How many solutions?
4x - y = 18 and -4x + y = -18

a. one
b. infinitely many
c. no solutions

The calculations for break even point is 5000 customers, and the solution to the system of equations were shown. Mr. Bro's Chick-fil-A franchise would be more profitable as it required less initial borrowing, broke even sooner and generated more income than Ms. Kramer's Popeye's franchise.

To solve this problem, we need to set up a system of equations. Let's use "b" to represent the amount each owner had to borrow to open their restaurant, "x" to represent the number of customers, and "y" to represent the total profit.

For Mr. Bro's Chick-fil-A

After 500 customers: y = -4000

After 3000 customers: y = 1000

We can use these two equations to find the slope of the line: m = (1000 - (-4000)) / (3000 - 500) = 1.8

Using the point-slope form of a line y - (-4000) = 1.8(x - 500)

Simplifying, we get: y = 1.8x - 3400

For Ms. Kramer's Popeye's

After 2000 customers: y = -6000

After 4500 customers: y = 1500

We can use these two equations to find the slope of the line: m = (1500 - (-6000)) / (4500 - 2000) = 1.4

Using the point-slope form of a line: y - (-6000) = 1.4(x - 2000)

Simplifying, we get: y = 1.4x - 5400

Now, we can set the two equations equal to each other to find the break-even point

1.8x - 3400 = 1.4x - 5400

0.4x = 2000

x = 5000

This means that both restaurants need to serve 5000 customers to break even.

To compare the total income of the two restaurants, we can find the y-value for both equations when x = 5000

Chick-fil-A: y = 1.8(5000) - 3400 = $5,000

Popeye's: y = 1.4(5000) - 5400 = $1,000

From this analysis, it is clear that owning Chick-fil-A is more profitable than owning Popeye's.

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The value of   logarithm log5 5/3 is approximately equal to 0.3174.

Using the approximation of ≈ 0.4307 for log5 2 and ≈ 0.6826 for log5 3, we can approximate the value of log5 5/3 by subtracting the two approximations.

log5 5/3 = log5 5 - log5 3 ≈ 1 - 0.6826 ≈ 0.3174


To explain further, logarithms are a way to express the relationship between exponential growth or decay and the input values. In this case, we are using the base of 5 to represent the exponent and trying to find the logarithm of 5/3.

By using the approximation values of log5 2 and log5 3, we can estimate the value of log5 5/3 by subtracting the two approximations. This approximation is useful in situations where we need a quick estimate of a logarithmic function without having to do complex calculations.

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Part A: The equation to represent this situation is: 0.50x + 3 = 18.50
Part B: The equation to represent this situation is: 0.75x + 3 - 0.10x = 21.00
Part C: The equations differ in the following ways:
1. Sydney's equation involves only the price per cup and the tip, while Daria's equation also considers the cost of the plastic cups.
2. The price per cup for Sydney and Daria are different.

Part A: The equation to represent this situation is:

18.50 = 0.50x + 3

Where x represents the number of cups of lemonade sold.

Part B: The equation to represent this situation is:

21.00 = 0.75x + 3 - 0.10x

Where x represents the number of cups of lemonade sold.

Part C: The equations from Part A and Part B differ in that Part B takes into account the cost of each plastic cup used to serve the lemonade, while Part A only considers the revenue from selling each cup of lemonade and the tip received. This means that the profit in Part B is calculated after deducting the cost of each plastic cup from the revenue earned, while the profit in Part A does not account for any costs incurred.

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The total cost to transport 12 tons of sugar is $8,600. The equation relating the total cost (c) to the amount of sugar transported (s) is: c = 175s + 6500

To find the total cost to transport 12 tons of sugar, we substitute s = 12 into the equation: c = 175(12) + 6500, c = 2100 + 6500, c = 8600

Therefore, the total cost to transport 12 tons of sugar is $8,600.

The equation shows that the total cost increases by $175 for each additional ton of sugar transported, and there is also a fixed cost of $6,500 for renting the trucks, which is added to the variable cost.

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To solve the equation 8 x five sixths, we first convert the fraction to a decimal by dividing the numerator (5) by the denominator (6), which gives us 0.83.

We then multiply 8 by 0.83 to get the final answer of 6.64. Therefore, 8 x five sixths = 6.64.

In general, to multiply a whole number by a fraction, we can convert the fraction to a decimal and then multiply the whole number by the decimal.

Alternatively, we can convert the whole number to a fraction with a denominator of 1 and then multiply the two fractions by cross-multiplying and simplifying.

In this case, we could also write 8 as 8/1 and multiply it by 5/6 to get (8 x 5)/(1 x 6) = 40/6, which simplifies to 6 and 4/6 or 6.67 (rounded to two decimal places). However, converting the fraction to a decimal is often simpler and more practical.

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If the vertex of a parabola is at (5,0) and it opens UPWARD, it will have one solution.

Since the parabola opens upward, its vertex is the minimum point, and therefore, it will have only one solution.

A parabola is a U-shaped curve in mathematics that can be formed by the graph of a quadratic function. It is a type of conic section, along with circles, ellipses, and hyperbolas.

Mathematically, a parabola can be defined as the set of all points in a plane that are equidistant from a fixed point called the focus and a fixed line called the directrix. The focus lies on the axis of symmetry of the parabola, and the directrix is perpendicular to the axis of symmetry.

If the vertex of a parabola is at (5,0) and it opens UPWARD, it will have one solution.

Your answer: one

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Answer:

Step-by-step explanation:

tried my best as the first two got me stuck

wouldn't recommend trying my answer and Id wait for another answer

The best prediction possible for the number of times you will roll a one number when a 6-sided die is rolled 12 times = (0.167)¹²

Events occur as the outcome of an experiment. But one cannot be satisfied with these events until a degree of measurement of the likeliness of its occurrence is not provided. Probability is a statistical tool used widely to obtain predictive value.

Here, 6-sided die rolled 12 times.

If a 6-sided die is rolled, possible outcomes are {1, 2, 3, 4, 5, 6}

So, total number of outcomes = 6

So, number of favorable outcomes = 1

Probability of getting 1 is 1/6 = 0.167

The best prediction possible for the number of times you will roll a one number when a 6-sided die is rolled 12 times = (0.167)¹²

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If for "c" tickets, Suzie paid an amount of $324, then the cost of each ticket is represented by "324/c".

The number of tickets that Suzie bought is = c tickets, and

Let "x" be the cost of "each-ticket for "rock-festival".

The total amount spent for "c" tickets is = $324,

Therefore, we can write the cost-equation as;

⇒ c × x = 324,

To find the value of "x", we solve for it by dividing both sides of the equation by "c":

⇒ x = 324/c,

So, the cost of each ticket is $324 divided by the number of tickets "c" that Suzie bought.

Therefore, Each tickets cost is 324/c.

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The circumference of a circle with a diameter of 8.7 units is approximately 27.318 units, calculated using the formula Circumference = πd. So, the correct answer is D).

The formula for the circumference of a circle is given by

Circumference = πd

where d is the diameter of the circle.

Substituting the given value of the diameter of circle a, we get:

Circumference = π x 8.7

Using the approximation of π = 3.14, we get

Circumference = 3.14 x 8.7

Circumference = 27.318 units (rounded to three decimal places)

Therefore, the circumference of the circle with a diameter of 8.7 units is approximately 27.318 units. So, the correct option is D).

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--The given question is incomplete, the complete question is given

" The diameter of circle a is 8.7 units. find the circumference of the circle.

a. 17.4 units

b. 75.69 unit

c. 8.7 units

d. 27.318 units "--

Shown that if f has no local minima nor local maxima on i, then f is either increasing or decreasing on i.

Since f has no local minima nor local maxima on i, it means that for any point x in i, either f is increasing or decreasing in a small interval around x. In other words, either f'(x) > 0 or f'(x) < 0 for all x in i.

Now suppose there exist two points a and b in i such that a < b and f(a) < f(b). We want to show that f is increasing on i.

Consider the interval [a,b]. By the Mean Value Theorem, there exists a point c in (a,b) such that f'(c) = (f(b) - f(a))/(b - a). Since f(a) < f(b), we have (f(b) - f(a))/(b - a) > 0, which implies f'(c) > 0. Since f'(x) > 0 for all x in i, it follows that f is increasing on [a,c] and on [c,b]. Therefore, f is increasing on i.

A similar argument can be made if f(a) > f(b), which would imply that f is decreasing on i.

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Answer:

See explanation.

Step-by-step explanation:

The arc BX, central angle BCX, and inscribed angle BNX are connected through the following relationships:

1. The central angle BCX subtends the arc BX. This means that the central angle is formed by two radii connecting the center of the circle to the endpoints of the arc BX.

2. The inscribed angle BNX subtends the same arc BX. This means that the inscribed angle is formed by two chords connecting a point on the circumference of the circle to the endpoints of the arc BX.

3. The relationship between the central angle BCX and the inscribed angle BNX is given by the Inscribed Angle Theorem, which states that the measure of an inscribed angle is half the measure of the central angle subtending the same arc. In other words, if θ is the measure of the central angle BCX and α is the measure of the inscribed angle BNX, then:

[tex]\alpha =\frac{1}{2}[/tex] θ

The probability of getting heads and an even number is 1/4, and the probability of getting tails and a prime number less than 4 is 1/6.

To solve this, we need to use the multiplication rule of probability, which states that the probability of two independent events occurring together is the product of their individual probabilities.

Let's first find the probability of getting heads and an even number. Since there are two equally likely outcomes when flipping a coin (heads or tails), and three equally likely outcomes when rolling a die (1, 2, 3, 4, 5, or 6), the probability of getting heads and an even number is:

P(heads and even) = P(heads) x P(even)

= 1/2 x 3/6

= 1/4

Next, let's find the probability of getting tails and a prime number less than 4. The prime numbers less than 4 are 2 and 3. So, the probability of getting tails and a prime number less than 4 is:

P(tails and prime) = P(tails) x P(prime)

= 1/2 x 2/6

= 1/6

Therefore, the probability that Oscar gets heads and an even number is 1/4, and the probability that Oscar gets tails and a prime number less than 4 is 1/6.

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The actual length of the truck is 15.6 meters and the actual width is 3.24 meters.

The actual length of the truck can be calculated by multiplying the length of the model by the scale factor:

Similarly, the actual width of the truck can be calculated as:

Therefore, the actual length of the truck is 15.6 meters and the actual width is 3.24 meters.

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Answer:

0.48 = 48/100

48/100 ÷ 4/4 = 12/25

0.48 = 12/25 =A

When the pretax financial income is negative (indicating a loss), the taxable income will also be negative. This means that the company can use the loss to offset future profits and reduce its tax liability.

To calculate the taxable income (loss) for each year, we need to apply the corresponding tax rate to the pretax financial income (or loss) figures. Here's the breakdown:

2017:

Taxable income = Pretax financial income * Tax rate

Taxable income = $77,000 * 0.25

Taxable income = $19,250

2018:

Taxable income = Pretax financial income * Tax rate

Taxable income = ($38,000) * 0.20

Taxable income = ($7,600)

2019:

Taxable income = Pretax financial income * Tax rate

Taxable income = ($33,000) * 0.20

Taxable income = ($6,600)

2020:

Taxable income = Pretax financial income * Tax rate

Taxable income = $122,000 * 0.20

Taxable income = $24,400

2021:

Taxable income = Pretax financial income * Tax rate

Taxable income = $90,000 * 0.20

Taxable income = $18,000

Please note that when the pretax financial income is negative (indicating a loss), the taxable income will also be negative. This means that the company can use the loss to offset future profits and reduce its tax liability.

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Answer:

there is a lot of words

Step-by-step explanation:

6209

The cost of a flight from Hong Kong to Tokyo with Galois Airways is 1429.99 HKD.

We start by calculating the Porson's product-moment correlation coefficient between the distance and airfare data. The value of the correlation coefficient ranges from -1 to +1. A value of -1 indicates a perfect negative correlation, 0 indicates no correlation, and +1 indicates a perfect positive correlation.

In this case, the correlation coefficient between distance and airfare for Galois Airways flights is 0.948, indicates a strong positive correlation between the distance and airfare.

The regression line is expressed as:

y = a + bx

where y is the dependent variable (airfare), x is the independent variable (distance), a is the intercept (the value of y when x is zero), and b is the slope (the change in y for a one-unit change in x).

The regression equation for Galois Airways flights is:

y = 553.51 + 0.292x

Now, we can use the regression equation to estimate the cost of a flight from Hong Kong to Tokyo, which is 2900 km away.

y = 553.51 + 0.292(2900) = 1429.99 HKD

Therefore, we estimate that the cost of a flight from Hong Kong to Tokyo with Galois Airways is 1429.99 HKD.

Finally, we need to explain why it is valid to use the regression equation to estimate the airfare between Hong Kong and Tokyo. We can do this by examining the assumptions of linear regression. The two main assumptions are that there is a linear relationship between the variables, and that the residuals (the differences between the actual and predicted values) are normally distributed with constant variance.

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Complete question is  Galois Airways has flights from Hong Kong International Airport to different destinations. The following table shows the distance, x kilometres, between Hong Kong and the different destinations and the corresponding airfare, y, in Hong Kong dollars (HKD) Destination Bali, Sydney, Bengaluru. Auckland, Bangkok, Indonesia Australia India Singapore New Thailand Zealand 3400 7400 4000 2600 9200 1700 Distance x, (km Airfare y, (HKD) 1550 3600 2800 1300 4000 1400 The Porson's product-moment correlation coefficient for this data is 0.948, correct to three significant figures. Use your prophio display calculator to find the equation of the regression line y on x.  b. The distance from Hong Kong to Tokyo is 2900 km. Use your regression equation to estimate the cost of a flight from Hong Kong to Tokyo with Calois Airways. c. Explain why it is valid to use the regression equation to estimate the airfare between Hong Kong and Tokyo.

Bob's minimum monthly credit card payment needs to be B) $129.00 to reach his dti goal of 36%.

Bob's total monthly debt payments are $1,947.00 ($1,250.00 mortgage + $349.00 auto loan + $348.00 credit cards). To achieve a dti ratio of 36%, his total monthly debt payments should be no more than $1,728.00 ($4,800.00 * 36%).

Therefore, he needs to reduce his monthly credit card payment by $219.00 ($1,947.00 - $1,728.00). Since his current minimum monthly credit card payment is $348.00, he needs to reduce it to d) $129.00 ($348.00 - $219.00) to reach his dti goal.

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Since t > 0, the time when the particle has a velocity of 20 m/s is approximately t ≈ 4.27 seconds.

A particle has a position function s(t) = t^3 - 4t^2 - 20t + 2 + 20t, t > 0. To find the time when the particle has a velocity of 20 m/s, we first need to find the velocity function by taking the derivative of the position function with respect to time:

v(t) = ds/dt = 3t^2 - 8t - 20.

Now set v(t) equal to 20 and solve for t:

20 = 3t^2 - 8t - 20.

40 = 3t^2 - 8t.

Now solve the quadratic equation for t:

t ≈ 4.27, -3.10.

To find the time when the acceleration is 0, we need to find the acceleration function by taking the derivative of the velocity function with respect to time:

a(t) = dv/dt = 6t - 8.

Now set a(t) equal to 0 and solve for t:

0 = 6t - 8.

t = 8/6 = 4/3.

So, the acceleration is 0 at t = 4/3 seconds.

The variance in acceleration signifies a change in the motion dynamics of the particle. When the acceleration is 0, it indicates that the particle is neither speeding up nor slowing down at that moment, resulting in a constant velocity.

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Answer:

(1,3)

Step-by-step explanation:

The midpoint formula is:

[tex](\frac{x1+x2}{2}),(\frac{y1+y2}{2})[/tex]

We have our 2 points, (-4,-2) and (2,8).

For this sake and for this explanation, point 1 is (-4,-2), and point 2 is (2,8).

We can substitute in our values:

[tex](\frac{-4+2}{2}),(\frac{-2+8}{2})[/tex]

substitute

[tex](\frac{2}{2}),(\frac{6}{2})[/tex]

Our midpoint is located at (1,3)

Hope this helps! :)

Answer:

(-1,3)

Step-by-step explanation:

To find the midpoint of a line segment, you want to find the change in x and y.

From (-4,-2) to (2,8), you move right by 6 and up by 10.

The midpoint is exactly half of this, meaning right by 3 and up by 5.

Therefore, the midpoint is (-1,3).

The  correct way to solve this equation for m in terms of y is  m = b - y/x

It is important to note that subject of formula is the variable that is made to stand alone in an equation.

It is described as the variable that is being worked out in an equation.

The subject of formula in an equation is worked to stand alone on on end of the equality sign.

Example of equations

x = y - 2

The variable 'x' is the subject of formula

From the information given, we have that;

y= mx+b

collect the terms

mx = b - y

Divide by the coefficient

m = b - y/x

The equation for m is m = b - y/x

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The complete question:

The equation y=mx+b is used to express the equation of a line. Which solution is a correct way to solve this equation for m in terms of y?

The number of Americans to leave a tip of more than 20% in 1500 is 90

If only 6% of Americans leave a tip of more than 20% for satisfactory service in a restaurant, we can assume that the same proportion of restaurant customers will do so.

Therefore, out of 1,500 restaurant customers, we would expect:

6% of 1,500 = (6/100) x 1,500 = 90

So we would expect 90 restaurant customers to leave a tip of more than 20%.

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The perimeter of the shaded region is approximately 85.67 cm The area of the shaded region is approximately 91.84 cm² (rounded to the nearest tenth).

To calculate the perimeter and area of the shaded region, we first need to find the radius of each circle.

The larger circle has a diameter of 21 cm, which means its radius is 10.5 cm (half of the diameter). The smaller circle has a diameter of 10 cm, so its radius is 5 cm.

To find the perimeter of the shaded region, we need to add the circumference of both circles and subtract the overlap (the length of the shared segment). The circumference of the larger circle is 2π(10.5) ≈ 65.97 cm, and the circumference of the smaller circle is 2π(5) ≈ 31.42 cm.

To find the length of the shared segment, we can use the Pythagorean theorem. The distance between the centers of the circles is 15 cm (the sum of the radii), so we can form a right triangle with legs of 10.5 cm and 5 cm. Using the Pythagorean theorem, we get:

c² = a² + b²
c² = 10.5² + 5²
c² ≈ 137.25
c ≈ 11.72

So the length of the shared segment is approximately 11.72 cm.

Therefore, the perimeter of the shaded region is approximately 65.97 + 31.42 - 11.72 = 85.67 cm (rounded to the nearest tenth).

To find the area of the shaded region, we need to subtract the area of the smaller circle from the area of the larger circle, and then subtract the area of the overlap (the area of the shared segment).

The area of the larger circle is π(10.5)² ≈ 346.36 cm², and the area of the smaller circle is π(5)² ≈ 78.54 cm².

To find the area of the shared segment, we can use the formula for the area of a sector of a circle:

A = (θ/360)πr²

where θ is the central angle of the sector. In this case, the sector has a central angle of 2cos⁻¹(5/10.5) ≈ 105.2°, so:

A = (105.2/360)π(10.5)²
A ≈ 91.84 cm²

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-3.8 is the slope of the secant line connecting (1, f(1)) and (9, f(9)).

To get the slope of the secant line, we must first compute the values of f(1) and f(9):

f(1)

= 1² - 5(1)

= -4

f(9)

= 9² - 5(9)

= 36 - 45

= -9

The formula for the slope of the secant line running between these two locations is:

slope = (y-change)/(x-change)

= (f(9)-f(1))/(9-1)

Substituting f(1) and f(9) values and simplifying yields slope ,

= (-9-(-4))/(9-1)

= -5/8

= -0.625

When we round this to two decimal places, we get:

slope = -0.63

The slope of the secant line connecting (1, f(1)) and (9, f(9)) is thus -0.63.

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If the largest single rough diamond ever found, the Cullinan diamond, weighed 3106 carat, it weighs approximately 621,200 milligrams and 1.37 pounds.

The Cullinan Diamond, the largest single rough diamond ever found, weighed 3,106 carats. To convert its weight to milligrams and pounds, we'll use the conversion factor of 1 carat = 0.2 grams.

First, convert carats to grams:
3,106 carats * 0.2 grams/carat = 621.2 grams

Next, convert grams to milligrams:
621.2 grams * 1,000 milligrams/gram = 621,200 milligrams

Lastly, convert grams to pounds:
621.2 grams * 0.00220462 pounds/gram ≈ 1.37 pounds

So, the Cullinan Diamond weighs approximately 621,200 milligrams and 1.37 pounds.

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The probability of a passengers waiting at the stop less than 5 minutes and more than 10 minutes is equal to 1/6 and 2/3 respectively.

Probability that the passenger waits less than 5 minutes for the train,

Area under the probability density function (PDF) of the arrival time distribution from 7:00am to 7:05am.

Distribution is uniform,

PDF is a constant function over the interval [7:00am, 7:30am] .

With height 1 / (30 minutes - 0 minutes) = 1/30.

Area under the PDF from 7:00am to 7:05am is,

Probability of waiting less than 5 minutes

= area under PDF from 7:00am to 7:05am

= (1/30) ×(5 - 0) minutes

= 1/6

Probability that the passenger waits less than 5 minutes for the train is 1/6.

Probability that the passenger waits more than 10 minutes for the train is

= Area under the PDF from 7:00am to 7:30am -  area under the PDF from 7:00am to 7:10am.

Area under PDF from 7:00am to 7:30am

= (1/30) × (30 - 0) minutes

= 1

Area under PDF from 7:00am to 7:10am

= (1/30) × (10 - 0) minutes

= 1/3

Area under PDF from 7:10am to 7:30am

= 1 - 1/3

= 2/3

Probability of waiting more than 10 minutes

= area under PDF from 7:10am to 7:30am

= (1/30) × (30 - 10) minutes

= 2/3

Probability that the passenger waits more than 10 minutes for the train is 2/3.

Therefore, the probability of waiting less than 5 minutes and waiting more than 10 minutes is equal to 1/6 and 2/3 respectively.

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The scale of the drawing is 1:33 1/3, because the actual size of each grid square in the kitchen floor tile is 33 1/3 times larger than its size in the drawing.

The scale of a architectural drawing represents the proportional relationship between the size of an object in the drawing and its actual size in real life.

In this case, the floor tiles in the Jackson family's kitchen are square with a length of 8 3/4 inches on each side, while each grid square in the drawing measures 1/4 inch on each side.

To determine the scale of the drawing, we need to find the ratio between the actual size of a grid square and its size in the drawing.

Using proportions, we can set up an equation to solve for the scale. Let x be the scale of the drawing, then we have:

8 3/4 inches / (1/4 inch) = x

Simplifying the left side of the equation gives us:

35 inches = x

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