The first floor of a tiny house has has a length of 11 feet. The width of the kitchen if is 7 feet and the width of the bathroom is 4 feet. The expression 11(7+4) represents the total area in square feet. Write an expression to represent the total area as the sum of the areas of each room

After considering the given data we conclude that the answer for the sub questions are
a) Jeff consumes 33.33 units of good x.
b) the compensating variation is:
\(CV=W'-W=2(50)-200=-100CV\)
c) The income effect is negative, indicating that Jeff will consume less of good x due to the decrease in purchasing power caused by the price increase.

a. To find Jeff's demand function for good x, we can use the following equation:
\(\frac{\partial U}{\partial x}=\frac{1}{x}=\frac{p_x}{p_y}=\frac{1}{2}\)
Solving for x, we get:
\(x=\frac{1}{2}y\)
Substituting the given values, we get:
\(x=\frac{1}{2}(200/3)=33.33\)
Therefore, Jeff consumes 33.33 units of good x.
b. If Px increases to 2, the new demand function for good x is:
\(x'=\frac{1}{2}y'\)where y'  is the amount of good y consumed at the new prices and income. To find the compensating variation, we need to find the amount of income Jeff would need at the original prices to achieve the same level of utility as he does at the new prices. We can use the following equation:
\(W'=W+CV\) where W is the original income, W' is the new income, and CV is the compensating variation.
Substituting the given values, we get:
\(8.51=\ln(33.33)+\ln(66.67)8.51=ln(33.33)+ln(66.67)\)
\(y'=\frac{W'}{2}\)
\(x'=\frac{1}{2}y'\) Solving for y', we get:
y'=100
Solving for x', we get:
x'=50
Therefore, the compensating variation is:
\(CV=W'-W=2(50)-200=-100CV\)
c. To calculate the total effect, substitution effect, and income effect of the price change, we can use the following equations:
\(TE=\frac{\Delta U}{U_0}\)
\(SE=\frac{\Delta x_s}{x_0}\)
\(IE=\frac{\Delta x_i}{x_0}\)where \(\Delta U\)is the change in utility, \(U_0\) is the initial utility,\(\Delta x_s\) is the change in consumption due to the substitution effect, \(x_0\) is the initial consumption, and \(\Delta x_i\) is the change in consumption due to the income effect.
The change in consumption due to the price change can be calculated as:
as:
\(\Delta x=x'-x_0=\frac{1}{2}y'-\frac{1}{2}y_0\)
where \(y_0=2x_0\) and \(y'=2x'\)
Substituting the given values, we get:
\(\Delta x=x'-x_0=50-33.33=16.67\)
The substitution effect can be calculated as:
\(SE=\frac{\Delta x_s}{x_0}=\frac{x_s'-x_0}{x_0}=\frac{1}{2}\frac{y_0-y_s'}{x_0}=\frac{1}{2}\frac{p_x}{p_y}\frac{y_0}{x_0}\)
Substituting the given values, we get:
\(SE=\frac{1}{2}\frac{1}{2}\frac{2x_0}{4x_0}=\frac{1}{4}\)
The income effect can be calculated as:
\(IE=\frac{\Delta x_i}{x_0}=\frac{\Delta W}{W_0}=\frac{CV}{W_0}\)
Substituting the given values, we get:
\(IE=\frac{-100}{200}=-0.5\)
The total effect can be calculated as:
\(TE=SE+IE=\frac{1}{4}-0.5=-0.25\)
Therefore, the total effect of the price change is negative, indicating that Jeff will consume less of good x as a result of the price increase. The substitution effect is positive, indicating that Jeff will consume more of good x due to the relative price change. The income effect is negative, indicating that Jeff will consume less of good x due to the decrease in purchasing power caused by the price increase.
To learn more about income effect
https://brainly.com/question/15300267
#SPJ4

The ratio of the least common multiple of 180 and 594 to the greatest common factor of 180 and 594 is 7,140:18.

The greatest common factor (GCF) of 180 and 594 is 18.

The least common multiple (LCM) of 180 and 594 is 7,140.

Therefore, the ratio of the LCM to the GCF is 7,140:18.

The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 180 and 594, you can use the prime factorization method. First, you need to prime factorize each number.

180 = 2 x 2 x 3 x 3 x 5 and 594 = 2 x 7 x 17.

Then, you need to identify the greatest common factor among the prime factors of each number. The prime factors of 180 and 594 that are common to both are 2 and 2, which means that the GCF of 180 and 594 is 18. The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers. To find the LCM of 180 and 594, you can use the prime factorization method. First, you need to prime factorize each number. 180 = 2 x 2 x 3 x 3 x 5 and 594 = 2 x 7 x 17. Then, you need to identify the least common multiple among the prime factors of each number. The LCM of 180 and 594 is 2 x 2 x 3 x 3 x 5 x 7 x 17, which is 7,140.

Therefore, the ratio of the LCM to the GCF is 7,140:18.

Learn more about ratio here

https://brainly.com/question/13419413

#SPJ4

2+2 expotentially put is given as \(2^{2}\). The solution has been obtained by using the concept of exponents.

What is an exponent?

The multiplicity of a given number is shown by the exponent, which is the number's representation. For instance, multiplying the number 2 by four times is represented by the expression 2^4. To 2*2*2*2, it has been increased. As a number's power, an exponent is also referred to. A whole number, fraction, negative number, or decimal can be used.

We are given 2+2 which is to be represented exponentially.

We know that 2+2 is 4

We can interpret that we are adding the number two, two times.

So this means we are multiplying 2 by 2 which gives us 4.

We know that if same numbers are multiplied then, they can be written in exponent form.

Here, since two is being multiplied by itself, so, the exponential form for this is \(2^{2}\).

Hence, 2+2 expotentially put is given as \(2^{2}\).

Learn more about exponent from the given link

https://brainly.com/question/13669161

#SPJ1

To find the selling price that will yield the maximum profit, we need to find the vertex of the quadratic function given by the profit equation y = -5x² + 286x - 2275.The x-coordinate of the vertex can be found using the formula:

x = -b/2a

where a = -5 and b = 286.

x = -b/2a

x = -286/(2(-5))

x = 28.6

So, the selling price that will yield the maximum profit is $28.60 (rounded to the nearest cent).

Therefore, the widgets should be sold for $28.60 to maximize the company's profit.

Hope I helped ya...

Answer:

29 cents

Step-by-step explanation:

The amount of profit, y, made by the company selling widgets, is related to the selling price of each widget, x, by the given equation:

\(y=-5x^2+286x-2275\)

The maximum profit is the y-value of the vertex of the given quadratic equation. Therefore, to find the price of the widgets that maximises profit, we need to find the x-value of the vertex.

The formula to find the x-value of the vertex of a quadratic equation in the form y = ax² + bx + c is:

\(\boxed{x_{\sf vertex}=\dfrac{-b}{2a}}\)

For the given equation, a = -5 and b = 286.

Substitute these into the formula:

\(\implies x_{\sf vertex}=\dfrac{-286}{2(-5)}\)

\(\implies x_{\sf vertex}=\dfrac{-286}{-10}\)

\(\implies x_{\sf vertex}=\dfrac{286}{10}\)

\(\implies x_{\sf vertex}=28.6\)

Assuming the value of x is in cents, the widget should be sold for 29 cents (to the nearest cent) to maximise profit.

Note: The question does not stipulate if the value of x is in cents or dollars. If the value of x is in dollars, the price of the widget should be $28.60 to the nearest cent.

Here is your answer :

Answer 1 :

Volume of the Cylinder = πr²h

Therefore, The Volume of the Cylinder is 50.27 Feet

By Rounding, 50 Units/Feet

Answer 2 :

So, volume is always cubed since you have l x w x h.

A cubic ft is 12 in x 12 in x 12 in = 1728 in3.

35328.78/1728 = 20.44  

20.44 x 7.48 = 152.89

About 153 gallons

HOPE IT HELPS

Answer:

d=rt In this problem we are looking for the distance, but we will have to go about it indirectly. If she's traveling the same exact road going and returning, then the distance traveled both ways is exactly the same. Since d = rt, and d is the same, by the substitution property, if and , then , and . So we need to rt for the trip going, rt for the trip returning and set them equal to each other and solve for t. Going is a rate of 24, and the time is t (since we don't know t), and returning is a rate of 30, and the time is 13 1/3-t. (If the whole trip takes 13 1/3 hours, and t is the time going, then the time returning is the difference between the total time and the going time. That concept is one that baffles most algebra students!). So our r1t1 is 24t, and our r2t2 is 30(13 1/3 - t). Set them equal to each other and that will look like this: That fraction of 40/3 is 13 1/3 made into an improper fraction. Distributing that we will have and 54t = 400. That means that t = 7.407. We have time, and that's great, but we need distance! Go back to one of your equations for distance and sub in t and solve for d. d = 24t, and d = 24(7.407), so d = 177.768 miles.

Answer:

$10000 Total cost to transport 14 tons

Step-by-step explanation:

The total cost C(S) = $6500 + ($250/ton)S.  This is a linear function with initial value $6500 and slope $250/ton.

C(14) = $6500 + ($250/ton)(14) = $10000 = Total cost to transport 14 tons

Answer:

hello! the answer is below!

Step-by-step explanation:

Let's write the equation.

6500 + 250s = c

Now put in our value for s.

6500 + 250 · 19 = 4750

The answers are

6500 + 250s = c

And

4750

Hope this helps! :)

Answer: C

Step-by-step explanation:

13-3=10

Answer: B is correct

Step-by-step explanation:

if you do 2 ÷ 5 you get 0.4. But that isn't an option. So, the only other possibility would be -2 ÷ 5 which gives us -0.4, and that makes sense.

I'm not the greatest at explaining this one but hopefully, this helps!

Answer:

£5300

Step-by-step explanation:

-first you find 3% of 5000, which is £150

-£150 only represents the intreset for one year, but becky invests for 2 years, so:

150*2= 300

-add them together:

300+5000=5300

An inverse function or  anti function is defined as a function, in which the graph can be  reverse into another function. hence commonly , if any type of function “f” takes x to y then, the inverse of “f”  function will take y to x.  hence  the function is represented as ‘f’ or ‘F’, then the inverse function is denoted by \(f^{-1} and F^{-1}\).

let us assume that  f and g are inverse functions, then the condition for  f(x) = y if and only if g(y) = x

when the graph is represented in an original function which has to be  one-to-one function in order  to assure that its inverse is an function. A function is said to be a one to one function only if  function of every second element corresponds to the first value .

The graph of function is  the inverse of a function which  reflects two things, that is , one represents the  function and second represents the inverse of the function, over the line y = x. This line in the graph passes through the origin and which  has slope value  equal to 1 and represented as;

y = f-1(x)     which is equal to     x = f(y)

This relation is basically  similar to y = f(x), which tells that  graph of f but the part of x and y are reversed here. So if we have to draw the graph of f-1, then we have to manipulate the positions of x and y in coordinate axes.

To know more about inverse function , click here:

brainly.com/question/2541698

#SPJ4

Answer:

The circumference of a circle is given by the formula:

C = 2πr

where C is the circumference and r is the radius.

In this problem, we know that the circumference of the lake is 15 miles. So we can set up the following equation:

15 = 2πr

Solving for r, we get:

r = 15 / (2π)

r ≈ 2.4 miles (rounded to the nearest tenth)

So the approximate radius of the lake is 2.4 miles.

The area of a circle is given by the formula:

A = πr^2

where A is the area and r is the radius.

Using the radius we just found, we can calculate the approximate area of the lake:

A = π(2.4)^2

A ≈ 18.1 square miles (rounded to the nearest tenth)

Therefore, the approximate area of the lake is 18.1 square miles.

Answer:

$480

Step-by-step explanation:

From the above question, we are told that:

A saleswoman earns 60% commission on all that she sells. Last month she sold $800 worth of merchandise.

The amount of commission (In dollars) she earned last month is calculated as:

60% of $800

= 60/100 × $800

= $480

Therefore, the amount of commission shoe earned last month in dollars = $480

Answer:

X=-11/6

Steps

f(x)=6x+11

simplify,

0=6x+11

-6x+11

Divide both sides,

Answer is x = -¹¹/6

Answer:

2(2.5) + 2(4.5) + 2(1.75) + 3.25

= 5 + 9 + 3.5 + 3.25 = 14 + 6.75 = 20.75

= 20 3/4 feet

The length of the wall is 20 3/4 feet.

The possible number of pizza special is (7 x 11 x 6 x 3 x 2 = 2772 variations.

Answer:

1.66 £

Step-by-step explanation:

(2 * 3.25 + 1.80) : 5 =

8.3 : 5

1.66 £

Answer:

75%

Step-by-step explanation:

Thus, ∫25 f (x) dx = ∫52 f (x) dx + ∫2−2 f (x) dx - ∫22 f (x) dx∫25 f (x) dx = 15 + 4 - 4 = 15Therefore, the value of the integral ∫25 f (x) dx is 15.

Suppose that f is continuous, ∫5−2 f (x) dx = 11 and ∫2−2 f (x) dx = 4. Find the value of the integral ∫25 f (x) dx.In this question, it is given that f is continuous and ∫5−2 f (x) dx = 11 and ∫2−2 f (x) dx = 4.We need to find the value of the integral ∫25 f (x) dx.The Integral Calculus is an interesting topic and it deals with finding the integrals of the functions. In calculus, the integral is a concept that can be used to find the area between the graph of a function and the x-axis.Suppose that f is continuous on the interval [a, b] and the function g(x) is defined by g(x) = ∫a xf(t) dt. If we take the derivative of g(x), we get:g′(x) = f(x)This is known as the First Fundamental Theorem of Calculus.Using this, we can solve this question as follows:Since ∫5−2 f (x) dx = 11, we can write ∫52 f (x) dx - ∫22 f (x) dx = 11∫52 f (x) dx - 4 = 11∫52 f (x) dx = 11 + 4 = 15Again, ∫2−2 f (x) dx = 4Thus, ∫25 f (x) dx = ∫52 f (x) dx + ∫2−2 f (x) dx - ∫22 f (x) dx∫25 f (x) dx = 15 + 4 - 4 = 15Therefore, the value of the integral ∫25 f (x) dx is 15.

Learn more about Integral

brainly.com/question/18125359

#SPJ11

Answer:

Explanation:

Mathematically, we know that:

In simple terms, when we have the same base, we simply go on to add the powers

We do the same thing here as follows:

When searching for the value 10 in the array [2, 3, 5, 6, 9, 13, 16, 19], a recursive binary search algorithm will return false since the element is not found in the array.

About Binary Search Algorithm

The binary search algorithm, applied on arrays are of recursive type. The broad strategy is to look at the middle item on the list. The procedure of the binary search algorithm is either terminated (key found), the left half of the list is searched recursively, or the right half of the list is searched recursively, depending on the value of the middle element.

The function carrying out the binary search algorithm in a code returns true if the desired element is found in the array, else returns false. Since the element 10 is not present in the given array: [2, 3, 5, 6, 9, 13, 16, 19], the binary search algorithm will return false.

Learn more about binary search algorithm here:

https://brainly.com/question/20734425

#SPJ4

The independent set in a graph is a set of vertices that contain no edges. So, no neighboring vertices are included. The max independent set problem is to get an independent set of maximum size in graph G.

The solution for this question is discussed below:

a) The integer linear program for the max independent set problem is as follows:

maximize ∑x_i Subject to: x_i+x_j ≤ 1 {i,j} ∈ E;x_i ∈ {0, 1} ∀i. The variable x_i can represent whether the ith vertex is in the independent set. It can take on two values, either 0 or 1.

b) The LP relaxation for the max independent set problem is as follows:

Maximize ∑x_iSubject to:

xi+xj ≤ 1 ∀ {i, j} ∈ E;xi ≥ 0 ∀i. The variable xi can take on fractional values in the LP relaxation.

c) The family of graphs is as follows:

Consider a family of graphs G = (V, E) defined as follows. The vertex set V has n = 2^k vertices, where k is a positive integer. The set of edges E is defined as {uv:u, v ∈ {0, 1}^k and u≠v and u, v differ in precisely one coordinate}. It can be shown that the size of the max independent set is n/2. Using LP, the value can be determined. LP provides a value of approximately n/4. Therefore, the ratio LP-OPT/OPT is at least c/4. Therefore, the ratio is in for a constant c>0.

d) The size of a max-independent set is equivalent to the number of vertices minus the minimum vertex cover size.

e) The 2-approximation algorithm for vertex cover implies a 2-approximation algorithm for the max independent set.

To know more about the independent set, visit:

brainly.com/question/31418821

#SPJ11

Answer:

B. 34.4

General Formulas and Concepts:

Pre-Algebra

Trigonometry

Step-by-step explanation:

Step 1: Define

∠ = 24°

opposite = 14

hypotenuse = x

Step 2: Find x

And we have our final answer!

Answer: The answer is 1600.

Step-by-step explanation:

Answer:

1600

Step-by-step explanation:

40 * 40 = 1600

an easy way to figure this out is

4 * 4 = 16

add two zeros (since there are two zeros in 40 and 40)

1600 is your answer

hope this helps :)

Answer:

Step-by-step explanation:

1. The probability of not drawing a white scrap is **3/10**. There are 10 scraps in total, and 5 of them are not white (2 pink scraps and 3 blue scraps). Therefore, the probability of not drawing a white scrap is 5/10 or 1/2.

2. The probability of not drawing a pink scrap is **7/10**. There are 10 scraps in total, and 8 of them are not pink (3 blue scraps and 5 yellow scraps). Therefore, the probability of not drawing a pink scrap is 8/10 or 4/5.

I hope this helps answer your questions!

Answer: -2/5x

Step-by-step explanation:

That is the slope

Y = mx + b says that

y = -2/5x + 7

There's your answer. Hope this helps.

Using Z-table ,

the required probability that their mean total body protein is between 12.2 and 12.4 kg is 0.691..

We have given that,

The sample is Normal distribution,

the mean of sample(X-bar,) = 12.3 kg

standard deviations of sample(sigma) = 0.4 kg

sample size(n) = 4

confidence interval= (12.2, 12.4)

we have to find the probability that mean body protein is between 12.2 and 12.4 kg

Using the confidence interval formula, for finding the value of Z-value ,

C.I = X-bar +- Z(s/√n)

put all avaliabile values we get,

12.2 = 12.3 + Z(0.4/√4) = 12.3 + Z(0.2)

=> Z = - 0.5

or 12.4 = 12.3 + Z(0.2)

=> Z = 0.1/0.2 = 1/2 = 0.5

so, -0.5 < Z< 0.5

now , using the z-value we can easily calculate the value of p i.e. probability

Use the Z-table , we get p -value is 0.691

Hence , probability that their mean total body protein is between 12.2 and 12.4 kg is 0.691

To learn more about P-value or critical value, :

https://brainly.com/question/4621112

#SPJ4

Answer:

Step-by-step explanation:

Use synthetic division:

The coefficients of 2x^3 - 1 are {2, 0, 0, -1}.  Setting up synthetic division, we get:

1    /    2    0    0    -1

                2     2    2

    ---------------------------

          2     2    2     1

Note that the remainder is 1.  The same result would be obtained through long division.

The quotient is 2x^2 + 2x + 2 with a remainder of 1.