Two Ferris wheels are side-by-side are rotating at the Math Fair. The first Ferris wheel has a radius of 7m and makes one complete revolution every 16 s. The bottom of the wheel is 1.5 m above ground. The second Ferris has a radius of 8m and completes one revolution every 20 s. The bottom of this wheel is 2 m above the ground. What are the equations of both Ferris wheels using sine as the base function? Graph each equation and estimate the times where the heights of a gondola are the same.

Answer:

option D. DE = 11

Step-by-step explanation:

The line DF is equivalent in length to the blue line,

(x + 7) + 7 = 4x + 2

Solve:

x + 14 = 4x + 2

subtract 14 from both sided to get x alone,

x + 14 - 14 = 4x + 2 - 14

x = 4x - 12

subtract 4x from both sided,

x - 4x = 4x - 4x - 12

-3x = -12

divided both sides by -3,

-3x / 3 = -12 / -3

x = 4

Plug in x into DE equation:

x + 7: (4) + 7 = 11

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Given that the AC and BC are perpendicular, their slopes are the negative inverse of each other which gives that the product of the slopes of AC and BC is -1

The completed proof is presented as follows;

The slope of AC or GC is GF/FC by definition of slope. The slope of BC or CE is DE/CD by definition of slope.

<FCD = <FCG + <GCE + <ECD by angle addition property <FCD = 180° by the definition of a straight angle, and <GCE = 90° by definition of perpendicular lines. So by substitution property of equality 180° = <FCG + 90° + <ECD. Therefore 90° - <FCG = <ECD, by the subtraction property of equality . We also know that 180° = <FCG + 90° + <CGF by the triangle sum theorem and by the subtraction property of equality 90° - <FCG = <CGF, therefore <ECD = <CGF by the substitution property of equality. Then <ECD ≈ <CGF by the definition of congruent angles. <GFC ≈ <CDE because all right angles are congruent. So by AA ∆GFC ~ ∆CDE. Since the ratio of corresponding sides of similar triangles are equal then GF/CD = FC/DE or GF•DE = CD•FC by cross product. Finally, by the division property of equality GF/FC = CD/DE. We can multiply both sides using the slope of using the multiplication property of equality to get GF/FC × -DE/CD = CD/DE × -DE/CD. Simplify so that GF/FC × -DE/CD = -1. This shows that the product of the slopes of AC and BC is -1.

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Answer:

Let the angle be x

∘

. Then it's complement = (4x)

∘

.

We know that if the sum of two angles is equal to 90

∘

then the angles are said to be complementary.

Step-by-step explanation:

4x+x=90°

5x=90°

x=90°/5

x=18

4×18=72°

This is the complete solution!

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Answer:

-0.61

Step-by-step explanation:

0.55/2=0.275

Read 0.275 from normal distribution tables

Gives -0.61

The area of the base of cube B is 25/9 times larger than the area of the base of cube A.

Because the cubes are similar, then we know that the dimensions of cube B are a dilation of scale factor K of the dimensions of cube A.

Then, the volume of cube B is K³ times the volume of cube A.

The area of any face of cube B is K² times the area of any face of cube A

From this we can write:

125 in³ = K³*27in³

(125/27) = K³

If we apply the cubic root in both sides, we get:

∛(125/27) = K = 5/3

Then the relation between the areas is equal to:

K² = (5/3)^2 = 25/9

The area of the base of cube B is 25/9 times larger than the area of the base of cube A.

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Answer:

25/9

Step-by-step explanation:

I Just Took the Test.

By using the given distances and directions, we have;

Part A: 1083.5 feet

Part B: 1921.37 feet

Part C: 58.05°

The distance between David and Lacey = 2000 feet

David's angle to the boat = 70°

Lacey's angle to the boat = 32°

Part A

The distance of the boat from David is found as follows;

Imaginary lines drawn from the boat to David and then to Lacey form a triangle.

In the triangle, let A = 70°

B = 32°

Therefore by the sum of angles in a triangle, we have;

C = 180° - (70° + 32°) = 78°

By using sine rule we have;

[tex] \frac{a}{sin(A)} = \frac{b}{sin( B )} = \frac{c}{sin(C)}[/tex]

David's distance from the boat, b, is therefore;

[tex] \frac{b}{sin( 32 )} = \frac{2000}{sin(78)}[/tex]

The angle subtended by the coastline, C, is therefore;

[tex] b = \frac{2000}{sin(78)} \times sin( 32 ) = 1083.5 [/tex]

Part B

The distance between the boat and Lacey is found as follows;

[tex] \mathbf{ \frac{a}{sin( 70)} }= \frac{2000}{sin(78)}[/tex]

[tex] a = \frac{2000}{sin(78)} \times sin( 70 ) = 1921.37 [/tex]

Part C

When b = 1200 feet, we have;

Finding the vertical distance of the boat from the coastline, we have;

1083.5 × sin(70) = 1018.17

We have;

[tex] \frac{1200}{sin(90)} = \frac{1018.17}{sin( B' )} [/tex]

[tex] {sin( B' )} = \frac{sin(90)}{1200} \times 1018.17 [/tex]

The angle between the coastline and his view to the boat, B', is therefore;

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Answer:

C.

Step-by-step explanation:

The boundary of a circle is the circle itself.

The radius of a circle is a segment from the center of the circle to any point of the circle.

In a circle, every radius has the same length.

Answer: C.

The correct information based on the equation is that the functions f and g have the same axis of symmetry, and the maximum value of f is greater than the maximum value of g.

From the graph of f(x):

⇒ Axis of symmetry will be at x = 2

⇒ The maximum value of f(x) = 4

From the table of g(x):

⇒ Axis of symmetry will be at x = 2

⇒ The maximum value of g(x) = 3

The graph is attached.

The functions f and g have the same axis of symmetry, and the maximum value of f is greater than the maximum value of g.

Here is the other part of the question:

Which statement is true?

The functions f and g have the same axis of symmetry, and the maximum value of f is less than the maximum value of g.

The functions f and g have the same axis of symmetry, and the maximum value of f is greater than the maximum value of g.

The functions f and g have different axes of symmetry and different maximum values.

The functions f and g have the same axis of symmetry and the same maximum values.

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Answer:

B

Step-by-step explanation:

[tex](f-g)(x)=4x^2+5x-3-(4x^3-3x^2+5)\\\\=-4x^3+7x^2+5x-8[/tex]

Hence B is correct.

a)

Gain on disposal=$12,900

b)

Loss on disposal=$5,900

Prepare a tabular summary to show the cost of equipment disposed of, the accumulated depreciation, and gain or loss recorded on disposal?

Note that initially when the equipment was purchased, it would be debited to an asset account, whereas, it would be credited upon disposal since the company no longer owns it.

The accumulated depreciation was originally a credit entry in the balance sheet and needs to be debited now that the equipment has been sold.

Note that the excess of the sum of the accumulated depreciation and the cash received over the initial cost of the equipment is a gain and the reverse means a loss was recorded on disposal.

Account                                DR                  CR

Asset                     $49,600

Gain on disposal      $12,900

Accumulated depreciation                               $24,600  

Cash received                                              $37,900  

gain on disposal=$24,600+$37,900-$49,600

gain on disposal=$12,900

Account                                 DR                    CR

Asset                                                           $49,600

Accumulated depreciation   $24,600  

Cash received                         $19,100  

Loss on disposal                     $5,900  

Loss on disposal=$49,600-$24600-$19,100

Loss on disposal=$5,900

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This is a very simple transformation problem and can be solved by observation. The correct answer is Option D where g(x) = f(x-3) + 6. See the attached graph for the full question.

In mathematics, transformation is the process of converting one figure, expression, or function into another of equivalent value.

Note that on an x-axis, moving past zero to the left gets you into the negative, and vice versa.

On the y-axis moving upwards past zero gets you into the positive.

Recall that g(x) is a transformation of f(x). This means that the original image is f(x).

Notice that F(x) is transformed three degree beyond 0 on the -axis and 6 degrees beyond zero on the y-axis. Hence the correct equation is:

g(x) = f(x-3) + 6.

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Using the hypergeometric distribution, it is found that there is a 0.0002 = 0.02% probability that exactly 6 patients will die.

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of the parameters for this problem are:

N = 25, k = 6, n = 8.

The probability that exactly 6 patients will die is P(X = 6), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 6) = h(6,25,8,6) = \frac{C_{6,6}C_{19,2}}{C_{25,8}} = 0.0002[/tex]

0.0002 = 0.02% probability that exactly 6 patients will die.

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An appropriate viewing rectangle is the set of minimum and maximum values of x and y on which all important attributes of the graph are clearly displayed.

We have been given a rational function:

[tex]f(x)=\frac{x^{2} -81}{x^{2} -11x+18}[/tex]

And we are required to determine an appropriate viewing rectangle for the graphing calculator.

Hence, An appropriate viewing rectangle is the set of minimum and maximum values of x and y on which all important attributes of the graph are clearly displayed.

For the given function, an appropriate viewing rectangle will be [-20,20,2]  by [-20,20,2].

This function, when graphed using a graphing calculator on the said viewing rectangle, it appears as attached.

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The type of transformation that preserves the symmetry of an even function f(x) but does not preserve the symmetry of an odd function g(x) is vertical translation.

Vertical translation of a graph is done by moving the base graph up or down in the y-axis direction. Each point on a graph is moved k units vertically to translate the graph by that many units.

The vertical translation is the movement of the curve along the y-axis by a certain number of units without altering the function's shape or domain.

The function's form is preserved in the case of vertical translation.

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Answer:

Mikhail is 44 years old.

Step-by-step explanation:

Set both Gabrielle and Mikhail's age to a variable.

Gabrielle is x, Mikhail is also x.

Now create an equation using the variables with the sum.

Age1 + Age2 + 15 = 103

x + x + 15 = 103

Now we solve.

1. Combine like terms

2x + 15 = 103

2. Make all the numbers on one side of the equation, and the variables of the other, so subtract.

2x + 15 - 15 = 103 - 15

2x = 88

3. Simplify further by dividing.

x = 44

Mikhail is 44 years old.

Check your work:

44 + (x + 15) = 103

x + 15 = 59

x = 44

Answer:

Step-by-step explanation:

Let Gabrielle's age be x.

The age of the milk will be x - 15.

x + (x - 15) = 103.

2x - 15 = 103

2x = 118

x = 59

The milk's age = x - 15 = 59 - 15 = 44.

Answer:

90

Step-by-step explanation:

slope

Answer:

formula is equal to rice run is equal to y 2 -y 1 X2 minus X1

Answer:

D.  -924 feet

Step-by-step explanation:

For this problem, we'll need the relationship [tex]d=vt[/tex] where "d" is the distance traveled, "v" is the velocity the object is traveling, and "t" is the amount of time that it traveled.

Velocity is a "vector" quantity, which has both a magnitude and a direction.  The magnitude is the speed (42 feet per second) and the direction is downward.  Collectively, the velocity is -42 feet per second.  This will address the change in altitude and signify that the change in altitude is downward.

All quantities should be using units that match.

In this case, the distances provided in the answers are all measured in feet, and the speeds are measured in feet per second, so the feet match.

Also, the times are measured in seconds, and the speeds are measured in feet per second, those also match.

[tex]d=vt[/tex]

[tex]d=(\frac{-42\text{ feet}}{\text{second}})(22\text{ seconds})[/tex]

[tex]d=-924 \text{ feet}[/tex]

Answer: False

Step-by-step explanation:

[tex]\sqrt{5x}=\sqrt{x} \sqrt{5} \neq x\sqrt{5}[/tex]

Answer:

3 nikels and 2 cents

Step-by-step explanation:

1 niquel = 5 cents

5+5+5= 15

15+ 2= 17

A percentage is a way to describe a part of a whole. The percetage decrease in the price of CD is 33.33%.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

The price of the CD decreases from $18 to $12. Therefore, the percentage decrease is,

Percentage Decrease = ($18-$12)/$18 × 100% = 33.33%

Hence, the percetage decrease in the price of CD is 33.33%.

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Answer:16.67

Step-by-step explanation:

880 of 5280 can be written as:

880

5280

To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100

880

5280

×

100

100

= (

880 × 100

5280

) ×

1

100

=

16.67

100

Therefore, the answer is 16.67%

If you are using a calculator, simply enter 880÷5280×100 which will give you 16.67 as the answer.

The miles Sophia drove is 60 miles

The distance Sophia drove is represented in fractions.

A number is expressed as a quotient where a numerator is divided by a denominator. In a simple fraction, both are integers.

A fraction consists of a numerator and a denominator. An example of a fraction is 1/2 where 1 is the numerator and 2 is the denominator.

In order to determine the miles Sophia drove, the total distance of the trip would be multiplied by the fraction of the time Sophia drove.

Miles Sophia drove = 3/5  x 100

                                = 60 miles

So sophia drove 60 miles in 500 miles.

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Answer: 14.25

Step-by-step explanation:

Because 14 and 10 inches don't indicate that the ruler can measure to the nearest 0.25 inches. They indicate that the ruler can measure to the nearest inch.

14.2598 inches cannot be measured with this ruler.

That leaves 14.25.

Hope this helped.

Answer:

A = 1.16d

Step-by-step explanation:

Multiplying by 1 + the percentage value is equivalent to adding the percentage.

0.16 = 0.16161616... as a ratio of integers is 16 : 99

The equation is given as:

0.16 = 0.16161616...

The above is a non-terminating decimal.

It can be represented as:

a/b - 1

Where

a = 16

b = 100

So, we have:

16/100 - 1

Evaluate the difference

16/99

Express as ratio

16 : 99

Hence, 0.16 = 0.16161616... as a ratio of integers is 16 : 99

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The measure of an interior angle of a regular nonagon (9-sided polygon) is 140°

The formula for sum of interior angles of a polygon is given as;

= ( n -2) × 180

Recall that a nonagon has nine sides, so , n = 9

Substitute the value into the formula

= ( 9 -2) × 180

= 7× 180

= 1260°

Since the sum of the angles =  1260°

One of the angles = 1260/ 9 = 140°

Therefore, the measure of an interior angle of a regular nonagon (9-sided polygon) is 140°

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Calculations:

Normal pop has mean of 20.0

standard deviation = 4.0

XNN(20.0, 4.0)

a).

[tex]z=\frac{x-h}{z}[/tex]

[tex]=\frac{25-20}{4.0} =\frac{5}{4} =1.25[/tex]

Z = 1.25

b).

The proportion between 20 and 25 is P(20 <x<25.0)

[tex]=p(\frac{20-20}{4} < z < \frac{25-0}{4} )[/tex]

[tex]=P(0 < z < 1.25)[/tex]

[tex]=P(Z < 1.25)-P(z < 0)[/tex]

[tex]=0.8944-0.5000[/tex]

P(20 < x < 25)=0.3944

c).

The proportion value is less than 18 when

[tex]P(x < 18)=p(\frac{x--4}{6} < \frac{18-20}{4}[/tex]

[tex]=P(z < \frac{-2}{4})[/tex]

[tex]=P(z < -0.5)[/tex]

P(x<18) = 0.3085

Answer:

A 256/3

Step-by-step explanation:

1/3 * 4^4 =

1/3 * (4*4*4*4) =

1/3 * 256 = 256/3

Answer:

A = 256/3

Step-by-step explanation:

F(x) = 1/3 × 4ˣ = 4ˣ/3

F(4) = 4⁴/3 = 256/3

Answer:

[tex]\sf \dfrac{1}{4} \pi \quad or \quad \dfrac{7}{9}[/tex]

Step-by-step explanation:

The width of a square is its side length.

The width of a circle is its diameter.

Therefore, the largest possible circle that can be cut out from a square is a circle whose diameter is equal in length to the side length of the square.

Formulas

[tex]\sf \textsf{Area of a square}=s^2 \quad \textsf{(where s is the side length)}[/tex]

[tex]\sf \textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}[/tex]

[tex]\sf \textsf{Radius of a circle}=\dfrac{1}{2}d \quad \textsf{(where d is the diameter)}[/tex]

If the diameter is equal to the side length of the square, then:
[tex]\implies \sf r=\dfrac{1}{2}s[/tex]

Therefore:

[tex]\begin{aligned}\implies \sf Area\:of\:circle & = \sf \pi \left(\dfrac{s}{2}\right)^2\\& = \sf \pi \left(\dfrac{s^2}{4}\right)\\& = \sf \dfrac{1}{4}\pi s^2 \end{aligned}[/tex]

So the ratio of the area of the circle to the original square is:

[tex]\begin{aligned}\textsf{area of circle} & :\textsf{area of square}\\\sf \dfrac{1}{4}\pi s^2 & : \sf s^2\\\sf \dfrac{1}{4}\pi & : 1\end{aligned}[/tex]

Given:

[tex]\implies \sf \textsf{Area of square}=6^2=36\:in^2[/tex]

[tex]\implies \sf \textsf{Area of circle}=\pi \cdot 3^2=28\:in^2\:\:(nearest\:whole\:number)[/tex]

Ratio of circle to square:

[tex]\implies \dfrac{28}{36}=\dfrac{7}{9}[/tex]

The correct option is the second one:

We know that:

We have the operation:

x - y + (-z)

Notice that because y is negative, then -y is positive.

Because z is positive, -z is negative.

Then we have:

positive + positive + negative

Or, in the number line:

right, right, left.

Second question:

Can we conclude the sign of the outcome?

No, we can't, the sign will depend on the values of x, y, and z.

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Answer:The correct option is the second one:i) right, right, left.ii) Undefined.

Step-by-step explanation: