The price-demand equation for hamburgers at Yaster's Burgers is
x+406 p = 2,950,
where p is the price of a hamburger in dollars and is the number of hamburgers demanded at that price. Use this information to answer questions below.
If the current price of a hamburger at Yaster's Burgers is $3.33, will a 2% price increase cause revenue to
1. increase
2. decrease?

If the current price of a hamburger at Yaster's Burgers is $4.94, will a 4% price increase cause revenue to
1. increase
2. decrease?

Answers

Answer 1

1. a 2% price increase will cause revenue to decrease. Hence the correct option is 2.

2. a 4% price increase will cause revenue to increase. Hence the correct option is 1.

1.The price-demand equation for hamburgers at Yaster's Burgers is x + 406p = 2950, where p is the price of a hamburger in dollars and x is the number of hamburgers demanded at that price.

We need to find out if a 2% price increase will cause revenue to increase or decrease when the current price of a hamburger is $3.33.

Let us substitute p = 3.33 in the above equation,

x + 406(3.33) = 2950x + 1340.98 = 2950x = 2950 - 1340.98x = 1609.02 / x = 1609.02

We know that the current price of a hamburger is $3.33, thus x = 1609.02/3.33 ≈ 483.07

Let us increase the price by 2%, then new price = 3.33 + (2/100) × 3.33 = 3.40

New value of x = 1609.02/3.40 ≈ 473.24

Revenue = Price × Quantity demanded at that price (p * x)

Revenue before increase = 3.33 * 483.07 ≈ $1610.89

Revenue after 2% increase in price = 3.40 * 473.24 ≈ $1609.82

Therefore, a 2% price increase will cause revenue to decrease.

Hence the correct option is 2.

2. Let us again use the price-demand equation for hamburgers at Yaster's Burgers, x + 406p = 2950.

Let us substitute p = 4.94 in the above equation,

x + 406(4.94) = 2950

x + 1992.64 = 2950

x = 2950 - 1992.64

x = 957.36

We know that the current price of a hamburger is $4.94, thus x = 957.36/4.94 ≈ 193.91

Let us increase the price by 4%, then new price = 4.94 + (4/100) × 4.94 = 5.13

New value of x = 957.36/5.13 ≈ 186.71

Revenue before increase = 4.94 * 193.91 ≈ $954.96

Revenue after 4% increase in price = 5.13 * 186.71 ≈ $958.46

Therefore, a 4% price increase will cause revenue to increase.

Hence the correct option is 1.

To know more about price-demand equation, visit:

https://brainly.com/question/32089845

#SPJ11


Related Questions

What is the cardinality (number of elements) of ?
A) 18
B) 19
C) 20
D) 21
E) None of the given

Answers

D) 21

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

By means of the Routh criterion analyze the stability of the given characteristic equation. Discuss how many left half plane, right half plane and jo poles do the system have? s5+2s++ 24s3+ 48s2 - 25s - 50 = 0

Answers

The given characteristic equation has two poles in the right half plane and three poles in the left half plane or on the imaginary axis.

To analyze the stability of the given characteristic equation using the Routh-Hurwitz criterion, we need to arrange the equation in the form:

s^5 + 2s^4 + 24s^3 + 48s^2 - 25s - 50 = 0

The Routh table will have five rows since the equation is of fifth order. The first two rows of the Routh table are formed by the coefficients of the even and odd powers of 's' respectively:

Row 1: 1   24   -25

Row 2: 2   48   -50

Now, we can proceed to fill in the remaining rows of the Routh table. The elements in the subsequent rows are calculated using the formulas:

Row 3: (2*(-25) - 24*48) / 2 = -1232

Row 4: (48*(-1232) - (-25)*2) / 48 = 60325

Row 5: (-1232*60325 - 2*48) / (-1232) = 2

The number of sign changes in the first column of the Routh table is equal to the number of roots in the right half plane (RHP). In this case, there are two sign changes. Thus, there are two poles in the RHP. The remaining three poles are in the left half plane (LHP) or on the imaginary axis (jo poles).

Learn more About imaginary axis from the given link

https://brainly.com/question/1142831

#SPJ11

Suppose that 1x/(5+x) = [infinity]∑n=0cnxn
Find the first few coefficients

Answers

The first few coefficients of the power series representation of f(x) = 1x/(5+x) are: c0 = 1/5, c1 = 1/5, c2 = -1/5 and c3 = 1/5.

To find the coefficients c0, c1, c2, ... of the power series representation of the function f(x) = 1x/(5+x), we can use the method of expanding the function as a Taylor series.

The Taylor series expansion of f(x) about x = 0 is given by:

f(x) = f(0) + f'(0)x + f''(0)x²/2! + f'''(0)x³/3! + ...

To find the coefficients, we need to compute the derivatives of f(x) and evaluate them at x = 0.

Let's begin by finding the derivatives of f(x):

f(x) = 1x/(5+x)

f'(x) = (d/dx)[1x/(5+x)]

= (5+x)(1) - x(1)/(5+x)²

= 5/(5+x)²

f''(x) = (d/dx)[5/(5+x)²]

= (-2)(5)(5)/(5+x)³

= -50/(5+x)³

f'''(x) = (d/dx)[-50/(5+x)³]

= (-3)(-50)(5)/(5+x)⁴

= 750/(5+x)⁴

Evaluating these derivatives at x = 0, we have:

f(0) = 1/5

f'(0) = 5/25 = 1/5

f''(0) = -50/125 = -2/5

f'''(0) = 750/625 = 6/5

Now we can express the function f(x) as a power series:

f(x) = f(0) + f'(0)x + f''(0)x²/2! + f'''(0)x³/3! + ...

Substituting the values we found:

f(x) = (1/5) + (1/5)x - (2/5)x²/2! + (6/5)x³/3! + ...

Now we can identify the coefficients:

c0 = 1/5

c1 = 1/5

c2 = -2/5(1/2!) = -1/5

c3 = 6/5(1/3!) = 1/5

Therefore, the first few coefficients of the power series representation of f(x) = 1x/(5+x) are:

c0 = 1/5

c1 = 1/5

c2 = -1/5

c3 = 1/5

To learn more about functions visit:

brainly.com/question/29769447

#SPJ11

Evaluate the first partial derivatives of the function at the given point. f(x,y,z)=x2yz2;fx​(1,0,2)=fy​(1,0,2)=fz​(1,0,2)=​ TANAPMATH7 12.2.033.MI. Evaluate the first partial derivatives of the function at the given point. f(x,y,z)=x2yz2fx​(2,0,3)=fy​(2,0,3)=fz​(2,0,3)=​ (2,0,3)

Answers

The first partial derivatives of the function f(x, y, z) = x^2yz^2 at the point (2, 0, 3) are:

f_x(2, 0, 3) = 0

f_y(2, 0, 3) = 36

f_z(2, 0, 3) = 0

To evaluate the first partial derivatives of the function f(x, y, z) = x^2yz^2 at the given point, we need to find the partial derivatives with respect to each variable (x, y, and z) and then substitute the given values into those derivatives.

Let's find the first partial derivatives:

f_x(x, y, z) = 2xy*z^2

f_y(x, y, z) = x^2z^2

f_z(x, y, z) = 2x^2yz

Now, substitute the given values (2, 0, 3) into each of the partial derivatives:

f_x(2, 0, 3) = 2 * 2 * 0 * 3^2

= 0

f_y(2, 0, 3) = 2^2 * 3^2

= 36

f_z(2, 0, 3) = 2 * 2^2 * 0 * 3

= 0

Therefore, the first partial derivatives of the function f(x, y, z) = x^2yz^2 at the point (2, 0, 3) are:

f_x(2, 0, 3) = 0

f_y(2, 0, 3) = 36

f_z(2, 0, 3) = 0

To know more about derivatives visit

https://brainly.com/question/25324584

#SPJ11

The first partial derivatives of the function f(x,y,z) = x²yz² at the point (2,0,3) are: fx(2, 0, 3) = 0, fy(2, 0, 3) = 0,

fz(2, 0, 3) = 0.

To evaluate the first partial derivatives of the function at the given point (2,0,3),

let's first differentiate the function f(x, y, z) = x²yz² with respect to x, y, and z one by one.

After that, we can substitute the point (2,0,3) into the derivative functions to obtain the desired partial derivatives of f(x,y,z) at the point (2,0,3).

Differentiation of f(x, y, z) = x²yz² with respect to x:

When we differentiate f(x, y, z) with respect to x, we assume that y and z are constants, and only x is the variable.

We apply the power rule of differentiation which states that the derivative of x^n with respect to x is nx^(n-1).

Using this rule, we obtain:

fx(x, y, z) = d/dx(x²yz²)

= 2xyz²

When we substitute (2,0,3) into fx(x, y, z),

we get:

fx(2, 0, 3) = 2(0)(3²) = 0

Differentiation of f(x, y, z) = x²yz² with respect to y:

When we differentiate f(x, y, z) with respect to y, we assume that x and z are constants, and only y is the variable.

We apply the power rule of differentiation which states that the derivative of y^n with respect to y is ny^(n-1).

Using this rule, we obtain:

fy(x, y, z) = d/dy(x²yz²) = x²z²(2y)

When we substitute (2,0,3) into fy(x, y, z), we get:

fy(2, 0, 3) = (2²)(3²)(2)(0) = 0

Differentiation of f(x, y, z) = x²yz² with respect to z:

When we differentiate f(x, y, z) with respect to z, we assume that x and y are constants, and only z is the variable.

We apply the power rule of differentiation which states that the derivative of z^n with respect to z is nz^(n-1).

Using this rule, we obtain:

fz(x, y, z) = d/dz(x²yz²) = x²(2yz)

When we substitute (2,0,3) into fz(x, y, z), we get:

fz(2, 0, 3) = (2²)(2)(3)(0) = 0

Therefore, the first partial derivatives of the function f(x,y,z) = x²yz² at the point (2,0,3) are:

fx(2, 0, 3) = 0fy(2, 0, 3) = 0fz(2, 0, 3) = 0.

Answer: fx(2, 0, 3) = 0, fy(2, 0, 3) = 0, fz(2, 0, 3) = 0.

To know more about partial derivatives, visit:

https://brainly.com/question/32387059

#SPJ11

Consider the given function. f(x)=e^x−8 Evaluate the Riemann sum for 0≤x≤2, with n=4, correct to six decimal places, taking the sample points to be midpoints.

Answers

We need to evaluate the Riemann sum for[tex]0≤x≤2[/tex], with n=4,

correct to six decimal places, taking the sample points to be midpoints using the given function.

f(x) = e^x - 8

We need to find the Riemann sum which is given by;

Riemann sum = [f(x1) + f(x2) + f(x3) + f(x4)]Δx

Where,[tex]Δx = (b - a)/n = (2 - 0)/4 = 1/2 = 0.5And, x1 = 0.25, x2 = 0.75, x3 = 1.25 and x4 = 1.75[/tex]

We need to find the value of f(xi) at the midpoint xi of each subinterval.

So, we have[tex]f(0.25) = e^(0.25) - 8 = -7.45725f(0.75) = e^(0.75) - 8 = -6.23745f(1.25) = e^(1.25) - 8 = -3.83889f(1.75) = e^(1.75) - 8 = 0.08554[/tex]

Now, putting these values in the Riemann sum, we get

Riemann[tex]sum = [-7.45725 + (-6.23745) + (-3.83889) + 0.08554] × 0.5= -9.72328 × 0.5= -4.86164[/tex]

Riemann sum for 0 ≤ x ≤ 2, with n = 4, correct to six decimal places, taking the sample points to be midpoints is equal to -4.86164 (correct to six decimal places).

Hence, the correct option is (d) -4.86164.

To know more about Riemann visit :

https://brainly.com/question/30241844

#SPJ11

Find the area of the following region. The region inside one leaf of the rose r=3cos(7θ) The area of the region is square units. (Type an exact answer, using π as needed).

Answers

The area of the region is square units.. 19.855.

The equation of the rose is r=3cos(7θ). Here is its graph :The area of one leaf of the rose can be calculated as follows:This implies that the area of the region inside one leaf of the rose r=3cos(7θ) is 19.855 square units. 

To know more about area visit:

brainly.com/question/28393668

#SPJ11

Use the linear approximation (1 + x)^k = 1 + kx, as specified.
Find an approximation for the function f(x) = 2/(1-x) for values of x near zero. O f(x) = 1 + 2x
O f(x) = 1-2x
O f(x) = 2 - 2x
O f(x) = 2 + 2x

Answers

We take the first term of the power series expansion, which gives us the first-order linear approximation. Hence, option (D) is correct

The given function is f(x) = 2/(1 - x).

To find an approximation for the function f(x) = 2/(1-x) for values of x near zero, we will use the linear approximation (1 + x)^k = 1 + kx.

We will find the first-order linear approximation of the given function near x = 0.

Therefore, we have to choose k and compute f(x) = 2/(1-x) in the form kx + 1.

Using the formula, (1 + x)^k = 1 + kx to find the linear approximation of f(x), we have:(1 - x)^(–1)

= 1 + (–1)x^1 + k(–1 - 0).

Comparing this equation with the equation 1 + kx, we have: k = –1.

Therefore, the first-order linear approximation of f(x) isf(x) = 1 – x + 1 + x,

which simplifies to f(x) = 2.

Since the first-order linear approximation of f(x) near x = 0 is 2, we can conclude that the correct option is O f(x) = 2 + 2x

Hence, option (D) is correct.

Note: To get the first-order linear approximation, we first expand the given function into a power series by using the formula (1 + x)^k.

Then, we take the first term of the power series expansion, which gives us the first-order linear approximation.

To know more about linear visit:

https://brainly.com/question/31510530

#SPJ11

is 100+x−0.001x2+0.00003x3 (in dollars per unit).
Find the increase in revenue if the production level is raised from 1,100 units to 1,700 units. \
a. 551,366,000
b. $51,367,000
c. S17,765,250
d. $26,866,667
e. $37,974,583

Answers

The revenue function given is R(x) = 100x - 0.001x² + 0.00003x³ dollars per unit. The production level is raised from 1,100 units to 1,700 units.

Let's start by finding the revenue generated by producing 1,100 units:

R(1,100) = 100(1,100) - 0.001(1,100)² + 0.00003(1,100)³

        = 110,000 - 1.21 + 4.2

        = 108,802.79 dollars

Now, let's find the revenue generated by producing 1,700 units:

R(1,700) = 100(1,700) - 0.001(1,700)² + 0.00003(1,700)³

        = 170,000 - 4.89 + 10.206

        = 175,115.31 dollars

Thus, the correct option is a)551,366,000.

To know more about production visit :

https://brainly.com/question/30333196

#SPJ11

For each of the methods we've learned so far:
(a) integration.
(b) e^rt,
(c) separation of variables,
(d) Laplace transform,
state whether the method works for the given problem. Briefly explain why (it works or fails).

Answers

The effectiveness of each method depends on the characteristics of the differential equation. Integration works for equations that can be directly integrated, e^rt is useful for linear homogeneous equations, separation of variables is applicable to first-order equations, and the Laplace transform is suitable for linear equations with constant coefficients.  

(a) Integration: This method works for problems where the equation can be directly integrated. By integrating both sides of the equation, we can find the antiderivative and obtain the general solution. However, not all differential equations can be solved through integration alone, especially those that involve nonlinear or higher-order terms.

(b) e^rt: This method is effective for solving linear homogeneous equations with constant coefficients. By assuming a solution of the form y = e^rt and substituting it into the differential equation, we can determine the values of r that satisfy the equation. However, it may not work for nonlinear or non-homogeneous equations.

(c) Separation of variables: This method works well for first-order ordinary differential equations that can be separated into two variables. By rearranging the equation and integrating each side separately, we can find the solution. However, it may not be applicable to higher-order differential equations or equations with nonlinear terms.

(d) Laplace transform: The Laplace transform method is suitable for solving linear ordinary differential equations with constant coefficients. By applying the Laplace transform to both sides of the equation and manipulating the resulting algebraic equation, we can obtain the solution. However, it may not be practical for solving certain boundary value problems or equations with complicated initial conditions.

Learn more about antiderivative here:

https://brainly.com/question/33243567

#SPJ11

Justify whether the systems are causal or non-causal. (i) \( y[n]=5 x[n]+8 x[n-3] \), for \( n \geq 0 \) (ii) \( y[n]=9 x[n-1]+7 x[n+1]-0.5 y[n-1] \) for \( n \geq 0 \)

Answers

The first system (i) [tex]\(y[n] = 5x[n] + 8x[n-3]\) for \(n \geq 0\)[/tex] is non-causal, while the second system (ii) [tex]\(y[n] = 9x[n-1] + 7x[n+1] - 0.5y[n-1]\) for \(n \geq 0\)[/tex] is causal.

To determine whether a system is causal or non-causal, we need to examine the range of values for the time index n in the system's equations.

(i) [tex]\(y[n] = 5x[n] + 8x[n-3]\) for \(n \geq 0\):[/tex]

In this system, the output y[n] at any time index n depends on the input x[n] and the delayed input x[n-3].
The presence of the term x[n-3] indicates that the system depends on the input's future values. Therefore, this system is non-causal.

(ii) [tex]\(y[n] = 9x[n-1] + 7x[n+1] - 0.5y[n-1]\) for \(n \geq 0\)[/tex]

In this system, the output y[n] at any time index n depends on the input x[n-1], the input x[n+1], and the delayed output y[n-1].
All the terms involve either the current or past values of the input or output. There is no dependency on future values. Therefore, this system is causal.

Learn more about causal system here:

https://brainly.com/question/32685220

#SPJ11

Look at the following conditionals: If it is not recess, then
Caleb is playing solitaire. If Caleb is playing solitaire, then it
is not recess. Is the second conditional the converse,
contrapositive,

Answers

The second conditional is the converse of the first conditional.The given conditionals are: If it is not recess, then Caleb is playing solitaire.

If Caleb is playing solitaire, then it is not recess.The second conditional is the converse of the first conditional.In logic, the converse of a conditional statement is obtained by interchanging the hypothesis and conclusion of the given conditional statement.

Therefore, if p → q is a given conditional statement, then its converse is q → p. In this case, the given first conditional statement is "If it is not recess, then Caleb is playing solitaire." Its converse is "If Caleb is playing solitaire, then it is not recess." Thus, the second conditional is the converse of the first conditional.

Learn more about converse from the given link

https://brainly.com/question/31918837

#SPJ11

Use the formula κ(x)=|f"(x)|/[1+(f’(x))^2]^3/2 to find the curvature.
y=5tan(x)
κ(x)=10 sec^2 (x) tan(x) /[1+25sec^4(x)]^3/2

Answers

The value of the curvature κ(x) = 10 sec^2 x tan x /[1+25 sec^4 x]^3/2.

To find the curvature using the formula κ(x)=|f"(x)|/[1+(f’(x))^2]^3/2 with the function y = 5 tan x, we need to differentiate y twice and substitute the values in the formula.

Given function is y = 5 tan x.

The first derivative of y = 5 tan x is: y' = 5 sec^2 x.

The second derivative of y = 5 tan x is: y'' = 10 sec^2 x tan x.

Substitute the value of f"(x) and f'(x) in the formula of curvature κ(x) = |f"(x)|/[1+(f’(x))^2]^3/2 :κ(x) = |10 sec^2 x tan x|/[1+(5 sec^2 x)^2]^3/2κ(x) = 10 sec^2 x tan x /[1+25 sec^4 x]^3/2

Therefore, the value of the curvature κ(x) = 10 sec^2 x tan x /[1+25 sec^4 x]^3/2.

To know more about curvature visit:

brainly.com/question/33155369

#SPJ11

Which scenarios describe data collected in a biased way? Select all that apply.

Answers

The scenarios that describe data collected in a biased way are: A principal interviewed the 25 students who scored highest on a reading test. Trey picked 10 numbers from a bag containing 100 raffle tickets without looking. Josh asked the first 25 people he met at the dog park if they preferred dogs or cats.

Here are the scenarios that describe data collected in a biased way:

A principal interviewed the 25 students who scored highest on a reading test. This is biased because it only includes the opinions of students who are already good at reading. It does not include the opinions of students who are struggling with reading.Trey picked 10 numbers from a bag containing 100 raffle tickets without looking. This is biased because it is possible that Trey picked more numbers from one section of the bag than another. This could skew the results of his data.Josh asked the first 25 people he met at the dog park if they preferred dogs or cats. This is biased because it only includes the opinions of people who are already at the dog park. It does not include the opinions of people who do not like dogs or who do not go to the dog park.

The other scenario, where Kiara puts the names of all the students in her school into a hat and then draws 5 names, is not biased. This is because Kiara is using a random sampling method. This means that every student in the school has an equal chance of being selected.

For such more question on principal:

https://brainly.com/question/25720319

#SPJ8

Question 3 2 pts A widget factory produces n widgets in t hours of a single day. The number of widgets the factory produces is given by the formula n(t) = 10,000t - 25t2, 0≤t≤9. The cost, c, in dollars of producing n widgets is given by the formula c(n) = 2040 + 1.74n. Find the cost c as a function of time t that the factory is producing widgets.
A) c(t) = 2040 + 17,400t - 43.5t²
B) c(t) = 2045 +17,400t - 42.5t²
C) c(t) = 2045 +17,480t - 42.5t²
D) c(t) = 2040 + 17,480t - 43.5t²

Answers

Option A. Answer: A) c(t) = 2040 + 17,400t - 43.5t².Given that a widget factory produces n widgets in t hours of a single day. The number of widgets the factory produces is given by the formula,n(t) = 10,000t - 25t², 0 ≤ t ≤ 9

and the cost, c, in dollars of producing n widgets is given by the formula c(n) = 2040 + 1.74n.

We need to find the cost c as a function of time t that the factory is producing widgets.

To find the cost c as a function of time t that the factory is producing widgets, we substitute n(t) in the formula of c(n) as follows;

c(t) = 2040 + 1.74 × [n(t)]c(t)

= 2040 + 1.74 × [10000t - 25t²]c(t)

= 2040 + 17400t - 43.5t²

Hence, the cost c as a function of time t that the factory is producing widgets is

c(t) = 2040 + 17,400t - 43.5t²,

which is option A. Answer: A) c(t) = 2040 + 17,400t - 43.5t².

To know more about factory produces visit:

https://brainly.com/question/29698347

#SPJ11

pls
help, lost here.
Given numbers \( =(63,80,41,64,38,29) \), pivot \( =64 \) What is the low partition after the partitioning algorithm is completed? (comma between values) What is the high partition after the partition

Answers

The low partition after the partitioning algorithm is completed is `(63,41,38,29)` and the high partition after the partition is `(80)`.

Given numbers \(=(63,80,41,64,38,29)\),

pivot \(=64\)

The low partition after the partitioning algorithm is completed is  `(63,41,38,29)` and the high partition after the partition is `(80)`.

Explanation:

The given numbers are:

\(=(63,80,41,64,38,29)\)

Pivot = 64

The steps to partition the above numbers are:

Choose the last element of the given array as the pivot element. In this case, pivot=64.

Partition the given array into two groups: a low group and a high group. The low group will contain all elements strictly less than the pivot element.

The high group will contain all elements greater than or equal to the pivot element.

Now partition the array around the pivot value (64). The result of the partitioning is that all the elements less than the pivot value (64) are moved to the left of it, and all the elements greater than the pivot value (64) are moved to the right of it. After partitioning, the array will look like this: `(63,41,38,29,64,80)`.

So, the low partition after the partitioning algorithm is completed is `(63,41,38,29)` and the high partition after the partition is `(80)`.

To know more about partition visit

https://brainly.com/question/32329065

#SPJ11

. Six years from now, P 5M will be needed to pay for a building renovation. In order to generate this surn, a sinking fund consisting of three beginaineof-year deposits (A) starting today is establishod. No further payments will be made after the said annual deposits. If money is worth 8% per annum, the value of A is closest io a) P1,132,069 c) P 1,457,985 sunk b) 1,222,635 d) P1,666,667

Answers

The value of A is closest to P1,132,069.

To determine the value of A, we can use the concept of a sinking fund and present value calculations. A sinking fund is established by making regular deposits over a certain period of time to accumulate a specific amount of money in the future.

In this scenario, we need to accumulate P5M (P5,000,000) in six years. The deposits are made at the beginning of each year, and the interest rate is 8% per annum. We want to find the value of each deposit, denoted as A.To calculate the value of A, we can use the formula for the future value of an ordinary annuity:

FV=A×( r(1+r)^ n −1 )/r

where FV is the future value, A is the annual deposit, r is the interest rate, and n is the number of periods.

Substituting the given values and Solving this equation, we find that A is approximately P1,132,069.

Therefore, the value of A, closest to the given options, is P1,132,069 (option a).

Learn more about Substituting here:

brainly.com/question/30336794

#SPJ11

Find the number of units that must be produced and sold in order to yield the maximum profit given the equations below for reve R(x)=6xC(x)=0.01x2+1.3x+20​ A. 365 units B. 470 units C. 730 units D. 235 units

Answers

Therefore, to yield the maximum profit, 235 units must be produced and sold.

To find the number of units that must be produced and sold in order to yield the maximum profit, we need to consider the profit function. The profit function is given by subtracting the cost function from the revenue function.

Given:

Revenue function R(x) = 6x

Cost function [tex]C(x) = 0.01x^2 + 1.3x + 20[/tex]

The profit function P(x) is obtained by subtracting the cost function from the revenue function:

P(x) = R(x) - C(x)

[tex]= 6x - (0.01x^2 + 1.3x + 20)[/tex]

To find the maximum profit, we need to determine the value of x that maximizes the profit function P(x). We can do this by finding the critical points of P(x) and evaluating their second derivatives.

Taking the derivative of P(x) with respect to x:

P'(x) = 6 - (0.02x + 1.3)

Setting P'(x) equal to 0 and solving for x:

6 - (0.02x + 1.3) = 0

0.02x = 4.7

x = 235

To determine whether x = 235 corresponds to a maximum or minimum, we can take the second derivative of P(x).

Taking the second derivative of P(x) with respect to x:

P''(x) = -0.02

Since the second derivative P''(x) is negative for all x, the critical point x = 235 corresponds to a maximum.

To know more about maximum profit,

https://brainly.com/question/30887890

#SPJ11

Can you just do problems c and d please? Thank you very much
The vector \( \vec{A}=2 \tilde{a}_{s}-5 \tilde{a}_{a} \) is perpendicular to which one of the following vectors? a. \( 5 \tilde{a}_{x}+2 \bar{a}_{y}+2 a_{x} \) b. \( 5 \tilde{a}_{x}+2 \dot{a}_{y} \) c

Answers

Neither option (c) nor option (d) is perpendicular to \(\vec{A}\).

Given that the vector \( \vec{A}=2 \tilde{a}_{s}-5 \tilde{a}_{a} \) is perpendicular to the vectors given as options.

Now, to find which vector is perpendicular to \(\vec{A}\), we can find the dot product between \(\vec{A}\) and each option and check which one gives 0.

Dot Product: If \(\vec{u} = u_{x} \tilde{a}_{x}+u_{y} \tilde{a}_{y}+u_{z} \tilde{a}_{z}\) and \(\vec{v} = v_{x} \tilde{a}_{x}+v_{y} \tilde{a}_{y}+v_{z} \tilde{a}_{z}\) are two vectors, then the dot product of the two vectors is given by:\(\vec{u} \cdot \vec{v} = u_{x}v_{x} + u_{y}v_{y} + u_{z}v_{z}\)

For option (c), the vector is \( 2 \tilde{a}_{x}+2 \tilde{a}_{y}+5 \tilde{a}_{z} \)

Therefore,\(\vec{A} \cdot \vec{c} = 2(2) - 5(5) + 0 = -21\) As the dot product is not zero, option (c) is not perpendicular to \(\vec{A}\).

Hence, option (c) is incorrect. Now, we can check option (d) For option (d), the vector is \( 5 \tilde{a}_{x}+2 \dot{a}_{y} \) Therefore,\(\vec{A} \cdot \vec{d} = 2(5) - 5(0) + 0 = 10\). As the dot product is not zero, option (d) is not perpendicular to \(\vec{A}\). Hence, option (d) is incorrect.

Therefore, neither option (c) nor option (d) is perpendicular to \(\vec{A}\).

To  know more about perpendicular visit:
brainly.com/question/29017140

#SPJ11

Data for motor vehicle production in a country for the years 1997 to 2004 are given in the table. Year 19971998199920002001200220032004 Thousands 1,5781,6281,8052,009 2,332 3,251 4,444 5,092 (A) Find the least squares line for the data, using x=0 for 1990 . y= (Use integers or decimals for any numbers in the expression. Do not round until the final answer. Then round to the nearest tenth as needed.) (B) Use the least squares line to estimate the annual production of motor vehicles in the country in 2011. The annual production in 2011 is approximately vehicles.

Answers

To find the least squares line for the given data, we will perform linear regression using the method of least squares. We'll consider the years (x-values) as the independent variable and the motor vehicle production (y-values) as the dependent variable.

Let's first calculate the necessary sums:

n = number of data points = 8

Σx = sum of x-values = 1997 + 1998 + ... + 2004

Σy = sum of y-values = 1578 + 1628 + ... + 5092

Σxy = sum of x*y = (1997 * 1578) + (1998 * 1628) + ... + (2004 * 5092)

Σ[tex]x^2[/tex] = sum of x^2 = (1997^2) + (1998^2) + ... + (2004^2)

Once we have these sums, we can use the following formulas to calculate the coefficients of the least squares line:

slope, m = (n * Σxy - Σx * Σy) / (n * Σx^2 - (Σx)^2)

intercept, b = (Σy - m * Σx) / n

Let's calculate these values:

Σx = 1997 + 1998 + 1999 + 2000 + 2001 + 2002 + 2003 + 2004 = 16016

Σy = 1578 + 1628 + 1805 + 2009 + 2332 + 3251 + 4444 + 5092 = 22139

Σxy = (1997 * 1578) + (1998 * 1628) + ... + (2004 * 5092) = 24979962

Σ[tex]x^2[/tex] = ([tex]1997^2[/tex]) + (1998^2) + ... + (2004^2) = 32096048

Now we can substitute these values into the formulas:

slope, m = (8 * 24979962 - 16016 * 22139) / (8 * 32096048 - (16016)^2)

intercept, b = (22139 - m * 16016) / 8

Performing the calculations:

slope, m ≈ 0.8259

intercept, b ≈ -161423.375

Therefore, the equation of the least squares line is:

y ≈ 0.8259x - 161423.375

To estimate the annual production of motor vehicles in the country in 2011, we substitute x = 2011 into the equation:

y ≈ 0.8259 * 2011 - 161423.375

Calculating this expression:

y ≈ 1661.136 - 161423.375

y ≈ -159762.239

The estimated annual production of motor vehicles in the country in 2011 is approximately -159,762 vehicles.

To know more about linear regression this:

https://brainly.com/question/32339599

#SPJ11

Wse a graphing utity to groph the equation and graphically approximate the values of \( x \) that satisfy the specified inequalitieg. Then solve each inequality algebraically. \[ y=x^{3}-x^{2}-16 x+16

Answers

The given inequality is y ≤ 0.We will use a graphing utility to graph the equation and approximate the values of x that satisfy the inequality.

In order to graph the given inequality, we need to graph the equation y = x³ - x² - 16x + 16 first. We can use the graphing utility to graph this equation as shown below:

graph{y=x^3-x^2-16x+16 [-10, 10, -5, 5]}

From the graph, we can see that the values of x that satisfy the inequality y ≤ 0 are the values for which the graph of the equation y = x³ - x² - 16x + 16 is below the x-axis.

We can approximate these values by looking at the x-intercepts of the graph. We can see from the graph that the x-intercepts of the graph are at x = -2, x = 2, and x = 4.

Therefore, the values of x that satisfy the inequality y ≤ 0 are approximately x ≤ -2, -2 ≤ x ≤ 2, and 4 ≤ x.

To solve the inequality algebraically, we need to find the values of x that make y ≤ 0. We can do this by factoring the expression y = x³ - x² - 16x + 16:

y = x³ - x² - 16x + 16= x²(x - 1) - 16(x - 1)= (x - 1)(x² - 16)= (x - 1)(x - 4)(x + 4)

The inequality y ≤ 0 is satisfied when the value of y is less than or equal to zero. Therefore, we need to find the values of x that make the expression (x - 1)(x - 4)(x + 4) ≤ 0.

To find these values, we can use the method of sign analysis. We can make a sign table for the expression (x - 1)(x - 4)(x + 4) as shown below:x-441Therefore, the values of x that make the expression (x - 1)(x - 4)(x + 4) ≤ 0 are approximately x ≤ -4, 1 ≤ x ≤ 4.

Therefore, the solution to the inequality y ≤ 0 is approximately x ≤ -2, -2 ≤ x ≤ 2, and 4 ≤ x, or -4 ≤ x ≤ 1 and 4 ≤ x.

To know more about inequality visit:

https://brainly.com/question/20383699

#SPJ11

Problem 3
3. (2 points) Let \( \varepsilon \) be any of the roots of the equation \( x^{2}+x+1=0 \). Find \[ \frac{1+\varepsilon}{(1-\varepsilon)^{2}}+\frac{1-\varepsilon}{(1+\varepsilon)^{2}} \]

Answers

The value of the given expression [tex]\[ \frac{1+\varepsilon}{(1-\varepsilon)^{2}}+\frac{1-\varepsilon}{(1+\varepsilon)^{2}} \][/tex]  is equal to 1.

To find the value of the expression [tex]\(\frac{1+\varepsilon}{(1-\varepsilon)^2} + \frac{1-\varepsilon}{(1+\varepsilon)^2}\)[/tex] , where [tex]\(\varepsilon\)[/tex] is any of the roots of the equation [tex]\(x^2 + x + 1 = 0\)[/tex].

Let's find the roots of the equation . We can solve this quadratic equation using the quadratic formula:

[tex]\[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\][/tex]

For this equation, a=1, b=1, and c= 1, so:

[tex]\[x = \frac{-1 \pm \sqrt{1 - 4}}{2} = \frac{-1 \pm \sqrt{-3}}{2} = \frac{-1 \pm i\sqrt{3}}{2}\][/tex]

Now, let's substitute [tex]\(\varepsilon\)[/tex] with one of these roots in the given expression:

[tex]\[\frac{1+\varepsilon}{(1-\varepsilon)^2} + \frac{1-\varepsilon}{(1+\varepsilon)^2} = \frac{1 + \left(\frac{-1 + i\sqrt{3}}{2}\right)}{\left(1 - \left(\frac{-1 + i\sqrt{3}}{2}\right)\right)^2} + \frac{1 - \left(\frac{-1 + i\sqrt{3}}{2}\right)}{\left(1 + \left(\frac{-1 + i\sqrt{3}}{2}\right)\right)^2}\][/tex]

To simplify this expression, let's calculate each term separately.

First, let's simplify the numerator of the first fraction:

[tex]\[1 + \frac{-1 + i\sqrt{3}}{2} = \frac{2}{2} + \frac{-1 + i\sqrt{3}}{2} = \frac{1 + i\sqrt{3}}{2}\][/tex]

Next, let's simplify the denominator of the first fraction:

[tex]\[1 - \left(\frac{-1 + i\sqrt{3}}{2}\right) = 1 - \frac{-1 + i\sqrt{3}}{2} = \frac{2}{2} - \frac{-1 + i\sqrt{3}}{2} = \frac{3 + i\sqrt{3}}{2}\][/tex]

Therefore, the first fraction becomes:

[tex]\[\frac{1 + \varepsilon}{(1 - \varepsilon)^2} = \frac{\frac{1 + i\sqrt{3}}{2}}{\left(\frac{3 + i\sqrt{3}}{2}\right)^2} = \frac{1 + i\sqrt{3}}{3 + i\sqrt{3}} = \frac{(1 + i\sqrt{3})(3 - i\sqrt{3})}{(3 + i\sqrt{3})(3 - i\sqrt{3})}\][/tex]

Expanding and simplifying the numerator and denominator, we get:

[tex]\[\frac{(1 + i\sqrt{3})(3 - i\sqrt{3})}{(3 + i\sqrt{3})(3 - i\sqrt{3})} = \frac{3 - i\sqrt{3} + 3i\sqrt{3} + 3}{9 - (i\sqrt{3})^2} = \frac{6 + 2i\sqrt{3}}{9 + 3} = \frac{6 + 2i\sqrt{3}}{12} = \frac{1}{2} + \frac{i\sqrt{3}}{2}\][/tex]

Substituting \(\varepsilon = \varepsilon_2\) into the expression:

[tex]\[\frac{1 + \varepsilon}{(1 - \varepsilon)^2} = \frac{1 + \left(\frac{-1 - i\sqrt{3}}{2}\right)}{\left(1 - \left(\frac{-1 - i\sqrt{3}}{2}\right)\right)^2} + \frac{1 - \left(\frac{-1 - i\sqrt{3}}{2}\right)}{\left(1 + \left(\frac{-1 - i\sqrt{3}}{2}\right)\right)^2}\][/tex]

Simplifying the numerator of the first fraction:

[tex]\[1 + \frac{-1 - i\sqrt{3}}{2} = \frac{2}{2} + \frac{-1 - i\sqrt{3}}{2} = \frac{1 - i\sqrt{3}}{2}\][/tex]

Simplifying the denominator of the first fraction:

[tex]\[1 - \left(\frac{-1 - i\sqrt{3}}{2}\right) = \frac{2}{2} - \frac{-1 - i\sqrt{3}}{2} = \frac{3 - i\sqrt{3}}{2}\][/tex]

Therefore, the first fraction becomes:

[tex]\[\frac{1 + \varepsilon_2}{(1 - \varepsilon_2)^2} = \frac{\frac{1 - i\sqrt{3}}{2}}{\left(\frac{3 - i\sqrt{3}}{2}\right)^2} = \frac{1 - i\sqrt{3}}{3 - i\sqrt{3}} = \frac{(1 - i\sqrt{3})(3 + i\sqrt{3})}{(3 - i\sqrt{3})(3 + i\sqrt{3})}\][/tex]

Expanding and simplifying the numerator and denominator, we get:

[tex]\[\frac{(1 - i\sqrt{3})(3 + i\sqrt{3})}{(3 - i\sqrt{3})(3 + i\sqrt{3})} = \frac{3 + i\sqrt{3} - 3i\sqrt{3} + 3}{9 - (i\sqrt{3})^2} = \frac{6 - 2i\sqrt{3}}{9 + 3} = \frac{6 - 2i\sqrt{3}}{12} = \frac{1}{2} - \frac{i\sqrt{3}}{2}\][/tex]

Now, we can sum the two fractions:

[tex]\[\frac{1 + \varepsilon}{(1 - \varepsilon)^2} + \frac{1 - \varepsilon}{(1 + \varepsilon)^2} = \left(\frac{1}{2} + \frac{i\sqrt{3}}{2}\right) + \left(\frac{1}{2} - \frac{i\sqrt{3}}{2}\right) = \frac{1}{2} + \frac{1}{2} = 1\][/tex]

Therefore, the value of the given expression is equal to 1.

Learn more about Quadratic Equation here:

https://brainly.com/question/30098550

#SPJ4

The question attached here is inappropriate, the correct question is

Let [tex]\( \varepsilon \)[/tex] be any of the roots of the equation [tex]\( x^{2}+x+1=0 \)[/tex].

Find the value of  [tex]\[ \frac{1+\varepsilon}{(1-\varepsilon)^{2}}+\frac{1-\varepsilon}{(1+\varepsilon)^{2}} \][/tex].

Given that the system has a relationship between input \( x(t) \) and output \( y(t) \), it can be written as a differential equation as follows: \[ \frac{d^{3} y}{d t^{3}}+2 \frac{d^{2} y}{d t^{2}}+1

Answers

The given system has a relationship between the output \( y(t) \) and its derivatives. It can be represented by the differential equation \(\frac{d^3 y}{dt^3} + 2\frac{d^2 y}{dt^2} + 1 = 0\).

The given differential equation represents a third-order linear homogeneous differential equation. It relates the output function \( y(t) \) with its derivatives with respect to time.

The equation states that the third derivative of \( y(t) \) with respect to time, denoted as \(\frac{d^3 y}{dt^3}\), plus two times the second derivative of \( y(t) \) with respect to time, denoted as \(2\frac{d^2 y}{dt^2}\), plus one, is equal to zero.

This equation describes the dynamics of the system and how the output \( y(t) \) changes over time. The coefficients 2 and 1 determine the relative influence of the second and first derivatives on the system's behavior.

Solving this differential equation involves finding the function \( y(t) \) that satisfies the equation. The solution will depend on the initial conditions or any additional constraints specified for the system.

LEARN MORE ABOUT differential equation here: brainly.com/question/32645495

#SPJ11

Water is pumped out of a holding tank at a rate of r(t) = 5-6e^-0.25t liters per minute, where t is in minutes since the pump started.

1. How much water was pumped out of the tank, 30 minutes after the pump started?
________
2. If the holding tank contains 1000 liters of water
when the pump is started, then how much water is in the tank 1 hour (60 minutes) after the pump has started?
_______

Answers

The volume of water in the tank 1 hour (60 minutes) after the pump has started is approximately 530.6 liters.

1) The rate at which water is being pumped out of the tank is given by:

r(t) = 5-6e^(-0.25t) liters per minute. The integral of r(t) from 0 to 30 will give the volume of water pumped out in the first 30 minutes of operation. So, the volume of water pumped out in 30 minutes is given by:
= ∫r(t)dt

= [5t + 24e^(-0.25t)]_0^30

= [5(30) + 24e^(-0.25(30))] - [5(0) + 24e^(-0.25(0))]

≈ 117.6 liters
The volume of water pumped out of the tank 30 minutes after the pump started is approximately 117.6 liters.

2) We need to find the volume of water left in the tank after 60 minutes of pump operation. Let V(t) be the tank's water volume at time t.

Then, V(t) satisfies the differential equation:

dV/dt = -r(t) and the initial condition:

V(0) = 1000.

We can use the method of separation of variables to solve this differential equation:
dV/dt = -r(t)

⇒ dV = -r(t)dt
Integrating both sides from t = 0 to t = 60, we get:
∫dV = -∫r(t)dt
⇒ V(60) - V(0)

= ∫[5 - 6e^(-0.25t)]dt

= [5t + 24e^(-0.25t)]_0^60

= [5(60) + 24e^(-0.25(60))] - [5(0) + 24e^(-0.25(0))]

≈ 530.6 liters
The volume of water in the tank 1 hour (60 minutes) after the pump has started is approximately 530.6 liters.

Water is being pumped out of the tank at a given rate, and we are given the value of r(t) in liters per minute, where t is in minutes since the pump started.

To know more about the separation of variables, visit:

brainly.com/question/30417970

#SPJ11

b. Now you can compare the functions. In each equation, what do the slope and y-intercept represent in terms of the situation?
PLEASE HELP>

Answers

Answer: the slope represents the amount of weight the puppy gains each week. The y-intercept represents the puppy's starting weight.

Step-by-step explanation:

Camille's puppy:

slope: 0.5

y-intercept: 1.5

Camille's puppy started at 1.5 pounds and gains 0.5 pounds every week.

Just an example hope it helps :)

For the given cost function C(x)=128√x+ x^2/1000 find
a) The cost at the production level 1850
b) The average cost at the production level 1850
c) The marginal cost at the production level 1850
d) The production level that will minimize the average cost.
e) The minimal average cost.
Give answers to at least 3 decimal places.

Answers

The cost at the production level 1850 is $11260. The average cost at the production level 1850 is $6.086. The marginal cost at the production level 1850 is $15.392.

a) To find the cost at the production level 1850, substitute x = 1850 into the cost function C(x). The cost at this production level is $11260.

b) The average cost is obtained by dividing the total cost by the production level. At x = 1850, the total cost is $11260 and the production level is 1850. Therefore, the average cost at this production level is $6.086.

c) The marginal cost represents the rate of change of the cost function with respect to the production level. To find the marginal cost at x = 1850, take the derivative of the cost function with respect to x and substitute x = 1850. The marginal cost at this production level is $15.392.

d) The production level that minimizes the average cost can be found by setting the derivative of the average cost function equal to zero and solving for x. The production level that minimizes the average cost is 12800 units.

e) To find the minimal average cost, substitute the production level 12800 into the average cost function. The minimal average cost is $5.532.

Learn more about average cost : brainly.com/question/29509552

#SPJ11

Investigate the sequence {a_n} defined by
(a_1 = 5, a_(n+1) = √ (5a_n).

Answers

The sequence {a_n} defined by a_1 = 5 and a_(n+1) = √(5a_n) is investigated. The explanation below provides insights into the behavior of the sequence.

To investigate the sequence {a_n}, we start with a_1 = 5 and recursively compute the terms using the formula a_(n+1) = √(5a_n). By substituting the value of a_n into the formula, we can find the next term in the sequence. For example, a_2 = √(5a_1) = √(5*5) = √25 = 5. Similarly, we can find a_3, a_4, and so on. As we continue this process, we observe that each term is equal to the previous term, indicating that the sequence remains constant.

Therefore, the sequence {a_n} is a constant sequence, where all terms are equal to 5.

Learn more about substituting here: brainly.com/question/24807436

#SPJ11

please solve it....

Answers

The total amount of sales is approximately Rs. 870000.

Let's break down the problem step by step to find the total amount of sales.

Let's denote the total annual sales as "S" in rupees.

According to the given information:

The agent receives a commission of 10% on the total annual sales.

The agent also receives a bonus of 2% on the excess of sales over Rs. 20000.

The total amount of commission and bonus is Rs. 104000.

To calculate the commission and bonus, we can set up the following equation:

Commission + Bonus = Rs. 104000

The commission can be calculated as 10% of the total sales:

Commission = 0.10S

The bonus is applicable only on the excess of sales over Rs. 20000. So, if the sales exceed Rs. 20000, the bonus amount can be calculated as 2% of (Total Sales - Rs. 20000):

Bonus = 0.02(S - 20000)

Substituting the values of commission and bonus in the equation:

0.10S + 0.02(S - 20000) = 104000

Simplifying the equation:

0.10S + 0.02S - 400 = 104000

0.12S = 104400

Dividing both sides of the equation by 0.12:

S = 104400 / 0.12

S ≈ 870000

Therefore, the total amount of sales is approximately Rs. 870000.

for such more question on total amount

https://brainly.com/question/25109150

#SPJ8

Question

a commission of 10% is given to an agent on the total annual sales with the addittion of bonus 2% on the excess of sales over rs. 20000 if the total amount of commission and bonus is rs.104000 find the total amount sales

Find the indefinite integral. Check your work by differentiation. ∫6x(9−x)dx ∫6x(9−x)dx=__

Answers

Therefore, the indefinite integral of ∫6x(9−x)dx is [tex]27x^2 - 2x^3 + C[/tex], where C is a constant.

To find the indefinite integral of ∫6x(9−x)dx, we can expand the expression and then integrate each term separately:

∫6x(9−x)dx = ∫[tex](54x-6x^2)dx[/tex]

Using the power rule for integration, we have:

∫54xdx =[tex](54/2)x^2 + C_1[/tex]

[tex]= 27x^2 + C_1[/tex]

∫[tex]-6x^2dx = (-6/3)x^3 + C_2 \\= -2x^3 + C_2[/tex]

Combining the results, we have:

∫6x(9−x)dx[tex]= 27x^2 - 2x^3 + C[/tex]

To check our work, we can differentiate the obtained result:

[tex]d/dx (27x^2 - 2x^3 + C) = 54x - 6x^2[/tex]

which matches the original integrand 6x(9−x).

To know more about indefinite integral,

https://brainly.com/question/31969670

#SPJ11

Given the definition of f(x) below, how is the function best described at x=0?
{x²+2x-2 if x < 0
Let F(x) = {2x² + 3x -2 if 0 ≤ x < 3
{-2x²-3x - 1 if x ≥ 3

Answers

At x = 0, the function f(x) is best described as having a "corner" or a "discontinuity" due to a change in the definition of the function at that point.

The function f(x) is defined differently for different ranges of x. For x < 0, f(x) = x^2 + 2x - 2. For 0 ≤ x < 3, f(x) = 2x^2 + 3x - 2. And for x ≥ 3, f(x) = -2x^2 - 3x - 1.

At x = 0, the function has a change in its definition. For x < 0, the expression x^2 + 2x - 2 is used to define f(x), while for x ≥ 0, the expression 2x^2 + 3x - 2 is used. Since 0 is the boundary between these two ranges, the function changes its definition at x = 0.

This change in definition results in a discontinuity or a "corner" in the graph of the function at x = 0. It means that the behavior of the function on the left side of 0 is different from its behavior on the right side of 0. Therefore, at x = 0, the function f(x) is best described as having a corner or a discontinuity.

Learn more about function here:

https://brainly.com/question/30721594

#SPJ11

Which of the following statements is true about the sum of a rational and an irrational number?
A.
The sum of a rational and irrational number is always an irrational number.

B.
The sum of a rational and irrational number is always a rational number.

C.
The sum of a rational and irrational number is never an irrational number.

D.
The sum of a rational and irrational number is sometimes a rational number.

Answers

It is incorrect to say that the sum of a rational and an irrational number is always irrational (A) or always rational (B). Similarly, it is incorrect to say that the sum is never irrational (C). The correct statement is that the sum of a rational and irrational number is sometimes a rational number (D).

The correct answer is D. The sum of a rational and irrational number is sometimes a rational number.

To understand why, let's consider an example. Let's say we have a rational number, such as 2/3, and an irrational number, such as √2.

When we add these two numbers together: 2/3 + √2

The result is a sum that can be rational or irrational depending on the specific numbers involved. In this case, the sum is approximately 2.94, which is an irrational number. However, if we were to choose a different irrational number, the result could be rational.

For instance, if we had chosen π (pi) as the irrational number, the sum would be:2/3 + π

In this case, the sum is an irrational number, as π is irrational. However, it's important to note that there are cases where the sum of a rational and an irrational number can indeed be rational, such as 2/3 + √4, which equals 2.

for more search question sum

https://brainly.com/question/30442577

#SPJ8

Other Questions
Measured values: Object distance do = 62 cm 320 cm image distance di = 1/62+1/320=1/1 f= 51.94 cm Calculated value: focal length f= 51 cm Comment on how well your measure and calculated values off agree. I think my measure and calcualtion, boyth are quite similar D. MAGNIFICATION You should have observed above that the size of the image changes depending on the position of the object. The magnification of the image is defined as the ratio of the image size to the object size, but it is also related to the image and object distances by: M=d/d. (2) Dan AE Using the equations (1) and (2), show that the image will be the same size as the object when de = di (.e. just substitute do = d). Then show that this occurs when do = di = 2f Is this conclusion confirmed by the simulation when do = di = 2f? 02) a) Find the period of ze given by S LT 137 FindH) for hin] =8) +26m-1)+28-2+6n-3) and show that the ter has a linear phase term Determine and plot the result in of convolution between xin) and hin] given below n = n + I20 + s - 48 2) -[n+2)+50[n+1+30[m] zin) = cos (1.1rn) + sin (0.7mm) The most common isotope of uranium, 238U, is an a-emitter with a half-life of 4.47 billion years. What mass of uranium would have the same activity as that of one gram of radium (1 curie)? This year (2022), Evan graduated from college and took a job as a deliveryman in the city. Evan was paid a salary of $73,800 and he recelved $700 in hourly pay for part-time work over the weekends. Evan summarized his expenses as follows: Calculate Evan's AGl and taxable income if he files single. Assume that interest payments were initially required on Evan's student loans this year. the long-run growth framework focuses on factors affecting: MarkshisandWhich steps should be used to compare the fractions andO Find a common numerator.O Add the numerators and denominators to determine which sum is larger.O Use the "greater than" symbol to show which denominator is larger.O Multiply the first fraction by 2 and the second fraction by 3 Wilson Ivanhoe is a leading producer of vinyl replacement windows. The company's growth strategy focuses on developing domestic markets in large metropolitan areas. The company operates a single manufacturing plant in Kansas City with an annual capacity of 500,000 windows. Current production is budgeted at 450,000 windows per year, a quantity that has been constant over the past threc years. Based on the budget, the accounting department has calculated the following unit costs for the windows: The company's budget includes $5,400,000 in foxed overhead and $3,150,000 in fixed seling and administrative expenses. The windows sell for $150.00 each. A 2% distributoris commission is included in the selling and administrative expenses. E Your answer is partially correct. Calculate variable overhead per unit and variable selling and administrative costs per unit. (Round answers to 2 decimal places, eg. 15.25.) Variable overhead per unit $ Variable selling and administrative costs per unit $ eTextbook and Media Last saved 1 second ago. Attempts: 2 of 3 used Bridgeport, Finland's second largest homebuilder, has approached Wilson with an offer to buy 75,000 windows during the coming year, Given the size of the order, Bridgeport has requested a 35% volume discount on Wilson's normal selling price. Calculate the contribution from special order. (If net contribution is negative, enter amount with a negative sign, eg. 5,285 or parentheses, e. (5,285). Round onswer to 0 decimal places, es. 8.971) Net contribution from special order Should Wilson grant Bridgeport's request? iok and Media Mer: Attempts: 0 of 3 used Return to the original data. Monk Builders has just signed a contract with the state government to replace the windows in lowincome housing units throughout the state. Monk needs 80,000 windows to complete the job and has offered to buy them from Wilson at a price of $110.00 per window. Monk will pick up the windows at Wilson's plant, so Wilson will not incur the $2 per window shipping charge. In addition, Wilson will not need to pay a distributor's commission, since the windows will not be sold through a distributor. Calculate the contribution from special order, contribution lost from regular sales and the net contribution from special order. Contribution from special order Contribution lost from forgone regular sales Net contribution from special order Should Wilson accept Monk's offer? Wilson accept Monk's offer. If Wilson decides to accept Monk's offer, it will need to find an additional 30,000 windows to meet both the special order and normal sales. Metlock Panes has offered to provide them to Wilson at a price of $130.00 per windowi Metlock Panes will deliver the windows to Wilson, and Wilson would then distribute them to its customers. Calculate total contribution from outsourcing. Total contribution from outsourcing Should Wilson outsource the production of the extra windows to Metlock Panes? 1.5% per year, with a beta of 0.50. Genentech have to suffer if it were not insured to justify purchasing the insurance? The actuarially fair insurance premium to cover Genentech's loss is s million. (Round to two decimal places.) Evaluate. Be sure to check by differentiating.e9x+8dxe9x+8dx=(Type an exact answer. Use parentheses to clearly denote the argument of each function). Given an acceleration vector, initial velocity u0,v0,w0, and initial position x0,y0z0, find the velocity and position vectors for t0 a(t)=7t,et,11,u0,v0,w0=0,0,2,x0,y0z0=3,0,0What is the velocity vector? v(t)=What is the position vector? r(t)= The nurse is discharging a baby with clubfoot who has had a cast applied. The nurse should provide additional teaching to the parents if they make which statement?-"I should call if I see changes in the color of the toes under the cast."-"I should use a pillow to elevate my child's foot as he sleeps."-"My baby will need a series of casts to fix her foot."-"Having a cast should not prevent me from holding my baby." 48 yr old woman with complex medical history, her legs are stikcs and her belly is getting bigger, is fatigued and does not have excessive daytime somnolence.has been homeless for most of 5 years, but lives in care for last 12 month.PE she is distractible and has inappropriate affect but is cooperative.Neuro and mental exam is otheriwse nromal. There is loss of adipose tissue from extremities and face, with noticeable inc in abdominal girth.Which of the following meds is most likely responsible for patients symptoms? . Let X be the 6-point DFT of x = [1, 2, 3, 4, 5, 6]. Determine the sequence y whose DFT Y[k] X-k)6], for k = 0,1,...,5. A third person to whom a joint tenant's interest is transferred becomes a(n):a. joint tenant.b. general partner.c. tenant in common.d. tenant by the entirety. A major focus in health care finance is the managing of third-party reimbursement. True or False? an expansion of the domestic money supply can be offset by the sale of foreign reserves. this technique is called Matching QuestionMatch the lifting technique to its respective situation.The Core LiftThe Team LiftBrace YourselfTake a kneeTwo-Hand GripThe Quick PickRetrieving a 45-pound object off thefloorLifting a 75-pound bag of potatoesPlacing items in a cooler withoutstretched armsRetrieving an object from the bottom ofa deep bin or barrelBending down to pick or retrievesomething from the floorRepetitive motion e.g. scanning What is the average angular speed of the Earth in radians per second as it (i) orbits the Sun? (ii) rotates about its own axis? The radius of the Earth is 6400 km. (iii) At what speed is someone on the equator travelling relative to the centre of the Earth? (iv) Hamid lives in Pabna in Bangladesh; the latitude there is 24 N. At what speed does he travel relative to the centre of the Earth? Give your answer in kmh 1to the nearest 10kmh 1. (i) 1.9910 7rads 1(ii) 7.2710 5rads 1(iii) 465 m s 1(iv) 1530kmh 1 in a buildings main electrical service panel the line side would For a geometric sequence with first term =2, common ratio =2, find the 9 th term. A. 512 B. 512 C. 1024 D. 1024 A B C D