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Examine the steps used to solve the equation.
-3y + 2/3 = 2y - 4

1. 2/3 = 5y - 4
2. 14/3 = 5y
3. (1/5) 14/3 = (1/5) 5y

Evaluate the steps used to solve the equation, and then describe each step.

Step 1. (add 3y to both sides, subtract 3y form both sides, add 2y to both sides, subtract 2y to both sides)

Step 2. (add 4 to both sides, subtract 4 from both sides, multiply both sides by 4, divide both sides by 4)

Step 3. (add 5 to both sides, add 1/5 to both sides, subtract 5 from both sides, multiply both sides by 1/5)

What is the solution to the equation? y = (14/5 , 14/15 , 7/8 , 70/3)

Answer:

2/3

Step-by-step explanation:

To know the fraction of men over women, we just need to divide the total number of men in the academy by the total number of women in the academy. So, we have that:

Fraction = men / women = 24 / 36 = 2/3

So the fraction we want to know is 2/3, that is, for every 2 men, there are 3 women in the academy.

Answer:

1. Subtract starting value minus final value.

2.divide that amount by the absolute value of the starting value.

3. Multiplt by 100 to get a percent decrease.

4. if the percentage is negative, it means there was an increase and not an decrease

Answer:

Step-by-step explanation:

A percent of increase (or decrease) is a ratio of the amount of increase (or decrease) to the original amount. To find the percent of increase (decrease): Determine the amount of increase (or decrease). Divide this result by the given original amount.

Answer:

Step-by-step explanation:

Let the no of cars be x and no of buses be y.

x + y = 60 -> y = 60 - x

6x + 30y = 600

with the available equations let us calculate the values of x and y.

6x + 30 * (60-x) = 600

6x + 1800 - 30x = 600

24x = 1200

x cars = 50

y buses = 10

maximum profit = 50 * 2.5 + 10 * 7.5 = $200

a) The objective function to maximize profit is: 2.5C + 7.5B using constraints 6C + 30B ≤ 600 and C + B ≤ 60. b) The parking lot should accept 50 cars and 10 buses to maximize profit. The maximum profit will be $200.

We need to set up a linear programming model to maximize profit from parking cars and buses.

A. Model Formulation:

Let C represent the number of cars and B represent the number of buses.

Objective Function: Maximize Profit = 2.5C + 7.5B

Constraints:

B. Solution:

First, we convert the inequalities to equations and solve:

We solve these equations simultaneously:

1. C + 5B = 100 (Equation 1)

2. C + B = 60 (Equation 2)

Subtract Equation 2 from Equation 1:

(C + 5B) - (C + B) = 100 - 60

⟶ 4B = 40 ⟶ B = 10

From Equation 2, we get:

C + 10 = 60 ⟶ C = 50

Maximum Profit Calculation:

Substituting C = 50 and B = 10 into the objective function:

Profit = 2.5(50) + 7.5(10) = 125 + 75 = 200

Therefore, to maximize profit, the attendant should accept 50 cars and 10 buses.

Maximum profit is $200.

Complete question:

The area of a parking lot is 600 square meters. A car requires 6 square meters. A bus requires 30 square meters. The attendant can handle only 60 vehicles. If a car is charged $2.50 and a bus $7.50. How many of each should be accepted to maximize Profit?

a. Set up for the solution of this Linear Programming (LP) problem.

b. Using part (a), how many of each should be accepted to maximize Profit? What is the maximum profit?

Answer:

the measure of angle x is 80

Step-by-step explanation:

Answer:

the answer is 3.71

Step-by-step explanation:

Answer:

3.71428571429

Step-by-step explanation:

Answer:

Row 2

Step-by-step explanation:

6+5+3+0+4=16

4+5+3+5+6=23

7+1+4+5+3=20

4+2+5+6+3=20

23 is bigger than all of those so it would be row two.

Answer:

Row 2

Explanation:

Answer: I believe the answer is 9 days.

Step-by-step explanation: 16 divided by 1.75 (1 and three-fourths) is equal to 9.143, which is only enough to feed him 9 full days.

Answer:

The answer to your question is 9 days.

Step-by-step explanation:

Data

Food needed = 1 3/4 cups

Total food = 16 cups

Number of days = ?

Process

1.- Convert the mixed fraction into an improper fraction

              1 3/4 = (4 + 3)/4 = 7/4

2.- Divide the total food by the food needed

              16/1 ÷ 7/4 = 64/7

-Simplify                     9        Quotient

                          7   64

                                 1          Remainder

3.- Mark can feed his dog 9 days and there will be 1/7 of the bag left.

Answer:

Exact Form:

x = 6 5 , 6

Decimal Form:

x = 1.2 , 6

Mixed Number Form:

x = 1  1 /5 , 6

Step-by-step explanation:

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

The value of x to this equation are as follows:

x = 6 or 6 /5

5x² - 36x + 36 = 0

-b ± √b² - 4ac / 2a

Using quadratic formula,

where,

a = 5

b = -36

c = 36

Therefore,

x = 36 ± √(-36)² - 4 × 5 × 36 / 2 × 5

x = 36 ± √1296 - 720 / 10

x = 36 ± √576 / 10

x = 36 ± 24 / 10

x = 36 + 24 / 10 or 36 - 24 / 10

x = 60 / 10  or 12 / 10

x = 6 or 6 / 5

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Answer:

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Answer: the surface area of the larger cylinder is 16 times that of the smaller cylinder.

Step-by-step explanation:

The formula for determining the total surface area of a cylinder is expressed as

Total surface area = 2πr² + 2πrh

Where

r represents the radius of the cylinder.

h represents the height of the cylinder.

π is a constant

Considering the larger cylinder,

radius = 8 cm

Height = 12 cm

Therefore,

Total surface area = (2 × π × 8²) + (2 × π × 8 × 12)

= 128π + 192π = 320π

Considering the smaller cylinder,

Total surface area = 56π

radius = 8/4 = 2cm

Height = 12/4 = 3 cm

Therefore,

Total surface area = (2 × π × 2²) + (2 × π × 2 × 3)

= 8π + 12π = 20π

Ratio of the surface area of the larger cylinder to the smaller cylinder is

320π/20π = 16

Answer:

After 10 seconds

Step-by-step explanation:

In this problem, the height of the object after t seconds is described by the function

[tex]h(t)=-16t^2+144t+160[/tex]

where

160 ft is the initial height of the object at t = 0

+144 ft/s is the initial velocity

[tex]-32 ft/s^2[/tex] is the acceleration due to gravity (downward)

Here we want to find the time at which the object hits the ground, so the time t at which

[tex]h(t)=0[/tex]

Therefore we can write

[tex]-16t^2+144t+160 =0[/tex]

Simplifying (dividing each term by 16), we get

[tex]-t^2+9t+10=0[/tex]

This is a second-order equation in the form

[tex]ax^2+bx+c=0[/tex]

Which has solutions given by the formula

[tex]t_{1,2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex] (2)

Here we have:

a = -1

b = 9

c = 10

Substituting into (2) we find the solutions:

[tex]t_{1,2}=\frac{-9\pm \sqrt{9^2-4(-1)(10)}}{2(-1)}=\frac{-9 \pm 11}{-2}[/tex]

Which gives:

[tex]t_1=10 s\\t_2 =-1 s[/tex]

Since time cannot be negative, the only solution is

t = 10 seconds

There are 120 possible combinations of phone models, colors, and calling plans.

To calculate the number of possible combinations of phone models, colors, and calling plans, we need to multiply the number of choices for each category together. In this case, there are 4 phone models, 6 colors, and 5 calling plans. So the total number of combinations is 4 x 6 x 5 = 120.

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Answer:

11

Step-by-step explanation:

8.7A+10=105.7

8.7A=95.7

A=11

The solution set is where the black dot is located, which is on the number 5.

The solution would be 5

Answer: -2

Step-by-step explanation:

Because I know

Answer: it will take the larger hose 37.5 minutes to fill the pool.

Step-by-step explanation:

Let t represent the number of minutes it will take the larger hose to fill the pool by itself. It means that the rate at which larger hose fills the pool per minute is 1/t

It takes the smaller hose twice as long to fill the swimming pool as it does the larger hose. It means that the number of hours it takes smaller hose to fill the pool is 2t and it fills it alone, then the rate at which it fills the pool per minute is 1/2t

By working together, they would work simultaneously and their individual rates are additive. It takes both hoses working together 25 minutes to fill the pool. It means that the rate at which they fill the pool together per minute is 1/25. Therefore,

1/t + 1/2t = 1/25

3/2t = 1/25

Cross multiplying, it becomes

2t = 3 × 25 = 75

t = 75/2 = 37.5 minutes

Final answer:

To find the time it takes for the larger hose to fill the pool alone, we set up an equation based on their combined work rate and solve for the larger hose's time, finding that it would take 75 minutes.

Explanation:

The question is about determining how long it will take for the larger hose alone to fill the pool, given that it takes twice as long for a smaller hose to complete the same task, and together they can fill the pool in 25 minutes. To solve this problem, let's denote the time it takes for the larger hose to fill the pool by itself as x minutes. Therefore, the smaller hose takes 2x minutes to fill the pool by itself.

Since the problem involves rates of work, we can use the formula Work done = Rate × Time. The rate can be considered as the portion of the pool filled per minute. So, the larger hose's rate is 1/x and the smaller hose's rate is 1/(2x). Working together, their combined rate is 1/25 of the pool per minute, following the equation 1/x + 1/(2x) = 1/25.

By solving this equation: 2/2x + 1/2x = 1/25 ⇒ 3/(2x) = 1/25 ⇒ x = 75. Therefore, it would take the larger hose 75 minutes to fill the pool by itself.

Answer: 130 degree

Step-by-step explanation:

Given that

The distance from

Dallas to Charleston = 980 miles Charleston to Indianapolis = 595 miles,

Indianapolis to Dallas is 764 mies.

If Dallas and Charleston lie on the same latitude, find the bearing from Charleston to Indianapolis.

Let us use cosine formula to find the angle at Charleston

764^2 = 980^2+595^2-2(980)(595)cosØ

583696 = 1314425-1166200cosØ

-1166200cosØ = -730729

CosØ = 0.6266

Ø = 51.2

Let us also calculate the angle at Indianapolis by using sine rule

980/sinI = 764/sin 51.2

Reciprocal both sides

SinI/980 = sin 51.2/764

Sin I = 980 × sin52.1/764

Sin I = 0.9996

I = 88.5 degree

The bearing = 270 - ( 51.2 + 88.5)

= 270 - 140

= 130 degree.

In this exercise we have to use the knowledge of triangles to calculate the angle of this geometric figure, in this way we can say that:

130 degree

Given that the distance from dallas to Charleston and Charleston to Indianapolis and Indianapolis to Dallas, we can use the the cosine formula to find the angle at Charleston, so we have:

[tex]764^2 = 980^2+595^2-2(980)(595)cos\phi\\583696 = 1314425-1166200cos\phi\\-1166200cos\phi = -730729\\Cos\phi = 0.6266\\\phi = 51.2[/tex]

Let us also calculate the angle at Indianapolis by using sine rule:

[tex]980/sin\theta = 764/sin (51.2)\\Sin\theta/980 = sin 51.2/764\\Sin\theta = 980 * sin52.1/764\\Sin \theta = 0.9996\\\theta = 88.5 degree = 270 - ( 51.2 + 88.5)\\= 270 - 140\\= 130 degree.[/tex]

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Answer:

The volume in terms of π is 144 ft³

The volume rounded to the nearest tenth is 452.4 ft³

Step-by-step explanation:

The formula of the volume of a cone is V = [tex]\frac{1}{3}[/tex] π r² h , where r is its radius and h is its height

The formula of the area of a circle is A = π r²

∵ The area of the base of the cone is 36π ft²

- Equate the formula of the area of the circle by 36π to find r

∵ πr² = 36π

- Divide both sides by π

∴ r² = 36

- Take √ to both sides

∴ r = 6 ft

∵ The height of the cone is equal to twice the radius

∵ The radius of the cone is 6 ft

- Multiply 6 by 2 to find the height

∴ h = 2(6) = 12 ft

∴ The height of the cone is 12 ft

Substitute the values of h and r in the formula of the volume of the cone to find it

∵ V = [tex]\frac{1}{3}[/tex] π(6)²(12)

∴ V = 144 π ft³

∴ V = 452.3893421 ft³

- Round it to the nearest tenth

∴ V = 452.4 ft³

Answer:

432 square meters

Step-by-step explanation:

The lateral area means the area that's not the bases. We have to add up all the lateral faces.

2(big rectangle area) + 2(small rectangle area) = total lateral area

2(144) + 2(72) = total lateral area

total lateral area = 432 square meters

Answer:

432

Step-by-step explanation:

432

Final answer:

To write the expression 6(-5r-4)-2(r-7s-3) in standard form, distribute the numbers outside the parentheses across the terms within and combine like terms to get -32r + 14s - 18.

Explanation:

To write the expression 6(-5r-4)-2(r-7s-3) in standard form, we must distribute the numbers outside the parentheses to each term inside the parentheses and then combine like terms.

Distribute the 6: 6 × (-5r) = -30r and 6 × (-4) = -24, giving us -30r - 24.

Distribute the -2: -2 × r = -2r, -2 × (-7s) = +14s and -2 × (-3) = +6, giving us -2r + 14s + 6.

Combine the two resulting expressions: -30r - 24 - 2r + 14s + 6.

Combine like terms: The terms -30r and -2r combine to -32r, and the constants -24 and +6 combine to -18.

The standard form of the expression is -32r + 14s - 18.

Check the answer to see if it is reasonable.

Answer:

3 ft by 4/3 feet.

Step-by-step explanation:

We have been given that a card is 9 inches by 4 inches. A printing shop will enlarge it so that the longer side is any lengths up to 3 ft. We are asked to find the dimensions of biggest enlargement.

We will use proportions to solve our given problem.

[tex]\frac{\text{Card width}}{\text{Card length}}=\frac{\text{Enlarged width}}{\text{Enlarged length}}[/tex]

Upon substituting our given values, we will get:

[tex]\frac{\text{4 inches}}{9 \text{ inches}}=\frac{\text{Enlarged width}}{\text{3 ft}}[/tex]

[tex]\frac{4}{9}=\frac{\text{Enlarged width}}{\text{3 ft}}[/tex]

[tex]\frac{4}{9}\times \text{3 ft}=\frac{\text{Enlarged width}}{\text{3 ft}}\times \text{3 ft}[/tex]

[tex]\frac{4}{3}\times \text{ft}=\text{Enlarged width}[/tex]

Therefore, the dimensions of the biggest enlargement  would be 3 ft by 4/3 feet.

To convert the word form of the time to decimal form, add 10.00 and 0.62 to get the final number representation of 10.62 seconds.

To write the time of ten and sixty-two hundredths seconds as a number, we need to convert the word form into decimal form. The word form tells us that there are ten whole seconds and sixty-two hundredths of a second. To convert this to decimal form, we write 10 as 10.00 and 62 hundredths as 0.62. Then, we add the two decimal numbers together to get the final result: 10.00 + 0.62 = 10.62. Therefore, the number representation of the given time is 10.62 seconds.

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Answer:

Alex has 110 shells

Benji has 132 shells

Carmen has 66 shells

Step-by-step explanation:

In this question, we are tasked with calculating the number of shells each of the friends have.

We proceed as follows;

Since Alex is the linking point between the other two friends, we say that let the number of shells Alex has be A

Now, Benji has 20% more shells

This mathematically means that the number of shells owned by Benji = (20% × A) + A = 0.2A + A =  1.2A

Carmen has 40% fewer shells than Alex;

Mathematically, this means that the number of shells owned by Carmen is A - (40% × A) = A - 0.4A = 0.6A

To find A, we simply add all together and equate to 308

Mathematically, we have;

A + 1.2A + 0.6A = 308

2.8A = 308

Divide both sides by 2.8

A = 308/2.8

A = 110

This means Alex has 110 shells

Benji has 1.2A = 1.2 × 110 = 132 shells

Carmen has 0.6A = 0.6 × 110 = 66 shells

Answer: 1.6x + 1.75y ≤ 10

Step-by-step explanation:

Let x represent the number of pounds of strawberries that Joey can buy.

Let y represent the number of pounds of raspberries that Joey can buy.

Strawberries cost $1.60 per pound and raspberries cost $1.75 per pound. It means that the cost of x pounds of strawberry and y pounds of raspberry is expressed as

1.6x + 1.75y

if she only has $10 to spend on berries, then the inequality that can be used to represent the situation is

1.6x + 1.75y ≤ 10

Answer:

b and d

Step-by-step explanation:

Answer:

7.5 gallons

Step-by-step explanation:

2^-3= 0.125

0.125*60= 7.5

Final answer:

The gas pump fills 7.5 gallons of gasoline in one minute.

Explanation:

If a gas pump fills 2-3 gallon of gasoline per second, we first need to understand how much that is in gallons. 2-3 is the same as 1/23 or 1/8. Therefore, the pump fills 1/8 gallon per second.

To find out how many gallons the pump fills in one minute, we multiply the amount filled per second by the number of seconds in a minute:

Gallons per minute = gallons per second × seconds per minute

Gallons per minute = 1/8 gallon/second × 60 seconds/minute

Gallons per minute = 60/8 gallons

By reducing this fraction, we get:

Gallons per minute = 7.5 gallons

Thus, the gas pump fills 7.5 gallons of gasoline in one minute.

Answer:

8 × 7

Step-by-step explanation:

(4 × 2) × 7

We can multiply what is inside the parentheses

(8) × 7

Answer:

8*7

Step-by-step explanation:

Multiply what is inside the parentheses first, (PEMDAS)

(4*2)*7

8*7

Hope this helps! :)

Answer:

Each Exterior Angle = (360 degrees) ÷ (Number of Sides)

Each Exterior Angle = 360 / 30

Each Exterior Angle = 12 degrees

Step-by-step explanation:

The measure of each exterior angle of a regular 30-gon will be 12°.

Based on the information, it should be noted that the value of the total angles will be 360°.

Therefore, the measure of each exterior angle of a regular 30-gon will be:

= 360/30

= 12°

Therefore, the measure of each exterior angle of a regular 30-gon is 12°.

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Answer: 1. C

2. B

Step-by-step explanation:)

The rotation rule describes the rotation about the origin in mathematics. The new coordinates of a point (x, y) after rotation can be determined using trigonometric functions. The angle of rotation can be calculated using the arc length formula.

In mathematics, the rule that describes rotation about the origin is referred to as the rotation rule or the radian rule. When a point (x, y) is rotated about the origin, the new coordinates (x', y') can be determined using the following formulas:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

The angle of rotation can be calculated using the arc length formula:

Angle = (Arc Length / Circle Circumference) * 360 degrees

For example, if the arc length separating the two hands of a clock is 1.0 meter and the radius of the clock is 0.70 meters, the angle of rotation can be calculated as follows:

Angle = (1.0 / (2 * pi * 0.70)) * 360 = 81 degrees