A small business invests $10,000 in equipment to produce

a new soft drink. Each bottle of the soft drink costs $0. 65 to

produce and is sold for $1. 20. How many bottles must be

sold before the business breaks even?

The number line in the image below shows the solution to the inequality 3x - 8 > 7.

How to Create a Number Line that Shows the Solution of an Inequality?

Before we can create a number line that represents the solution of an inequality, we have to solve to find the solution first.

Given the inequality 3x - 8 > 7, solve for x:

3x - 8 + 8 > 7 + 8 (addition property of equality)

3x > 15

3x/3 > 15/3 (division property of equality)

x > 5

The solution is x > 5, therefore, the image attached below shows the number line of the solution.

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Answer:

Step-by-step explanation:

To find the probability that exactly 35 vehicles pass through the drive-thru during the lunch hour rush on a given day, we can use the probability density function of the normal distribution. In this case, the mean is 38 and the standard deviation is 5.7.

The probability of a specific value x in a normal distribution is given by the formula:

P(x) = (1/(σ * √(2π)) * e^((-1/2) * ((x - μ)^2 / σ^2))

Where x is the specific value we are trying to find the probability of, μ is the mean, and σ is the standard deviation.

plugging in the given values, we get:

P(35) = (1/(5.7 * √(2π)) * e^((-1/2) * ((35 - 38)^2 / 5.7^2))

The result is very close to zero, the probability of exactly 35 vehicles passing through the drive-thru during the lunch hour rush is very low, almost impossible.

55 rooms should be set aside for full-paying skiers.

Now, According to the question:

Let C represents the contribution that is lost when a reservation is breached.

H represents the loss of opportunity that is associated with not having the availability of anything.

D rep the no- shows with regard to experience in the past

X represents the overbooked number.

All the values here represent the critical probability for yield management.

Let X rep the reserved seats for passengers with full fare

D rep the full fare tickets

F rep the price of full fare

D rep the price of discounted fare

Now, Solving the problem :

P(d< x) < (F -D)/ p × F

= (299 - 109)/0.8 × 299

=  71,012.5

The Z value for 0.71 probability is 0.5

U + Z* standard deviation = 50 + 0.5 *10

= 55 rooms

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The price per ounce is given as follows:

$0.15 = 15/100.

The price per ounce is obtained applying the proportions in the context of this problem, dividing the total price by the number of ounces.

The parameters for this problem are given as follows:

Hence the price per ounce is calculated as follows:

2.25/15 = $0.15.

The total price was of $2.25 for 15 ounces, and the problem asks for the price per ounce.

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The height of the cube brick is 7 units and the volume is equal to 343 unit³

The volume of a cube is defined as the total number of cubic units occupied by the cube. The formula is given as V = a³ where "a" is the length of edge or sides.

The length of an edge for the cube brick is 7 units which implies the height represented by h is also 7 units and the volume is calculated as follows:

volume of cube brick = 7 units × 7 units × 7 units

volume of cube brick = 343 units ³

Therefore, the height of the cube brick is 7 units and the volume is equal to 343 unit³

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Answer:

32 & 12

Step-by-step explanation:

let age of andy = x

let age of brett = y

x + y = 44        (eq 1)

x= 8 + 2y         (eq 2)

putting the value of x from 2 in 1

8 + 2y + y = 44

3y = 36

y = 12

x = 8 + 2(12)

x = 32

Jetlag is a condition associated with crossing multiple time zones is experienced by sports tourists from Argentina travelling to Japan.

People who travel quickly between different time zones may experience jet lag, a sleep disorder.

Jet lag causes sporadic sleep problems. It occurs when signals from a new time zone cause the body's biological clock to become out of sync. Feeding times and light exposure are two examples of cues.

The term "jet lag" originated from the fact that it was uncommon to travel far and quickly enough to cause desynchronosis prior to the development of passenger jet aircraft. Propeller-driven travel was slower and covered less ground than jet flights, so it had a negligible impact on the issue.

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You can have 43 packs of the 645 markers (645 ÷ 15 = 43)

Step-by-step explanation:

First, you can make 42.33 packs of markers with 645 markers and 15 markers per pack. This is calculated by dividing the total number of markers (645) by the number of markers per pack (15), which gives you 42.33.

The center of dilation if Quadrilateral N' is the image of quadrilateral N under a dilation is; Point C

The center of dilation is defined as a reference point that is used to appropriately scale the dilation of a figure.

Now, if we imagine that the corresponding vertices of the two quadrilaterals are extended, then it will be clear that the extensions intersect at a point C.

Therefore we can conclude that point C is the center of dilation by the fact that corresponding parts of a paragraphic intersect at a point.

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Answer:

10x+5y-30

Step-by-step explanation:

5(2x+y -6)

5x2=10

5x (-6)= -30

=10x+5y-30

The volume of the container is 4,500 cm3.

Calculate the volume of the two cubes that make up the container.

For the cube on the left, the volume can be found by multiplying the length (15 cm) by the width (10 cm) by the height (10 cm).

15 cm × 10 cm × 10 cm = 1,500 cm3

For the cube on the right, the volume can be found by multiplying the length (20 cm) by the width (15 cm) by the height (10 cm).

20 cm × 15 cm × 10 cm = 3,000 cm3

Add the two volumes together to find the total volume of the container.

1,500 cm3 + 3,000 cm3 = 4,500 cm3

Therefore, the volume of the container is 4,500 cm3.

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Mean with frequency represented by the number of times people visits the shop is equal to 1.9.

Let 'v' represents the visits of the people.

'f' represents the frequency that is number of times group of people visits the shop.

To calculate mean results of the table are as follow:

Visits ( v)       frequency ( f)         fv

0                            5                     0

1                             14                   14

2                            18                   36

3                            7                     21

4                            6                     24

Mean of the number of visits

= ( Sum of all the fv ) / ( Sum of all the frequency)

= ( 0 + 14 + 36 + 21 + 24 ) / ( 5 + 14 + 18 + 7 + 6 )

= 95 / 50

= 1.9

Therefore, the mean of the number of visits with the given frequency is equal to 1.9.

The above question is incomplete, the complete question is :

A group of people answer the question:

How many times did you shop at Ascobury's last week?

Here are the results:

Visits ( v)       frequency ( f)         fv

0                           5

1                             14

2                            18

3                            7  

4                             6

Find the mean number of visits.?

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Marcella started with 56 candles during her initial purchase

The given problem can be solved by arithmetic approach

Given,

After 8 weeks she has 160 candles

And also, she buys 13 more candles every week

To find her initial number of candles purchased,

Let her initial number of purchase of candles be 'x'

According to the question,

Initial number of candles + (8 weeks * 13 candles/week) = 160 candles

Substituting x, we get

x+(13*8)=160

or, x+104=160

or, x=160-104

or, x=56

Thus, we can say that initially Marcella had bought 56 candles.

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-37. 44 / 4. 8 gives  -7.8 when dividing -37.44 by 4.8 by simple dividing rule whereas after rounding off -37.44 and 4.8 that will be -37 and 5 will be 7.4.

In the given problem Division is = 4. 8 and dividend is = -37. 44, And as per law Division is divided by dividend  (Division/dividend), and the result produced, is called quotient In this case in this case, Quotient is -7.8.

And -37.44 is approximately -37 As .44 is rounded off to .00 (As per law 0-4 is 0 and 5-9 is rounded up to the next digit. And 4.8 could be around off to 5. And now if -37 is divided by 5 estimated will be 7.4.

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The hypotenuse of the 45-45-90 triangle measures x / √2 units.Identify the given information. The given information is that the legs of a 45-45-90 triangle each measure x units. The question can be solved by following the steps :

1. Use the Pythagorean Theorem to solve for the hypotenuse. The Pythagorean Theorem states that a2 + b2 = c2 where a and b are the legs of the triangle and c is the hypotenuse. In this case, x2 + x2 = c2.

2. Simplify the equation. When two of the same numbers are added together, the sum is twice that number. Therefore, 2x2 = c2.

3. Solve for c. To solve for c, divide both sides of the equation by 2. This yields x2 = c2 / 2.

4. Take the square root of both sides. Taking the square root of both sides yields x = c / √2.

5.The answer to the question is that the hypotenuse of the 45-45-90 triangle measures x / √2 units.

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Reporting on a mission, initiative, or the data obtained from it is known as debriefing. Debriefing can reduce problems associated with the use of deception by a researcher. So option a is correct.

Debriefing is the act of reporting on a mission, project, or the data gleaned from it. After an activity or event, a structured procedure examines the actions performed.

Technically speaking, it refers to a method of active intervention that is specialized and developed into more formal meanings like operational debriefing. It is divided into various categories, including, among others, psychological, military, and experiential debriefing.

The following crucial components are often included in effective debriefings:

1. Active participation that goes beyond merely taking criticism in a passive manner.

2. Developmental aim centred on growth and learning

3. A discussion of particular incidents

4. Information from several sources

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Is that a question? You don't seem to have anything linked or a question posted?

The price of the delivery is $15 and the mileage is 40.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

Given that the rosebud flower shop has a basic delivery charge of 5$ plus a rate of 25 cents per mile.

Total cost = basic delivery fee + (rate per mile x number of miles)

=$5 + (0.25 x m)

= $5 + 0.25m

The linear expression that represents the total delivery cost from Rosebud Flower Shop ;

Total cost = basic delivery fee + (rate per mile x number of miles)

=$7 + (0.2 x m)

$7 + 0.2m

When the costs are the same, the two expressions would be;

$7 + 0.2m = $5 + 0.25m

$7 - $5 = 0.25m - 0.20

$2 = 0.05m

m = 2 / 0.05

m = 40

Price = $7 + 0.2(40)

$7 + 8 = $15

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The length of MN for this problem is given as follows:

MN = 12.

The law of sines states that the sine of each angle is proportional to the side length opposite the angle.

The angle opposite to side MN is given as follows:

O.

Which is congruent to angle M, and the side opposite to angle M is:

NO = 12.

Hence the length of MN is also given as follows:

MN = 12.

(as it is opposite to a congruent angle to the opposite side with length of 12).

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Here there is a 10% decrease in the number of streams each week after the song's release. From calculations the number of streams after sixth week is 8,503,056.

Let's look into the data given.

The initial number of streams, X₀ = 16,000,000

The percent decrease is 100- 90 = 10%

So the rate of decrease = 10/100 = 0.10

The period of time, n = 6

The equation to find the final number of streams, X =  X₀ (1-r)ⁿ

                                               = 16,000,000× (1-0.01)⁶

                                               = 8503056.

So the number of streams in the sixth week is 8,503,056

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Answer:

(B) 9,447,840

Step-by-step explanation:

Week         Streams

1                  16,000,000 x 90

2                 14,400,000 x 90

3                 12,960,000 x 90

4                 11,664,000 x 90

5                 10,497,600 x 90

6                 9,447,840 x 90

Therefore, the answer would be 9,447,840

Answer: Based on the formula I was taught, for your first problem it'd be the option that says 813.9 ft and for the second one it'd be your option with 2076.3 square inches.

Answer: D) 813.9 inches

Step-by-step explanation:

Formula for surface area of cylinder is:

A=2πrh+2πr2

r = 6

h = 15.6

A = 2π(6)(15.6) + 2π(6)^2

A = 187.2π + 2π(36)

A = 187.2π + 72π

A = 259.2π

If π is 3.14,

A = 259.2(3.14) = 813.9

Answer:

= 16m² - 9

Step-by-step explanation:

(4m+3)(4m-3)

= 4m*4m + 4m*3 + 3*4m + 3*-3

= 16m² + 12m -12m - 9

= 16m² - 9

Liling will end up with four triangles if she starts with two tiny squares of material and cuts them on the diagonal. Knowing the areas of each of the four triangles will help us calculate the size of the larger square quilt block.

We are aware that the area of a square can be calculated by multiplying one side's length by itself (A = s2). Each of the small squares' ensuing triangles has a base and height that are equal to one-half of its side because the small squares were cut on the diagonal. Therefore, each triangle has a surface area of (1/2) x (1/2) x s2 = (1/4) x s2 = (s2)/4.

If the large quilt block is made up of four of these triangles, then the area of the quilt block is 4 x (s^2)/4 = s^2. Since the area of the large quilt block is 36 square inches, we can set up the equation:

s^2 = 36

To find the length of one side of the large quilt block (s), we can take the square root of both sides of the equation:

s = √36

s = 6 inches

So, the length of one side of the large quilt block is 6 inches, and the area of the block is 36 square inches.

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The two trapezoids below are similar. The value of Ef will be 6.

If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.

Given that there are two trapezoids ABCD and GHEF. The length of EF = x will be calculated as:-

Apply the similarity property in the two trapezoids.

AB / FE = DC / GH

24 / x = 30 / 7.5

x = ( 24 x 7.5 ) / 30

x = ( 1800 / 300 )

x = 6

Hence, the value of the side x = EF = 6.

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Answer:

B(-5, 3)

Step-by-step explanation:

(1 + x)/2 = -2

1 + x = -4

x = -5

(7 + y)/2 = 5

7 + y = 10

y = 3

B(-5, 3)

A table with two rows and columns of data represent a linear function.

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12 is the least common denominator between 3/4 and 7/12.

The least common denominator (LCD) of two or more fractions is the smallest number that can be divided by the denominators of each of the fractions without leaving a remainder.

The smallest number among all the common multiples of the denominators is the least common denominator when two or more fractions are provided.

Finding the least common multiple (LCM) of the denominators 4 and 12 will allow you to get the least common denominator of 3/4 and 7/12.

12 is the least frequent multiple of 4 and 12. Therefore, 12 is the least common denominator between 3/4 and 7/12.

Finding the denominators' multiples is another way to locate it. 43 = 12 is the least common multiple and the least common denominator, respectively.

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Graphs (C) and (D) having median value larger than the mean value.

What Is a Histogram?

A histogram is a graphical representation of data points organized into user-specified ranges.

In graphs (C) and (D), the median value is larger than the mean value as the distribution is skewed to the left which means most values are large but there are few exceptionally small values because of which means shift towards the left and thus the mean is less than the median, or we can say that the median value is larger that the mean value.

So, graphs (C) and (D) having median value larger than the mean value.

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Answer: a. $12, b. $12, c. $13, d. $12

Step-by-step explanation:

a. 1+1+1+1+1+1 = 6, 2+2+2=6, 6+6=12

b. 1+1+1+1=4, 2+2+2+2=8, 4+8=12

c. 1+1+1+1+1=5, 2+2+2+2=8, 5+8=13

d. 1+1+1+1+1+1+1+1=8, 2+2=4, 8+4=2

Step-by-step explanation:

To find the factor by which the dimensions of cylinder A were multiplied to produce the corresponding dimensions of cylinder B, we can use the fact that they are similar solids. This means that the ratio of corresponding dimensions is the same for both cylinders.

Since the base of cylinder A has a circumference of 4π units and the base of cylinder B has an area of 9π units, we can use these measurements to find the ratio of the radii of the two cylinders.

The circumference of a circle is given by 2πr, where r is the radius, so the radius of cylinder A is 4π/2π = 2 units.

The area of a circle is given by πr^2, so the radius of cylinder B is sqrt(9π/π) = sqrt(9) = 3 units.

The ratio of the radius of cylinder A to cylinder B is 2/3. Since similar solids have the same ratio for all dimensions, this means that the dimensions of cylinder A were multiplied by a factor of 2/3 to produce the corresponding dimensions of cylinder B.