a furniture store sells 48 tables for every 60 chairs in a given week. what is the unit rate of tables to chairs? reduce the unit rate.

The bus must be used 30 times in a month for the total monthly cost without the discount pass to be the same as the total monthly cost with the discount pass.

The mathematical problem deals with determining the number of times one must take a bus ride for a monthly discount pass to be as cost-effective as individual fare payments. To solve it, we must set up an equation based on the cost of bus rides. Let's denote the number of bus rides as 'n'.

Without the pass, each ride is $1.25, so n rides would cost 1.25n dollars.

With the pass, each ride is $0.75 and you also need to pay $15 for the monthly pass, so n rides would cost 0.75n + 15 dollars.

To find out the break-even point, we set these two expressions for the total cost equal to each other:

1.25n = 0.75n + 15

Solving this equation gives us:

0.5n = 15, n = 15/0.5 = 30.

Therefore, the bus must be used 30 times in a month for the total monthly cost without the discount pass to be the same as the total monthly cost with the discount pass.

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Answer:

3/2 (or 1 1/2)

Step-by-step explanation:

-4 1/6 + 5 2/3​   (express as improper fractions)

= -25/6 + 17/3  (convert fractions common denominator i.e 6)

= -25/6 + (17/3)(2/2)

= -25/6 + (17 x 2)/6

= -25/6 + 34/6

= 9/6

= 3/2

=1 1/2

Answer:

-4 = h(x)

Step-by-step explanation:

[tex]6 - 10 = -4[/tex]

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Answer:

D

Step-by-step explanation:

[tex]\frac{f(x)}{g(x)}[/tex]

= [tex]\frac{2x+4}{2x^2+4x}[/tex]

Factor out 2 on the numerator and 2x on the denominator.

= [tex]\frac{2(x+2)}{2x(x+2)}[/tex]

Cancel the factor (x + 2) on the numerator/ denominator

= [tex]\frac{2}{2x}[/tex] ← cancel the 2 on numerator/ denominator

= [tex]\frac{1}{x}[/tex] : x ≠ 0

Answer:

Step-by-step explanation:

Whole, integer, rational, real

Answer:

The distance (d) between two points (x1,y1) and (x2,y2) is given by the formula

d = √  ((X2-X1)2+(Y2-Y1)2)

d = √ (5-2)2+(3-8)2

d = √ ((3)2+(-5)2)

d = √ (9+25)

d = √ 34

The distance between the points is 5.8309518948453

The midpoint of two points is given by the formula

Midpoint= ((X1+X2)/2,(Y1+Y2)/2)

Find the x value of the midpoint

Xm=(X1+X2)/2

Xm=(2+5)/2=3.5

Find the Y value of the midpoint

Ym=(Y1+Y2)/2

Ym=(8+3)/2=5.5

The midpoint is: (3.5,5.5)

Graphing the two points, midpoint and distance

P1 (2,8)

P2 (5,3)

Midpoint (3.5,5.5)

The length of the black line is the distance between the points (5.8309518948453)

Find the slope of the line connecting the two points

Slope =  (Y2-Y1)  =  (3-8)  =  (-5)  = -1.66666666666667

(X2-X1) (5-2) (3)

Find the equation of the line passing through the two points

The general equation for a straight line is

y = mx + b

Where m represents the slope of the line which we found in the previous step to be -1.66666666666667

y = -1.67x + b

We substitute x and y for the values from one of our points (2,8)

8 = -1.67×2 + b

8 = -3.33 + b

8--3.33 = b

11.33 = b

Knowing both b and m, we can contruct the equation of the line

y= -1.67x+ 11.33

X and Y intercepts

The x-intercept is a point on the graph where y is zero

Using the equation we found in the previous step and substituting zero for y

y= -1.67x+ 11.33

0= -1.67x+ 11.33

1.67x= 11.33

x= 11.33/1.67 = 6.80

The x intercept for this straight line is 6.80

The y-intercept is a point on the graph where x is zero

Using the equation we found in the previous step and substituting zero for x

y= -1.67×0+ 11.33

y= 11.33

The y intercept for this straight line is 6.80

References

refernce image showing the distance between two points on the xy plane

Step-by-step explanation:

The distance between the two points will be √34. The correct option is c

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

The distance (d) between two points (x₁,y₁) and (x₂,y₂) is given by the formula:-

d = √  ((X₂-X₁)²+(Y₂-Y₁)²)

d = √ (5-2)²+(3-8)²

d = √ ((3)²+(-5)²)

d = √ (9+25)

d = √ 34

Therefore, the distance between the two points will be √34. The correct option is c

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Answer:

12

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

81 - 49y^2 = (9 - 7y)(9 + 7y)

FOIL the equation.

(9 - 7y)(9 + 7y)

81 + 63y - 63y - 49y^2

81 - 49y^2

The correct answer is option A. 81 - 49y².

It exists easily identified by looking at the numbers, the number shows a perfect square, and the variable y exists also squared

That is 9² = 81 and 7² = 49

Also, the sign in-between them must be a negative sign, when the expression consists of the above, then it provides a different square.

81 - 49y²

9² - 7²y²

(9 - 7y)(9 +7y)

Opening back the parenthesis to verify our answer

(9 - 7y)(9 +7y)

9(9+7y) -7y(9+7y)

81 +63y -63y -49y²

81 - 49y²

Therefore, the correct answer is option A. 81 - 49y².

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Answer:

$157.89

Step-by-step explanation:

The original price is x

you took away 5%, making the new price 95% of x, or .95x

Put it in an equation

.95x = 150

x = 150/.95

x = 30/.19

x = 3000/19

x=157 17/19

x is about $157.89

The amount Nat's paid at the club before the discount is $157.90

Given:

Total bill including discount = $150

Discount = $5

Amount before discount = x

Total bill including discount = Amount before discount - (Discount × Amount before discount)

150 = x - (5% × x)

150 = x - (0.05 × x)

150 = x - 0.05x

150 = 0.95x

divide both sides by 0.95

x = 150 / 0.95

x = 157.89473684210

Approximately,

x = $157.90

Therefore, amount Nat's paid at the club before the discount is $157.90

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Assuming one salad requires 1 cup of tomatoes, Karl can make 5 salads as shown by the division equation 5 cups / 1 salad = 5 salads. The multiplication equation 5 salads x 1 cup = 5 cups demonstrates the amount of tomatoes needed for 5 salads.

To properly answer this question, we first need to know the number of cups of tomatoes required to make one salad. However, if we suppose that one salad requires 1 cup of tomatoes, then the division equation is 5 cups / 1 salad = 5 salads. This equation illustrates that Karl can make 5 salads with the amount of tomatoes he has.

On the other hand, the multiplication equation would be 5 salads x 1 cup = 5 cups. This equation pertains to how many cups of tomatoes are needed to make 5 salads. Please note that these equations assume that 1 cup of tomatoes is needed for a single salad, but the proportions may vary depending on the actual recipe.

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Karl can make 5 salads using 5 cups of tomatoes.

Assuming Karl makes salads that require 1 cup of tomatoes each, we can determine the number of salads he can make using division:

Number of salads = Total tomatoes (cups) / Tomatoes per salad (cups)

Number of salads = 5 cups / 1 cup/salad

Therefore, Karl can make 5 salads using 5 cups of tomatoes.

A multiplication equation can be used to express the relationship between the number of salads, the number of tomatoes per salad, and the total number of tomatoes:

Total tomatoes (cups) = Number of salads × Tomatoes per salad (cups)

5 cups = 5 salads × 1 cup/salad

Both equations demonstrate the same relationship between the number of salads, the number of tomatoes per salad, and the total number of tomatoes.

Answer:

8.) x = 5, x=-12

9.)x = 5, x = -8

10.)x = -1/5, x = -2

Hope I helped :)

Answer:

10. -2, -⅕ = x

9. -8, 5 = x

8. -12, 5 = x

7. -5, 6 = x

Step-by-step explanation:

10. [tex]5{x}^{2} + 11x + 2 = 0 \\ \\ (5{x}^{2} + x) + (10x + 2) = 0 \\ x(5x + 1) + 2(5x + 1) \\ \\ (x + 2)(5x + 1) = 0 \\ \\ -2, \: - \frac{1}{5} = x[/tex]

9.

[tex]2{x}^{2} + 6x - 80 = 0 \\ \\ (2{x}^{2} + 16x) - (10x - 80) = 0 \\ 2x(x + 8) -10(x + 8) = 0 \\ \\ (x + 8)(2x - 10) = 0 \\ \\ -8, \: 5 = x[/tex]

8.

[tex] {x}^{2} + 8x - 65 = x - 5 \:→ {x}^{2} + 7x - 60 \\ \\ ({x}^{2} - 5x) + (12x - 60) \\ x(x - 5) + 12(x - 5) \\ \\ (x + 12)(x - 5) = 0 \\ \\ 5, \: -12 = x[/tex]

7.

[tex] {x}^{2} = x + 30 → - {x}^{2} + x + 30 \\ \\ (-{x}^{2} - 5x) + (6x + 30) \\ -x(x + 5) + 6(x + 5) \\ \\ -(x - 6)(x + 5) = 0 \\ \\ -5, \: 6 = x[/tex]

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The lines that are parallel to each other are as follows;

When parallel lines are cut by a transversal, angles relationship are formed.

This angle relationship includes corresponding angles, alternate angles, vertical angles and many more.

Therefore, the lines that are parallel are as follows;

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Answer:

20 children and 20 adults

Step-by-step explanation:

20 + 20 = 40

Answer:

20 adults 20 children

Step-by-step explanation:

if theres the same amount of children and adults just do 40/2

Answer:

6.59

Step-by-step explanation:

52.72 ÷ 8 = 6.59

So the answer is 6.59

Answer:

[tex]y> \frac{2}{3}x+3[/tex]

Step-by-step explanation:

we have the points

(-3,1) and (0,3)

step 1

Find the slope m of the line

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values

[tex]m=\frac{3-1}{0+3}[/tex]

[tex]m=\frac{2}{3}[/tex]

step 2

Find the equation of the line in slope intercept form

[tex]y=mx+b[/tex]

we have

[tex]m=\frac{2}{3}[/tex]

[tex]b=3[/tex] ----> the y-intercept is the point (0,3)

substitute the values

[tex]y=\frac{2}{3}x+3[/tex]

step 3

Find the equation of the inequality

we know that

The slope is positive

Everything to the left of the line is shaded ( The inequality is of the form y > ax+b or y ≥ ax+b)

Is a dashed line (The inequality is of the form y > ax+ b or y < ax+b)

therefore

The equation of the inequality is of the form y > ax+b

The inequality is

[tex]y> \frac{2}{3}x+3[/tex]

see the attached figure to better understand the problem

Answer:

c

Step-by-step explanation:

Graph C of ordered pairs shows a proportional relationship.

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value time the other.

A proportional relationship is one where there is multiplying or dividing between the two numbers. A linear relationship can be a proportional one (for example y=3x is proportional), but usually, a linear equation has a proportional component plus some constant number (for example y=3x +4).

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Answer:

(4, -1)

Step-by-step explanation:

Since it takes negative two to get from 3 to 1, you also have to deduct 2 from 1, which is -1 [y-coordinate]. Now, since it takes six to get from -8 to -2, you also have to add 6 to -2, which is 4 [x-coordinate].

So, point B is (4, -1).

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Answer:

<1 ,1>..., square root of two

Step-by-step explanation:

Component of vector PQ...,

; Q - P...where you subtract the x coordinate of Q by the x coordinate of P and the same for the y coordinate

; <(6-5),(9-8)>

; < 1,1 >

And the magnitude of PQ...,

;square root of( 1^2 + 1^2 )

;square root of 2

Final answer:

The component form of vector PQ is <1, 1>, and the magnitude is the square root of 2, thus the correct answer is <1, 1>, square root of 2.

Explanation:

To find the component form and magnitude of vector PQ, we calculate the difference in the x-coordinates and the y-coordinates of points P and Q. The component form of a vector is obtained by subtracting the coordinates of the initial point from the coordinates of the terminal point. In this case, the initial point is P(5, 8) and the terminal point is Q(6, 9).

The component form of vector PQ is therefore:

Vector PQ = (Qx - Px, Qy - Py)

Vector PQ = (6 - 5, 9 - 8)

Vector PQ = <1, 1>

Next, to find the magnitude of vector PQ, we use the Pythagorean theorem, which is the square root of the sum of the squares of the components:

Magnitude of PQ = √(1^2 + 1^2)

Magnitude of PQ = √(2)

Magnitude of PQ = √2

Therefore, the correct answer is <1, 1>, √2.

Answer:

A

Step-by-step explanation:

The general formula for the volume of a right cone is as follows (also see attached):

V = (1/3) π r² h; where r = radius of base and h = height

In this case, it is given that r = x

also given :

height = 2 (base radius)

or

h = 2x.

Hence the formula becomes:

V = (1/3) π r² h

V = (1/3) π x² (2x)

V = (2/3) π x³  (answer A)

3 is the correct answer bebe :)

6*3=18

18+4=22

Mean absolute deviation of the following would be the best measure of center. Option A is correct.

A boxplot is a visual representation of a data set's dispersion and centers.

The interquartile range and the mean of the data set are two examples of spread measures. The mean, average, and median are examples of center measures.

A box plot is a graph that allows us to readily compare the median number of teeth in mammals and reptiles.

The scatter plot below shows how many visits to fast food establishments each of his classmates made throughout the previous week.

The best indicator of the center would be the mean absolute deviation of the following.

Hence option A is correct.

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Answer:

11

Step-by-step explanation:

Final answer:

Reading decimal numbers requires understanding the places to the right of the decimal point: tenths, hundredths, thousandths, etc. The least significant place value—which in 0.604 is the thousandth place—helps in reading, rounding, and performing operations like moving the decimal point or using scientific notation.

Explanation:

Understanding how to read decimal numbers is important in mathematics. When reading the digits to the right of the decimal point, the name of each place value position helps you determine the value of the digit. For example, in the number 0.604, the digit '6' is in the tenth place, which means it represents six tenths, the digit '0' is in the hundredth place, acting as a placeholder, and the '4' is in the thousandth place, representing four thousandths. Similarly, in 1.604, the '1' is in the ones place, the '6' is in the tenth place, the '0' is a placeholder in the hundredth place, and the '4' is in the thousandth place.

Knowing the least place value is also important when rounding or when dealing with operations that affect the decimal point. For instance, if we need to move the decimal point or deal with scientific notation, recognizing the least significant digit's place value informs us how to maintain numerical accuracy. If you understand that the least significant digit in 1.604 is the '4' in the thousandth place, you would keep the decimal up to three places if you were to round or shift the decimal in calculations.

Answer:

229

Step-by-step explanation:

100+40+6+80+3

ok why is your math so easy

Answer:

34

Step-by-step explanation:

Substitute the given values for a and b into the expression

7(4) - 2(- 3) = 28 - (- 6) = 28 + 6 = 34

Answer:

2 cubic centimeters per minute

Step-by-step explanation:

8 cubic centimeters filled per 4 minutes

divide 8 by 4 = 2

2 cubic centimeters per minute

Answer: 2 cubic centimeters

Step-by-step explanation:

Given : As lucia fills her fish tank, she notices that it fills 8 cubic centimeters of water in 4 minutes.

i.e. Time taken to fills 8 cubic centimeters of water = 4 minutes

By UNITARY METHOD, we have

Amount of water it fills in 1 minute (i.e. Unit rate) = [tex]\dfrac{\text{8 cubic centimeters }}{\text{4 minutes}}[/tex]

= [tex]\dfrac{8}{4}=2[/tex] cubic centimeters

Therefore, it fills 2 cubic centimeters in 1 minute.

Hence, the correct answer is 2 cubic centimeters.

Answer

2

Step-by-step explanation:

as -6+12-4

Answer: A, 17 inch

The box is 21 inches long, anything longer and it won't fit. 17 inch is the only thing shorter than 21.

Answer:

the green means its right at the top

Step-by-step explanation: