A bicycle wheel has a diameter of 62 cm. The wheel makes 80 full turns. How far does the bicycle travel? Provide your answer in meters

Answer:

lines are perpendicular

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

line 1

4x + 2y = 12 ( subtract 4x from both sides )

2y = - 4x + 12 ( divide through by 2 )

y = - 2x + 6 ← in slope- intercept form

slope of line 1 = - 2

line 2

3x - 6y = 18 ( subtract 3x from both sides )

- 6y = - 3x + 18 ( divide through by - 6 )

y = [tex]\frac{1}{2}[/tex] x - 3 ← in slope- intercept form

slope of line 2 = [tex]\frac{1}{2}[/tex]

• Parallel lines have equal slopes

Clearly the lines are not parallel

• the product of the slopes of perpendicular lines = - 1

- 2 × [tex]\frac{1}{2}[/tex] = - 1

then Line 1 and Line 2 are perpendicular to each other

Answer:1. 2

2. 20

3. 5499999.5 or5500000

Step-by-step explanation:

Answer:

1. 2

2. 20

3. 5,499,999.5 = 5,500,000

A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.

3² = 3 X 3 = 9

4³ = 4 x 4 x 4 = 64

[tex]2^{6}[/tex] = 2 x 2 x 2 x 2 x 2 x 2 = 64

The exact value in fractions are:

a) 1/9

b) 1/64

c) 1/64

A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

[tex]3^{-2}[/tex]

= 1/3²

3² = 3 X 3 = 9

= 1/9

[tex]4^{-3}[/tex]

= 1/4³

4³ = 4 x 4 x 4 = 64

= 1/64

[tex]2^{-6}[/tex]

= 1/[tex]2^{6}[/tex]

[tex]2^{6}[/tex] = 2 x 2 x 2 x 2 x 2 x 2 = 64

= 1/64

Thus.,

The exact value in fractions are:

a) 1/9

b) 1/64

c) 1/64

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The system of inequalities is as follows:

30x + 20y ≥ 63,000

x ≤ 1900

x + y ≤ 2800

A relationship between two expressions or values that are not equal to each other is called 'inequality'.

Given that, for a concert event, there are 30 reserved seat tickets and 20 general admission tickets. There are 1,900 reserved seats available, and fire regulations limit the number of paid ticket holders to 2,800.

The system of inequalities can be explained as follows:

30x + 20y ≥ 63,000 → Indicating a take in of at least $63,000 in ticket sales.

x ≤ 1900  → Indicating that 500 reserved seats are available.

x + y ≤ 2800 → Indicating limits of the paid ticket holders to 2800.

x ≥ 0  → Indicating ticket x must be equal or greater than 0.

y ≥ 0  → Indicating ticket y must be equal or greater than 0.

Hence, The system of inequalities is as follows:

30x + 20y ≥ 63,000

x ≤ 1900

x + y ≤ 2800

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Answer:

x = 10

Step-by-step explanation:

Those are opposite interior angles, meaning that they have the same angle measure, so just set them equal to each other to solve for x:

32-x = 3x-8

32 = 4x-8

40 = 4

10 =

By evaluating the linear function we will get the 3 points:

A. (-2, 8)

B. (2, -4)

C. (7, -19)

You can see the graph on the image at the end.

Well, the first thing we need to do is get these points, to do so, we need to evaluate the linear function in the given values.

We have f(x) = -3x + 2

if x = 2

f(2) = -3*2 + 2 = -4

if x = -2

f(-2) = -3*-2 + 2 = 8

if x = 7

f(7) = -3*7 + 2 = -19

So we have the points (-2, 8), (2, -4), and (7, -19)

The graph of these 3 points can be seen in the image below.

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The range between the moon's minimum and maximum temperature in degrees Fahrenheit is 640°F

From the question, we have

Time of Day     Temperature

   Day                 253°F

   Night              -387°F

the moon's minimum temperature =  -387°F

and maximum temperature =  253°F

range = 253 - (-387) =  640°F

Subtraction:

Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.

The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.

Complete question:

The table shows the high temperature on the moon during the day and the overnight low temperature.

Time of Day Temperature

Day 253°F

Night –387°F

What is the range between the moon's minimum and maximum temperature in degrees Fahrenheit?

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Jeriel pays $75 for an additional 2 GB of data, and 45+15x for every further 1 GB of data.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Let's examine the writing of phrases. The other number is x, and a number is 6 greater than half of it. In a mathematical expression, this proposition is denoted by the equation x/2 + 6.

Here,

For 6 GB, the cost is $45.

For per GB extra the cost is $15.

The cost of data paid by Jeriel,

=45+2*15

=$75

For x GB, the cost is,

=45+15x

The cost of data paid by Jeriel for 2 GB extra data is $75 and for x GB, the cost paid is 45+15x.

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Answer:

5

Step-by-step explanation:

By the Pythagorean Theorem:

[tex] {x}^{2} + {10}^{2} = {(5 \sqrt{5} )}^{2} [/tex]

[tex] {x}^{2} + 100 = 125[/tex]

[tex] {x}^{2} = 25[/tex]

[tex]x = 5[/tex]

Answer: 4x+1

Step-by-step explanation:

1.  5(2x-3)-2(3x-8)

2. 10x-15-2(3x-8)

3. 10x-15-6x+16

4. 10x+1-6x

5. 4x+1

Answer:

4x+1

Step-by-step explanation:

First you have to expand it like 10x-15-2(3x-8) Basically multiplying 5 with 2x and -3.

Then take -2 multiply with 3x and -8  which will make it  10x-15-6x+16

Now Put together the like terms 10x-6x -15+16

Which makes it 4x+1

Hope it helped! I am a student too.

Brainly wont be there to help you in life its better to study.

If you want to guarantee that two cards are from the same suit, you need only draw five cards (since there is no way you can draw five cards without at least two of them being the same suit)

Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.

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Steve claims that the points (-4,8) (8,8) and (-4,3) form a right triangle. Yes, Steve is correct.

The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

As we know the distance between (a, b) and (c, d) is:

distance = √( (a - c)² + (b - d)²)

The distance between (-4, 8) and (8, 8) is:

d₁ = √( (-4 - 8)² + (8- 8)²) = 12

The distance between (8, 8) and (-4, 3) is:

d₂ = √( (8 + 4)² + (8- 3)²) = 13

The distance between (-4, 8) and (-4, 3) is:

d₃ = = √( (-4 + 4)² + (8 - 3)²) = 5

If the Pythagorean theorem is correct, then the square of the larger side must equal the sum of the squares of the two shorter sides, which means that:

5² + 12² = 13²

Solving that we get:

25 + 144 = 169

169 = 169

Thus, Steve claims that the points (-4,8) (8,8) and (-4,3) form a right triangle. Yes, Steve is correct.

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The correct order of the steps used to derive the identity is (A.) 4, 3, 5, 1, 2.

The trigonometry identity is given as:  tan(2x)

When the tangent formula is applied, we have: Tan (2x)  = Sin (2x)/Cos (2x)......................(4)

Expand Sin (2x) and Cost 2x)

Tan (2x) = 2 Sin (x) Cos (x)/Cos (x) - Sin²(x)..........................(3)

It can be inferred therefore that the list that obeys the above order is:
Option (a) 4, 3, 5, 1, 2.

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Full Question:²

What is the correct order of the steps used to derive the identity?

A.) 4, 3, 5, 1, 2

B.) 4, 5, 3, 1, 2,

C.) 3, 4, 5, 1, 2

D.) 3, 4, 1, 5, 2

The difference shows that woman on average pays higher than men.

What  is mean/ average?

Mean is that the average of the given ranges and is calculated by dividing the add of given numbers by the whole number of numbers.

Main body:

The wider range in prices may be due to the higher number of observation.

females have a bigger spread and overall higher cost. 50% of females spend between $20-$75 on a haircut, while 50% of men only spend between $9.25-$20. The median for Female is also significantly higher.

The mean is higher due to the high max valves that are bringing the mean up.

Hence from observing we can say that woman on average pays higher than men.

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Answer: The difference between sum of first 20032003 even numbers and sum of first 20032003 odd numbers is “-20032003”.

Step-by-step explanation:

The sum of first 20032003 even numbers:

[tex]Summation E=E_{1}+E_{2}+E_{3}+ . . . . . +E_{20032003}[/tex]

The sum of first 20032003 odd numbers:

[tex]Summation O=O_{1}+O_{2}+O_{3}+ . . . . . +O_{20032003}[/tex]

Difference between the sum of first 20032003 even numbers and the sum of first 20032003 odd numbers:

[tex]Difference=Summation E - Summation O=(E_{1}+E_{2}+E_{3}+ . . . . . . . +E_{20032003})-(O_{1}+O_{2}+O_{3}+ . . . . . . . +O_{20032003})[/tex]

[tex]Difference=(E_{1}-O_{1})+(E_{2}-O_{2})+(E_{3}-O_{3})+ . . . . . . . +(E_{20032003}-O_{20032003})[/tex]

Even numbers start as 0, 2, 4, 6…. While odd numbers start as 1, 3, 5, 7…..

(assuming that we are taking non-negative even/odd numbers into account only)

As we know, every nth even number is one behind their respective odd number (i.e. 0 lags 1, 2 lags 3, 4 lags 5 and so on)

Thus, our equation of difference becomes,

[tex]Difference=(-1)_{1}+(-1)_{2}+(-1)_{3}+ . . . . . . . +(-1)_{20032003} =(-1)*20032003=-20032003[/tex]

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The sides of the base of pyramid is 2ft long.

the height of pyramid = 6ft

Volume of pyramid = 8cubic ft

Area of base = A

Formula:

Volume of pyramid = (Area of the base)*(height)/3

8 = (A)*6/3

8 = (A)*2

A = 8/2

A = 4

the total area is 4ftsquare , so

each base is 2 ft.

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Population in 20 years is 2654 .So option(2) is correct

A percentage is a percentage of something expressed as a number between 0 and 100 rather than as a fraction. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent.

Given that a population of 1000 people were to increase by 5% every year

We have to determine the population be in 20 years

P = 1000

R = 5

T = 20

Population in 20  years = P[(1+(r/100)]t

= 1000[1 + 5/20]20

= 1000(21/20)20

= 1000 x 2.6538

= 2653

Therefore population in 20 years is 2654

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Ken will run 3 laps and Hamid will run 4 laps in 80 and 60 seconds.

To find this, we first find the number of seconds that will have passed when they meet again.  We use the LCM, or least common multiple, for this.  First we find the prime factorization of each number:

LCM of 80 and 60 = 2X2X5X4X3

                             = 4X5X4X3

                             = 240

Now, divide the respective seconds from the total 240, we get

for Ken, 240÷ 80 = 3 laps

For Hamid, 240÷ 60 = 4 laps

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As the amount of space a rhombus encloses in a two-dimensional space can be defined as its area, the ABCD rhombus's area is A = 12 d1 d2.

A particular type of rhombus is a parallelogram. In a rhombus, the opposing sides or angles are parallel as well as equal. A rhombus also has sides that are each the same length, and its diagonals come together at right angles to make its shape. A diamonds or rhombus is also referred to as a "rhombus."

The diagonal lines are parallel. A rhombus is what it is. The parallelogram is a rectangle, rhombus, and square since the diagonals are all congruent and perpendicular to one another. It is a rhombus, ABCD.

Rhombus Area Calculation Formulas

Diagonal Use, A = ½ x d1 x d2

A = b h using Base and Height

Trigonometry is used, A = b2 × Sin (a)

Where b = length of any side, h = height of rhombus, d1 = length of diagonal 1, d2 = length of diagonal 2, a = measure of any inner angle

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The expression that could represent the amount of sodium per serving, in milligrams, in the new soup recipe would be = (1 - 33/100)X but when simplified it can be represented with 0.67x.

Sodium is defined as an element that is made up of 11 electrons revolving round it's atomic orbit. It serves as the major component of common salt found in food products.

From the question;

The new soup recipe = - 33% = - 33/100

The old soup recipe = X milligrams.

Since the new recipe is 33/100 less than the old soup recipe.

The new soup recipe would be = (1 - 33/100)X

When further simplified;

= 1 - 33/100

= 100-33/100

= 67/100

= 0.67x

Therefore, the new soup recipe can be represented with the above derived expressions such as (1 - 33/100)X and 0.67x when simplified.

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The option that is an example of a linear function in two variables is b. 3.1y - 6 = 7x

Linear functions have a straight line as their graph. The following is the form of a linear function. y = f(x) + a+bx There is one independent variable and one dependent variable in a linear function.

A straight line on the coordinate plane is represented by a linear function. For example, y = 3x - 2 denotes a straight line on a coordinate system.

Linear equations are classified into three types: point-slope, standard, and slope-intercept.

In this case, we can see that the variables are x and y. Therefore, the correct option is B.

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Using compound interest, it is found that:

a) The amount of money that she will have is of £2377.

b) The interest she will have earned is of £377.

The balance of an investment of P in compound interest after t years is modeled as follows:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which the remaining parameters are:

The values of these parameters in this problem are given as follows:

P = 2000, r = 0.025, n = 1, t = 7.

Hence the balance of the account after 7 years will be of:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]A(7) = 2000\left(1 + \frac{0.025}{1}\right)^{7}[/tex]

A(7) = 2377.

The interest earned is calculated as the final balance subtracted by the principal, hence:

I(7) = A(7) - P

I(7) = 2377 - 2000

I(7) = 377.

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There is one solution to the equation.

What is solution of the equation?

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.

Given: Kelsey buys several pairs of uniform pants for $17.95 each, and a sweater for $24.

Jeana shops at a different store and buys several pairs of uniform pants for $18.95 each, plus a sweater for $18.

The equation represents the situation is,

17.95x + 24 = 18.95x + 18

Subtract 18 from both sides,

17.75x + 24 - 18 = 18.95x + 18 - 18

        17.95x + 6 = 18.95x

18.95x - 17.95x = 6

                       x = 6

Therefore, there is one solution to the equation.

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For the given figure, the value of the variable x is 14° and the value of the variable y is 37°.

Variable:

Variable is known as an alphabet which is used to represent the unknown number.

Given,

Here we have the figure with the expressions

(9x + 12)°

3x°

(4y - 10)°

Now, we have to find the value of the variables x and y.

Here we know that the "If two lines which are parallel are intersected by a transversal then the pair of interior angles on the same side of the transversal are supplementary."

So, here we have write the given values as,

=> (9x + 12)° + 3x° = 180°

=> (12x + 12)° = 180°

=> 12x° = 168°

=> x = 14°

Similarly, the value of y s calculated as,

=> (4y - 10)° + 3x° = 180°

We know the value of x, then the value of y is,

=> (4y - 10)° + 3(14)° = 180°

=> 4y - 10 + 42 = 180°

=> 4y = 148

=> y = 37°

Therefore, the value of the variable x is 14° and the value of the variable y is 37°.

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The simplified form of this expression is x^4y-3x+y^2x^3-3y

From the question, we have

(x+y)(x^3 y-3)

= xx^3 y-x⋅3+yx^3 y-y⋅3

=x^4y-3x+y^(1+1) x^3-3y

=x^4y-3x+y^2 x^3-3y

The simplified form of this expression is x^4y-3x+y^2 x^3-3y

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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Answer:

f(- 4) = 22

Step-by-step explanation:

substitute x = = - 4 into f(x)

f(- 4) = 2(- 4)² + 7(- 4) + 18 = 2(16) - 28 + 18 = 32 - 10 = 22

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The equivalent expression is;

⇒ ln (e⁴) = 4

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ ln (e⁴)

Now,

Since, We know that;

ln (eˣ) = x

So, We can apply the above rule, we get;

⇒ ln (e⁴) = 4

Thus, The equivalent expression is;

⇒ ln (e⁴) = 4

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