus+carousel+for+63,640$,+including+sales+tax.+if+the+sales+tax+rate+is+6%,+then+what+was+the+cost+of+the+carousel+before+the+tax? DQuestion 4The Axis Age was a time of spiritual change and renewal from 200-500 C.E.TrueO FalseQuestion 5 WILL GIVE BRAINLIEST IF YOU GUYS ANSWER THIS SIMPLE GRADE 7 QUESTION How should raw meats be shelved prior to cooking?in a separate cooler from all cooked foodsbased on first in-first out principlesaccording to freshnessby order of internal cooking temperatures explain the reasons why trade developed between East Africa coast before the v century (5x + 9) + (8x - 30) = 180 Which command can be used to define the range segments for single-value visualization? ___and___help the body use and breakdown carbohydrates, proteins and fats? ndclhdabcDC.sbdcb.dschsd Cobalt is element 27. Cobalt-60 is used in the medical treatment of cancer. How many neutrons and protons are contained in the nucleus of this isotope?33 neutrons, 33 protons27 neutrons, 27 protons33 neutrons, 27 protons27 neutrons, 33 protons Hi can someone please help me with these! (1+-1)8+7(1+-1) I cant find answer to this one it was on my map test Answers please help me J. J. Thomson created an apparatus composed of a sealed glass tube with electrodes of different polarities fixed at each end. By passing a high voltage through gas in the sealed tube, he was able to create a cathode ray. What did thompson call the particles that make up a cathode ray?. What group in England gradually developed into the formal legal body known as parliament? The bishops The Great Council The Estates-General The common laws 18. What is a verb phrase in sentence 5? (1 point)Owould have givenOgiven himOwas soOwould have REALLY NEED HELP ON THIS!! Triangle MNO is formed by connecting the midpoints of the side of triangle JKL.The measures of the interior angles of triangle JKL are shown. Find the measure ofLKNM. Figures not necessarily drawn to scale.8054NM46K What does it mean to say that strategy and structure have a reciprocal relationship? A court should overturn its precedents unless there is a compelling reason not to._____. A(1,7), B(1,2), and C(5,2) area