MODELING REAL LIFE Bowling alley A charges $3.75 to rent shoes and $4 per game. Bowling alley B charges $2.50 to rent shoes and $4.50 per game. a. For what numbers of games is the total cost, including a pair of rental shoes, less at bowling alley A? at bowling alley B? Bowling alley A: ___ or more games. Bowling alley B: ___ or___ games .
b. Bowling alley A increases the cost per game by $0.50. How does this affect your answer in part (a)? Explain.

The dimensions of the concrete patio should be 23ft x 12ft x 0.5feet.

Since a rectangle is two-dimensional, while a cube is three-dimensional, the dimensions of the concrete patio include its length, width, and height or thickness.

The quantity of concrete required = 138ft³

The perimeter of the patio = 70 feet

Height = 6 inches or 1/2 foot or 0.5 ft

Perimeter = 2(L + W)

70 = 2(L + W)

L + W = 35 (70/2)

The possibilities for the length and width include 20 and 15, 25 and 10, and lastly, 23 and 12, which are also the two pair factors of 276.

Let L = 23 (the length is always longer than the width)

W = 12 (35 - 23)

Check:

Volume of concrete = 138ft³

Area = 276ft² (138ft³/0.5ft)

Two pair factors of 276 are 92 and 3, 46 and 6, 23 and 12, 2 and 138, and 1 and 276.

Given also that (23 + 12)2 = 70 (perimeter)

The dimensions that meet the two requirements are:

Length = 23 feet

Width = 12 feet

and Height = 0.5 feet

= 23 x 12 x 0.5 = 138

Thus, the dimensions of the concrete patio should be 23ft x 12ft x 0.5feet.

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Answer:

8

Step-by-step explanation:

The range of a data set in statistics is the difference between the largest and the smallest values. While range does have different meanings within different areas of statistics and mathematics, this is its most basic definition, and is what is used by the provided calculator. Using the same example:

2,10,21,23,23,38,38

38 - 2 = 36

The range in this example is 36. Similar to the mean, range can be significantly affected by extremely large or small values. Using the same example as previously:

2,10,21,23,23,38,38,1027892

The range, in this case, would be 1,027,890 compared to 36 in the previous case. As such, it is important to extensively analyze data sets to ensure that outliers are accounted for.

Answer: Range is all the values of the y-axis therefore, the range of the graph is {0,4,6,8}

Answer:

answer is 251.5

Mark as branliest if helped a bit

The 17th term of the sequence is 289

The nth term is given as

Sn = n^2

The 17th term of the sequence implies that

n = 17

So, we have

S17 = 17^2

Evaluate

S17 = 289

Hence, the 17th term of the sequence is 289

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The geometric transformation which will not  produce the image ∆A'B'C' is an option (B) reflection across the x-axis followed by a reflection across the y-axis

In this question, we have been given a triangle ABC and the transformed triangle A'B'C'

Also, in the graph the first triangle is at A(-3, 0), B(-2, 3), C(- 1, 1) and the Second triangle is at A prime (0, -3), B prime (3, -2), C prime (1, -1).

Consider the graph as shown below.

From the coordinates of vertex of triangle ABC and triangle A'B'C' we can observe that,

A(-3, 0) -> A'(0, -3)

B(-2, 3) -> B'(3, -2)

C(-1, 1) -> C'(1, -1)

For each vertex,

x coordinate of triangle ABC = y coordinate of triangle A'B'C'

and y coordinate of triangle ABC = x coordinate of triangle A'B'C'

This means, the geometric transformation of triangle ABC is reflection across the line y = x

But the reflection across the x-axis followed by a reflection across the y-axis.

Therefore, the geometric transformation which will not  produce the image ∆A'B'C' is an option (B) reflection across the x-axis followed by a reflection across the y-axis

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Answer:

Average= [tex]\frac{25}{72}[/tex]

Step-by-step explanation:

o find the average add up the values and divide the sum by the number of values.

Rewriting all values as fractions, rewriting any negatives if necessary and, setting up as an addition problem

The least common denominator (LCD) is: 24.

Rewriting as equivalent fractions with the LCD:

Rewriting numerators over the common denominator,

Totaling the numerator:

= [tex]\frac{25}{24}[/tex]

Dividing by the number of values: 3

[tex]\frac{25}{24}[/tex] ÷3 =[tex]\frac{25}{24}[/tex] ×[tex]\frac{1}{3}[/tex] = [tex]\frac{25}{72}[/tex]

Average of the fractions is:

Average= [tex]\frac{25}{72}[/tex]

The integers from 6 to 10 (inclusive).will be D. {6, 7, 8, 9, 10}.

It should be noted that the integers given are from 6 to 10 (inclusive).

In this case, this simply means the numbers from 6 to 10.

Therefore, the appropriate number will be: D.

{6, 7, 8, 9, 10}

In conclusion, the correct option is D.

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the graph of the new line ,Graph the line (-3,1) that is perpendicular to the line with the equation 2x+5y=10.

Definition:Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter. Each object in a graph is called a node.

x = 3

The points are on a vertical line because they share the same x-coordinate. A vertical line has the equation x=constant. The x-coordinate of the points must match the constant:

x = 3 . . . . formula for the line

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Answer:

  (c)  $95,400

Step-by-step explanation:

You want the listing price of your house such that you can clear $92,500 after paying a 3% commission to the buyer's realtor.

The buyer's agent will receive 3% of the sale price (P), so you receive that amount less. You want your share to be $92,500.

  (1 -3%)P = 92,500

Dividing by the coefficient of P, we get ...

  P = 92,500/0.97 ≈ 95,361

We are asked to round this value to the nearest $100. That makes the listing price ...

  $95,400 . . . . listing price

__

Additional comment

You can estimate the listing price by adding 3% of 92500 to that value, and you can estimate the added amount as 3%×90,000 = 2700. That is, you know the listing price needs to be slightly higher than ...

  92500 +2700 = 95,200

Only one of the answer choices is above that value and rounded to the nearest $100. (You can eliminate the first two choices, because they are not properly rounded.)

Answer:

40°

Step-by-step explanation:

At point C, the angle is shown as 110°.
Since a line is 180°, you now know that the other side of point C is 70°.
Line A-B and A-C are equal (shown by the short lines), meaning the angle at point B is also 70°,
A triangle is 180° in total, so the equation would be 180° - 2(70°) = 180° - 140° = 40°

given ∛1000

∛1000 = ∛(10 × 10 × 10)

∛1000 = 10

hi

-(3a-3) =   -3a +3    

you cannot do much more.  

You can  rewrite it as  3 ( -a +1)   or as  -3 ( a -1)  but nothing more really.

Answer: the ratio is 1.13

Step-by-step explanation:

The ratio of non-black sedans to black sedans is 40/31, as of the given condition.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,

The total number of sedans in the parking lot is,
496 black sedans + 640 non-black sedans = 1136 sedans.

The ratio of non-black sedans to black sedans can be found by dividing the number of non-black sedans by the number of black sedans:

Ratio = 640 non-black sedans / 496 black sedans
Ratio  = 640/496
Ratio = 40/31

So, the ratio of non-black sedans to black sedans is 40/31.

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Answer:

0

Step-by-step explanation:

since a function maps only one member in the co-domain

Answer:

0

Step-by-step explanation:

[tex]n(S \cup T)=n(S)+n(T)-n(S \cap T) \\ \\ 15=15-n(S \cap T) \\ \\ n(S \cap T)=0[/tex]

The distance between -10 and 5 on a number line is 15

From the question, we are to determine the distance between the given points on a number line

The given points are -10 and 5

On a number line, the distance between any two points is the difference between the largest number and the smallest number

That is,

Distance between two points on a number line = Value of the largest number - Value of the smallest number

The given points are -10 and 5

The largest number is 5

and

The smallest number is -10

Thus,

Distance between -10 and 5 on a number line = 5 - -10

Distance between -10 and 5 on a number line = 5 + 10

Distance between -10 and 5 on a number line = 15

Hence, the distance between -10 and 5 on a number line is 15

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The answer and all work is shown in the provided screenshot! :)

Have a great day!

Answer: Point B will be at (4,-3)

Point C will be (-2,-3)

Point D will be (6,3)

Answer:

y = 8

Step-by-step explanation:

y + y + 2 = 18

2y + 2 = 18

     -2     -2    (+ 2 and - 2 cancel out each other)

   2y   = 16    

    2       2

     y = 8

The corresponding angles of both triangles are not congruent to each other, therefore: B. ΔRST is not similar to ΔUVW.

If two triangles are similar to each other, their corresponding interior angles measures would be congruent to each other, while their corresponding side lengths would be proportional to each other.

Angle R = 55°

Angle T = 45°

Angle S = 180 - 55 - 45 = 80°.

Angle U = 55°

Angle V = 75°

Angle W = 180 - 55 - 75 = 50°

Thus, we can state that, the corresponding angles of both triangles are not congruent to each other, therefore: B. ΔRST is not similar to ΔUVW.

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Answer:

===============================

Parallel lines have equal slopes.

Find the slope of the first line, mn:

Find the slope of the second line, ab:

Compare the slopes and find the value of k:

Answer:

[tex]k=\dfrac{3}{2}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4.3 cm}\underline{Slope formula}\\\\$m=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\ are points on the line.\end{minipage}}[/tex]

Segment MN

[tex]\implies \textsf{slope}=\dfrac{y_N-y_M}{x_N-x_M}=\dfrac{1-0}{5-0}=\dfrac{1}{5}[/tex]

Segment AB

[tex]\implies \textsf{slope}=\dfrac{y_B-y_A}{x_B-x_A}=\dfrac{k-2 \frac{1}{4}}{-2\frac{1}{4}-1\frac{1}{2}}=\dfrac{k-2 \frac{1}{4}}{-2\frac{1}{4}-1\frac{2}{4}}=\dfrac{k-2 \frac{1}{4}}{-3\frac{3}{4}}[/tex]

Parallel lines have the same slope.  

Therefore, equate the found slopes for the two segments and solve for k:

[tex]\implies \dfrac{k-2 \frac{1}{4}}{-3\frac{3}{4}}=\dfrac{1}{5}[/tex]

Cross multiply:

[tex]\implies 5 \left(k-2 \frac{1}{4}\right)=-3\frac{3}{4}[/tex]

[tex]\implies 5k-10 \frac{5}{4}=-3\frac{3}{4}[/tex]

[tex]\implies 5k-11 \frac{1}{4}=-3\frac{3}{4}[/tex]

Add 11 ¹/₄ to both sides:

[tex]\implies 5k-11 \frac{1}{4}+11 \frac{1}{4}=-3\frac{3}{4}+11 \frac{1}{4}[/tex]

[tex]\implies 5k=(-3+11)+\left(-\frac{3}{4}+\frac{1}{4}\right)[/tex]

[tex]\implies 5k=8-\frac{1}{2}[/tex]

[tex]\implies 5k=7\frac{1}{2}[/tex]

Divide both sides by 5:

[tex]\implies 5k \div 5=7\frac{1}{2} \div 5[/tex]

[tex]\implies 5k \div 5=\dfrac{15}{2} \div 5[/tex]

[tex]\implies k=\dfrac{3}{2}[/tex]

Therefore, the value of k for which the two segments are parallel is ³/₂.

Answer:

1st one is the right option

Answer:

f(4) = 5

Step-by-step explanation:

locate x = 4 on the x- axis, go vertically up to meet the line at (4, 5 ) , then

f(4) = 5

The number of students from country C using mathematical operations is 113,115.

The mathematical operations are addition, subtraction, multiplication, and division.

These mathematical operations are used to determine the output value, given some input values.

The number of foreign students from country B = 138,000

Students from country B are 22% more than the number of students from country C.

Assume that the number of students from country C = 100%

Then the number of students from country B = 122% (100 + 22)

If the number of foreign students from country B is 138,000, which is 22% more, then the number of students from country C is as follows:

The number of students from country C = 113,115 (138,000/1.22)

Thus, the number of students from country C using mathematical operations is 113,115.

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This number is 22​% more than the number of students from country C.

Answer:

n = 4

Step-by-step explanation:

8 * n = 32

Solve for n

Divide each side by 8

8*n/8 = 32/8

n = 4

Answer:

26

Step-by-step explanation:

Comment

Irrational means that the number cannot be represented as a fraction. This question means that the square root itself is between 5 and 7. Be careful how you read the question.

That means you have to take the square root of the given number and see where it lands.

√13 = 3.61 which is not between 5 and 7

√6 is going to be even smaller. Not the answer

√25 = 5 The question says between. Not the answer.

√26 = 5.09 which is greater than 5 and and less than 7

The correct option is C, if f(x) has a domain only with positive values, the graph will be on the first and fourth quadrant.

We know that the domain of f(x) is only the set of positive real numbers. Now remember that the domain of a function is the set of the inputs of that function (the inputs are on the horizontal axis).

Then the graph of f(x) will only be on the positive side of the horizontal axis.  We know that the two quadrants that are on that region are the first quadrant and the fourth quadrant.

Then if f(x) has a domain only with positive values, the graph will be on the first and fourth quadrant, this means that the correct option is C.

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Answer:

first we find out how much is three dozens?

3 x 12 =36

now we multiply 26 and 36 to find out the number of cookies

26 x 36 = 936

936 cookies is your answer

Answer:

2.5

Step-by-step explanation:

Mu choices are 2.5 or 2.6 .

2.53 would be closer to 2.5 than to 2.6

The distances would be

2.50, 2.51. 2.52, 2.53, 254. 2.55, 2.56, 2.57, 2.58, 2.59, 2.60

Another name for 2.5 would be2.50 and another name for 2.6 would be 2.60.  Do you see from the list above that 2.53 would be closer to 2.50 than 2.60