Rolling is a combination of linear and rotating motion. When a wheel makes one full rotation, it moves
forward a distance equal to the wheel's circumference.
a. A child's first bicycle has 12-inch tires. These tires have a 6-inch radius. How far does the bicycle move
forward each time the wheel makes one complete rotation? Give your answer in meters.
(1 inch = 0.022 meters)
b. A woman's ten-speed bicycle has 27-inch tires (13.5-inch radius). How far does this bicycle move
forward each time the wheel makes one complete rotation? Give your answer in meters.
6C Circular Motion
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c. How many times does the child's bicycle tire have to rotate for the bicycle to travel 1 kilometer?
d. How many times does the woman's bicycle tire have to rotate for the bicycle to travel 1 kilometer?
A wheel moves forward one circumference in one rotation
Contact
point
Circumference
of wheel

Answer:

101.8 unit sqaure

Step-by-step explanation:

Solution Given:

no of side(n)=8

radius(r)=6

Area =?

we have

[tex]\boxed{\bold{Area\: of \:regular\: polygon =nr^2sin(\frac{180}{n})Cos(\frac{180}{n})}}[/tex]

where

r is the radius and n is no of the side.

Now

Substituting Value:

[tex]Area\: of \:regular\: polygon =8*6^2sin(\frac{180}{8})Cos(\frac{180}{8})\\=8*36*0.38268*0.923879\\=101.823[/tex]

in nearest tenth 101.8 unit square

Answer:

101.8 square units

Step-by-step explanation:

The given diagram shows a regular octagon with a radius of 6 units.

The radius of a regular polygon is the distance from the center of the polygon to one of its vertices.

Therefore:

To find the area of a regular polygon given its radius and number of sides, we can use the following formula:

[tex]\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=nr^2\sin \left(\dfrac{180^{\circ}}{n}\right)\cos\left(\dfrac{180^{\circ}}{n}\right)$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

Substitute n = 8 and r = 6 into the formula and solve for A:

[tex]A=8\cdot 6^2\sin \left(\dfrac{180^{\circ}}{8}\right)\cos\left(\dfrac{180^{\circ}}{8}\right)[/tex]

[tex]A=288\sin \left(22.5^{\circ}\right)\cos\left(22.5^{\circ}\right)[/tex]

[tex]A=101.823376...[/tex]

[tex]A=101.8\; \sf square\;units\;(nearest\;tenth)[/tex]

Therefore, the area of a regular octagon with a radius of 6 units is 101.8 square units, to the nearest tenth.

Answer: x=9

Step-by-step explanation:

Combine like terms

Add 7 to both sides

Simplify the expression

Subtract 4x from both sides

Simplify the expression

The solution sets are  {√5, -√5}, {√61, -√61}, {5√2, -5√2}, {5√2, -5√2},  {3√3, -3√3}, {2√2, -2√2}, {7√3, -7√3}, {2√7, -2√7},  {√2, -√2}, {2√21, -2√21}

Let's solve each quadratic equation one by one:

1. 3x^2 + 4x^2 = 35

Combine like terms:

7x^2 = 35

Divide by 7:

x^2 = 5

Take the square root of both sides:

x = ±√5

Solution set: {√5, -√5}

2. 3x^2 – 28 = 2x^2 + 33

Combine like terms:

x^2 = 61

Take the square root of both sides:

x = ±√61

Solution set: {√61, -√61}

3. x^2 – 25 = 25

Move 25 to the other side:

x^2 = 50

Take the square root of both sides:

x = ±√50

Simplify the square root:

x = ±5√2

Solution set: {5√2, -5√2}

4. 2x^2 – 30 = 70

Move 30 to the other side:

2x^2 = 100

Divide by 2:

x^2 = 50

Take the square root of both sides:

x = ±√50

Simplify the square root:

x = ±5√2

Solution set: {5√2, -5√2}

5. 8x^2 – 6x^2 = 54

Combine like terms:

2x^2 = 54

Divide by 2:

x^2 = 27

Take the square root of both sides:

x = ±√27

Simplify the square root:

x = ±3√3

Solution set: {3√3, -3√3}

6. 3x^2 – 6 = 34 – 2x^2

Move all terms to one side:

5x^2 = 40

Divide by 5:

x^2 = 8

Take the square root of both sides:

x = ±√8

Simplify the square root:

x = ±2√2

Solution set: {2√2, -2√2}

7. x^2 + 49 = 196

Move 49 to the other side:

x^2 = 147

Take the square root of both sides:

x = ±√147

Simplify the square root:

x = ±7√3

Solution set: {7√3, -7√3}

8. 5x^2 – 40 = 100

Move 40 to the other side:

5x^2 = 140

Divide by 5:

x^2 = 28

Take the square root of both sides:

x = ±√28

Simplify the square root:

x = ±2√7

Solution set: {2√7, -2√7}

9. 9x^2 = 4x^2 + 10

Move 4x^2 to the other side:

5x^2 = 10

Divide by 5:

x^2 = 2

Take the square root of both sides:

x = ±√2

Solution set: {√2, -√2}

10. x^2 – 4 = 80

Move 4 to the other side:

x^2 = 84

Take the square root of both sides:

x = ±√84

Simplify the square root:

x = ±2√21

Solution set: {2√21, -2√21}

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Jane because she has a higher credit score.

Given,

Jane and Stephanie both borrow $15,000 from the same bank to purchase the same make and model car. Jane's credit score is 732 and Stephanie's credit score is 588 .

Now,

For taking loan from the bank the most important thing is the credit score of the individual. If the individual has higher credit score than the person gets loan more easily and will pay less finance charges.

In our case,

Jane has a credit score of 732 which is higher than that of Stephanie .

So, jane will pay less finance cost as compared to Stephanie.

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After gaining 2.3 ounces, the weights of the kittens are 5.9 ounces, 6.5 ounces, and 5.6 ounces, respectively.

To determine the weights of the kittens after gaining 2.3 ounces, we need to add this amount to their initial weights.

The initial weights of the kittens were 3.6 ounces, 4.2 ounces, and 3.3 ounces. Adding 2.3 ounces to each of these weights, we have:

Kitten 1: 3.6 + 2.3 = 5.9 ounces

Kitten 2: 4.2 + 2.3 = 6.5 ounces

Kitten 3: 3.3 + 2.3 = 5.6 ounces

It's worth noting that these calculations assume that all kittens gained the same amount of weight. In reality, weight gain can vary between individuals, and other factors such as health and nutrition can also influence weight. The given information provides a simplified scenario for calculating the weight changes based on a uniform weight gain of 2.3 ounces.

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x = 180-73 = 107

6z-103 = x = 107

6x = 107+103 = 210

z = 35

The calculated measure of the angle ABC is 57.5 degrees

From the question, we have the following parameters that can be used in our computation:

Arc AC = 115 degrees

The angle ABC subtends the arc AC

using the above as a guide, we have the following:

Angle ABC = 1/2 * Arc AC

substitute the known values in the above equation, so, we have the following representation

Angle ABC = 1/2 * 115 degrees

Evaluate the equation

Angle ABC = 57.5 degrees

Hence, the measure of angle ABC is 57.5 degrees

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The correct option is,

D. Yes, because each x-value has exactly one corresponding y-value

We have to given that,

The graph of a quadratic equation is shown in image.

Since, We know that,

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable and another variable (the dependent variable).

Now, When we apply Vertical line test on the graph.

We get;

Each x-value has exactly one corresponding y-value.

Therefore, The graph of equation is function because each x-value has exactly one corresponding y-value.

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(a): The cost, C, depends on the number of people attending, g, and the base cost is $250.

(b):    C(g) = 11g + 250

(c):  C(46) = 806.

(d):         g = 121.

(a) The given equation is,

C= 11g +250

This represents the total cost, in dollars, for a sports banquet when g people attend.

This means that the cost, C, depends on the number of people attending, g, and the base cost is $250.

b) The function can be written as follows,

⇒  C(g) = 11g + 250

c) To determine C(46),

Substitute g = 46 into the function.

So, C(46) = 11(46) + 250

                = 806.

This number represents the total cost, in dollars, for the sports banquet when 46 people attend.

d) To determine the value of g when C(g) = 1581,

Solve the equation 11g + 250 = 1581 for g.

First, we can subtract 250 from both sides to get

⇒ 11g = 1331

Then, we divide both sides by 11 to get

⇒ g = 121.

This number represents the number of people attending the sports banquet when the total cost is $1581.

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39 * (1-15/100) = 39*0.85 = 33.15 (dollars)

Based on the given options, the closest choice to the value of the upper quartile is "O. 54 056."

To find the value of the upper quartile, we first need to arrange the given run times in ascending order:

40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59

Next, we calculate the position of the upper quartile. Since the upper quartile represents the 75th percentile, we divide the data into four equal parts. The upper quartile is located at the position (3/4) * (n + 1), where n is the total number of data points.

In this case, n = 20, so the position of the upper quartile is (3/4) * (20 + 1) = (3/4) * 21 = 15.75. Since the position is not an integer, we can take the average of the values at positions 15 and 16 to find the upper quartile.

The values at positions 15 and 16 are 55 and 56, respectively. Taking the average, we get (55 + 56) / 2 = 111 / 2 = 55.5.

Therefore, the value of the upper quartile is 55.5 seconds.

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The equivalent decimal and mixed number for given letter C is,

⇒ C = 8.2 ; 8 2/10

We have to given that,

A number line is shown in image.

Since,

A number lines are the horizontal straight lines in which the integers are placed in equal intervals.

And, All the numbers in a sequence can be represented in a number line. This line extends indefinitely at both ends.

Now, By given number line,

Point C is two point left from point 8.

Hence, The point C is denoted as,

⇒ C = 8.2

⇒ C = 82/10

⇒ C = 8 2/10

Therefore, the equivalent decimal and mixed number for given letter C is,

⇒ C = 8.2 ; 8 2/10

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Answer:

diameter = 2(radius)

Step-by-step explanation:

not sure what your question is but the diameter of a circle is equal to 2 times the length of its radius

The order of G is 24, and the only Subgroups of order 12 are isomorphic to A4 or S3 x Z2, neither of which contain N.

Let us first understand the definitions of subgroups and maximal subgroups.A subgroup is a set of elements in a group that are themselves a group under the group operation.

In other words, a subgroup is a subset of a group that contains the identity element, and is closed under group multiplication and taking inverses.

A maximal subgroup of a finite group G is a proper subgroup M of G, which is not equal to G itself, and such that there are no proper subgroups of G that contain M. In other words, M is as large as possible among all proper subgroups of G.

This means that M is not a subset of any larger proper subgroup of G.Example: Let G be the symmetric group S4 and let H be the subgroup of G generated by (1 2 3) and (1 2).

Then H is not a maximal subgroup of G because it is contained in the larger subgroup K generated by (1 2 3) and (1 2) and (1 3) and (2 4).

On the other hand, if we consider the subgroup N generated by (1 2) and (3 4), then N is a maximal subgroup of G because there are no proper subgroups of G that contain N. This can be seen by noting that any proper subgroup of G must have order 12,

since the order of G is 24, and the only subgroups of order 12 are isomorphic to A4 or S3 x Z2, neither of which contain N.

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Answer:

one solution (- 6, 2 )

Step-by-step explanation:

- 3x + y = 20 → (1)

x + y = 4 ( subtract x from both sides )

y = - x - 4 → (2)

substitute y = - x - 4 into (1)

- 3x - x - 4 = 20

- 4x - 4 = 20 ( add 4 to both sides )

- 4x = 24 ( divide both sides by - 4 )

x = - 6

substitute x = - 6 into (2)

y = - x - 4 = - (- 6) - 4 = 6 - 4 = 2

solution is (- 6, 2 )

The value of the fifth term of the sequence is 1/256

From the question, we have the following parameters that can be used in our computation:

Third term, a(3) = 1/4

Common ratio, r = -1/8

Using the above as a guide, we have the following:

The fifth term = Third term * Common ratio * Common ratio

substitute the known values in the above equation, so, we have the following representation

The fifth term = 1/4 * -1/8 * -1/8

Evaluate

The fifth term = 1/256

Hence, the value of the fifth term is 1/256

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The circle centered at the point (3, 1) and has a radius of length 2 is,

⇒ (x - 3)² + (y - 1)² = 2²

Given that,

Center ⇒ (3, 1)

Radius ⇒ 2

We know that,

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle possesses rotational symmetry around the center

And the standard equation of circle is,

(x - a)² + (y - b)² = r²

Where (a, b) is center of circle

R is radius of circle

So here,

(a, b) = (3, 1)

r = 2

Therefore the required equation of circle is,

⇒ (x - 3)² + (y - 1)² = 2²

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The probability of rolling the number 3 or more when a die is thrown is 2/3.

The sample space of rolling dice = {1, 2, 3, 4, 5, 6}.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

Probability of getting the number 3 = 1/6

Probability of getting the number more than 3 = 3/6

So, probability of getting event = 1/6 + 3/ 6

= 4/6

= 2/3

Therefore, the probability of rolling the number 3 or more when a die is thrown is 2/3.

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Answer:

Answer below.

Step-by-step explanation:

Just take f(x) and subtract g(x) expression

So that equals....  4-x^2 -(2-x)

Always write exponents in descending order -x^2-(-x)+4-2

answer = -x^2+x+2

Answer:

2 + 3 + 1 + 8 + 4 = 18

3 + 1 + 8 = 12

18 - 12 = 6

6 + 5 = 11

11 + 8 + 2 + 4 = 25

25 - 7 = 18

18 + 2 + 1 + 8 + 3 = 32

32 + 6 = 38

Therefore, the length of the space rock is 38 inches.

Step-by-step explanation:

The numerical value of x in the triangle is approximately 2.67.

The figure in the image are two similar triangles.

Side length A of the smaller triangle = 8

Side length B of the smaller triangle = 6

Side length A of the bigger triangle = ( 8 + x )

Side length B of the biger triangle = ( 6 + 2 )

To solve for the value of x, we use ratios and proportions, since the triangles are similar.

Hence:

Side length A of the smaller triangle : Side length B of the smaller triangle = Side length A of the bigger triangle : Side length B of the biger triangle

Plug in the values:

8 : 6 = ( 8 + x ) : ( 6 + 2 )

8/6 = ( 8 + x ) / ( 6 + 2 )

Cross multiply:

6( 8 + x ) = 8( 6 + 2 )

6( 8 + x ) = 8( 8 )

6( 8 + x ) = 8( 8 )

48 + 6x = 64

6x = 64 - 48

6x = 16

x = 16/6

x = 2.67

Therefore, the value of x is approximately 2.67.

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y-(-9) = -6(x-(-4)), y = -6x-33

The value of the segment RS for the secant through R which intersect the circle at points S and T is equal to 46.4 to the nearest tenth.

Circle theorems are a set of rules that apply to circles and their constituent parts, such as chords, tangents, secants, and arcs. These rules describe the relationships between the different parts of a circle and can be used to solve problems involving circles.

For the tangent RS and the secant through R which intersect the circle at points S and T;

RQ² = RS × ST {secant tangent segments}

42² = x × 38

1764 = 38x

x = 1764/38

x = 46.4211

Therefore, the value of the segment RS for the secant through R which intersect the circle at points S and T is equal to 46.4 to the nearest tenth.

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Answer:

x=12

Step-by-step explanation:

Dividing by 3x is not a reliable way to solve the equation because it captures only one solution of the equation, instead of the two solutions.

The equation in the context of this problem is defined as follows:

3x² = 6x.

We must bunch together all the terms with the variable x, hence:

3x² - 6x = 0

3x(x - 2) = 0.

Hence, applying the factor theorem, the solutions are given as follows:

Dividing both sides, we have that:

3x = 6

x = 2.

Hence only one solution would be captured.

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Answer:

  C.  no solution

Step-by-step explanation:

You want to know the solution to the system of equations ...

Equations are best examined for the possible number of solutions when they are written in the same form. Here, we can put both equations into slope-intercept (y=) form by multiplying the second equation by -1.

  -y = -x + 11 . . . . . . . .second equation

  y = x - 11 . . . . . . . . equivalent equation; multiplied by -1

Now, you see that these slope-intercept equations have the same slope (x-coefficient = 1), but different intercepts (11, -11).

Lines with the same slope and different intercepts are parallel lines. They never meet, so never have any points in common. There are no values of x and y that satisfy both equations at the same time.

There are no solutions.

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well, let's first find out how much is the bill plus tip.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20\% of 100.50}}{\left( \cfrac{20}{100} \right)100.50}\implies 20.10~\hfill~\stackrel{ 100.50~~ + ~~20.10 }{\text{\LARGE 120.60}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{120.60}{\underset{\textit{divided by 2}}{2}}\implies \text{\LARGE 60.30} ~~ \textit{each person}[/tex]

To find the number of distinct proper subsets of a set, we need to consider that a proper subset is a subset that includes some, but not all, of the elements of the original set.

The set N = {2, 50, 62, 13, 40} contains 5 elements. For each element, we have two choices: include it in a subset or exclude it. This means that for each element, there are 2 possibilities: it can be in the subset or not in the subset.

Therefore, the total number of distinct subsets of a set with 5 elements is 2^5, which is equal to 32.

However, since we are looking for proper subsets, we need to exclude the empty set and N itself from the count. So, the total number of distinct proper subsets of the set N = {2, 50, 62, 13, 40} is 32 - 2 = 30.

Step-by-step explanation:

Using the laws of logorithms, this equals

2 ln (x-1) = 3      

ln(x-1) = 3/2             now   e^x both sides

e^( ln (x-1) =  e^(3/2)  

(x-1)  = e^(3/2)

x = 5.4817