4. Greg plans to purchase a bicycle. Bike A costs $270 and has an expected maintenance cost of $36 per year. Bike B costs $360 and has an expected maintenance cost of $20 per year.

a. Write a rational function for the average yearly cost of Bike A.

b. Write a rational function for the average yearly cost of Bike B.

c. Which bike has the lowest average yearly cost if Greg owns the bike for 5 years? Justify your
answer with numbers and words.

The diagonal length of a right rectangular prism is given by the formula (l2 + w2 + h2) units. The length of the diagonal of this rectangular box is 5√2 cm.

Therefore, the equation for the diagonal length of a right rectangular prism is (l2+w2+h2), where l is the length, b is the breadth, and h is the height.

d2 = l2 + w2 + h2

Take the square root of either side of the equation to find the value of d:

d =  √(d2) = √(l2 + w2 + h2)

d = √(l2 + w2 + h2)

The diagonal length is as follows given that the rectangular box in question is 6 cm x 8 cm x 5 cm in size:

d = √(36 + 64 + 25)

d = √(125)

d = √(62.5)·√(2)

d = 5√(2)

Therefore, the length of the diagonal of this rectangular box is 5√2 cm.

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Answer:

the answer I think is the 1st

Step-by-step explanation:

as the change (+4) is in y

not in x

The graph of f-1(x) is (d)

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

f(x) = 2x + 4

This means that

y = 2x + 4

Swap x and y

So, we have

x = 2y + 4

Make y the subject

So, we have

y = 0.5x - 2

This equation is represented by graph (d)

Hence, the graph is (d)

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Answer: $14.10

Step-by-step explanation:

11.25 * 9 = 101.25

101.25/100 = 1.0125

11.25 + 1.0125 = 12.2625

--
12.2625 * 26 = 282.0375

282.0375/100 = 2.820375

11.25 + 2.820375 = 14.070375
--

14.070375 rounded = 14.10

Answer:

[tex]x^{2} - 14 = 50[/tex]

Step-by-step explanation:

Let x = Unknown number

Number squared = [tex]x^{2}[/tex]

Difference between the number squared and 14 is 50:

= [tex]x^{2} - 14 = 50[/tex]

= [tex]x^{2} = 14 + 50[/tex]

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

(NOTE: It cannot be [tex]14 - x^{2} = 50[/tex] since:

[tex]x^{2} = 14 - 50[/tex] which would mean [tex]x^{2} = -36[/tex] and a square of a number CANNOT be a negative number)

Taking the square root of both sides to get rid of the square:

= [tex]x = \sqrt{64}[/tex]

= x = ±8

Answer:

x = 2

Step-by-step explanation:

We can start by rewriting the equation as follows:

100 * (1/5)^x / 4 = 4

Next, we'll multiply both sides by 4 to cancel out the division by 4:

400 * (1/5)^x = 16

Finally, we'll divide both sides by 400 * (1/5)^x to isolate (1/5)^x:

1/((1/5)^x) = 16 / 400 = 1/25

Taking the reciprocal of both sides:

(1/5)^x = 25

Taking the power of 5 to both sides:

x = log(25)/log(5) = 2

So x = 2 is the solution to the equation.

The area of shape B is 312.5 cm²

Let us assume that the area of the shape B is m square units.

Here, the dimensions of shape A is 12 cm and the area of the shape A is 200 cm²

The dimensions of shape B is 15 cm and the area of the shape B is m cm²

Since A and B are two similar 2D shapes their dimensions must be in proportion.

So, we get an equation,

⇒ A² / B² = 200 / m

⇒ 12² / 15² = 200 / m

⇒ 144 / 225 = 200 / m

⇒ m = (225/144) × 200

⇒ m = 312.5 cm²

Therefore, the area of shape B is 312.5 cm²

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The complete question is:

A and B are two similar 2D shapes. The area of shape A which is 12cm is 200cm squared. Calculate the area of shape B which is 15cm.

Kari can buy 30 AA batteries and 30 D batteries. We used simple LCM for this solution.

To find the smallest number of each battery type that Kari can buy, we must find the least common multiple (LCM) of 6 and 10. The LCM is the smallest multiple that both numbers can divide into evenly. To find the LCM, we can list the multiples of each number until we find a common multiple. In this case, the LCM of 6 and 10 is 30. So, Kari can buy 30 AA batteries and 30 D batteries, which gives her an equal number of both battery types.

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The final coordinates of the vertices of quadrilateral A'B'C'D';

A''(12, 9)

B''(16, 2)

C''(12, -2)

D''(13, 2)

A transformation is a dramatic change in form or appearance. An important event like getting your driver's license, going to college, or getting married can cause a transformation in your life. A transformation is an extreme, radical change.

here, we have to,

to interpret the sequence of transformations,

The coordinates of the quadrilateral ABCD are;

A(-3, 4)

B(-7, -3)

C(-3, -7)

D(-4, -3)

Now, the first sequence of transformation is reflection across the y-axis. Now, the transformation rule for reflection across the y-axis is;

(x, y) → (−x, y) .

Thus, we now have;

A'(3, 4)

B'(7, -3)

C'(3, -7)

D'(4, -3)

It is now translated 9 units left and as such the transformation rule is;

((x + 9), y)

We now have;

A'(12, 4)

B'(16, -3)

C'(12, -7)

D'(13, -3)

It is now translated 5 units up and as such, the final coordinates are;

A''(12, 9)

B''(16, 2)

C''(12, -2)

D''(13, 2)

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Answer:

This one is quite tough as I too was stuck on this one, I believe the answer is B. I hope this helps.

Answer: the answer is 0=0

Step-by-step explanation:

5-12=-7

x-7=x-7        x-7+7=x-7+7

x=x     x-x=x-x

0=x-x

0=0

The equation to solve for your normal hourly rate is x = (612.5 - 1.5 * 46 + 46 * x) / 40.

In this equation, x represents your normal hourly rate. The first term in the parentheses, 612.5, is your total earnings for the week. The second term, 1.5 * 46, represents the overtime pay you received for working 6 hours over 40 hours. The third term, 46 * x, represents the amount you earned for your 40 hours of regular pay. The final term, 40, represents the number of hours you worked at your regular rate. By dividing both sides of the equation by 40, we can isolate x and solve for your normal hourly rate.

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Complete Question:

You are paid 1.5 times your normal hourly rate for each hour you work over 40 hours in a week. you worked 46 hours this week and earned $612.50. part a: which equation can you use to solve for x , your normal hourly rate?

Answer:

.17 miles per minute

Step-by-step explanation:

You are trying to figure out how many Miles he ran in EACH minute, so you would do 8(Miles)/47(minutes)

8/47 = .17

the maximum number of data points that fall below the second quantile is 4.

4 data points.

Quantiles divide a set of data into four equal parts, each with an equal number of data points. In this case, 36 data points are divided into 9 quantiles, meaning each quantile contains 4 data points. Therefore, the maximum number of data points that fall below the second quantile is 4.

Quantiles divide a set of data into equal parts, each with an equal number of data points. The number of quantiles is determined by the total number of data points. For example, if there are 36 data points, then it is divided into 9 quantiles, each with 4 data points. The lower the quantile, the lower the value of the data points it contains. Therefore, the maximum number of data points that fall below the second quantile is 4.

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The answer is:

A frequency distribution for a collection of data is shown in the accompanying table.

The intervals or ranges of the data are displayed in the left column of the table, and the frequency or number of observations within each interval is displayed in the right column.

For instance, the first row demonstrates that 4 observations fall within the range of 10 to 19 while the second row demonstrates that 5 observations fall within the range of 20 to 29.

We only combine the frequencies to determine the total number of observations:

Total observations equal 25 (4 + 5 + 8 + 7 + 1 = 25)

By averaging the bottom and upper interval bounds, we can also determine each interval's midpoint. As an illustration, the first interval's midway (10-19) is as follows:

Midpoint: (14.5) (10 + 19) / 2

This may be done for each interval, and to display the midpoints, we can add a third column to the table.

The cumulative frequency, which is the overall frequency as we progress from the shortest interval to the longest interval, can then be calculated. The cumulative frequency can be displayed in the table by using a fourth column.

The finished table is shown here:

Interval Frequency Midpoint Cumulative Frequency

10-19 4 14.5 4

20-29 5 24.5 9

30-39 8 34.5 17

40-49 7 44.5 24

50-59 1 54.5 25

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Answer:

3

Step-by-step explanation:

8(3x + 9)

24x + 72 =0

24x = -72

x = -72/24

x = -3

The possible values of x % 10, where x is an integer, are integers between 0 and 9, inclusive, i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

The modulo operation (represented by the percent symbol %) returns the remainder of the division of one number by another. For example, when x is divided by 10, the result of x % 10 is the remainder of that division.

Since 10 is a positive integer, when x is divided by 10, the result is always a non-negative integer. Furthermore, since the range of x is all integers, the result of x % 10 will always be less than 10.

Therefore, the possible x % 10 are integers in the range of 0 to 9, including 0 and 9. These are the remainders that can result from dividing x by 10. For example:

7 % 10 = 7

17 % 10 = 7

27 % 10 = 7

In all of these cases, the remainder is 7 when the number is divided by 10.

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The expression which represents Arizona and Florida is 5a - 8 and 2f + 25 respectively.

Number of countries in Arizona= a

Number of countries in Florida= f

Florida:

5a - 8

Georgia:

2f + 25

Therefore, 5a - 8 and 2f + 25 represents the expression of each country respectively.

Complete question:

Write an expression for the number of counties in Georgia.

Florida has 8 less than 5 times the number of counties, a, in Arizona.

Georgia has 25 more than twice the number of counties, f, in Florida.

a. Write an expression for the number of counties in Florida.

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The value of the expression is 1/(9x)^2

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

(-9x)^-2

We can write the expression without negative exponents by using a fraction with a positive exponent:

(-9x)^-2 = 1/(-9x)^2

And without parentheses, this expression becomes:

1/(9x)^2

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On solving the provided question, we can say thatthe equations will be each moth will be 564/x = 564/12 = $47 and 2 moths will be = 47x = 47*2 = $94

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

Tonya saved $564 in one year.

the equations will be

each moth will be 564/x

= 564/12 = $47

2 moths will be = 47x = 47*2 = $94

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An approximate size which does not represent any of the actual dimensions of the unit is nominal value.

The phrase "nominal number" is said to be quite new and rarely used. It seems to have come from the statistical phrase "nominal data," which is reportedly defined as data revealing "...merely declarations of qualitative category of membership," as it is used in school textbooks. The meaning of the word "nominal" in this use is "name."

Nominal numbering is mathematically a one-to-one and onto function from a set of named objects to a set of numbers, which may change (typically growing) over time. It is a function because each named object is assigned a single number; it is one-to-one because different objects are assigned different numbers; and it is onto because every number in the set at a given time has a single named object associated with it.

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Step-by-step explanation:

put the 3-digit on top and 2-digit on bottom

multiply last # on the 2-digit by by the 3digit then add a 0 placeholder then reapeat

Elena spent an amount of $4.10 + p more than Taniy.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Let's represent the amount spent by Elena and Taniy as E and T, respectively. We know that:

E = 8.25 + 4p (since Elena bought a watermelon for $8.25 and 4 pounds of cherries for 4p)

T = 4.15 + 3p (since Taniy bought a pineapple for $4.15 and 3 pounds of cherries for 3p)

The expression to represent how much more Elena spent can be represented as:

E - T = (8.25 + 4p) - (4.15 + 3p)

Expanding the right side:

E - T = 8.25 + 4p - 4.15 - 3p

Combining like terms:

E - T = 4.10 + p

So Elena spent $4.10 + p more than Taniy.

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Participants in a study on the effects of viagra are assigned to groups, the independent variable is The viagra.

In an algebraic equation, an independent variable is a variable whose values are not impacted by changes. It is claimed that the value of y is a function of the value of the independent variable (x), also known as the x value, and the value of y is known as the dependent variable, in an algebraic equation with two variables (x and y), if any value of x is related to any other value of y.

The alphabetic letter that conveys a numerical value or a number is known as a variable in mathematics. In algebraic equations, a variable is used to represent an unknowable quantity.

For these variables, any alphabet from a to z may be used. Most frequently, the variables "a," "b," "c," "x," "y," and "z" are utilised in equations.

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a) The probability that among the first songs played​  you like 2 of​ them

= 0.404

b)The probability that among the first songs played​  you like 3 of​ them

= 0.2246

c) The probability that among the first songs played​  you like all of​ them

= 0.0024

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.

Given:

Total tracks= 18

a) The probability that among the first songs played​  you like 2 of​ them

=  C(7 , 2) x C( 11, 3) /C(18, 5)

= 21 x 165 / 8568

= 0.404

b)The probability that among the first songs played​  you like 3 of​ them

= C(7 , 3) x C( 11, 2) /C(18, 5)

= 35 x 55 / 8568

= 0.2246

c) The probability that among the first songs played​ you like all of​ them

= C(7 , 5) x C( 11, 0) /C(18, 5)

= 0.0024

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The sample space of a fair, 7-sided number cube rolled while playing a board game is,

S = {1, 2, 3, 4, 5, 6, 7}

The correct option is C.

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of potential experiment results. Depending on the experiment, a sample area could contain a variety of results.

Given:

7-sided number cube rolled while playing a board game.

The sample space is the collection of all the numbers.

So, the sample space is,

S = {1, 2, 3, 4, 5, 6, 7}

Hence, S = {1, 2, 3, 4, 5, 6, 7}.

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Answer & Step-by-step explanation:

To multiply these two binomials, we can use the distributive property as follows:

(2x+5)(3x+1) = 2x(3x+1) + 5(3x+1)

Now, we can simplify each term:

2x(3x+1) = 6x^2 + 2x

5(3x+1) = 15x + 5

Putting these back together, we get:

(2x+5)(3x+1) = 6x^2 + 2x + 15x + 5

Simplifying the middle two terms, we get:

(2x+5)(3x+1) = 6x^2 + 17x + 5

Therefore, the expression that is equivalent to (2x+5)(3x+1) is 6x^2 + 17x + 5.

Answer: Let x be the number of shirts that David buys.

The cost of the shirts can be represented by the equation: $15x.

The total amount of money that David has spent can be represented by the equation: $32.25 + $15x.

Since David has a total of $65 to spend, we can write the inequality:

$32.25 + $15x ≤ $65

Solving for x, we get:

$15x ≤ $65 - $32.25 = $32.75

$15x ≤ $32.75

$x ≤ $32.75 / $15 = 2.183333

Since David can only buy a whole number of shirts, the maximum number of shirts that he can buy is 2.

So, the maximum number of shirts David can buy is 2.

Step-by-step explanation:

Answer:

4:7, 16:28, 32:56, 64:112

Step-by-step explanation:

You can go down 1, and you can also keep doubling. I hope this helped, I hope you get it right! Have a Good Day!