pls help quickly . with explanation

The optimal number of square feet of space to be added is approximately 101 square feet.

We have,

To determine the optimal number of square feet of space to maximize the restaurant's profit, we need to analyze the relationship between the additional square footage, the number of new customers, and the resulting profit.

Let's start by defining some variables:

Let "x" represent the number of additional square feet of space to be added beyond the initial 100 square feet.

Let "C(x)" represent the cost in dollars to add x square feet of space. In this case, C(x) = $100 * x.

Let "N(x)" represent the number of new customers attracted per month when x square feet of space is added.

Let "P(x)" represent the profit generated per month when x square feet of space is added. In this case, P(x) = $50 * N(x).

Given the information provided, we know that each additional square foot of space attracts 2 new customers per month.

So, N(x) = 2x.

However, the number of new customers per month is expected to decrease by 1% for every 10 square feet of additional space beyond the initial 100 square feet.

To incorporate this, we can modify our equation for N(x) as follows:

N(x) = 2x * (1 - 0.01 * (x - 100) / 10)

Now, we can express the profit function P(x) in terms of x:

P(x) = $50 * N(x)

= $50 * [2x * (1 - 0.01 * (x - 100) / 10)]

= $100x * (1 - 0.01 * (x - 100) / 10)

To find the optimal number of square feet of space that maximizes profit, we need to find the value of x that maximizes P(x).

We can do this by taking the derivative of P(x) with respect to x, setting it equal to zero, and solving for x.

dP(x)/dx = $100 * (1 - 0.01 * (x - 100) / 10) + $100x * (-0.01 / 10)

= $100 - $1 * (x - 100) + $100x * (-0.01 / 10)

= $100 - $1x + $100 * (-0.01 / 10) - $1x

= $100 - $2x - $0.01x + $10x

= $100 + $7x - $0.01x

Setting dP(x)/dx equal to zero:

$100 + $7x - $0.01x = 0

$7x - $0.01x = -$100

0.99x = $100

x ≈ $100 / 0.99

x ≈ 101.01

Since we're dealing with square footage, we can round the result to the nearest whole number.

Therefore,

The optimal number of square feet of space to be added is approximately 101 square feet.

Learn more about derivatives here:

https://brainly.com/question/29020856

#SPJ4

The complete question:

The manager of a restaurant is considering expanding the seating area. She wants to determine how many additional square feet of space should be added to maximize the restaurant's profit. The cost to add new space is $100 per square foot, and the profit generated per square foot is estimated to be $50 per month. The manager expects that each additional square foot of space will attract 2 new customers per month. However, the number of new customers per month is expected to decrease by 1% for every 10 square feet of additional space beyond the initial 100 square feet.

What is the optimal number of square feet of space that should be added to maximize the restaurant's profit?

Given parameters:

Simba temperature in the morning  = 6°C

Temperature drop = 9°C

Unknown:

Temperature during the night = ?

Solution:

 Since the temperature in the morning is given;

 Temperature at night  = Morning temperature  - drop in temperature

  Temperature at night = 6°C - 9°C = -3°C

The temperature at night is  -3°C

Answer:

A. and D.

Step-by-step explanation:

Hey there!

In order to to find the point at which these two equations intersect at, you need to first rewrite the equations if needed so that they are in the form:

\(y=mx+b\)

or

\(y=ax^2+bx+c\)

The first equations needs to be rewritten

\(3x+5=y+4x\)

make \(y\) by itself

\(3x+5-4x=y\)

Simplify LHS

\(y=-x+5\)

Now we have it in slope-intercept form

Looking at the equation, we can tell that the slope of the line is \(-1\) and the y-intercept is 5

Now you can graph this equation easily (image down below)

The second equation is already in form so there is no need to rewrite anything

We can go straight to graphing (image down below)

Now plot both equations on the same graph (image down below)

The slope of the line that passes through the points (-2, 2) and (-4, -1) is 3/2 i.e. 1.5 .

How can we define the slope for a given line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. Therefore, the relationship between the change in the y-coordinate and the change in the x-coordinate is provided by the formula m = change in y/change in x = Δy/Δx, where "m" is the slope of a line.
Mathematically, slope of a line = m = (y₂ - y₁)/(x₂ - x₁)

Given, the line passes through the points (-2, 2) and (-4, -1)
Now, using the formula established in the literature, we get:
slope = m = (y₂ - y₁)/(x₂ - x₁) = (-1 - 2)/(-4 - (-2)) = -3/-2 = 3/2 = 1.5
Therefore, the slope of the line that passes through the points (-2, 2) and (-4, -1) is 3/2 i.e. 1.5 .

To learn more about slope of a line, tap on the link below:
https://brainly.com/question/16949303

#SPJ13

Calculate the sum of the white sugar and the brown sugar quantities. Given that the cake requires 2/3 cup of white sugar and 1/4 cup of brown sugar, we can add this fractions together to find the total sugar needed.

To combine fractions, we first need to find a common denominator. The least common multiple of 3 and 4 is 12. We can convert the fractions to have a common denominator of 12 by multiplying the numerator and denominator of each fraction by appropriate factors.

For the white sugar:

2/3 cup = (2/3) * (4/4) = 8/12 cup

For the brown sugar:

1/4 cup = (1/4) * (3/3) = 3/12 cup

Now, we can add the fractions together:

8/12 cup + 3/12 cup = 11/12 cup

Therefore, the total amount of sugar needed for the cake is 11/12 cup.

To learn more about fractions  click here : brainly.com/question/10354322

#SPJ11

Answer:

4x 6y

Step-by-step explanation:

14x -10=4

The Project Triangle is also known as the triple constraints model and consists of three elements: cost, time and scope.

The Project Triangle is also known as the Iron Triangle or Triple Constraints and is a graphical representation of the connection between project costs, schedule, and scope. It is one of the key principles of project management, and it is utilized to help organizations and project managers understand and handle trade-offs between different objectives of a project.

The three elements of the Project Triangle are:

To know more about Project Triangle, visit:

https://brainly.com/question/33122965

#SPJ11

Answer:

The graph of the data presented is shown in the attached image to this solution.

It shows that the relationship between distance travelled in miles and the time take in hours is D = 55t

Step-by-step explanation:

The distance travelled with the corresponding time taken are presented in the table

Note: D - Distance travelled (miles)

t - Time (hours)

D | t

55 | 1

110 | 2

165 | 3

220 | 4

275 | 5

330 | 6

We are then told to plot these distance travelled on a graph with the time taken.

The distance travelled is plotted on the y-axis and the time in hours is plotted on the x-axis.

The image of the graph of this function will be attached to this answer

It is evident that the graph shows the relationship between the distance travelled and time taken to be D = 55t

Hope this Helps!!!

Graph of relationship \(D=55t\) on coordinate plane attached below.

Since, the table below shows the distance traveled as a function of time.

Time(t)                                           Distance (D)

1                                                       55

2                                                      110

3                                                      165

4                                                      220

5                                                      275

6                                                      330

In the graph, X - axis represent timer in hours and Y - axis represent that distance travelled in miles.

Slope = \(\frac{y}{x} =\frac{55}{1}=\frac{110}{2}=\frac{165}{3} =55\)

It is observed that, in each relationship slope is same .Therefore, relationship is a line passing through the origin.

Relationship is,      \(D=55t\)

Graph is attached below,

Learn more:

https://brainly.com/question/13828699

Answer:

True, as the the equation for circumference is πd, so 7 x 2 = 14, and if we round π to 3.14, the answer would be around 42 as 3x14=42

Answer:

Step-by-step explanation:

Let's simplify the expression:

-4d(5d^2-12)+7(d+5)

First, let's distribute the -4d to the terms inside the parentheses:

-20d^3 + 48d + 7(d+5)

Next, let's distribute the 7 to the terms inside the parentheses:

-20d^3 + 48d + 7d + 35

Combine like terms:

-20d^3 + 55d + 35

So the final simplified expression is:

-20d^3 + 55d + 35.

If a line went through a point of 2,5 and the slope of 5/3 what is y-value of the point

The method of induction is a mathematical proof technique that involves showing that a statement holds for a base case, and then showing that if it holds for n, it also holds for n+1. This process is repeated until the statement is shown to hold for all positive integers.

This statement can be proven by induction.

Base Case:

For n = 1, there are 3 airports. Let the 3 airports be A, B, and C. If an airplane from airport A is heading towards airport B, then the airplane from airport B must be heading towards airport C, and the airplane from airport C must be heading towards airport A. Hence, there is no airport that none of the airplanes are heading towards.

Inductive Step:

Assume that the statement holds for n = k, where k is a positive integer.

We need to prove that the statement holds for n = k + 1, where there are 2(k + 1) + 1 = 2k + 3 airports.

Let the 2k + 3 airports be A1, A2, ..., A2k + 3. Without loss of generality, let the airplane from airport A1 be heading toward airport A2.

Since the distances between any two airports are all different, we have two cases to consider:

If there exists an airport Ai, such that Ai is the closest airport to A1, then airplanes from Ai must be heading towards A1.

If there is no airport Ai that is closest to A1, then there must be the closest pair of airports, say Ai and Aj, such that Ai is the closest to A1 and Aj is the closest to Ai.

In the first case, none of the airplanes are heading towards Ai, and in the second case, neither Ai nor Aj is the closest airport to any other airport. Hence, in both cases, there is an airport that none of the airplanes are heading towards.

By induction, the statement holds for all positive integers n.

To know more about induction refer to:

brainly.com/question/13079664

#SPJ4

The ΔABC placed on top of ΔADE, and having angles ∠ABC and ∠BAC congruent to ∠ADE and ∠DAE in ΔADE is similar to ΔADE. The side CB is 3 indicating that the side ED, which has a length of x = 5

Similar triangles are triangles that have similar (the same shape), such that one triangles has side lengths that are a constant multiple of the other.

Please find attached a possible drawing that is based on the parameters of the question

From the question and the drawing created with MS Word, we have;

Length of AB = 9

Side CB = 3

Segment BD = 6

∠ABC = ∠ADE = 90°

∠ABC ≅ ∠ADE by definition of congruency

From the drawing, ∠BAC ≅ ∠BAC by reflexive property of equality

Triangle ΔBAC is similar to triangle ΔDAE by AA similarity postulate

Segment AD = Segment AB + Segment BD by segment addition postulate

AD = 9 + 6 = 15

The pair of corresponding sides of similar triangles are proportional, therefore;

\(\dfrac{\overline{AB}}{\overline{AD}} = \dfrac{\overline{BC}}{\overline{DE}}\)

Which gives;

\(\dfrac{9}{15} = \dfrac{3}{x}\)

9 × x = 15 × 3 = 45

x = 45 ÷ 9 = 5

The  length of side ED, x = 5

Learn more about similar triangles in geometry here:

https://brainly.com/question/2644832

#SPJ1

Answer: 12

Step-by-step explanation: Because 9 x 2 is 18, and 7 x 2 is 14, we want to multiply 6 by 2. This gives us the answer 12.

9 x 2 = 18

7 x 2 = 14

6 x 2 = 12

Answer:

The distance from Durham to Fuquay-Varina is 30 miles.

Step-by-step explanation:

Given that the cities of Raleigh, Durham, and Fuquay-Varina approximate a right triangle, and the distance from Raleigh to Durham is 24 miles, while the distance from Raleigh to Fuquay-Varina is 18 miles, to determine what is the distance from Durham to Fuquay-Varina, the following calculation must be performed, applying the Pythagorean theorem:

18 ^ 2 + 24 ^ 2 = X ^ 2

324 + 576 = X ^ 2

√ 900 = X

30 = X

Therefore, the distance from Durham to Fuquay-Varina is 30 miles.

Using trigonometric ratio and the angle of depression, the altitude of the plane is 98m

The angle of depression is an angle formed by a horizontal line and a line of sight from a point above that line to an object below that line. It is used in trigonometry to calculate the distance between the observer and the object of interest.

Using trigonometric ratio, we can calculate the height or altitude which the plane is flying.

Data;

Using tangent of the angle;

tan θ = opposite / adjacent

tan 27 = x / 193

x = 193 * tan27

x = 98m

The altitude is 98m

Learn more on angle of depression here;

https://brainly.com/question/2096694

#SPJ1

Answer:

500 ml

Step-by-step explanation:

1 liter = 1 000 ml

1 / 2 liters = 1000 ml /2 = 500 ml

1000ml - 500 ml = 500 ml

Answer:

(-4, 3/2)

Step-by-step explanation:

(x1 + x2/2  ,   y1 + y2 / 2)

[-1 + (-7)/2    ,  -3 + 6/2]

[-8/2, 3/2]

(-4, 3/2)

PART A

From the figure,

PQ is a tangent (given)

OP is a radius (given)

Therefore, Triangle QOP is a right-angled triangle

So to calculate side OP, we use the Pythagoras theorem

Therefore, OP is equal to 7 units.

PART B

To get line TQ,

TQ = TO + OQ

OQ = 25 (given)

TO = OP (they are both radii of the circle, hence they are the same)

TO = 7

TQ = 7 + 25

TQ = 32

Therefore, TQ is equal to 32 units.

Given statement solution is :- We cannot find the missing value from the given options (3656, 2739, 1841, 5418, or 3556).

The given sequence is: 5 2 1 4 0 0 7 2 8 1 m m 7 m 5 m A.

To find the missing value, let's analyze the pattern in the sequence. We can observe the following pattern:

The first number, 5, is the sum of the second and third numbers (2 + 1).

The fourth number, 4, is the sum of the fifth and sixth numbers (0 + 0).

The seventh number, 7, is the sum of the eighth and ninth numbers (2 + 8).

The tenth number, 1, is the sum of the eleventh and twelfth numbers (m + m).

The thirteenth number, 7, is the sum of the fourteenth and fifteenth numbers (m + 5).

The sixteenth number, m, is the sum of the seventeenth and eighteenth numbers (m + A).

Based on this pattern, we can deduce that the missing values are 5 and A.

Now, let's calculate the missing value:

m + A = 5

To find a specific value for m and A, we need more information or equations. Without any additional information, we cannot determine the exact values of m and A. Therefore, we cannot find the missing value from the given options (3656, 2739, 1841, 5418, or 3556).

For such more questions on Missing value: Indeterminable.

https://brainly.com/question/30389332

#SPJ8

Answer: 4.15

Step-by-step explanation:

If a sample of 35 such reviews is selected then approximately 38.97% of the 35 reviews will take more than an hour.

For calculating what percent of reviews will take more than an hour, we can use the standard normal distribution to answer this question.

First, we need to standardize the review time of an IRS examiner by subtracting the mean and dividing by the standard deviation:

z = (60 - 55.1) / 17.6 = 0.278

where 60 is the number of minutes in an hour.

This means that a review time of one hour (60 minutes) corresponds to a standard score of 0.278.

To find the probability that a review time is more than an hour (60 minutes), we need to find the area under the standard normal curve to the right of this z-score:

P(Z > 0.278) = 0.3897

Using this probability, we can conclude that approximately 38.97% of the 35 reviews will take more than an hour.

To know more about probability refer here :

https://brainly.com/question/29173387#

#SPJ11

The harmonic coefficients an are 0.5, 1.2, 0, 0.125, 0, 0, ...

Hence, the correct option is 0.5,1.2,0,0.125,0,..., 0.

Question 1:

If the Fourier series coefficient an=-3+j4

The value of a_n isO-3+j4

The complex conjugate of an is a*-3-j4

On finding the magnitude of an by using the formula

|an|=sqrt(Re(an)^2+Im(an)^2)

=sqrt((-3)^2+(4)^2)

=5

The value of a_n is -3+j4.

Hence, the correct option is O-3+j4.

The given harmonic coefficients are:

y(t)=0.5+sin(60πt)+4cos(30πt)-0.125sin(90πt+120°)

On comparing the given signal with the standard equation of Fourier series:

y(t) = a0/2 + an cos(nω0t) + bn sin(nω0t)

The coefficients of cosnω0t and sinnω0t are given by

an = (2/T) * ∫[y(t) cos(nω0t)]dt,

bn = (2/T) * ∫[y(t) sin(nω0t)]dt

Here,ω0 = 2π/T

= 2π,

T = 1.

The value of a0 is given by

a0 = (2/T) * ∫[y(t)]dt

Now, let's find the values of a0, an and bn.

The coefficient a0 is given by

a0 = (2/T) * ∫[y(t)]dt

= (2/1) * ∫[0.5+sin(60πt)+4cos(30πt)-0.125sin(90πt+120°)]dt

= 1.125

The coefficient an is given by

an = (2/T) * ∫[y(t) cos(nω0t)]dt

When n = 1

an = (2/T) * ∫[y(t) cos(ω0t)]dt

= (2/1) * ∫[0.5+sin(60πt)+4cos(30πt)-0.125sin(90πt+120°)] cos(ω0t)dt

= 0.5

The coefficient bn is given by

bn = (2/T) * ∫[y(t) sin(nω0t)]dt

When n = 1

bn = (2/T) * ∫[y(t) sin(ω0t)]dt

= (2/1) * ∫[0.5+sin(60πt)+4cos(30πt)-0.125sin(90πt+120°)] sin(ω0t)dt

= 0

Now, let's find the values of a2 and a3.

The coefficient an is given by

an = (2/T) * ∫[y(t) cos(nω0t)]dt

When n = 2

an = (2/T) * ∫[y(t) cos(2ω0t)]dt

= (2/1) * ∫[0.5+sin(60πt)+4cos(30πt)-0.125sin(90πt+120°)] cos(2ω0t)dt

= 1.2

The coefficient an is given by

an = (2/T) * ∫[y(t) cos(nω0t)]dt

When n = 3

an = (2/T) * ∫[y(t) cos(3ω0t)]dt

= (2/1) * ∫[0.5+sin(60πt)+4cos(30πt)-0.125sin(90πt+120°)] cos(3ω0t)dt

= 0.125

Now, the harmonic coefficients an are 0.5, 1.2, 0, 0.125, 0, 0, ...

Hence, the correct option is 0.5,1.2,0,0.125,0,..., 0.

To know more about coefficients visit

https://brainly.com/question/13431100

#SPJ11

Answer:

I believe y would be 70°

Step-by-step explanation:

Hope this helps!

Answer:

97/113

Step-by-step explanation:

67 robots have legs only, 21 have wheels only, and 9 have both legs and wheels.  The total number of robots with legs and/or wheels is 97.

The probability is 97/113.

Answer:

98÷7=14 cuz 14×7=98

Step-by-step explanation:

The solution of the given system of equations is (-1, 2).

What is system of equations?

A group of equations involving one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations intersect, are the solutions to systems of equations.

Consider, the given system of equations.

x^2 - x + 3y - 8 = 0           ..(1)

x - y + 3 = 0                       ..(2)

From equation (2),

x = y - 3            ..(3)

Plug the value of x in equation (1).

⇒ (y - 3)^2 - (y - 3)  + 3y - 8 = 0

y^2 - 6y + 9 - y + 3 +3y - 8 = 0

y^2 - 4y + 4 = 0

y^2 - 2y - 2y + 4 = 0

y(y - 2) - 2(y - 2) = 0

(y - 2)(y - 2) = 0

(y - 2)^2 = 0

y = 2

Now plug y = 2 in equation (3)

x = 2 - 3

x = -1

hence, the solution of the given system of equations is (-1, 2).

To know more about system of equations, click on the link

https://brainly.com/question/13729904

#SPJ1

a. the standard deviation of ln(X) to be approximately 0.371. b. the probability that X is at most 15,000 kg/day/km is approximately 0.747. c. the distribution has a higher probability of values exceeding the mean compared to values below the mean. d. 17,000 kg/day/km is above the 95th percentile of the distribution.

a. The mean value of ln(X) can be calculated by taking the natural logarithm of the mean value of X. In this case, the mean value of X is 10,281 kg/day/km. Taking the natural logarithm of this value gives us the mean value of ln(X), which is approximately 9.238.

To calculate the standard deviation of ln(X), we need to use the coefficient of variation (CV) provided. The formula to calculate the standard deviation of ln(X) is: σ[ln(X)] = √(ln(1 + CV^2)). Plugging in the value of CV = 0.40, we can calculate the standard deviation of ln(X) to be approximately 0.371.

b. To find the probability that X is at most 15,000 kg/day/km, we can use the properties of the lognormal distribution. We need to convert the given value of 15,000 kg/day/km to ln(X). Taking the natural logarithm of 15,000 gives us approximately 9.615.

Next, we can use the cumulative distribution function (CDF) of the lognormal distribution with the calculated mean value of ln(X) and the standard deviation of ln(X) to find the probability. The CDF represents the probability that X is less than or equal to a certain value. By evaluating the CDF at ln(X) = 9.615, we find that the probability that X is at most 15,000 kg/day/km is approximately 0.747.

c. The probability that X exceeds its mean value is not 0.5 because the lognormal distribution is skewed. Skewness indicates an asymmetry in the distribution, where the tail on one side is longer or heavier than the other. In the case of the lognormal distribution, the right tail is typically longer. This means that the distribution has a higher probability of values exceeding the mean compared to values below the mean.

d. To determine if 17,000 kg/day/km is the 95th percentile of the distribution, we can use the quantile function of the lognormal distribution. The quantile function gives us the value below which a certain percentage of the distribution falls.

By plugging in the desired percentile of 95% into the quantile function with the given mean value of ln(X) and the standard deviation of ln(X), we can find the corresponding value in the original X scale. Evaluating the quantile function at 95%, we find that the value is approximately 15,571 kg/day/km.

Therefore, 17,000 kg/day/km is above the 95th percentile of the distribution.

Learn more about probability here

https://brainly.com/question/13604758

#SPJ11