A sales manager collected the following data on x = annual sales and y = years of experience. The estimated regression equation for these data is y = 80 + 4x.
Years of Experience Annual Sales ($1000s)
1 80
3 97
4 92
4 102
6 103
8 111
10 119
10 123
11 117
13 136
a. Compute SST, SSR, and SSE.
b. Compute the coefficient of determination r2. Comment on the goodness of fit.
c. What is the value of the sample correlation coefficient?

Answer:

In total, she would have 4100 milliliters of water.

The indefinite integral is 343/4 * (x/7)^4 + c.

We substitute x = 7 tan(θ) and then dx/dθ = 7 sec^2(θ), so dx = 7 sec^2(θ) dθ. Also, using the trigonometric identity sec^2(θ) = 1 + tan^2(θ), we have √49 x^2 = √49 (7 tan(θ))^2 = 49 * 7 tan^2(θ). Then:

∫ x/7 √49 x^2 dx = ∫ (7 tan(θ)/7) * (7 sec^2(θ)) * (49 * 7 tan^2(θ)) dθ

= ∫ 343 tan^3(θ) sec^2(θ) dθ

We can use the substitution u = tan(θ), which implies du/dθ = sec^2(θ), so dθ = du/sec^2(θ). Then:

∫ 343 tan^3(θ) sec^2(θ) dθ = ∫ 343 u^3 du = 343 * (u^4/4) + c

= 343 * (tan^4(θ)/4) + c

Finally, we substitute back x = 7 tan(θ), which implies tan^4(θ) = (x/7)^4, to get:

∫ x/7 √49 x^2 dx = 343/4 * (x/7)^4 + c

Therefore, the indefinite integral is 343/4 * (x/7)^4 + c.

Click the below link, to learn more about  indefinite integral :

https://brainly.com/question/17095530

#SPJ11

Confidence Interval = 47 ± 7.853 = (39.147, 54.853)

To construct an 80% confidence interval for the population mean (μ), we will use the formula:
Confidence Interval = ¯x ± (t * (s / √n))

where ¯x = 47 (sample mean), s = 20 (sample standard deviation), and n = 12 (sample size).

First, we need to find the t-value for an 80% confidence level with 11 degrees of freedom (n - 1 = 12 - 1 = 11). Using a t-distribution table, we find that the t-value is approximately 1.363.

Now, we can calculate the margin of error:
Margin of Error = 1.363 * (20 / √12) ≈ 7.853

Finally, we construct the 80% confidence interval:
Confidence Interval = 47 ± 7.853 = (39.147, 54.853)
So, the 80% confidence interval for the population mean (μ) is (39.147, 54.853) to three decimal places.

For more such questions on population mean, visit

brainly.com/question/30727743

#SPJ11

The probability that all the M&Ms a child selects are brown is approximately 0.2381.

Hi! To find the probability that all the M&Ms a child selects are brown, we will consider the candy dish that contains six brown and three red M&Ms.

Step 1: Calculate the total number of ways to choose 3 M&Ms from the dish. This is given by the combination formula C(n, r) = n! / (r!(n-r)!) where n is the total number of items and r is the number of items to be selected.

Total M&Ms (n) = 6 brown + 3 red = 9
M&Ms to be selected (r) = 3

C(9, 3) = 9! / (3!(9-3)!) = 84

Step 2: Calculate the number of ways to choose 3 brown M&Ms from the 6 available.

C(6, 3) = 6! / (3!(6-3)!) = 20

Step 3: Calculate the probability that all the M&Ms are brown by dividing the number of ways to choose 3 brown M&Ms by the total number of ways to choose 3 M&Ms.

Probability = (number of ways to choose 3 brown M&Ms) / (total number of ways to choose 3 M&Ms)
Probability = 20 / 84 ≈ 0.2381 (rounded to four decimal places)

So, the probability that all the M&Ms a child selects are brown is approximately 0.2381.

Learn more about probability

brainly.com/question/11234923

#SPJ11

The correct answer is D. After the loop, the last row of matrix is 0, 0, 0, 0, 10.

This is because the code initializes a 5x5 matrix with all elements set to 0. Then, the for loop iterates over the length of the last row (which is 5), and sets the values in the last row to 10. However, the loop also has a semicolon immediately after the condition, which effectively terminates the loop before it even starts executing the loop body.

Therefore, only the initialization statement (which does nothing) and the semicolon are executed, leaving the rest of the matrix unchanged except for the last element in the last row, which is set to 10.

In computer programming, an initialization statement is a statement used to set an initial value to a variable or constant when it is declared. This is typically done to ensure that the variable or constant starts with a known and expected value, and to avoid any unpredictable behavior that may result from uninitialized data.

To know more about initialization statement, refer here:

https://brainly.com/question/13089791

#SPJ11

Answer:

9$

Step-by-step explanation:

Answer:

about 19.3

Step-by-step explanation:

you are given two angles and a side so use Law of Sines

label all the angles and sides so it is easier: the square angle is angle A, the 48 degree angle is angle C, and the other angle is angle B. Therefore the side between A and C is side b, the side between A and B is side c, and the side between C and B is side a

use the Law of Sines; we already know the measure of angle C and the length of side c for reference

[tex]\frac{c}{sineC} =\frac{a}{sineA} \\\\\frac{14.3}{sin48} =\frac{a}{sine90} \\\\\frac{14.3}{0.74} =\frac{a}{1} \\\\19.3=\frac{a}{1} \\\\a=19.3[/tex]

so x measures about 19.3

Assuming that the amount of homework is constant and can be divided equally into four parts, it would take you 60 minutes (or 1 hour) to finish all of your homework. This is because 15 minutes is one fourth of 60 minutes.

Answer:

The answer is 1 hour

Step-by-step explanation:

I got this answer because I aleady know that 15 minutes is 1/4 of an hour and if you do that 4 times that is 60 minutes ( 1 hour)

The weighted average cost of capital for Android Corp. is 12.41%.

First, calculate the weight of each source of capital:

- Common stock: $50 million / ($50 million + $27 million) = 0.65
- Debt: $27 million / ($50 million + $27 million) = 0.35

Next, calculate the cost of each source of capital:
- Common stock: 18%
- Debt: 3%

Finally, calculate the weighted average cost of capital using the following formula:

WACC = (weight of common stock x cost of common stock) + (weight of debt x cost of debt)
WACC = (0.65 x 0.18) + (0.35 x 0.03)
WACC = 0.117 + 0.0105
WACC = 0.1275 or 12.41%

Hence the wieght  weighted average cost of capital for Android Corp. is 12.41%.

Learn more about weighted average cost.

brainly.com/question/28042295

#SPJ11

Answer:

The area of a parallelogram with adjacent sides u and v is given by the magnitude of the cross product of u and v:

A = |u x v|

We can find the cross product as follows:

u x v = (8)(-1) - (0)(-2), -(9)(-2) - (-3)(1), (9)(2) - (-3)(8) = (-8, -15, 42)

So the area of the parallelogram is:

A = |(-8, -15, 42)| = √(8^2 + 15^2 + 42^2) ≈ 46.09 square units

(a) The triple scalar product of three vectors u, v, and w is given by:

u . (v x w)

We can find the cross product v x w as follows:

v x w = (2)(1) - (-2)(1), (-2)(3) - (0)(1), (0)(1) - (2)(1) = (4, -6, -2)

So the triple scalar product is:

u . (v x w) = (-3)(4) - (4)(-6) - (-1)(-2) = -12 + 24 - 2 = 10

(b) The volume of a parallelepiped with adjacent edges u, v, and w is given by the scalar triple product of u, v, and w:

V = |u . (v x w)|

We already found u . (v x w) in part (a), so we just need to take the absolute value:

V = |10| = 10 cubic units

To find the distance from point P to the plane, we can use the formula:

d = |ax + by + cz + d| / sqrt(a^2 + b^2 + c^2)

where the equation of the plane is given by ax + by + cz + d = 0. In this case, we have:

a = 4, b = -1, c = 3, and d = -9

So the equation of the plane is 4x - y + 3z - 9 = 0. To find the distance from point P(2, 8, -7), we plug in these values:

d = |(4)(2) + (-1)(8) + (3)(-7) - 9| / sqrt(4^2 + (-1)^2 + 3^2) ≈ 5.61 units

Therefore, the distance from point P to the plane is approximately 5.61 units.

rate5* po and give thanks for more po! your welcome!

Answer: 100 minutes

Step-by-step explanation:

Let the hoses be A and B, with A being larger and B being smaller.

To fill the swimming pool:

The time taken by the two hoses = 20 mins

A + B = 20 mins

The time taken by the larger hose A = 25 mins

A = 25 mins

A + B = 20 mins

A = 25 mins

Take the Least Common Multiple (LCM) of 20 and 25.

The LCM of 20 and 25 = 100

Let the total volume of the swimming pool be 100 units.

Total time taken by both A and B = 20 mins.
The total volume of the pool = 100 units.
The rate of work done by the two hoses per minute is 100/ 20 = 5 units.
The two hoses together fill the pool at the rate of 5 units per minute.

A + B = 5 units --------- (1)

Total time taken by the larger hose A = 25 mins.
The total volume of the pool = 100 units.
The rate of work done by the hose A per minute is 100/ 25 = 4 units.
The larger hose A fills the tank at the rate of 4 units per minute.

A = 4 units ---------- (2)

Substituting the value of A from equation (2) in (1),
we get B = 1 unit/minute.
i.e., The total volume of the pool is 100 units, and B fills the tank at the rate of 1 unit per minute.

So the smaller hose takes 100 minutes to fill the pool.

To view a similar problem, read at
https://brainly.com/question/7222842

The solution to the differential equation for the motion of the spring is x(t) = (c1+ c2t) [tex]e^-\frac{3t}{5}[/tex], where c1 and c2 are constants determined by the initial conditions x(0) = -1 and dx/dt|t=0=4.

Since the spring is critically damped, it will not go past equilibrium as it returns to its equilibrium position without oscillating.

To solve the given differential equation, we first find the characteristic equation by replacing d²x/dt² with r², dx/dt with r, and x with 1: 375r² + 450r + 135 = 0.

Solving for r using the quadratic formula gives r = -0.6 and r = -0.9. Since the roots are equal, the general solution is x(t) = (c1 + c2t) [tex]e^-\frac{3t}{5}[/tex],  where c1 and c2 are constants determined by the initial conditions.

Using x(0) = -1, we get c1 = -1. To find c2, we differentiate x(t) with respect to t and use the initial condition dx/dt|t=0=4, giving c2 = 4. Thus, the solution is x(t) = (-1 + 4t) [tex]e^-\frac{3t}{5}[/tex] .

Since the spring is critically damped, the damping coefficient is equal to the undamped natural frequency, which means that it returns to equilibrium as quickly as possible without oscillating. Therefore, the spring will not go past equilibrium.

To know more about differential equation click on below link:

https://brainly.com/question/14620493#

#SPJ11

The function in standard form is: f(x) = x² + 4x - 21

A function is a rule that corresponds each input value from the domain to precisely one output value from the target set (called the range).

If the zeros of a quadratic function are -7 and 3, then the function can be factored as follows:

f(x) = a(x + 7)(x - 3)

where a is a constant that determines the shape and size of the quadratic function.

To write the function in standard form (ax² + bx + c), we need to expand the factored form by multiplying the two factors:

f(x) = a(x + 7)(x - 3)

f(x) = a(x² - 3x + 7x - 21)

f(x) = a(x² + 4x - 21)

We can see that the function is now in standard form, where a = the coefficient of the x² term, b = the coefficient of the x term, and c = the constant term:

f(x) = a(x² + bx + c)

In this case, a = 1, b = 4, and c = -21, so the function in standard form is:

f(x) = x² + 4x - 21.

To know more about function visit:

https://brainly.com/question/23712366

#SPJ1

The values of x and y that have the maximum product are x = 40 and y = 40. The maximum product of x and y is Q = 40 * 40 = 1600.

To solve this problem, we need to use the method of Lagrange multipliers, which involves finding the maximum or minimum of a function subject to a constraint. In this case, our function is Q = xy (the product of x and y), and our constraint is x + y = 80.

We start by setting up the Lagrangian function:

L(x,y,λ) = xy + λ(x+y-80)

where λ is the Lagrange multiplier. We then take partial derivatives of L with respect to x, y, and λ, and set them equal to zero:

∂L/∂x = y + λ = 0
∂L/∂y = x + λ = 0
∂L/∂λ = x + y - 80 = 0

Solving these equations simultaneously, we get:

x = y = 40
λ = -40

So the values of x and y that maximize the product are both 40 (integers), and the maximum product is:

Q = xy = 40*40 = 1600.

To maximize the objective function Q = xy subject to the constraint x + y = 80, follow these steps:

1. Rewrite the constraint equation to isolate one variable, for example, y: y = 80 - x.
2. Substitute this expression for y in the objective function: Q = x(80 - x).
3. Expand the equation: Q = 80x - x^2.
4. To find the maximum value of Q, take the first derivative of Q with respect to x: dQ/dx = 80 - 2x.
5. Set the first derivative equal to zero to find the critical points: 80 - 2x = 0.
6. Solve for x: x = 40.
7. Substitute the value of x back into the constraint equation to find the corresponding value for y: y = 80 - 40 = 40.

Learn more about Lagrange multiplier at: brainly.com/question/30889108  

#SPJ11

The dimensions of the region with the largest area are 45 feet by 45 feet.

To maximize the area enclosed by a given length of fencing, we want to use all of the fencings to create the perimeter of the region.

Let the length and width of the region be represented by L and W, respectively. We know that the perimeter of the region is 180 feet, so:

2L + 2W = 180

Simplifying this equation, we get:

L + W = 90

We want to maximize the area A of the region, given by:

A = LW

We can use the equation L + W = 90 to solve for one variable in terms of the other. For example, we can solve for W in terms of L:

W = 90 - L

Substituting this expression into the equation for the area, we get:

A = [tex]L(90 - L) = 90L - L^2[/tex]

To find the maximum area, we can take the derivative of A with respect to L and set it equal to 0:

dA/dL = 90 - 2L = 0

Solving for L, we get:

L = 45

Substituting this value back into the equation for W, we get:

W = 90 - 45 = 45

Therefore, the dimensions of the region with the largest area are 45 feet by 45 feet.

Learn more about derivative

https://brainly.com/question/31315615

#SPJ4

The rejection of the null hypothesis in a hypothesis testing at a 5% significance level means that there is evidence to suggest that the population mean pollution concentration in urban areas is not equal to 120 with 95% confidence. The correct answer is B).

We conducted a hypothesis testing at a 5% significance level and based on our analysis, we rejected the null hypothesis. It means that there is sufficient statistical evidence to reject the null hypothesis that the population mean pollution concentration in urban areas is equal to 120 at a 5% significance level, in favor of the alternative hypothesis that the population mean pollution concentration is different from 120.

The level of confidence cannot be determined solely from this information.

So, the correct option is B).

To know more about Null hypothesis:

https://brainly.com/question/28920252

#SPJ4

The probability of getting a Full House with 3 Kings and any pair except Kings is 24 / C(52, 5), which simplifies to 1 / 108290.

To calculate the probability of getting a Full House with 3 Kings, we first need to find the number of possible ways to get this hand. There are four Kings in a deck of 52 cards, so the number of ways to select 3 Kings from the deck is C(4, 3) = 4.

Next, we need to select the pair of cards that will complete the Full House. Since the pair can be any rank except Kings, we have 12 possible ranks to choose from. Once we have chosen the rank, there are 4 cards of that rank in the deck, so the number of ways to select 2 cards from that rank is C(4, 2) = 6.

Therefore, the total number of ways to get a Full House with 3 Kings is 4 * 6 = 24.

The denominator C(52, 5) represents the total number of 5-card hands that can be dealt from a deck of 52 cards. This is given by C(52, 5) = 2,598,960.

Know more about probability here:

https://brainly.com/question/30034780

#SPJ11

The given equation is second-order homogeneous linear differential equation with constant coefficients. It can be written in form of y'' + 10y' + 25y = 0', y'.  Solution of equation is [tex]y_p(t) = (-e^(5t)*sin(t) + 5*e^(5t)*cos(t))/34.[/tex], solving we get A = -1/34 and B = 5/34.

The characteristic equation of the differential equation is r^2 + 10r + 25 = 0, which can be factored as (r+5)^2 = 0. Hence, the roots of the characteristic equation are repeated and equal to -5. Therefore, the general solution of the differential equation is given by [tex]y(t) = (c1 + c2*t)*e^(-5t)[/tex], where c1 and c2 are arbitrary constants determined by the initial conditions.

To find the particular solution of the non-homogeneous part of the equation, we can use the method of undetermined coefficients. Since the right-hand side of the equation is of the form e^(5t)*sin(t), we assume that the particular solution has the form [tex]y_p(t) = A*e^(5t)*sin(t) + B*e^(5t)*cos(t),[/tex] where A and B are constants to be determined.

Taking the first and second derivatives of [tex]y_p(t), y'_p(t) = 5A*e^(5t)*sin(t) + 5B*e^(5t)*cos(t) + A*e^(5t)*cos(t) - B*e^(5t)*sin(t), and y''_p(t) = 10A*e^(5t)*cos(t) - 10B*e^(5t)*sin(t) + 20A*e^(5t)*sin(t) + 20B*e^(5t)*cos(t).[/tex]

Substituting these expressions into the original equation and equating the coefficients of sin(t) and cos(t), we obtain the system of equations: -10B + 25A = 0, 10A + 25B = 1

Solving this system, we get A = -1/34 and B = 5/34. Therefore, the particular solution of the equation is [tex]y_p(t) = (-e^(5t)*sin(t) + 5*e^(5t)*cos(t))/34[/tex]. Finally, the general solution of the differential equation is [tex]y(t) = (c1 + c2*t)*e^(-5t) + (-e^(5t)*sin(t) + 5*e^(5t)*cos(t))/34,[/tex] where c1 and c2 are determined by the initial conditions.

Know more about arbitrary constants here:

https://brainly.com/question/30466124

#SPJ11

Complete question is For The Following Equations Determine The Appropriate Type Of A Particular Solution To Be Used With The Method Of undetermind coefficients.

(a) y"-10y+ 25y = est + sin t;

(b) y"+25y = cos(5t) +t2;

(c) y" +16y= 4t sin(4t+)+4t;

(d) y"+y"=3t+e'

Option 2 allows Ms. Carlton to pay the smallest amount of interest, with a total interest of $548.00 compared to $920.00 for Option 1.

To determine which repayment option allows Ms. Carlton to pay the smallest amount of interest, we need to calculate the total amount of interest paid for each option.

For Option 1, the total amount paid over the 3-year period is:

Total payment = Monthly payment x Number of payments

Total payment = $95.00 x 36

Total payment = $3,420.00

Since Ms. Carlton borrowed $2,500, the total interest paid is:

Total interest = Total payment - Amount borrowed

Total interest = $3,420.00 - $2,500.00

Total interest = $920.00

For Option 2, the total amount paid over the 2-year period is:

Total payment = Monthly payment x Number of payments

Total payment = $127.00 x 24

Total payment = $3,048.00

Since Ms. Carlton borrowed $2,500, the total interest paid is:

Total interest = Total payment - Amount borrowed

Total interest = $3,048.00 - $2,500.00

Total interest = $548.00

Therefore, Option 2 allows Ms. Carlton to pay the smallest amount of interest, with a total interest of $548.00 compared to $920.00 for Option 1.

to know more about interest

brainly.com/question/30393144

#SPJ1

The solution to the initial-value problem x' + 2y' + x = 0, x(0) = 0 and x' - y' + y = 0, y(0) = 2 using Laplace transforms is x(t) = -2t*sin(t) and y(t) = 2*cos(t).


1. Apply Laplace transform to both equations: L{x'} + 2L{y'} + L{x} = 0 and L{x'} - L{y'} + L{y} = 0.

2. Use properties of Laplace transforms: sX(s) - x(0) + 2[sY(s) - y(0)] + X(s) = 0 and sX(s) - x(0) - [sY(s) - y(0)] + Y(s) = 0.

3. Substitute initial conditions: sX(s) + 2[sY(s) - 2] + X(s) = 0 and sX(s) - [sY(s) - 2] + Y(s) = 0.

4. Rearrange and solve for X(s) and Y(s): X(s) = (4sY(s) - 4)/(s² + 1) and Y(s) = (s² + 2s + 2)/(s² + 1).

5. Apply inverse Laplace transform to find x(t) and y(t): x(t) = -2t*sin(t) and y(t) = 2*cos(t).

To know more about Laplace transforms click on below link:

https://brainly.com/question/30759963#

#SPJ11

Therefore, the mass of the yogurt in the mixture is 74g.

The mass of yogurt, we need to know the ratio of yogurt to the total mixture. Since we only have the ratio of two of the components, we need to assume that the remaining portion is made up of the yogurt.

The total ratio of the mixture is 2:3. This means that for every 2 parts of the first component, there are 3 parts of the second component.

Let's assume that the first component is the yogurt, and the second component is something else. This means that for every 3 parts of the mixture, 2 parts are yogurt and 1 part is the other component.

We know that the total mass of the mixture is 185g. So, we can set up a proportion:

2/5 = x/185

where x is the mass of the yogurt.

Solving for x, we get:

x = 74g

So, the mass of the yogurt in the mixture is 74g.

Learn more about mass visit: brainly.com/question/86444

#SPJ4

Correct Question:

A desert has both fruit and yogurt inside altogether the mass of the desert is 185g the ratio of the mass to fruit to the mass of yoghurt is 2:3 what is the mass of yoghurt?

The postulate that explains why these triangles are congruent is: A. ASA.

The postulate that explains why two triangles are congruent is the Angle Side Angle theorem.

According to this postulate, if the added side of an angle and two angles are congruent to two angles and the added side of another angle, then the two triangles being evaluated are congruent. From the triangle, we can see that this postulate is satisfied because of the arrangement of the triangles.

Learn more about the Angle Side Angle theorem here:

https://brainly.com/question/3168048

#SPJ1

It appears that you have created a relative-frequency distribution graph for some data (possibly related to investment returns) and would like to use a normal density function to model future returns. The most important assumption to consider in this context is the assumption of normality.

The normality assumption states that the underlying data follows a normal distribution, also known as the Gaussian distribution or bell curve. This distribution is characterized by its symmetric bell shape and is defined by its mean (average) and standard deviation (a measure of variability). In a normal distribution, about 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

When using the normal density function to model future returns, it is crucial to assume that the data exhibits normality. This means that the relative frequencies of the returns in the dataset follow the pattern expected from a normal distribution. If the data significantly deviates from normality, the predictions made using the normal density function might not be accurate and could lead to poor decision-making in future investment scenarios.

In summary, the most important assumption to consider when using a normal density function to model future returns based on a relative-frequency distribution graph is that the data follows a normal distribution. This assumption allows for accurate predictions and better decision-making in investment planning.

Learn more about distribution  here:

https://brainly.com/question/29664127

#SPJ11

Applying the definition of congruent triangles, the perimeter of triangle ABC is: D. 180 ft.

Congruent triangles are two or more triangles that have the same size and shape, meaning that their corresponding sides and angles are equal.

We are told that triangles ABD and CBD are congruent, this means their corresponding sides lengths are equal. That is:

AB = BC = 50 ft

AD = CD = 40 ft

Perimeter of triangle ABC = AB + AD + CD + BC

= 50 + 40 + 40 = 50

= 180 ft.

Learn more about congruent triangles on:

https://brainly.com/question/31375021

#SPJ1

The circumference of the circle inscribed in a square of side 14 units is 43.96 units, on the basis of the fact that the diameter of the circle will be equal to the side of the square.

What is circumference?

Circumference is the length of a circle's boundary or the perimeter of any circular object or figure.A circle's circumference or an elliptical two-dimensional figure's perimeter are the same. Either the radius or the diameter of the circle are necessary components to calculate the circumference.

Circumference of circle=2πr       {where r=radius}

                                      =πd         {where d=diameter}

Given that the circle is inscribed in the square & it is the maximum possible circle that would fit inside the square of 14 units.

The diameter of circle= side of square that inscribes circle

                               d   = 14 units

Circumference of circle=πd

                                      =π(14)

                                      =14π      {in terms of π}

Circumference of circle=14π

                                      =14(3.14)            {taking π=3,14}

                                      =43.96 units

Circumference of circle=43.96 units

To know more about circumference, visit:

https://brainly.com/question/28757341

#SPJ1

Largest number of flights you would need to get from any destination to any other destination in Math world can be calculated using the concept of Graph theory.

Graph theory, a network of points (vertices) and lines (edges) is represented as a graph.

In the case of flights, the airports are the vertices, and the flights connecting them are the edges.
find the maximum number of flights needed, we need to find the diameter of the graph.

Diameter of a graph is the longest distance between any two vertices. In other words, it is the maximum number of edges that you need to travel to get from one vertex to another.
diameter of the graph will depend on the number of vertices and the connections between them.

In the case of Math world, we do not have a specific graph, so we cannot calculate the exact number of flights needed. we can estimate that the diameter of the graph will be large, given the number of airports and the complexity of the network.

For similar questions on Math World

https://brainly.com/question/22942374

#SPJ11

The equation that models this relationship is y = 0.1x + 80

An equation is an expression that shows how numbers and variables are related to each other using mathematical operations.

Let y represents his pay each night and x represents the waitstaff's tips.

The host at a Cuban restaurant is paid $80 plus 10% of the waitstaff's tips for each night, therefore:

y = 80 + 10% of x

y = 0.1x + 80

The equation is y = 0.1x + 80

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

The maximum r-values occur at θ = 0, π/2, π, 3π/2, etc.

To sketch the graph of the polar equation r = 5 cos 2θ, we can first create a table of values for r and θ.

θ r

0 5

π/8 4.14

π/4 2.93

3π/8 1.54

π/2    0

5π/8 -1.54

3π/4 -2.93

7π/8 -4.14

π -5

... ...

To plot the graph, we can use these values to find the corresponding points in the polar coordinate system.

We can also note that the polar equation r = 5 cos 2θ has symmetry about the y-axis, since replacing θ with -θ results in the same value of r.

Additionally, we can find the maximum r-values by finding the points where cos 2θ is equal to 1, which occur when 2θ is equal to 0 or a multiple of 2π.

So, the maximum r-values occur at θ = 0, π/2, π, 3π/2, etc.

To sketch the graph, we can plot the points from the table of values and connect them with a smooth curve.

Here is a rough sketch of the graph attached

Read more about rectangular equation at

https://brainly.com/question/14289251

#SPJ1

If a grocery delivery service subscriber pays $135.99 per year for unlimited deliveries. The amount  that  will have been paid instead of using cash is: $1.93.

First determine the monthly interest rate.

Annual interest rate (APR) = 16.999%

Monthly interest rate =16.999% / 12 = 1.416583%

Interest charges = $135.99 x 1.416583%

Interest charges  = $1.93

Now let find  much more would be paid instead of using cash

$135.99 + $1.93 = $137.92

Difference in cost=  $137.92 - $135.99 = $1.93

Therefore correct  option is C.

Learn more about amount paid here:https://brainly.com/question/26670496

#SPJ1

The required length of the road is given as 87.5 meters.

Given that,

A map of a city uses a scale of 1cm =3.5 meters. A road shown on the maps runs for 25cm how long is the road is to be determined.

We know that,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,

1 cm = 3.5 meters,

For a road of 25 cm on the map,

Length of the road = 25 × 3.5

Length of the road = 87.5 meters

Thus, the required length of the road is given as 87.5 meters.

Learn more about simplification here:

brainly.com/question/12501526

#SPJ1