For lunch you can pick a main item (pizza or sandwich), a side item (fruit, veggie or chips) and a drink (milk or juice). How many different lunches can be chosen?

To find the critical points at which profit is maximized given the total revenue TR = 4700 - 302 and total cost TC = 320/10,500, we need to compute the marginal revenue and marginal cost, equate MR = MC to find the optimal quantity Q∗, verify if Q∗ is a relative maximum point, and compute the maximum profit level (π) by evaluating π∗ = 9(π(Q∗)).

Marginal Revenue (MR) is the derivative of the total revenue function with respect to quantity (Q). In this case, MR = dTR/dQ. By taking the derivative of TR = 4700 - 302 with respect to Q, we can find the expression for MR.

Marginal Cost (MC) is the derivative of the total cost function with respect to quantity (Q). In this case, MC = dTC/dQ. By taking the derivative of TC = 320/10,500 with respect to Q, we can find the expression for MC.

To find the optimal quantity Q∗, we equate MR and MC by setting MR = MC and solve for Q. This is because profit is maximized when MR equals MC.

Once we have found Q∗, we need to verify if it is a relative maximum point. This can be done by checking the second derivative of the profit function and determining if it is negative at Q∗. If the second derivative is negative, it confirms that Q∗ is a relative maximum point.

Finally, to compute the maximum profit level (π∗), we evaluate π(Q∗) by substituting Q∗ into the profit function. In this case, we can multiply the value of π(Q∗) by 9 to obtain the maximum profit level (π∗).

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Answer:

Step-by-step explanation:

Total number marbles Stacia has = 28

The ratio of red to blue marbles = 1 : 6

As the total number of marbles is 28. Thus,

r + b = 28

As the ratio of red to blue marbles is 1 to 6.

It means for each red marble 'r', we have 6 blue 'b' marbles. Thus,

b = 6r

now substituting b = 6r in the equation r + b = 28

r + b = 28

r + 6r = 28

7r = 28

divide both sides by 7

7r/7 = 28/7

r = 4

Thus,

The total number of red marbles ⇒ r = 4

The total number of blue marbles ⇒ b = 6r = 6(4) = 24

Therefore,

Answer: I couldn't honestly help with that I would if I could

Step-by-step explanation:

Answer:

Given

x+y+z=0

⟹x+y=−z

Cubing on both sides

(x+y) 3 =(−z) 3

⟹x 3 +y 3 +3x 2y+3xy 2 =−z 3

⟹x 3 +y 3 +3xy(x+y)=−z 3

⟹x 3+y 3+3xy(−z)=−z 3

⟹x 3 +y 3−3xyz=−z 3

⟹x 3 +y 3 +z 3 =3xyz

Step-by-step explanation:

Hope it is helpful.....

\(\qquad \qquad \textit{sum of an infinite geometric sequence} \\\\ \displaystyle S=\sum\limits_{i=0}^{\infty}\ a_1\cdot r^i\implies S=\cfrac{a_1}{1-r}\quad \begin{cases} a_1=\stackrel{\textit{first term}}{\frac{1}{8}}\\ r=\stackrel{\textit{common ratio}}{\frac{2}{3}}\\ \qquad -1 < r < 1 \end{cases}\)

\(\displaystyle\sum_{k=0}^{\infty} ~~ \underset{a_1}{\frac{1}{8}}\underset{r}{\left( \frac{2}{3} \right)}^k\implies S=\cfrac{ ~~ \frac{1}{8} ~~ }{1-\frac{2}{3}}\implies S=\cfrac{ ~~ \frac{1}{8} ~~ }{\frac{1}{3}}\implies S=\cfrac{3}{8}\)

The point_dist with the distance between point (x1, y1) and point (x2, y2): point_dist = math.sqrt((x2 – x1) ** 2.0 + (y2 – y1) ** 2.0).

The program is the illustration of functions. Functions are the collections of defined program statements, which are executed when they are evoked.

In this case, the program in Python, in which comments are used to explain each line is as follows:

#This imports the math module

import math

#This defines the function

def calculate distance (x1, y1, x2, y2):

#This calculates the distance between the point_dist

point_dist = math.sqrt((x2 – x1) ** 2.0 + (y2 – y1) ** 2.0)

#This returns the calculated distance

return dist distance

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Although part of your question is missing, you might be referring to this full question: Assign point_dist with the distance between point (x1, y1) and point (x2, y2). The calculation is: Distance = SquareRootOf( (x2 - x1)2 + (y2 - y1)2 ). Sample output with inputs: 1.0 2.0 1.0 5.0. Points distance: 3.0.

Over the time interval [2,5], the object traveled a distance of 450 meters.

To find the distance traveled over the time interval [0,2], we can use the formula for distance traveled, which is given by:

distance = velocity x time

Since the velocity is given by v(t) = 18t m/s, we can substitute t = 2 seconds to find the velocity at time t=2:
v(2) = 18(2) = 36 m/s

Now we can use this velocity and the time interval [0,2] to find the distance traveled:
distance = velocity x time
distance = 18t x t = 18t²

For t = 2 seconds, the distance traveled is:
distance = 18(2)² = 72 meters

Therefore, over the time interval [0,2], the object traveled a distance of 72 meters.

To find the distance traveled over the time interval [2,5], we can use the same formula, but this time we need to find the velocity at t=5 seconds:
v(5) = 18(5) = 90 m/s

Now we can use this velocity and the time interval [2,5] to find the distance traveled:
distance = velocity x time
distance = 18t x t = 18t²

For t = 5 seconds, the distance traveled is:
distance = 18(5)² = 450 meters

Therefore, over the time interval [2,5], the object traveled a distance of 450 meters.

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Answer:

Hana is wrong

Step-by-step explanation:

savings=26+34

=60

savings left after spending=60-6-3

=51

Answer: The total volume of all the tanks at the aquarium after the new dolphin tank is installed will be 1.25x10^6 gallons + 250,000 gallons = 1.5x10^6 gallons.

This is the equivalent of 1,500,000 gallons.

Step-by-step explanation:

Answer:

1. All numbers between, including 0 and 15.

Step-by-step explanation:

The domain is the independent variable (x), so in this case, it's be the amount of time James spent typing. James types for 15 minutes, so of course 0 and 15 have to be included, as it'll give a complete graph of what he's done so far.

Answer:

11:29.

Step-by-step explanation:

10:47 - 11:00 is 13 minutes, which leaves 29 minutes. So then you add that to 11:00, 11:29.

Answer:11:29

Step-by-step explanation:

If Doug starts at 10:47 and sweeps for 42 minutes

First you add 42 minutes to the 47.

Remember there are 60 minutes in an hour.

So do 47+42=89

Next do 89-60 (because there are 60 minutes in an hour)

You get 29 minutes.

Add one to the 10

That makes 11:29

The correct person is Amanda, as we want to find the total number of shoes, and each pair is composed by two shoes.

The total number of shoes is obtained applying the proportions in the context of the problem.

In the closest there are S pairs of shoes, and each pair of shoes is composed by two shoes, hence the total number of shoes in the closet is obtained as follows:

2 x S = 2S.

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Answer:

\(y=\boxed{-\dfrac{1}{4}}\left(x-\boxed{-2}\:\right)^2+\boxed{4}\)

Step-by-step explanation:

The graph of a quadratic function is symmetrical.

The axis of symmetry is the vertical line through the vertex of the parabola so that the left and right sides of the parabola are symmetrical.

From inspection of the given table, the axis of symmetry is x = -2 as the y-values of x = -3 and x = -1 are both 3.75.

Therefore, the vertex is (-2, 4).

Vertex form of a quadratic equation:  

\(y=a(x-h)^2+k\)

where:

Substitute the vertex and one of the other points into the vertex formula and solve for a:

\(\begin{aligned}y&=a(x-h)^2+k\\\implies 3&=a(0-(-2))^2+4\\3&=a(2)^2+4\\3&=4a+4\\-1&=4a\\a&=-\dfrac{1}{4}\end{aligned}\)

Substitute the vertex (-2, 4) and the found value of a into the formula to create an equation for the function:

\(y=\boxed{-\dfrac{1}{4}}\left(x-\boxed{-2}\:\right)^2+\boxed{4}\)

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Answer:

-1/4   -2    4

Step-by-step explanation:

Answer:

9.4534218

Step-by-step explanation:

i might be wrong if i am im sorry

Answer:

Step-by-step explanation:

41 minutes

He finished reading at 8:57 AM. How many minutes did he read? >) 41 minutes.

can i get brainlyest thx

Answer:

He read for 39 minutes

Step-by-step explanation:

You just subtract 57 - 18

The product of the two matrices Q₁Q₂ is orthogonal

In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. ... {\displaystyle Q^{\mathrm {T} }Q=QQ^{\mathrm {T} }=I,} where QT is the transpose of Q and I is the identity matrix.

It is said to be an orthogonal matrix if its transpose is equal to its inverse matrix, or when the product of a square matrix and its transpose gives an identity matrix of the same order.

If A is an n*n orthogonal matric, then A*A¹ = A¹*A

Therefore A*A¹ = A¹*A  = 1

This implies that the product Q₁O₂ is orthogonal.

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Answer:

72\(\sqrt{3}\)

Step-by-step explanation:

The area (A) of a rhombus is calculated as

A = \(\frac{1}{2}\) × d₁ × d₂ (d₁ and d₂ are the diagonals )

The diagonals bisect each other at right angles

d₁ = 2 × 6 = 12

Use the tangent ration in the upper left right triangle and the exact value

tan60° = \(\sqrt{3}\)

tan60° = \(\frac{opposite}{adjacent}\) = \(\frac{opp}{6}\) = \(\sqrt{3}\) ( multiply both sides by 6 )

opp = 6\(\sqrt{3}\) , then

d₂ = 2 × 6\(\sqrt{3}\) = 12\(\sqrt{3}\)

Thus

A = \(\frac{1}{2}\) × 12 × 12\(\sqrt{3}\) = 6 × 12\(\sqrt{3}\) = 72\(\sqrt{3}\)

Answer:

7.92%

Step-by-step explanation:

Given the following

Weight of package at home = 20.2 ounces.

Weight of the package at the office = 18.6ounces

Decrement = 20.2 - 18.6

percentage error = decrement/wt at home * 100

percentage error = 1.6/20.2* 100

percentage error = 160/20.2

percentage error = 7.92

HEnce  the percent error in the weight of the package is 7.92%

Answer:

y = -2x + 23.

Step-by-step explanation:

If the line is parallel to

y = -2x - 5,

that means it has the SAME SLOPE. Parallel lines have the same slope, but they could have different y-intercepts.

The slope intercept form is:

y = mx + b.

m = slope.

b = y intercept.

In this case, the slope is -2.

So we know the answer will have a slope of -2.

So we can write:

y = -2x + b.

We just have to finish the answer by replacing "b" with a number.

To find out what "b" is, we plug in the point (8,7).

To plug this point in, we replace "x" with 8 and "y" with 7.

7 = -2(8) + b.

7 = -16 + b.

Now to get b by itself to solve for b, we have to add 16 to both sides.

7 + 16 = b.

b = 23.

So our final answer is: y = -2x + 23.

Answer:

43.94 in total

Step-by-step explanation:

18% of 37.24 is 6.70 which would be the tip and adding those two numbers together would equal 43.94

Hope this helps. Plz give brainliest.

Answer: 37.42

Step-by-step explanation: first you need to add and point to the 18% like this 0.18 and add it to the first number

Compare the number of degree recipients for each major in two years and calculate the maximum absolute difference.

To determine the biggest absolute difference, subtract the number of degree recipients for each major in one year from the corresponding number in the other year.

Take the absolute value of each difference to ensure it is positive. Repeat this process for each major and compare the absolute differences.

Identify the largest absolute difference among the majors, which represents the biggest disparity in the number of degree recipients between the two years.

This analysis helps to identify which major experienced the most significant change in the number of degree recipients over the given time period.

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The chances are that the emission from the manufacturing unit is within the permissible level or not within the permissible level is 0.5525.

The term probability describes the chance that an event will occur. In this case, we know that the probability that the company is exceeding the permissible level is 0.35.

We also know that; probability that the carbon emission is within the permissible level is 1 - 0.35 = 0.65.

The chances are that the emission from the manufacturing unit is within the permissible level or not within the permissible level, hence;  0.65 x 0.85 = 0.5525.

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At one time, the British advanced corporation tax system taxed British companies' foreign earnings at a higher rate than their domestic earnings.

This was put in place to discourage multinational corporations from artificially shifting profits earned in the UK to low-tax jurisdictions. The policy was aimed at preventing companies from avoiding tax by moving profits out of the UK and into tax havens. By imposing a higher tax rate on foreign earnings, the UK government hoped to make it less attractive for companies to engage in profit-shifting practices.

The policy was controversial and faced criticism from some business groups, who argued that it placed an unfair burden on companies operating overseas. However, the government defended the policy as necessary to ensure that companies paid their fair share of tax in the countries where they operated. Eventually, the policy was replaced by a territorial tax system, which only taxes companies on their profits earned in the UK. This change was made to simplify the tax system and make it more attractive for companies to invest in the UK.

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Answer:

70 mph

Step-by-step explanation:

Here we want to calculate average speed

Mathematically, average speed = Total distance/Total time

Kindly recall distance = speed * time

for the first part;

We have: 60 * 2 = 120 miles

For the second: 4 * 75 = 300 miles

Average speed = (300 + 120)/(4 + 2) = 420/6 = 70 mph

The distance from Dock A to the coral reef cannot be determined without the bearing angles provided in the question.

To find the distance from Dock A to the coral reef, we need the bearing angles from both Dock A and Dock B. However, the bearing angles are not provided in the question, so it is not possible to calculate the distance accurately.

Bearing angles are measurements used in navigation to indicate the direction of an object relative to a reference point. Without the bearing angles, we cannot determine the exact position of the coral reef relative to Dock A.

In order to find the distance from Dock A to the coral reef, we need to know the bearing angles from both Dock A and Dock B. Without this information, it is not possible to determine the distance accurately.

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Answer:

173.8 squared

Step-by-step explanation:

area = 0.5 * b * h

I hope this helps!

Answer:

The area of a triangle is b x h divided by 2.

Substituting in the given values,

25.75 x 13.5 / 2

347.625 / 2

173.8125

The area of the triangle is 173.8125 ft squared.

Hope this helps! :)

The expression 14x⁴y³ - 42x³y⁴ is rewritten to 14x³y³(x - y)

An algebraic expression can be described as a mathematical expression that is made up of terms, coefficients, variables, factors and constants.

They are also made up of some arithmetic operations, such as;

From the information given, we have the algebraic expression;

14x⁴y³ - 42x³y⁴

Now, factor the common numbers, we have;

14(x⁴y³ - 3x³y⁴)

Factor the common variables, we get;

14x³y³(x - y)

Hence, the expression is 14x³y³(x - y)

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By using the property of function, the result obtained is, When f(94) is divided by 1000, the remainder is 561

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here the functional equation is given by

\(f(x) + f(x - 1) = x^2\)

Now,

\(f(x) + f(x - 1) = x^2\)

\(f(x) = x^2 - f(x - 1)\\f(94) = 94^2 - f(93) = 94^2 - 93^2 + f(92) =\\94^2 - 93^2 + 92^2 - f(91) = 94^2 - 93^2 + 92^2 -91^2+f(90)\)

\(94 + 93 + 92 + 91 + ..... +20^2 - f(19)\)

\(94 + 93 + 92 + ..... + 21 + 400 - 94\) [Since \(94 - 93 = 93 - 92 = .... = 1\)]

\(\frac{74}{2}(21 + 94) + 400 -94\)

\(37 \times 115 + 400 - 94\\4255 + 400 - 94\\4561\)

So f(94) = 4561

When 4561 is divided by 1000, the remainder is 561

So, when f(94) is divided by 1000, the remainder is 561

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Complete Question

The function f has the property that, for each real number x

\(f(x)+f(x-1) = x^2\)

If f(19)=94 what is the remainder when f(94) is divided by 1000?