ramona owns a small coffee shop, where she works full-time. her total revenue last year was $200,000, and her rent was $5,000 per month. she pays her one employee $3,000 per month, and the cost of ingredients averages $1,000 per month. ramona could earn $55,000 per year as the manager of a competing coffee shop nearby. her economic profit last year was were....
a. $18,000
b. $37,000
c. $55,000
d. $66,000
e. $92,000

The solution to the differential equation y" - 8y' + 16y = 24x + 2 is y = (c1 + c2 x) e^(4x) - 3x + 1 plus any constants determined by initial or boundary conditions.

To solve the given differential equation y" - 8y' + 16y = 24x + 2 using the method of undetermined coefficients, we first find the complementary solution of the homogeneous equation y" - 8y' + 16y = 0:

The characteristic equation is r^2 - 8r + 16 = 0, which has a double root of r = 4. Therefore, the complementary solution is y_c = (c1 + c2 x) e^(4x).

Next, we need to find a particular solution for the non-homogeneous equation. Since the right-hand side has two terms, we can try a particular solution of the form y_p = Ax + B for the homogeneous term and y_p = C for the constant term.

Substituting this form into the differential equation, we get:

y_p" - 8y_p' + 16y_p = 24x + 2

Taking the derivatives and plugging them back into the equation, we get:

-8A + 16B + 16C = 2

0 + 0 + 16C = 24

Solving for A, B, and C, we get A = -3, B = -1/2, and C = 3/2.

Therefore, the particular solution is y_p = -3x - 1/2 + 3/2 = -3x + 1.

The general solution is then y = y_c + y_p = (c1 + c2 x) e^(4x) - 3x + 1.

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Answer:

7^4/3^10 is the correct answer

The slope is 10 and the y-intercept is 0, making this a linear equation in the slope-intercept format.

The basic form of a linear equation is y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept. A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. Many real-world situations, such as the connection between a product's price and the number of sales, or the relationship between a person's age and height, can be modelled using linear equations.

given

Let t be the number of hours and d be the number of miles that Sebi goes. Since Sebi consistently travels at 10 mph on his bicycle, we can apply the following equation:

Distance is determined by rate and duration.

When we change the numbers, we obtain:

d = 10t

The slope is 10 and the y-intercept is 0, making this a linear equation in the slope-intercept format.

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The probability of a wheelchair not needing to be serviced for the 16 weeks of the semester is 0.230.

The exponential distribution is a continuous probability distribution that describes the time between two consecutive events that occur randomly and independently of each other. This distribution is useful in the fields of reliability, physics, and finance, among others.

The exponential distribution has a single parameter known as the scale parameter, which is denoted by lambda (λ) and is typically expressed in terms of the mean time between failures.The mean, median, and standard deviation are three of the most common summary statistics used to describe a probability distribution.

The probability of a wheelchair not needing to be serviced for the 16 weeks of the semester can also be calculated using the exponential distribution.

Mean: The mean of the exponential distribution is equal to 1/λ.λ = 1/7 = 0.143

Therefore, the mean is 1/λ = 1/0.143 = 6.993.

Median: The median of the exponential distribution is equal to ln(2)/λ.λ = 1/7 = 0.143

Therefore, the median is ln(2)/λ = ln(2)/0.143 = 4.837.

Standard deviation: The standard deviation of the exponential distribution is equal to 1/λ.λ = 1/7 = 0.143

Therefore, the standard deviation is 1/λ = 1/0.143 = 6.993.

Probability: P(X > 16) = e^(-λx)λ = 1/7 = 0.143X = 16P(X > 16) = e^(-0.143 * 16) = 0.230

Therefore, the probability of a wheelchair not needing to be serviced for the 16 weeks of the semester is 0.230.

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Answer:

12 large boxes, 9 small boxes

Step-by-step explanation:

Let s = number of small boxes

l = number of large boxes

We set up and solve this system of equations:

s + l = 21------->3s + 3l = 63

3s + 5l = 87------>3s + 5l = 87

----------------

2l = 24

l = 12, s = 9

The given numbers are in decimal and binary system and the final result of the given operation is [tex](4675.31)_{10}[/tex].

A binary integer (base-2) is converted to an equivalent decimal number using the binary to decimal conversion formula. (base-10). In mathematics, integers are expressed using a number system. It is a method to display numerical data. The four various numeral systems are as follows:

System of Binary Numbers (Base-2)
system of octal numbers (Base-8)
System of Decimal Numbers (Base-10)
System of Hexadecimal Numbers (Base-16).
We are the two numbers:-

[tex](4623.56)_{10} , (110011.11)_{2}[/tex]

these are in decimal and binary system respectively.

now, we will express them in same system ( here we choose decimal system).

[tex](110011.11)_{2} = (2^{5} + 2^{4} + 0 + 0 + 2^{1} + 2^{0} + 2^{-1} + 2^{-2} )_{10} \\= (2^{5}+2^{4}+0*2^{4}+0*2^{3}+2^{1}+2^{0}+2^{-1}+2^{-2})_{10} \\= (32+16+2+1+0.5+0.25)_{10} \\= (51.75)_{10}[/tex]

Now, addition is done below:-

4623.56+51.75= 4675.31.

hence, the final result of the given operation= [tex](4675.31)_{10}[/tex]

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The area's estimated snapping turtIe popuIation, rounded to the cIosest whoIe number, is 56.

That is correct! As 0 is a whoIe number and aII whoIe numbers were integers, 0 is additionaIIy an integer.

The LincoIn-Petersen index method, which is frequentIy empIoyed to determine the size of a popuIation using a capture-mark-recapture approach, can be utiIized to resoIve this issue.

The estimated popuIation (N) is equaI to (M x C) / R using the foIIowing formuIa:

M is the quantity of peopIe incIuded in the initiaI sampIe (marked turtIes)

C is the second sampIe's size (totaI number of turtIes caught in the second sampIe)

R is the quantity of marked peopIe who were Iocated again in the specimen.

When we enter the specified vaIues into the equation, we obtain:

N = (15 x 15) / 4

N = 56.25

The area's snapping turtIe popuIation is thought to be 56, rounded off to the cIosest whoIe number.

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As a result, in order to make the most money, the widgets must be sold for $15.83, to the nearest cent.

The cost that consumers pay for a single piece of a good is known as the price at which it is sold. For instance, if a company produces lamps, the sales unit price is indeed the cost to customers of a single lamp. We must identify the x value that maximizes the profitability function y = -6x² + 190x - 826 in order to estimate the selling price for widgets that will yield the highest profit.

Calculus can be used in this process. The critical points, or maximum and lowest values of the function, can be found by taking the derivatives of a profitability function in relation to x and setting it to zero. The derivative test can then be used to assess if the crucial point is indeed a maximum or even a minimum. If we take the profit function's derivative with regard to x, we get:

y' = -12x + 190

By setting y' to zero and figuring out x, we obtain:

-12x + 190 = 0

x = 15.83

The critical value of x is therefore 15.83.

We must compute the second derivative of a profit function with respect to x to determine if this critical point is indeed a maximum or a minimum:

y'' = -12

The critical point at x = 15.83 corresponds to the greatest value of the money demand function since y" is negative. In order to optimize the profit, the widgets must be sold for $15.83, to the nearest cent.

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The number of bacteria  in an egg salad that is left out at room temperature is 256 option D.

The bacteria would double 4 times in 2 hours, so the total number of bacteria in the egg salad would be 256.

So we have 4 bacteria after 2 hours we have,

4 x 4 x 4 x 4 = 256 bacteria.

Probability denotes the likelihood of something happening. It is a mathematical discipline that deals with the occurrence of a random event. The value ranges from zero to one. Probability has been introduced in mathematics to predict the likelihood of occurrences occurring.

Probability is defined as the degree to which something is likely to occur. This is the fundamental probability theory, which is also utilised in probability distribution, in which you will learn about the possible results of a random experiment. To determine the likelihood of a particular event occurring, we must first determine the total number of alternative possibilities.

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Complete question:

There are four bacteria in an egg salad that is left out at room temperature. After two hours, how many bacteria will be in the egg salad?

- 32

- 2048

- 8

- 256

Answer:

d. 32 in.²

Step-by-step explanation:

Bottom face: 6 in. × 0.5 inch

Side faces: 2 × 5 in. × 0.5 in.

Front and back faces: 2 x 6 in. × 4 in. / 2

surface area = 3 in.² + 5 in.² + 24 in.²

surface area = 32 in.²

Answer: To solve the problem, we need to use the given time to find Michaela's swimming rate in meters per second, and then use that rate to calculate the distance she will swim in 10 minutes.

1 minute = 60 seconds

4 minutes and 50 seconds = 4 x 60 + 50 = 290 seconds

So, Michaela's rate is:

distance / time = x / 290 seconds

where x is the distance she can swim in 290 seconds.

Simplifying the equation:

x = distance = (time x distance) / time = (290 seconds x distance) / 290 seconds = distance

We know that Michaela can swim 500 meters in 290 seconds:

500 meters / 290 seconds = 1.724 meters per second

Therefore, in 10 minutes (600 seconds), she will swim:

distance = rate x time = 1.724 meters/second x 600 seconds = 1034.4 meters

So, Michaela will swim 1034.4 meters in 10 minutes.

Step-by-step explanation:

Answer:

p ≥ 228

Step-by-step explanation:

p ≥ 228

This inequality means the Bowlers have to score at least 228 points to move on.

Hope this helped!

The answer is C. Yes, the bases are parallel and the legs are congruent.

A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called bases, and the non-parallel sides are called legs. There are different types of trapezoids, including isosceles trapezoids where the legs are congruent and right trapezoids where one of the angles between a leg and a base is a right angle. A trapezoid is a quadrilateral with one pair of parallel sides. The parallel sides are called the bases, and the non-parallel sides are called the legs. The legs can be either congruent or non-congruent.

There are several types of trapezoids, based on the relationships between their sides and angles:

Isosceles trapezoid: This is a trapezoid where the legs are congruent. The bases may or may not be congruent.

Right trapezoid: This is a trapezoid where one of the angles between a leg and a base is a right angle (90 degrees).

Scalene trapezoid: This is a trapezoid where none of the sides are congruent.

Trapezium: In British English, a trapezium is a quadrilateral with no parallel sides. In American English, this shape is called a general quadrilateral.

Trapezoids are used in many areas of mathematics, including geometry and calculus. In geometry, they can be used to calculate the area and perimeter of various shapes. In calculus, they can be used to calculate integrals over regions with curved boundaries.

Here,

In an isosceles trapezoid, the legs (non-parallel sides) are congruent, and the bases (parallel sides) are also congruent.

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Peter makes a profit of Rs 60.00 by means of buying 30 apples at Rs 5.00 each and selling them at Rs 7.00 every.

Peter buys 30 apples at a value of R5.00 every, for a total price of R150.00. He then sells every apple at R7.00, for a complete sales of R210.00.

To calculate his earnings, we subtract his price from his revenue.

profit = revenue - cost

In this case, his income is R210.00 - R150.00 = R60.00. this means that Peter makes a profit of R60.00 from selling 30 apples.

Consequently, Peter makes a profit of Rs 60.00 by means of buying 30 apples at Rs 5.00 each and selling them at Rs 7.00 every.

The earnings made with the aid of Peter is the distinction between the sales generated via the income and the price of buying the apples. with the aid of subtracting the cost from the revenue, we are able to see the earnings he has made. This easy calculation can be used by organizations to decide their earnings and to make choices approximately pricing and stock.

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There are 6 ways for the student to select her lunch when she chooses from the given main course selection and chooses between water or tea for her drink selection. 3 × 2 = 6 ways.

The problem is about counting the number of ways that can be possible to select the meal for the student.

The student selects one main course and one drink. The main course consists of one of the following:

beef with broccoli, moo shu pork, or chicken with cashew. She can select water or tea for her drink. Therefore, the total number of ways that can be possible to select her lunch is obtained by multiplying the number of options for each course.For instance, there are three options for main course selection, and two options for drink selection. Therefore, the total number of ways that she can select her lunch

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There are 84 ways to buy two objects of different types.

To choose two objects of different types, we can choose one type of object first and then choose one object from that type and one object from the other two types.

The number of ways to choose one type of object is 3 (cups, saucers, or spoons). For each type of object, there are different numbers of objects to choose from:

So, the total number of ways to choose two objects of different types is:

3 x (5 x 4 + 5 x 2 + 4 x 2) = 3 x 28 = 84

Therefore, there are 84 ways to buy two objects of different types.

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Answer:

x=4.9

Step-by-step explanation:

using the Pythagorean theorem to find the leg of tringle A:

[tex]a^{2} +b^{2} =c^{2}[/tex]

[tex]y^{2} +3^{2} =7^{2}[/tex]

[tex]y^{2} +9=49\\y^{2} =40\\\sqrt{y^{2} } =\sqrt{40} \\y=\sqrt{40}[/tex]

we know that the hypotenuse for tringle B is [tex]\sqrt{40}[/tex] so, now we can find the value of x:

using the Pythagorean theorem:

[tex]a^{2} +b^{2} =c^{2}[/tex]

[tex]4^{2} +x^{2} =(\sqrt{40} )^{2}[/tex]

[tex]16+x^{2} =40\\x^{2} =24\\\sqrt{x^{2} } =\sqrt{24} \\x=4.9[/tex]

Answer:

X

Step-by-step explanation:

We first must check the total amount of breakfast. Y happens to have 130 instead of 125. Now, we see that W and Z have a majority on strawberries with oatmeal, which is not what we are looking for. The last answer we have is X, where there is a majority of oatmeal + blueberries and there is a total of 125 breakfasts.

Hope this helps!

The amount of time Sophie waited for Rana at the finish line can be calculated as 20/r - 20/s, where r is Rana's biking speed in mph and s is Sophie's biking speed in mph.

To find out how long Sophie waited for Rana at the finish line, we need to calculate the time it takes for each of them to complete the 20 mile trip. The time taken can be calculated using the formula: time = distance / speed.

Sophie's time to complete the trip can be calculated as follows:

time taken by Sophie = distance / speed of Sophie

time taken by Sophie = 20 / s

Similarly, Rana's time to complete the trip can be calculated as:

time taken by Rana = distance / speed of Rana

time taken by Rana = 20 / r

Since Sophie waits for Rana at the finish line, she would have to wait for the amount of time it takes for Rana to finish the trip. Therefore, the total waiting time would be the time taken by Rana to complete the trip minus the time taken by Sophie to complete the same trip:

waiting time = time taken by Rana - time taken by Sophie

waiting time = 20/r - 20/s

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Answer:

1. The graphs of f(x) and h(x) are both quadratic functions with a minimum point. However, the minimum point of f(x) is located at (6,0), while the minimum point of h(x) is located at (2,3).

2. The graphs of g(x) and h(x) both open upwards and are quadratic functions. However, the vertex of g(x) is located at the origin (0,0), while the vertex of h(x) is located at (2,3).

3. The graph of g(x) is a simple parabola that opens upwards, while the graphs of f(x) and h(x) are more complex parabolas with a minimum point and an upward opening. The graph of f(x) is centered at (6,0), while the graph of h(x) is centered at (2,3).

The time that Andrew can use to row his boat in still waters would be = 5.75 hrs.

The speed can be defined as the scalar quantity that shows that amount of distance that is covered with respect to time.

The formula that can be used to calculate speed = distance/time.

The speed of the current in the river = 2 mph

The distance covered downstream = 15miles

The distance covered upstream = 8

average distance = 15+8/2 = 11.5 miles

Given 2 miles = 1 HR

11.5 miles = X

Make X the subject of formula;

X = 11.5×1/2

= 5.75 hrs

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The circumference of circle has the formula 2xPixr

where, r = radius of circle.

The relation between radius (r) and diameter (d) of the circle is d = 2r

Circumference = pi x diameter = 3.14 x 25m = 78.5m

Circumference = 2 x pi x radius = 2 x 3.14 x 4.5cm = 28.26cm

Circumference = 2 x pi x radius = 2 x 3.14 x 28in = 175.84in

Circumference = pi x diameter = 3.14 x 19ft = 59.66ft

Circumference = 2 x pi x radius = 2 x 3.14 x 3mm = 18.84mm

Circumference = 2 x pi x radius = 2 x 3.14 x 35in = 219.8in

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If the box holds 2 layers with 15 cubes in each layer, the volume of the box is 56.25 cubic inches.

To find the volume of the box, we need to multiply the length, width, and height of the box. Since the cubes are all the same size, we can use the dimensions of a single cube to determine the size of the box.

Each cube has a side length of 1/2 inch, so its volume is (1/2)^3 = 1/8 cubic inch. Since there are 30 cubes in the box, the total volume of all the cubes is:

30 cubes x 1/8 cubic inch per cube = 3 3/4 cubic inches

The box has two layers, each with 15 cubes, arranged in a rectangular shape. Therefore, the length and width of the box are each 1/2 inch x 15 cubes = 7 1/2 inches.

The height of the box is equal to the height of two layers of cubes, which is 2 x 1/2 inch = 1 inch.

Now, we can calculate the volume of the box by multiplying its length, width, and height:

Volume of box = length x width x height = 7 1/2 inches x 7 1/2 inches x 1 inch = 56.25 cubic inches.

In summary, by using the dimensions of a single cube and the number of cubes in the box, we can calculate the total volume of the cubes. Then, by using the dimensions of the arrangement of the cubes, we can calculate the dimensions of the box, which allows us to find its volume by multiplying its length, width, and height.

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Answer: We have one km being covered in one minute. So how many km do we cover in one hour? Remember, there are 60 minutes in one hour. Do you think it might be 60 km in one hour? Can you say that a different way, say number of km in one hour? 60 km in one hour. Close. Very good. Now let’s clean up your answer and just say 60 km per hour or 60 ``````````````````````.

The number line which represents the solution bro the inequality 2x + 5 < 11 is:

First, we must solve the inequality so that it looks it's simplest form in order to be represented on a number line.

Solving the inequality is as follows:

In essence, representation of the inequality, y < 3 on the number line is as follows:

An open circle is at positive 3. Everything to the left of the circle is shaded.

PS: It is only a closed circle if the inequality includes an equal to sign.

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We may approximate the sin 165 angles using trigonometric formulas as: tan 165°/(1 + tan2(165°)) (1-cos2(165°))...

Trigonometric identities enable the expression of sin 165° as,

Sin (15°) = sin(180° - 165°)

(-sin 180 + -sin 165) = -sin 345

cos(-75°) = cos(-90° - 165°)

(90 + 165)/255 = -cos 255

Explanation: We know that cos(165) is negative and sin(165) is positive because 165 is in QII. We will use 330 with in half angle formulae because 165=3302.

165 degrees are somewhere between 90 and 180 degrees. Hence, it has an acute angle.

Hence, the 165° angle's addition is 15°. Q. Below are a few angles' measurements.

525 is a positive number of interactions angle, while 195 is a negative coterminal angle.

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A smaller sample size can offer a good estimate of the mean. The expressions population of working adults is not too vast to estimate the mean of the entire group using a sample.

An expression in mathematics is a collection of numbers, variables, and complex mathematical (such as addition, subtraction, multiplied, division, multiplications, and so on) that express a quantity or value.

Expressions might be as basic as [tex]"3 + 4"[/tex] or as complicated as [tex]"(3x2 - 2) / (x + 1)"[/tex] . They may also contain functions like "sin(x)" or "log(y)".

Expressions can indeed be evaluated by swapping values for the variables and performing the algebraic calculations in the order specified.

If [tex]x = 2[/tex] , for example, the formula [tex]"3x + 5"[/tex] equals  [tex]3(2) + 5 = 11[/tex] . Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.

If Fran chooses a random sample of the working adult population in her town, the mean for that group will most likely be close to the mean for the entire group.

Therefore,  A smaller sample size can offer a good estimate of the mean. The population of working adults is not too vast to estimate the mean of the entire group using a sample.

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Answer:

10/63

Step-by-step explanation:

Equation: 2/7 * 5/9

Multiply the numerators: 2*5=10

Multiply the denominators: 7*9=63

Your answer: 10/63

The size of the the matrix B if a matrix A is 5x3 and the product AB is 5x7 is B =[3x7].

Two matrices can only be multiplied if the first matrix has the same number of columns as the second matrix has. If the first matrix has dimensions of a x b and the second matrix has dimensions of c x d, then b = c and their product will have dimensions of a x d.

Let A is a 3 x 5 matrix and B is a 5 x 7 matrix

We know that matrix multiplication of A and B is possible if

Number of columns of A = Number of rows of B

Since in the given problem

Number of columns of A = Number of rows of B = 5

So the product is possible

Now the product AB is a matrix of order 3 × 7

Now the order of the product AB is 3 × 7

If a 3 x 5 matrix is multiplied by a 5 x 7 matrix then their product is a matrix of order 3 × 7.

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