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[tex]2x^4 + x^3 - x^2 +54x - 56[/tex] expression represents the area of Dylan’s room

Given that,

Length of room = [tex]x^2 -2x+8[/tex]

Width of room = [tex]2x^2 + 5x - 7[/tex]

To find: Expression that the area (lw) of Dylan’s room

Since bedroom is generally of rectangular shape, we can use area of rectangle

The area of rectangle is given as:

[tex]\text {area of rectangle }=\text { length } \times \text { width }[/tex]

Substituting the given expressions of length and width,

[tex]area = (x^2 -2x+8)(2x^2 + 5x - 7)[/tex]

We multiply each term inside first parenthesis with each term inside the second parenthesis.

So it becomes,

[tex]2x^4 + 5x^3 - 7x^2 -4x^3 -10x^2 +14x +16x^2 +40x - 56[/tex]

Now combine like terms,

[tex]2x^4 + x^3 - x^2 +54x - 56[/tex]

Thus the above expression represents the area of Dylan’s room

Answer:

c

Step-by-step explanation:

Question:

A car’s gas tank can hold 11 9/10 gallons of gasoline. It contains 8 3/4 gallons of gasoline. How much more gasoline is needed to fill the tank?

Answer:

[tex] 5\frac{3}{20}[/tex] more gasoline is needed to fill the tank?

Step-by-step explanation:

Given:

Capacity of the car tank = 11 9/10

Quantity of fuel already present = 8 3/4

To Find:

Quantity needed to fill the tank = ?

Solution:Let the quantity of the  gasoline needed to fill the tank be  x

Then

x = total capacity of the tank  -  quantity of fuel already present in the tank

x = [tex]11 \frac{9}{10}[/tex] - [tex]8 \frac{3}{4}[/tex]

x = [tex]\frac{119}{10}[/tex] - [tex]\frac{27}{4}[/tex]

x = [tex] 11.9[/tex] - [tex]6.75[/tex]

x = 5.15 or [tex] 5\frac{3}{20}[/tex]

Answer:x4+2x3+7x2+6x+12

Step-by-step explanation:

Answer:

The number of marbles Richard has 24 and John has 6.

Step-by-step explanation:

Richard has four times as many marbles as john.

If Richard have 18 to John they would have the same number.

Now, to find number of marbles each has.

Let the marbles of John be [tex]x[/tex].

And the marbles of Richard be [tex]4x.[/tex]

According to question:

[tex]4x=x+18.[/tex]

Subtracting both sides by [tex]x[/tex] we get:

[tex]3x=18.[/tex]

Dividing both sides by 3 we get:

[tex]x=6.[/tex]

Marbles of John = [tex]6.[/tex]

Marbles of Richard = [tex]4x=4\times 6=24[/tex]

Therefore, the number of marbles Richard has 24 and John has 6.

Final answer:

John has 12 marbles, and Richard has 48 marbles, as Richard has four times as many as John, and giving John 18 marbles would equalize their amounts.

Explanation:

To find the answer, we need to set up an equation based on the information provided: Richard has four times as many marbles as John, and if Richard gives John 18 marbles, they would have the same number.

Let's denote the number of marbles John has as J. Then Richard has 4J marbles. If Richard gives 18 marbles to John, Richard would have 4J - 18 marbles, and John would have J + 18 marbles. According to the problem, after the exchange, they have an equal number of marbles, so we can write the equation:

4J - 18 = J + 18

Solving for J, we move all the J terms to one side and numeric terms to the other side:

4J - J = 18 + 18

3J = 36

Dividing both sides by 3, we get:

J = 12

So, John has 12 marbles. Since Richard has four times as many, he has 4 x 12 = 48 marbles. Therefore, Richard has 48 marbles and John has 12 marbles.

The radius of can is 2.524 inches

Solution:

Given that large can of tuna fish that has a volume of 66 cubic  inches and a height of 3.3 inches

To find: Radius

Given a large can of tuna fish, we know that can is generally of cylinder shape, we can use the volume of cylinder formula,

The volume of cylinder is given as:

[tex]\text{ volume of cylinder}= \pi r^{2} h$[/tex]

Where,

"r" is the radius of cylinder

"h" is the height of cylinder

[tex]\pi[/tex] is a constant equal to 3.14

Substituting the given values in above formula,

[tex]66 = 3.14 \times r^2 \times 3.3\\\\66 = r^2 \times 10.362\\\\r^2 = \frac{66}{10.362}\\\\r^2 = 6.369\\\\r = 2.524[/tex]

Thus the radius of can is 2.524 inches

Answer:

see the explanation

Step-by-step explanation:

The complete question in the attached figure

Let

x ----> the number of movies

y ----> the amount of money remaining on her gift card

we know that

The slope of the linear equation is equal to the unit rate

take two points from the graph

(0,18) and (2,12)

Find the slope

[tex]m=(12-18)/(2-0)[/tex]

[tex]m=(-6)/(2)=-\$3\ per\ movie[/tex] ---> is negative because is a decreasing function

That means -----> Each movie she rents cost her $3, so her  gift card balance will decrease $3 for every movie rented

The linear equation is equal to

[tex]y=-3x+18[/tex]

For y=0

[tex]0=-3x+18[/tex]

[tex]x=6[/tex]

so

6 is the maximum number of movies that Elyse can rent on line

The unit rate is the ratio of the change in the y-coordinate value to the change in the x-coordinate value between any two strategically chosen points. Elyse's unit rate represents the cost per movie rental.

While the graph isn't directly available, the principle to find the unit rate of the graph is the same. The unit rate is the ratio of the change in the vertical (y-axis) value to the change in the horizontal (x-axis) value between any two distinct points on the graph. In the context of Elyse's movie rentals, the unit rate would represent the cost per movie.

To calculate this, you'd subtract the y-coordinate value of the second point from the y-coordinate value of the first point. This represents the change in the balance of the gift card. Then you'd subtract the x-coordinate value of the second point from the x-coordinate value of the first point, representing the number of movies rented. Dividing the change in balance by the number of movies gives the cost per movie, which is our unit rate.

For example, if she had $12 after renting 2 movies and $6 on her card after renting 4 movies, the unit rate would be computed as: (12 - 6) / (4 - 2) = $3 per movie. This means that for every movie that Elyse rents, she spends $3 from her gift card.

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Answer:

cost of each pie = $15.75

cost of each cake = $2.75

Step-by-step explanation:

Let x be the Pie and y be the cake.

Given:

The cost of two pies and five cakes is $45.25,

[tex]2x+5y=45.25[/tex]-----------(1)

The cost of 2 pies and three cakes is $39.75

[tex]2x+3y=39.75[/tex]--------------(2)

Now we subtract equation 2 from equation 1.

[tex]2y=5.5[/tex]

[tex]y=\frac{5.5}{2}[/tex]

y=2.75

Now we substitute the value of y in equation 1.

[tex]2x+5\times 2.75=45.25[/tex]

[tex]2x+13.75=45.25[/tex]

[tex]2x=45.25-13.75[/tex]

[tex]2x=31.5[/tex]

[tex]x=\frac{31.5}{2}[/tex]

x=15.75

So, The cost of each pie is $15.75

And the cost of each cake is $2.75

Final answer:

To find the cost of each pie and cake, two equations were set up based on the total cost of pies and cakes. By subtracting the second equation from the first, the cost of one cake was determined to be $2.75. Subsequently, the cost of one pie was calculated to be $15.75.

Explanation:

Calculating the Cost of Pies and Cakes

We have two equations based on the information provided:

2P + 5C = $45.25

2P + 3C = $39.75

Where P represents the cost of one pie, and C represents the cost of one cake. To solve for P and C, we can subtract the second equation from the first:

2P + 5C - (2P + 3C) = $45.25 - $39.75

2C = $5.50

C = $5.50 / 2

C = $2.75

Now that we know the cost of one cake, we can substitute C in one of the equations to find P:

2P + 5($2.75) = $45.25

2P + $13.75 = $45.25

2P = $45.25 - $13.75

2P = $31.50

P = $31.50 / 2

P = $15.75

Therefore, the cost of each pie is $15.75 and the cost of each cake is $2.75.

Answer:

Therefore,

Distance between XY is 878 ft and YB is 524 ft.

Step-by-step explanation:

Given:

BW = 1612 ft

∠ Y = 72°

∠ X = 49°

To Find:

XY = ?

YB = ?

Solution:

In right angle Triangle Δ WBY Tangent identity,

[tex]\tan Y= \frac{\textrm{side opposite to angle Y}}{\textrm{side adjacent to angle Y}}[/tex]

Substituting we get

[tex]\tan 72= \frac{WB}{YB}=\frac{1612}{BY}[/tex]

[tex]\therefore BY=\frac{1612}{3.077}=523.88=524\ ft...(approximate)[/tex]

Similarly,

In right angle Triangle Δ WBX Tangent identity,

[tex]\tan X= \frac{\textrm{side opposite to angle X}}{\textrm{side adjacent to angle X}}[/tex]

Substituting we get

[tex]\tan 49= \frac{WB}{XB}=\frac{1612}{XB}[/tex]

[tex]\therefore XB=\frac{1612}{1.15}=1401.73=1402\ ft...(approximate)[/tex]

Now For

[tex]XB = XY +BY[/tex].............Addition Property

Substituting we get

[tex]1402 = XY +524\\\\\therefore XY=1402-524=878\ ft[/tex]

Therefore

Distance between XY is 878 ft and YB is 524 ft.

The question is a Mathematics problem related to the concept of the Pythagorean Theorem. The solution entails considering the diagonal walk as the hypotenuse in a right triangle, whose sides' lengths are known (200 feet). The Pythagorean theorem is then used to calculate the hypotenuse's length.

The subject of this question is mathematics, specifically, the concept of the Pythagorean Theorem in geometry. The park is described as a perfect square, so the diagonal Mr. Carter and his wife plan to walk across can be thought of as the hypotenuse of a right triangle formed by two sides of the square.

Given that each side of the square is 200 feet, the length between points C and A can be calculated using the Pythagorean theorem, which is a² + b² = c². Here, both a and b are the lengths of the sides of the park, which is 200 feet. So the calculation would be: 200² + 200² = c². This simplifies to 40000 + 40000 = c², leading to a total of 80000 = c². To find c, which is the distance they will walk across the park, we take the square root of 80000, which can be rounded down to 283 feet if we use a calculator.

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Mr. Carter and his wife can find the distance they will walk across the park by using the Pythagorean theorem. They substitute the length of the sides of the square (200 feet) into the theorem's formula: sqrt (200^2 + 200^2) to calculate the distance.

The subject of this question is Mathematics, and it pertains to the topic of geometry, specifically the Pythagorean theorem. We are given a perfect square (Portage Park) with sides of 200 feet, and we want to find the distance from one corner (point C) to the diagonally opposite corner (point A). This distance forms the hypotenuse of a right triangle, where the sides of the square become the two legs of the triangle.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). So the distance  Mr. Carter and his wife will walk (d) can be described with the equation: d = sqrt (a^2 + b^2).

Since Portage Park is a perfect square, both a and b are 200 feet. You can substitute 200 for both a and b in the equation to find d: d = sqrt (200^2 + 200^2).

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Answer:

90-32 is the answer

Step-by-step explanation:

Because this is a right angle its total angle in degrees is 90 and if it is split in to then m1 and m2 must equal 90 degrees so if m2 is 32 degrees then m1 would be what's left which is 90-32

Answer: add over and over again

Step-by-step explanation:How do you get from 0 to 3? you add 3 to 0. Then, how do you get from 3 to 8? you add another 3 but then you a 2 too, so then 8. Lastly, my last example, how to get from 8 to 15. You take five, and then add 2 to it and add that number(then number you get when you add 5+1), 7 to 8.

Hope it helps u..............

The area of a triangle for one of the legs being 3 inches and the hypotenuse being 9 inches is 12.727 square inches

Solution:

Given that to find area of a triangle for one of the legs being 3 inches and the hypotenuse being 9 inches

From given information,

Let "c" = hypotenuse = 9 inches

Let "a" = length of one of the leg of triangle = 3 inches

To find: area of triangle

The area of triangle when hypotenuse and length of one side of triangle is given:

[tex]A = \frac{1}{2} a \sqrt{c^2 - a^2}[/tex]

Where, "c" is the length of hypotenuse

"a" is the length of one side of triangle

Substituting the given values we get,

[tex]A = \frac{1}{2} \times 3 \times \sqrt{9^2 - 3^2}[/tex]

[tex]A =\frac{1}{2} \times 3 \times \sqrt{81-9}\\\\A =\frac{1}{2} \times 3 \times \sqrt{72}\\\\A =\frac{1}{2} \times 3 \times 8.48528\\\\A = \frac{1}{2} \times 25.45584\\\\A = 12.727[/tex]

Thus area of triangle is 12.727 square inches

Part 1: The right answer is Option B.

Part 2: The right answer is Option B.

Step-by-step explanation:

Given,

1 hour = 120 calories

Part 1: How many calories are burned per minute when walking on a treadmill?

1 hour = 120 calories

1 hour = 60 minutes

Therefore,

60 minutes = 120 calories

1 minute = [tex]\frac{120}{60}=2\ calories[/tex]

2 calories are burned per minute.

The right answer is Option B.

Part 2: Assuming you walk at a constant rate and burn 120 calories per hour, how many minutes will it take to burn 75 calories.

From part 1;

1 minute = 2 calories

1 calorie = [tex]\frac{1}{2}\ minute = 0.5\ minutes[/tex]

75 calories = 75*0.5 = 37.5 minutes

The right answer is Option B.

Keywords: multiplication, division

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Answer:

$130 - ($20+$35) is the equation

The equation to represent the total amount spent on t-shirts and hoodies at the River Bluff High School store is 20t + 35h = 130, where t is the number of t-shirts and h is the number of hoodies purchased, and they total $130.

To represent the situation in which t-shirts cost $20 each and hoodies cost $35 each, and a total of $130 is spent, we can introduce variables to represent the quantity of t-shirts and hoodies purchased. Let's use t to represent the number of t-shirts and h to represent the number of hoodies. The equation for this situation in standard form, where Ax + By = C, would be:

20t + 35h = 130,

where 20 is the cost of one t-shirt, 35 is the cost of one hoodie, and 130 represents the total amount spent on t-shirts and hoodies combined.

Answer:

Part A:

An= 6 + 3(n-1)

Part B:

36 cars

Answer:

The diver's new depth is 14.4 feet.

Step-by-step explanation:

Given:

A scuba diver is swimming 18 feet below the water's surface.

The diver swims up slowly at 0.6 feet per second for 5 seconds and then swims up for 2 more seconds at 0.3 feet per second.

Now, to find the diver's new depth.

As given,

Total depth = 18 feet.

Total distance covered:

[tex]Distance\ covered = 0.6\times 5+0.3\times 2[/tex]

[tex]Distance\ covered = 3+0.6[/tex]

[tex]Distance\ covered =3.6[/tex]

Now, to get the new depth:

New depth = Total depth - distance covered.

[tex]New\ depth=18-3.6[/tex]

[tex]New\ depth=14.4\ feet.[/tex]

Therefore, the diver's new depth is 14.4 feet.

The probability that a freshman student at this school plays either a sport or a musical instrument is 0.74

Step-by-step explanation:

The addition rules in probability are:

∵ The probability that a freshman plays a sport is 0.55

∴ P(sport) = 0.55

∵ The probability that a freshman plays a musical instrument is 0.34

∴ P(music) = 0.34

∵ The probability that a freshman plays both a sport and a musical

    instrument is 0.15

∴ P(sport and music) = 0.15

To find the probability that freshman student at this school plays either a sport or a musical instrument use the second rule above because it is non-mutually exclusive

∵ P(sport or music) = P(sport) + P(music) - P(sport and music)

∴ P(sport or music) = 0.55 + 0.34 - 0.15

∴ P(sport or music) = 0.74

The probability that a freshman student at this school plays either a sport or a musical instrument is 0.74

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The probability that a freshman student at this school plays either a sport or a musical instrument is indeed 0.74

To find the probability that a freshman student plays either a sport or a musical instrument, we can use the principle of inclusion-exclusion for probability.

The principle states that for any two events A and B, the probability of the union of A and B is given by:

[tex]\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \][/tex]

Let event A be the event that a freshman plays a sport, and event B be the event that a freshman plays a musical instrument.

We are given the following probabilities:

P(A) = 0.55 (the probability that a freshman plays a sport)

P(B) = 0.34 (the probability that a freshman plays a musical instrument)

P(A and B) = 0.15 (the probability that a freshman plays both a sport and a musical instrument)

 Using the principle of inclusion-exclusion, we calculate the probability  Upon reviewing the calculation, it appears there was an error in the final step.

The correct calculation should be:

[tex]\[ P(\text{either A or B}) = P(A \cup B) \][/tex]

[tex]\[ P(\text{either A or B}) = 0.74 \][/tex]

Therefore, the probability that a freshman student at this school plays either a sport or a musical instrument is indeed 0.74, not 0.64 as initially stated.

The final answer is [tex]\(\boxed{0.74}\).[/tex]

Answer:

96 km/hr

Step-by-step explanation:

Average number of kilometers per hour = 4,608 km / 48 hours

Average number of kilometers per hour = 96 km/hr

Answer:

96

Step-by-step explanation:

IF they are not getting sleep all of their journey then they must faces 96 kilometers per hour but according to their long journey they must want to get sleep and thats way they must spend some time on rest or sleep.

To find the value of x for parallel lines with expressions (7x + 11) and (10x - 43), set them equal and solve the resulting equation, which gives x = 18.

If line a is parallel to line b and we have the expressions (7x + 11) for line a and (10x - 43) for line b, then the corresponding angles formed by these lines and a transversal would be equal. To solve for x, we set the two expressions equal to each other because the slopes of parallel lines are equal. The equation would be 7x + 11 = 10x - 43.

This is the value of x that makes the two expressions equal, thus confirming the lines are parallel.

Answer:

The solution set is given as:

B) [tex]\{x|x\epsilon R, x>-5\}[/tex]

Step-by-step explanation:

Given inequality:

[tex]x-5>-10[/tex]

To find the solution set for the given inequality.

Solution:

We have : [tex]x-5>-10[/tex]

Solving for [tex]x[/tex]

Adding 5 both sides.

[tex]x-5+5>-10+5[/tex]

[tex]x>-5[/tex]

Thus the solution set is all real numbers greater than -5. This can be given as:

[tex]\{x|x\epsilon R, x>-5\}[/tex]

Answer:

In summation form [tex]\sum_{n = 1} ^{5} 6(6)^{n - 1}[/tex]

Step-by-step explanation:

Within one hour, the first person gives a stack of flyers to six people and within the next hour, those six people give a stack of flyers to six new people.

So, in the first 5 hours, the summation of people that receive a stack of flyers not including the initial person will be given by

6 + (6 × 6) + (6 × 6 × 6) + (6 × 6 × 6 × 6) + (6 × 6 × 6 × 6 × 6).

So, in summation form [tex]\sum_{n = 1} ^{5} 6(6)^{n - 1}[/tex]

Therefore, Sigma-Summation Underscript n = 1 Overscript 5 EndScripts 6 (6) Superscript n minus 1, gives the correct solution. (Answer)

We can evaluate how many persons are getting flyer by each person then calculate summation.

Option A: [tex]\sum^5_{n=1}6(6)^{(n-1)}\\[/tex]summation form.

First person gives flyers to 6 people.

Those 6 persons give flyers to 6 new people, thus [tex]6 \times 6 = 36[/tex] people...

And so on five times for five hour as this process is done on hourly basis.

Thus, the summation without including first person, for five hours to count total number of people who received flyers is:

[tex]6 + (6 \times 6) + (6 \times 6 \times 6) + (6 \times 6 \times 6 \times 6 ) + (6 \times 6 \times 6 \times 6 \times 6)[/tex]

or in summation it can be rewritten as:

[tex]\sum^5_{n=1}6(6)^{(n-1)}\\[/tex]

Thus, Option A:  [tex]\sum^5_{n=1}6(6)^{(n-1)}\\[/tex] is the needed summation form.

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Answer:

who ever line crosses the y-axis at -4.

Step-by-step explanation:

Answer:

Ellis so c

Step-by-step explanation:

Answer: A) We need 1 1/2 ft of ribbon

B)$1.60 per foot

C)$2.40 is the total

Step-by-step explanation:

So if the length around the jar is 18 inches and we know that there is 12 inches in a foot, and 3 feet in a yard and $ 4.80 per every 3 feet. These become basis numbers. 18in- 12inch= 6 inch. So now we have 1 1/2 feet of ribbon to cover the circumference of the jar. Now we are left to answer the second question how much does it cost per foot? We can divide 4.80 by 3 to see the total cost of a foot of ribbon. That turns to 1.60 per foot. We divide that by two to cover the 6 inches. And the answer is $2.40 for 1 1/2 feet of ribbon

Answer:

It will cost $256542 to prepare the field for next weeks match.

Step-by-step explanation:

The maximum dimensions of a field according to FIFA rules is 110 m by 75 m.

So, the maximum area of a field is (110 × 75) = 8250 square meters.

Now, 1 square meters is equivalent to 1.196 square yards.

So, the maximum area of a field is (8350 × 1.196) = 9867 square yards.

Now, given that it costs to make ready each square yard of a full-size FIFA field, $26 before each game.

Therefore, it will cost $(26 × 9867) = $256542 to prepare the field for next week's match. (Answer)

Answer:

add

Step-by-step explanation:

Answer:

D) data shows no relationship between temperature and lemonade sales.  

Step-by-step explanation:

There is no correlation between temperature and lemonade sales. Sometimes two variables are not related. The data shows no relationship between temperature and lemonade sales.

The correct option will be D) data shows no relationship between temperature and lemonade sales.

Graphs are a not unusual place technique to visually illustrate relationships withinside the statistics. The reason for a graph is to provide statistics that are too severe or complex to be defined appropriately withinside the textual content and in much less space.

Given, The owner of Ray’s Deli wants to find out if there is a relationship between the temperature in summer and the number of glasses of lemonade he sells.

Since,

There is no correlation between temperature and lemonade sales. Sometimes two variables are not related. The data shows no relationship between temperature and lemonade sales.

Therefore, The correct option will be D) data shows no relationship between temperature and lemonade sales.

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Answer:

Step-by-step explanation:

twice a number is increased by 7.....let x represent the number

ur expression would be : 2x + 7

The maximum revenue occurs at [tex]\( n = 13 \).[/tex]

The correct option is (a).

To maximize the revenue for the tour company, we need to find the value of ( n ) that maximizes the revenue function [tex]\( R = 52n - 2n^2 \).[/tex]

1. Find the derivative of the revenue function:

  The derivative of a function gives us the rate of change of the function. We will find the derivative of the revenue function with respect to ( n ) to find where the revenue function is increasing or decreasing.

Given the revenue function [tex]\( R = 52n - 2n^2 \)[/tex], we'll find its derivative [tex]\( \frac{dR}{dn} \):[/tex]

[tex]\[ \frac{dR}{dn} = \frac{d}{dn}(52n - 2n^2) \][/tex]

[tex]\[ \frac{dR}{dn} = 52 - 4n \][/tex]

2. Set the derivative equal to zero to find critical points:

  To find the critical points, we set the derivative equal to zero and solve for ( n ):

[tex]\[ 52 - 4n = 0 \][/tex]

[tex]\[ 4n = 52 \][/tex]

[tex]\[ n = \frac{52}{4} \][/tex]

[tex]\[ n = 13 \][/tex]

3. Determine the nature of the critical point:

  To determine if ( n = 13 ) is a maximum or minimum, we use the second derivative test. If the second derivative is negative at the critical point, it's a maximum; if positive, it's a minimum.

Taking the second derivative of ( R ):

[tex]\[ \frac{d^2R}{dn^2} = \frac{d}{dn}(52 - 4n) \][/tex]

[tex]\[ \frac{d^2R}{dn^2} = -4 \][/tex]

Since the second derivative [tex]\( \frac{d^2R}{dn^2} = -4 \) is negative, \( n = 13 \)[/tex] corresponds to a maximum.

4. Verify the endpoints:

  Since the domain of ( n ) is not specified, we need to check if the endpoints of the domain have any maximum revenue. In this case, we don't have any specific domain constraints, so we don't need to check the endpoints.

5. Conclusion:

The maximum revenue occurs at [tex]\( n = 13 \).[/tex]

Therefore, the correct answer is option a) 13.

complete question given below:

A tour company has a ticket price that goes down $2 for every additional person who signs up for a group trip. They charge, per person, 52-2n Where n is the number of people that go on the trip. Their total revenue, R, as a function of the number of people who can go in the trip is R=52n-2n^2. How many people Maximize the revenue for the tour company

a.13

b.26

c.39

d.22

Maximized revenue for the tour company occurs with 13 people on the trip, yielding $676.

To maximize revenue, we need to find the maximum point of the revenue function [tex]\( R = 52n - 2n^2 \)[/tex]. We can do this by finding the derivative of the revenue function with respect to n and then setting it equal to zero to find the critical points. Then, we can determine whether these critical points correspond to a maximum or minimum by analyzing the second derivative.

So, let's start by finding the derivative of the revenue function:

[tex]\[ \frac{dR}{dn} = 52 - 4n \][/tex]

Setting this derivative equal to zero and solving for [tex]\( n \):[/tex]

[tex]\[ 52 - 4n = 0 \][/tex]

[tex]\[ 4n = 52 \][/tex]

[tex]\[ n = \frac{52}{4} \][/tex]

[tex]\[ n = 13 \][/tex]

Now, we need to check whether this critical point corresponds to a maximum or a minimum. To do this, we'll take the second derivative of the revenue function:

[tex]\[ \frac{d^2R}{dn^2} = -4 \][/tex]

Since the second derivative is negative, the critical point [tex]\( n = 13 \)[/tex]corresponds to a maximum.

So, the tour company will maximize its revenue when 13 people go on the trip.

Answer:

Celia make [tex]5\frac{1 }{4}[/tex] servings.

Step-by-step explanation:

Given:

Celia made 3 1/2 cups of rice.

A serving of rice is 2/3 cup.

Now, to find the number of servings Celia make.

Celia made [tex]3\frac{1}{2} =\frac{7}{2}\ cups.[/tex]

So, to get the number of servings we use unitary method:

If 2/3 cup of rice is of 1 serving.

So, 1 cup of rice is of = [tex]1\div\frac{2}{3}servings.[/tex]=[tex]\frac{3}{2}[/tex]

Then 7/2 cup of rice is of  [tex]=\frac{7}{2} \times \frac{3}{2}[/tex]

                                           [tex]=\frac{21}{4}=5\frac{1}{4}.[/tex]

Thus, 7/2 cup of rice is of [tex]5\frac{1 }{4}[/tex] servings.

Therefore, Celia make [tex]5\frac{1 }{4}[/tex] servings.

Ceila made 5.25 or 5 ¹/₄ servings of rice.

Ceila made 3 1/2 cups of rice. In improper fractions this is:

3 1 /2 = 7/2

The number of servings made by Ceila can be found by:

= Number of cups of rice Ceila made / Cups of rice in a serving

= 7 / 2 ÷ 2/3

= 7/2 × 3/2

= 21 / 4

= 5.25 servings

When dividing fractions, you can instead multiply the first fraction by the inverse of the second fraction.

In conclusion, Ceila made 5.25 or 5 ¹/₄ servings of rice.

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