A game stop membership cost $20 and includes one game A month for five dollars. Nonmembers can get one more game a month for seven dollars. What a system of a simulation in linear equations to use this information to decide whether to become a

Answer:

Option E is the correct answer (As the)

Step-by-step explanation:

Option A indicates that Joan, for 18 years, was the former chair; it is inappropriate to think that she would be attending meetings while she was the former chair. The sentence indicates that Joan served for 18 years as the chair lady, and during this time she attended meetings. Thus, option E is clearer and precise in its meaning than option A.

Answer:

179.2km

Step-by-step explanation:

The distance from their house to the beach is 448km. Now they have to drive to and from the beach. The total distance traveled by the family is 448km + 448km.

This is equal to 896km. Now we have 5 adults who took their turns to drive and they drove the same distance. The total distance traveled by each adult will be 896/5 = 179.2km

Hence, each adult in the family drove a distance of 179.2km

Answer:

66500

Step-by-step explanation:

114000:total budget

12:total bungalows

9500:budget for each bungalow

7: unfinished bungalows

66500: remaining budget for unfinished bungalows

hope this helped and good luck :D

The remaining budget for unfinished bungalows is $66500

The four basic arithmetic operations in Maths, for all real numbers, are: Addition (Finding the Sum; '+') Subtraction (Finding the difference; '-') Multiplication (Finding the product; '×') Division (Finding the quotient; '÷')

Given that, A total of $114,000 will be evenly spent to build 12 Bungalows, the first 5 bungalows have been completed and paid. We need to find the amount available for the remaining bungalows.

Amount used in each bungalow;

114000/12 = $9500

Therefore, each bungalow will need $9500

Amount used = $9500 × 5 = $47500

Amount remaining for remaining bungalows = $114,000 - $47500 = $66500

Hence, $66500 is remaining budget for unfinished bungalows.

For more references on arithmetical operations, click;

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System of inequalities are,  [tex]x+y<10[/tex]  and [tex]5x+8y\geq 56[/tex]

Let us consider, He does house cleaning job for x hours and sales job for y hours.

Since, he can work a total of not more than 10 hours each week at  two jobs.

So, inequality are,   [tex]x+y<10[/tex]

Since, house cleaning job pays $5. per hour and  sales job pays $8 per hours.

Thus, Total earn = 5x + 8y

But he need to earn at least $56 each week

So, inequality are , [tex]5x+8y\geq 56[/tex]

Learn more:

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Final answer:

The variables x and y represent the hours worked at the house cleaning and sales jobs, respectively. The system of inequalities x + y ≤ 10, 5x + 8y ≥ 56, and x ≥ 0, y ≥ 0 reflects the constraints on work hours and minimum earnings.

Explanation:

To solve the problem, we need to define two variables representing the hours worked at each job:

Let x be the number of hours worked at the house cleaning job.

Let y be the number of hours worked at the sales job.

Given the conditions of the problem, we can formulate the following system of inequalities:

The total working hours from both jobs cannot exceed 10 hours per week: x + y ≤ 10.

The total earnings must be at least $56 to pay bills: 5x + 8y ≥ 56.

The number of working hours cannot be negative: x ≥ 0 and y ≥ 0.

This system of inequalities represents the constraints on the number of hours you can work at each job and the minimum earnings required to pay your bills.

Answer:

[tex]2\frac{1}{4} inches.[/tex]

Step-by-step explanation:

Hi,

We see the plot line below, which shows that three crosses above [tex]\frac{3}{4} - inch[/tex] buttons, that means we have three such buttons available with us.

To find their total lengths, we have two methods:

[tex]\frac{3}{4} \times 3\\ = \frac{3 \times 3}{4}\\= \frac{9}{4}[/tex]

changing this improper fraction into a mixed fraction: [tex]2\frac{1}{4} inches.[/tex] will be the total length of three buttons lined up.

Answer:

a.) 10

b.) -2

c.) 6

d.) y = 6

e.) T = π

f.) y = -6cos(2t) + 4

Step-by-step explanation:

a.) Max value is the highest value in the y-axis. It peaks at y=10

b.) Min value is the lowest value in the y-axis. Peaks at y=-2

c.) Amplitude is how high the peak is from the midpoint. It could be found by taking the average of the peaks. (10 - (-2))/2 = 6

d.) y = 6

e.) T = π

f.) General equation for a sinusoidal wave is

y = Acos(ωt - Ф) + k

y = Acos((2π/T)t - Ф) + k

The graph started at it's min, so the amplitude must had been fliped upsidedown because it normally starts at the max. Therefore I must make my equation negative to flip it.

y = -Acos((2π/T)t - Ф) + k

y = -(6)cos((2π/(π))t - (0)) + (4)

y = -6cos(2t) + 4

Answer:

The maximum revenue is $1,20,125 that occurs when the unit price is $155.

Step-by-step explanation:

The revenue function is given as:

[tex]R(p) = -5p^2 + 1550p[/tex]

where p is unit price in dollars.

First, we differentiate R(p) with respect to p, to get,

[tex]\dfrac{d(R(p))}{dp} = \dfrac{d(-5p^2 + 1550p)}{dp} = -10p + 1550[/tex]

Equating the first derivative to zero, we get,

[tex]\dfrac{d(R(p))}{dp} = 0\\\\-10p + 1550 = 0\\\\p = \dfrac{-1550}{-10} = 155[/tex]

Again differentiation R(p), with respect to p, we get,

[tex]\dfrac{d^2(R(p))}{dp^2} = -10[/tex]

At p = 155

[tex]\dfrac{d^2(R(p))}{dp^2} < 0[/tex]

Thus by double derivative test, maxima occurs at p = 155 for R(p).

Thus, maximum revenue occurs when p = $155.

Maximum revenue

[tex]R(155) = -5(155)^2 + 1550(155) = 120125[/tex]

Thus, maximum revenue is $120125 that occurs when the unit price is $155.

Answer:

(1) -0.833

(2) 0.80

(3) 0.70

(4) 390

(5) 90

(7) 48

Step-by-step explanation:

Given:

E (X) = 100, E (Y) = 120, E (Z) = 130

Var (X) = 9, Var (Y) = 16, Var (Z) = 25

Cov (X, Y) = -10, Cov (X, Z) = 12, Cov (Y, Z) = 14

The formulas used for correlation is:

[tex]Corr (A, B) = \frac{Cov (A, B)}{\sqrt{Var (A)\times Var(B)}} \\[/tex]

(1)

Compute the value of Corr (X, Y)-

[tex]Corr (X, Y) = \frac{Cov (X, Y)}{\sqrt{Var (X)\times Var(Y)}} \\=\frac{-10}{\sqrt{9\times16}} \\=-0.833[/tex]

(2)

Compute the value of Corr (X, Z)-

[tex]Corr (X, Z) = \frac{Cov (X, Z)}{\sqrt{Var (X)\times Var(Z)}} \\=\frac{12}{\sqrt{9\times25}} \\=0.80[/tex]

(3)

Compute the value of Corr (Y, Z)-

[tex]Corr (Y, Z) = \frac{Cov (Y, Z)}{\sqrt{Var (Y)\times Var(Z)}} \\=\frac{14}{\sqrt{16\times25}} \\=0.70[/tex]

(4)

Compute the value of E (3X+4Y-3Z)-

[tex]E(3X+4Y-3Z)=3E(X)+4E(Y)-3E(Z)\\=(3\times100)+(4\times120)-(3\times130)\\=390[/tex]

(5)

Compute the value of Var (3X-3Z)-

[tex]Var (3X-3Z)=[(3)^{2}\times Var(X)]+[(-3)^{2}\times Var (Z)]+(2\times3\times-3\times Cov(X, Z)]\\=(9\times9)+(9\times25)-(18\times12)\\=90[/tex]

(6)

Compute the value of Var (3X+4Y-3Z)-

[tex]Var (3X+4Y-3Z)=[(3)^{2}\times Var(X)]+[(4)^{2}\times Var(Y)]+[(-3)^{2}\times Var (Z)]+[(2\times3\times4\times Cov(X, Y)]+[(2\times3\times-3\times Cov(X, Z)]+[(2\times4\times-3\times Cov(Y, Z)]\\=(9\times9)+(16\times16)+(9\times25)+(24\times-10)-(18\times12)-(24\times14)\\=-230[/tex]

But this is not possible as variance is a square of terms.

(7)

Compute the value of Cov (3X, 2Y+3Z)-

[tex]Cov(3X, 2Y+3Z)=Cov(3X,2Y)+Cov(3X, 3Z)\\=6Cov(X, Y)+9Cov(X,Z)\\=(6\times-10)+(9\times12)\\=48[/tex]

The correct answers to the given set of data are:

This refers to the measurement of spread between numbers which can be found in a set of data.

Hence, to compute the variance and covariance

Using the variance formula we can see that the given sets of data are:

Read more about variance here:
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The letter e is used for continuous compound, it is raised by the interest rate times the amount of time.

The formula would be 1200e^0.16t

The answer is C

Answer:

55 because if u take the 6 and 3 and multiply then subtract 4 and whatever you get that's your answer same with the others

Answer:

1. the answer is x=1/3y+1 y=3x−3

Step-by-step explanation:

Question refers to below content.

Three gallons of paint are used to paint 16 wooden signs. How many wooden signs can be painted with one gallon of paint?? Between what two whole numbers does the number lie?

Answer:

[tex]5 \frac{1}{3}[/tex] wooden sign can be painted from 1 gallon of paint.

The answer lies between number 5 and 6.

Step-by-step explanation:

Given:

Amount of paint = 3 gallons

Number of wooden signs = 16

We need to find the Number of wooden signs can be painted with 1 gallon of paint.

Solution:

Now we know that;

3 gallons of paint = 16 wooden signs painted

1 gallon of paint =  Number of wooden signs can be painted with 1 gallon of paint.

By using Unitary method we get;

Number of wooden signs can be painted with 1 gallon of paint = [tex]\frac{16}{3} \ \ Or \ \ 5 \frac{1}{3}[/tex]

Hence [tex]5 \frac{1}{3}[/tex] wooden sign can be painted from 1 gallon of paint.

Now we can say that;

[tex]5 \frac{1}{3}[/tex]  lies between 5 and 6.

Hence The answer lies between number 5 and 6.

Answer: 1 2/3 ounces of cinnamon is needed.

Step-by-step explanation:

1/3 ounce is cinnamon is needed for each 1 and 1/2 cups of flour. Converting 1 and 1/2 cups to improper fraction, it becomes 3/2 cups.

It means that the number of ounces of cinnamon need for 1 cup of flour would be

(1/3)/(3/2) = 1/3 × 2/3 = 2/9 ounces of cinnamon.

Converting 7 and 1/2 cups of flour to improper fraction, it becomes 15/2 cups of flour.

Therefore, the ounces of cinnamon needed to bake cookies with 15/2 cups of flour is

2/9 × 15/2 = 15/9 = 5/3

= 1 2/3 ounces of cinnamon

Answer: the bill for a glass of apple juice is $0.7 and the bill for a salad is $1.5

Step-by-step explanation:

Let x represent the bill for a glass of apple juice.

Let y represent the bill for a salad.

The bill for five glasses of apple juice and four salads is $9.50. It means that

5x + 4y = 9.5 - - - - - - - - - - - 1

The bill for four glasses of apple juice and five salads is $10.30. This means that

4x + 5y = 10.30- - - - - - - - - - - -2

Multiplying equation 1 by 4 and equation 2 by 5, it becomes

20x + 16y = 38

20x + 25y = 51.5

Subtracting, it becomes

- 9y = - 13.5

y = - 13.5/-9

y = 1.5

Substituting y = 1.5 into equation 1, it becomes

5x + 4 × 1.5 = 9.5

5x + 6 = 9.5

5x = 9.5 - 6 = 3.5

x = 3.5/5 = 0.7

The bill for a glass of juice and a salad would be $2.20.

To find the cost of a glass of apple juice and a salad, we need to set up a system of equations using the given information. Let's assign variables to the cost of a glass of apple juice and a salad. Let x be the cost of a glass of apple juice and y be the cost of a salad.

From the first sentence, we can write the equation 5x + 4y = 9.50. From the second sentence, we can write the equation 4x + 5y = 10.30.

To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method. Multiply the first equation by 4 and the second equation by 5 to eliminate x:

20x + 16y = 38.00

20x + 25y = 51.50

Subtract the first equation from the second:

9y = 13.50

Divide both sides by 9:

y = 1.50

Substitute this value of y into one of the original equations (let's use the first equation):

5x + 4(1.5) = 9.50

5x + 6 = 9.50

Subtract 6 from both sides:

5x = 3.50

Divide both sides by 5:

x = 0.70

Therefore, the bill for a glass of juice and a salad would be $0.70 + $1.50 = $2.20.

Final answer:

Marie used 4 1/2 cups of flour for the bread and had 6 1/2 cups left for the muffins. By adding these amounts together, we find that the original bag of flour contained 11 cups of flour in total.

Explanation:

To determine how much flour was initially in the bag, we need to add together the amount of flour used for the bread and the muffins.

Marie baked two loaves of bread, with each loaf requiring 2 1/4 cups of flour. Therefore, the total flour used for bread is:

2 loaves × 2 1/4 cups/loaf = 4 1/2 cups

After baking the bread, she used the remaining 6 1/2 cups of flour to make muffins. To find the initial amount of flour in the bag, we add the flour used for the bread to the flour used for the muffins:

4 1/2 cups + 6 1/2 cups = 11 cups

Therefore, the bag originally had 11 cups of flour.

Answer:

The value of [tex]x=8[/tex].

Step-by-step explanation:

Given:

[tex]\frac{x+3}{x}-\frac{x+1}{x+4}=\frac{5}{x}[/tex]

We need to solve this equation.

Solution:

First combining equation having same denominators we get;

[tex]\frac{x+3}{x}-\frac{5}{x}=\frac{x+1}{x+4}[/tex]

Now denominators are common so we will solve the numerators we get;

[tex]\frac{x+3-5}{x}=\frac{x+1}{x+4}\\\\\frac{x-2}{x}=\frac{x+1}{x+4}[/tex]

Now by cross multiplication we get;

[tex](x-2)(x+4)=x(x+1)[/tex]

Now Applying distributive property we get;

[tex]x^2+4x-2x-8=x^2+x\\\\x^2+2x-8=x^2+x[/tex]

Now Combining the like terms we get;

[tex]x^2+2x-x^2-x=8\\\\x=8[/tex]

Hence on solving we get the value of [tex]x=8[/tex].

Answer:The number of ounces of cereals left in the box is 3

Step-by-step explanation:

Tina and Joey share a 18-ounce box of cereal. By the end of the week, Tina has eaten 1/6 of the box. This means that the amount of cereal that Tina ate is

1/6 × 18 = 3 ounce

Also, by the end of the week, Joey has eaten 2/ 3 of the box of cereal. This that the amount of cereal that Joey ate is

2/3 × 18 = 12 ounce

The number of ounces of cereals left in the box would be

18 - (12 + 3) = 18 - 15

= 3

Answer: the height after 10 hours is 21 cm

Step-by-step explanation:

Assuming the rate at which the height of the candle is decreasing is in arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + (n - 1)d

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

If after seven hours of burning, a candle has high of 22.5 Centimeters, the expression is

22.5 = a + (7 - 1)d

22.5 = a + 6d - - - - - - - - - -1

If after 26 hours of burning, it's height is 13 cm. The expression is

13 = a + (26 - 1)d

13 = a + 25d - - - - - - - - - - - 2

9.5 = - 19d

d = 9.5/ - 19

d = - 0.5

Substituting d = - 0.5 into equation 1, it becomes

22.5 = a + 6 × - 0.5

22.5 = a - 3

a = 22.5 + 3

a = 25.5

The linear expression becomes

Tn = 25.5 - 0.5(n - 1)

The height of the candle after 10 hours would be

25.5 - 0.5(10 - 1)

= 25.5 - 4.5

= 21 centimeters

Step-by-step explanation:

The given four sides of quadrilateral = (2, 4), (3, 5), (4, 6) and (5,8)

To find, the area of the quadrilateral = ?

We know that,

The area of quadrilateral [tex]=\dfrac{1}{2} [x_{1}( y_{2}-y_{3})+x_{2}( y_{3}-y_{4})+x_{3}( y_{4}-y_{1})+x_{4}( y_{1}-y_{2})][/tex]

[tex]=\dfrac{1}{2} [2( 5-6)+3( 6-8)+4( 8-4)+5(4-5)][/tex]

[tex]=\dfrac{1}{2} [2(-1)+3(-2)+4(4)+5(-1)][/tex]

[tex]=\dfrac{1}{2} (-2-6+16-5)[/tex]

[tex]=\dfrac{1}{2} (16-13)[/tex]

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

Thus, the area of the quadrilateral is [tex]\dfrac{3}{2}[/tex] units.

The distance between (-3, 2) and (3, -8) is approximately 11.66.

To find the distance between two points, we can use the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, (-3, 2) can be denoted as (x1, y1) and (3, -8) can be denoted as (x2, y2). Substituting these values in the formula:

d = sqrt((3 - (-3))^2 + (-8 - 2)^2)

d = sqrt(6^2 + (-10)^2)

d = sqrt(36 + 100) = sqrt(136)

The distance between (-3, 2) and (3, -8) is approximately 11.66.

Final answer:

To calculate the distance between (-3, 2) and (3, -8), one must find the differences in both the x and y coordinates, square these differences, sum them, and take the square root of this sum, which yields approximately 11.66.

Explanation:

To find the distance between the points (-3, 2) and (3, -8), we use the Pythagorean Theorem. The distance d is calculated as the square root of the sum of the squares of the difference in the x-coordinates and the y-coordinates.

First, find the differences:
Δx = [tex]x_2 - x_1[/tex] = 3 - (-3) = 6
Δy = [tex]y_2 - y_1[/tex] = -8 - 2 = -10

Then calculate the distance squared:
d² = (Δx)² + (Δy)²
d² = (6)² + (-10)²
d² = 36 + 100
d² = 136

Take the square root of the distance squared to find the distance:
d = [tex]\sqrt{136}[/tex]
d ≈ 11.66

Answer:

The solution is (5, −2)

Step-by-step explanation :

x + y = 3 => y = 3 - x

                  y = x - 7  } =>

=> 3 - x = x - 7 => 3 + 7 = x + x => 2x = 10 => x = 5

x + y = 3

5 + y = 3

y = 3 - 5

y = - 2

Answer:

I feel bad for you I really would like to help you but I haven't even learn that stuff yet

Answer:

Step-by-step explanation:

(24.50+11 d)*(107/100)=108.61

24.50×107+1177 d=10861

1177 d=10861-24.50×107

=10861-2621.50

=8239.50

d≈7 days

Final answer:

The equation that can be used to determine the number of days d the car was rented is: $108.61 = $24.50 + ($11 * Number of days). By solving this equation, we find that the car was rented for 7 days.

Explanation:

To determine the number of days the car was rented, we can use the equation:

Total cost = Cost of renting a car + (Cost per day * Number of days)

In this case, the cost of renting a car is $24.50 and the cost per day is $11. The sales tax is 7%.

The equation becomes:

$108.61 = $24.50 + ($11 * Number of days)

Now, we can solve for the number of days:

Subtract $24.50 from both sides of the equation: $108.61 - $24.50 = $11 * Number of days

Calculate the difference: $84.11 = $11 * Number of days

Divide both sides of the equation by $11: Number of days = $84.11 / $11

Round the result to the nearest whole number: Number of days = 7

Answer:

  $6 for a 1-minute call

Step-by-step explanation:

For duration "d" the costs of the plans are identical when ...

  5 +1d = 1 +5d

  4 = 4d . . . . . . . . add -1-1d to both sides

  1 = d  . . . . . . . . . divide by 4. Duration in minutes.

Then the cost for this 1-minute call is ...

  5 + 1·1 = 6 . . . . dollars

Each plan will charge $6 for a 1-minute call.

Answer:

Step-by-step explanation:

Let x represent the call duration that would cost the same amount with either plans.

On her plan, christina pays $5 just to place a call and $1 for each minute. This means that the total cost of x minutes on this plan is

x + 5

When brenna makes an international call, she pays $1 to place the call and $5 for each minute. This means that the total cost of x minutes on this plan is

5x + 1

For both costs to be the same, the number of minutes would be

x + 5 = 5x + 1

5x - x = 5 - 1

4x = 4

x = 4/4 = 1

A call duration of 1 minute would cost exactly the same under both plans. The cost of the call would be

5 × 1 + 1 = $6

Answer:

It will cost is $828.75.

Step-by-step explanation:

Given:

Davis is putting tile in his rectangular kitchen. His kitchen is 13 feet long, and 17 feet wide. The tile davis is installing is $3.75 per square foot.

Now, to find the total cost.

Davis is putting tile in his rectangular kitchen.

Length = 13 feet.

Width = 17 feet.

So, to get the area of kitchen:

Area = length × width

Area = 13 × 17

Area = 221 square foot.

As, the unit rate is given.

Cost per square foot = $3.75.

Now, to get the total cost by using unitary method:

If cost of 1 square foot = $3.75.

So, the cost of 221 square foot = $3.75 × 221

                                                    = $828.75.

Therefore, it will cost  $828.75.

To find the total cost of tiling Davis' kitchen, we need to find the area of the kitchen in square feet by multiplying its length and width, then multiply the area by the cost per square foot. In this case, it will cost Davis $828.75 to tile his kitchen.

The question is about Davis installing tiles in his rectangular kitchen and how much the cost will be at $3.75 per square foot. First, we need to determine the total area of the kitchen. In this case, the kitchen is rectangular in shape and the area of a rectangle is calculated by multiplying the length by the width. Here, length is 13 feet and the width is 17 feet, hence the area of the kitchen is 13 x 17 = 221 square feet.

Now, the cost per square foot of tile is given as $3.75. So, we multiply the total area by the cost per square foot to determine the overall cost of the tile. The calculation is as follows, 221 square feet x $3.75 = $828.75.

Therefore, it will cost Davis $828.75 to tile his kitchen.

https://brainly.com/question/30694298

Answer:

Step-by-step explanation:

The large screen television is rectangular in shape. The diagonal divides the rectangle into two equal right angle triangles. The diagonal represents the hypotenuse of the right angle triangle.

He knows that the diagonal of the television measures 42.1 inches and the base is 34.3 inches. To determine the height,h of the triangle which is also the width of the rectangle, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

42.1² = 34.3² + h²

h² = 1772.41 - 1176.49 = 595.92

h = √595.92 = 24.41 inches.

Area of rectangle = Length × width

Area of Television = 34.3 × 24.41 = 837.3 inches²

Answer:

$2925

Step-by-step explanation:

To find the cost, we need to get the area of the triangular sale. This can be obtained by using the area of a triangle.

This is A = 1/2 * b * h

Where in this case, b = 12ft and h = 25ft

The area is thus 1/2 * 12 * 25 = 150sq.ft

Now we know that 1sq.ft is $19.50, 150 will be 150 * 19.5 = $2925

Answer:

a) 375m/s2

b) F = 0.045N

c) F/T =  0.00096

d) Tension = 46.9N

Step-by-step explanation:

The step by step calculation is as shown in the attached file.

Answer:

The heart is located in the middle of the 2 lung's in the middle of the chest and slightly to the left side of the chest.

Step-by-step explanation:

The heart is a muscular organ of the size of a fist just behind and to the left of the breastbone. The cardiovascular system is the heart pumping blood across the artery and vein network.Behind your sternum and between your two lungs your heart is found. The heart lies closer to the front of the chest and in the front of the spine. Your diaphragm, stomach and liver are underneath your heart.

Answer:

break even units for both the cases will be 5

Step-by-step explanation:

Data provided in the question:

For the case 1

Variable cost = $20 each

Selling cost = $50

Rent for the booth fair = $150

Now,

Let break even units be x

At break even

Total cost = Total revenue

Thus,

$20x + $150 = $50x

or

$50x - $20x = $150

or

$30x = $150

or

x = 5

Case 2

Variable cost = $15 per unit

Thus,

At break even

Total cost = Total revenue

Thus,

$15x + $150 = $50x

or

$50x - $15x = $150

or

$35x = $150

or

x = 4.28 ≈ 5

The break even point will still remain the same.

The break-even point is calculated by setting total cost equal to total revenue and solving for the number of units produced and sold (denoted as 'units').

Given the current variable cost per unit ($20), the sale price per unit ($50), and the fixed cost (booth rent - $150), we can set up the equation as follows:

Total Cost = Fixed cost (booth rent) + variable cost per unit * units
Total Revenue = sale price per unit * units

Setting these two equal to each other, we get:

150 + 20*units = 50*units

By rearranging this equation, we find:

units = 150 / (50 - 20)

This calculates out to 5 units. Therefore, Ray needs to sell 5 units to break even with his current costs.

If Ray is able to reduce his variable cost to $15 per unit, we will repeat the same calculation with the new variable cost:

units = 150 / (50 - 15)

This calculates out to approximately 4.29 units. Since Ray cannot sell a fraction of a unit, he would have to sell 5 units to fully cover his costs, but he would begin to make a profit sooner than with his current variable cost. In fact, from the 5th unit sold, part of the revenue would go towards profit. Therefore, with the reduced variable cost, his break-even point would be closer to 4 units, but practically still 5 units.

In conclusion, with his current costs, Ray's break-even point is at 5 units. If he is able to reduce his variable cost to $15 per unit, his break-even point would theoretically be lower at approximately 4.29 units, but practically still would round up to 5 units.

#SPJ3

Answer:

{x| x∈R, x > -2}

Step-by-step explanation:

You solve the inequality just like you would solve an equality.

Everything that has the x on the left side, everything without x on the right side.

Be careful that when you multiply by -1, the inequality signal changes(for example, lesser than becomes higher than

So

[tex]10 < x + 12[/tex]

[tex]-x < 12 - 10[/tex]

[tex]-x < 2[/tex]

Multiplying by -1

[tex]x > -2[/tex]

So the correct answer is:

{x| x∈R, x > -2}

{x| x∈R, x > -2}

Step-by-step explanation:

You solve the inequality just like you would solve an equality.

Everything that has the x on the left side, everything without x on the right side.

Be careful that when you multiply by -1, the inequality signal changes(for example, lesser than becomes higher than

So

Multiplying by -1

So the correct answer is:

{x| x∈R, x > -2}