A bicycle wheel is centimeters from top to bottom. When the wheel goes all the way around one time, the bicycle travels 198 centimeters. How can this information be used to estimate the value of π?

Answer:

[tex]\frac{5\sqrt{11} }{11}[/tex]

Step-by-step explanation:

To cancel out a square-rooted number at the denominator, we can multiply the square-rooted number by multiplying the square root number over again:

[tex]\frac{5}{\sqrt{11}}[/tex] * [tex]\frac{\sqrt{11}}{\sqrt{11}}[/tex]

Now, any same number of square root times another same number of a square root will cancel out the root. So [tex]\sqrt{11}[/tex] * [tex]\sqrt{11}[/tex] will equal 11.

With this information, we can now go back to the problem, so we will get:

[tex]\frac{5\sqrt{11}}{11}[/tex]

The y-intercept of the linear function is: C. 15.

The y-intercept of a linear function is defined as the starting or initial value, which is also the point on the y-axis where the line of the equation crosses.

In a given function represented as y = mx + b, the y-intercept is the value of b.

From the information given above, we have:

Initial value/y-intercept (b) = flat rate = $15

Slope/unit rate (m) = $10

Therefore, the y-intercept of the function is: C. 15.

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Solving systems of linear equations in two variables by substitution involves isolating one of the variables and substituting its value into the other equation.

This can be done by adding or subtracting the same term from both sides of one equation and then using that result to substitute into the other equation.

For example, consider the system of equations below:

2x + 3y = 8

3x + 2y = 7

Start by solving for x in the first equation by subtracting 3y from both sides:

2x + 3y = 8

2x = 8 - 3y

x = (8 - 3y)/2

Now substitute this expression for x in the second equation:

3(8 - 3y)/2 + 2y = 7

24 - 9y + 2y = 7

11y = 17

y = 17/11

Finally, solve for x, add y = 17/11 to the first equation as follows:

2x + 3(17/11) = 8  

2x + 51/11 = 8  

2x = 8 - 51/11  

x = (8 - 51/11)/2  

x = 21/22

The solution is x=21/22 and y=17/11.

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Answer:

the numbers are 13 and 17

Step-by-step explanation:

let the first number be a

let the second number be b

a+b=30.......a=30-b

a-b=4

substitute the first eq into the second one

30-b-b=4

30-2b=4

30-4=2b

26=2b

13=b

a=30-b

a=30-13

a=17

The letter E would be drawn roughly 40 times, but probably not exactly 20 times.

The area of mathematics known as probability deals with numerical representations of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an occurrence, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

P(A) = f / N determines probability, which quantifies the possibility of an event happening. Probability and odds are connected, but probability is necessary for odds to exist.

Statistical formula

P(A) stands for the likelihood that event A will occur.

f = Number of possible outcomes of an event (frequency)

N stands for the total number of outcomes.

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Answer:

The length of the shorter leg of the triangle can be calculated using the Pythagorean Theorem. The formula is a^2 + b^2 = c^2, where a is the length of the shorter leg, b is the length of the longer leg and c is the length of the hypotenuse. In this case, a^2 + 52^2 = c^2. The hypotenuse can be calculated by using the sine formula. c = (52/sinA). Substituting this value into the Pythagorean Theorem equation, a^2 + 52^2 = (52/sinA)^2. Solving for a, a = sqrt(52^2 - (52/sinA)^2).

Answer: 6 divided by 2/3 = 9

Step-by-step explanation:

For division always take the first number in the word problem so in this question the answer would be 6 then you take the 2/3 and divide it by 6. So it would be 6 divided by 2/3. then you take the 9 from the word problem  and do 6 divided by 2/3 equals 9. So in this question the answer would be option 2 or could also be called option B. And if this is it that means the answer is, 6 divided by 2/3 = 9.

The division equation which representant this situation is 6 ÷ 2/3 = 9.

Division equations are mathematical equations with the division operator in them. Division equations are useful not only in math class, but in everyday life as well. For example, if we wanted to evenly distribute a bag of candies among our friends, we could use division to find our answer. Assume we have 100 candy bars and four friends. Divide 100 by 4 to find out how many candies each person gets. We discover that our answer is 25, which means that each of our friends receives 25 candies.

It's our job to figure out what the division equals. This can be represented by a variable, such as x. As a result, our total division equation will be: 100/4=x. On both sides of the equals sign, we have things.

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a) The numeric value at x = 4 is given as follows: f(4) = 64.

b) The logarithmic expression is given as follows: x = log2(16).

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is defined as follows:

f(x) = 4(2)^x.

At x = 4, the numeric value is found replacing the lone instance of x by 4, hence:

f(4) = 4(2)^4 = 64.

For the logarithmic expression, we obtain the inverse function, hence:

64 = 4(2)^x.

2^x = 16

x = log2(16).

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The value of X of the vertical angles would be = 1.36

The vertical angles are the type of angles that are known to be directly opposite each other which are also equal angles.

The given vertical angles are ZA and ZB.

If m A = (8x – 20)°

m B = (3x – 5)º

The vertical angles are equal, to find X;

mA = mB

8x -20 = 3x - 5

Bring the like terms together;

8x + 3x = 20- 5

11x = 15

X= 15/11

X= 1.36

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Complete question:

ZA and ZB are vertical angles. If m A = (8x – 20)° and m B = (3x – 5)º, then find the value of x.

To solve a complex fraction, which is a fraction that contains one or more fractions in its numerator and/or denominator, you can follow these steps:

Factor the numerator and denominator of the complex fraction if possible. This will make it easier to cancel common factors.

Multiply both the numerator and denominator by the reciprocal of the fraction(s) in the denominator. This will eliminate the fraction(s) in the denominator, leaving a simplified expression.

Simplify the resulting expression by combining like terms, if possible.

Check your work by multiplying the numerator and denominator of the original complex fraction by the reciprocal of the fraction(s) in the denominator, and verifying that the simplified expression you obtained is equivalent.

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The scale factor is equal to 2.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

as given, K =(5,0) (10,0)

Solution:

Initial Coordinates=(5,0)=(xi,yi)→xi=5, yi=0

Final Coordinates=(10,0)=(xf,yf)→xf=10, yf=0

Scale factor=xf/xi=yf/yi

We divide the final coordinates by the initial coordinates. In this case the ordinates (yf and yi) are zero and we can't divide by zero, but the abscissas (xf and xi) are different of zero, then we can use them:

Scale factor=xf/xi=10/5

Scale factor=2

Therefore, the scale factor is equal to 2.

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The product of (X + A) + (X + B) is- [tex]x2 + xb + ax + ab[/tex]

The information provided in the question,

The outcome of multiplying two numbers together is known as the product. 12 is the result of the addition of 3 and 4, 20 is the sum of 4 and 5, and so on. Discovering the Product A multiplication problem has a solution in the product.

We must determine the of (x + a) and (x + b).

The product is the result of multiplying two numbers, as we all know.

So,

[tex]( x+ a)[/tex]   x  [tex]( x + b)[/tex]

[tex]x( x+b) + a( x + b)[/tex]

[tex]x[/tex]²[tex]+ bx + ax + ab[/tex]

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The dimensions for the scale drawing of the flag is 20 cm by 23 cm

A scale is a set of levels or numbers which are used in a particular system of measuring things or are used when comparing things.

Given that, A rectangular flag is 80 centimeters by 92 centimeters. we need to find dimensions of a scale drawing of the flag using the scale 1:4,

Therefore,

80 / 92 = 20 / 23

Hence, the dimensions for the scale drawing of the flag is 20 cm by 23 cm

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Answer:

20cm by 23cm

Step-by-step explanation:

The solution for this equation is x = -36

3/4 ( x + 8 ) = 1/2 ( x - 6)

(Opening the brackets)

(3x + 24)/4  = ( x - 6)/ 2

By cross multiplication,

2(3x + 24) = 4( x - 6 )

6x + 48 = 4x - 24

(Taking the Variable to  one side)

6x - 4x = - 24 - 48

2x = - 72

x= - 72/2

x = -36

Hence, the solution for this equation is x = -36

Answer:

follow me first

Step-by-step explanation:

i will answer that in 60 sec

Answer:

B

Step-by-step explanation:

1. Before anything, figure out the inequality symbol. Why? In the solutions, all of the inequalities are different so you narrow it down by figuring out the inequality sign.

2. "At most 50 pounds" means we can't go over 50 pounds, but the package can still equal 50, that's just the most it can be. This means we will have a line underneath because it includes the maximum number, 50, in the solution.

3. "At most" also means the package (x) cannot be over 50. The sign opening must face 50 because that shows x has to be less than. But it can equal 50, so the sign is [tex]x\leq 50[/tex]. That would be B.

4. About the numbers, the box weighs 2 pounds. This means it is x+2 because weight is not negative and it is ADDING weight to what we don't know. To isolate x, just do 50-2, and you get 48. That again proves b is the answer.

Answer:

sorry its so long

Step-by-step explanation:

We multiply the entire equation by the number

6

6 in order to get rid of the fractions.

2

�

+

3

�

=

6

5

�

=

6

�

=

6

5

=

1

1

5

1

1

5

ℎ

=

1

hour

12

minutes

2x+3x

5x

x

1

5

1

​

h

​

=6

=6

=

5

6

​

=1

5

1

​

The average rate of change from x = 1 to x = 5 is given as follows:

-1.25.

The average rate of change of a function is given by the change in the output divided by the change in the input.

The numeric values for the function graphed are given as follows:

Hence the change in the output is given as follows:

2.5 - 7.5 = -5.

The change in the input is given as follows:

5 - 1 = 4.

Hence the average rate of change is given as follows:

-5/4 = -1.25.

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The events from "Let George Do It!" in the right sequence will be:

From 1946 to 1954, Owen and Pauline Vinson produced the radio drama series Let George Do It in the United States.

In 1954, Olan Soule voiced the role of private eye George Valentine, which was portrayed by Bob Bailey. The scripts by David Victor and Jackson Gillis were directed by Don Clark.

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Step-by-step explanation:

fog(x)=f(x-3)

=(x-3)²+2

=x²-6x+9+2

=x²-6x+11

The coordinates of the vertex for f(x) = 3x²+6x+3 are (-1, 0).

For any equation of the type y=ax²+bx+c, the vertex is given by (h, k)

Where, h = -b/2a and k = (4ac - b²)/4a.

Given, the equation is y = 3x²+ 6x+3

Here, a = 3, b = 6 and c = 3

So, h = -6/2(3)

h = -6/6

h = -1

4ac = 4(3)(3)

4ac = 36

So, k = [36 - (6)2]/4(3)

k = (36 - 36)/12

k = 0

Therefore, the coordinates of the vertex are (h,k) = (-1, 0).

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Answer:

The required linear function for the temperature T, in degrees Fahrenheit, of the oven m minutes from the time it was turned on until it reaches the desired temperature is T = 54m + 80.

Step-by-step explanation:

Given that,

An oven is turned on and set to reach the desired temperature of 350 degrees Fahrenheit. The oven warms up at a constant rate. The oven’s temperature is 134 degrees Fahrenheit at 1 minute and it reaches its desired temperature at 5 minutes.

What are functions?

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is the independent variable while Y is the dependent variable.

Here,

At time m = 1 min, temperature T = 134 °F

At time m = 5 min. temperature T = 450 °F

Slope of the equation M = 450 - 134 / 5 - 1

                                        = 216 / 4

                                        = 54

Linat relationship can be given as,

T - 134 = 54 (m - 1)

T = 54m -54 + 134

T = 54m + 80

Thus, the required linear function for the temperature T, in degrees Fahrenheit, of the oven m minutes from the time it was turned on until it reaches the desired temperature is T = 54m + 80.

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Hope it helps :)

This type of insurance is designed to provide financial protection for the policyholder's loved ones in the event of their death.

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Answer:

(5n + 1)(3n - 2)

Step-by-step explanation:

Find what number multiplies into -7 and adds into -2, including the coefficient in 15n^2

Yes, The molar mass of a substance is defined as the mass of 1 mol of that substance, expressed in grams per mole, and is equal to the mass of 6.022 × 10²³(Avogadro's number) atoms, molecules, or formula units of that substance.

The Avogadro constant, A, is the number of particles (such as atoms, molecules, or ions) in one mole of something. Its value is modernly defined as exactly 6.022 140 76 × 10²³. (As it is a pure number, it has no units.)

So, in 1 mol of helium, which has a mass of (very close to) 4 g, there are A

atoms; in 1 mol of sucrose, with a mass of 342 g, there are A molecules.

We can have moles of other kinds of things, including subatomic particles. The amount of charge known as the faraday is the charge of one mole of electrons (A of them; about 96 500 C).

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Here you go mate!

7x + 10 = -11

answer : x = -3

-12(x + 5) = -144

Answer : x = 7

-9x - 9 = 27

Answer : x = -4

x/4 + 2 = 10

Answer : x = 32

Answer:

Step-by-step explanation: 3×6+1,3×6 is 18+1 is 19/6 is your answer

The percent of the games that was lost is 26.7%.

Percentage is the ratio of two numbers expressed as a number out of 100. The sign that is used to represent percentage is %.

Percentage of the games lost = (number of games lost / total number of games) x 100

Number of games lost = total number of games - number of games won

75 - 55 = 20

Percentage of the games lost = (20 / 75) x 100 = 26.7%

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Answer:

[tex]x\sqrt{x}[/tex]

Step-by-step explanation:

Use Exponent Power rule:

[tex]b^{1/n} =\sqrt[n]{b}[/tex]

Given [tex]\sqrt{x^3}[/tex] also known as [tex]\sqrt[2]{x^3}[/tex], rewrite with exponent power rule as [tex]x^{3/2}[/tex].

Factor [tex]x[/tex] from [tex]x^{3/2}[/tex] = [tex]x(x^{1/2})[/tex]

Rewrite as [tex]x\sqrt{x}[/tex]