help pleaseeeeee i need this asap

Answer:

Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.

Answer:

They are 12, 13, 14 and 15.

Step-by-step explanation:

If the least integer is x, then:

x + x + 1 + x + 2 + x + 3 = 54

4x + 6 = 54

4x = 48

x = 12.

the equation to find the slope between 2 points is

name the points

1=(11,9)

2=(12,9)

apply the formula

the slope between the points is 0.

a. The MRS is constant (not diminishing) at 1/3.

U(x,y) = 3x + y

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = 1 / 3

The MRS is constant (not diminishing) at 1/3.

b. The MRS is diminishing because as y increases, the MRS decreases.

U(x,y) = x * y

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = 1 / y

The MRS is diminishing because as y increases, the MRS decreases.

c. The MRS is diminishing because as y increases, the MRS decreases.

U(x,y) = x * y

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = 1 / y

Similar to the previous case, the MRS is diminishing because as y increases, the MRS decreases.

d. The MRS depends on the ratio of y to x and can vary.

U(x,y) = x^2 - y^2

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = -2y / 2x = -y / x

The MRS depends on the ratio of y to x and can vary. It is not necessarily diminishing.

e. The MRS depends on the values of x and y and can vary.

U(x,y) = x + y / (x * y)

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = -1 / (y^2) + 1 / (x^2 * y)

The MRS depends on the values of x and y and can vary. It is not necessarily diminishing.

Now let's move on to the second part of the question:

For parts a, b, and c, we need more specific information about the utility functions, such as the values of α and β, to calculate the demand curves for x and y, the indirect utility function, and the expenditure function.

To show that the demand curve is homogeneous in degree zero in terms of income and prices, we need the specific functional form of the utility functions and information about the prices of x and y. Please provide the necessary details for parts A, b, and c to continue the analysis.

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Answer:

5 movies

Step-by-step explanation:

Let x denotes number of movies that need to be ready each month for the total fees to be the same from either company.

Monthly membership fee charged by a video store = $7.50

Amount charged to rent each movie = $1.00

So,

total amount charged by the first store = \(7.50+(1)x=7.50+x\)

Monthly membership fee charged by another video store = $0

Amount charged to rent each movie = $2.50

So,

total amount charged by another store = \(0+2.50(x)=2.50x\)

To find number of movies that need to be ready each month for the total fees to be the same from either company,

solve \(7.50+x=2.50x\)

\(7.50+x=2.50x\\7.50=2.50x-x\\7.50=1.50x\\x=\frac{7.50}{1.50}\\ =5\)

Answer:

point A

Step-by-step explanation:

on the number line, point A represent -2

Answer:

Step-by-step explanation:

10

Answer:

A.y=|x|+7

Step-by-step explanation:

The solution of equation is x=-3

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given

The equation;√x+3=-6

Now,

√x=-6-3

√x=-9

x=-3

Therefore the answer of the given equation will be -3

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It should be hung 4 1/16 feet (Measurement unit) from each side of the wall.

what are measurement units(e.g. feet)?

Finding a number that represents the amount of something is what measurement is all about. A measuring unit is a unit of measurement that is used to express a physical quantity.

There are 7 measurement SI-units and these are following

Let, the wall hanging should be hung d feet from each end of wall

therefore,

Length of wall hanging=2 7/8 feet

Length of wall= 11 feet

length left after hanging the wall hanging=11 - 2 7/8

=8 1/8 feet

hence d=(8 1/8)/2

d=4 1/16 feet (distance from each end of wall)

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The volume of the largest rectangular box in the first octant with three faces in the coordinate planes, and one vertex in the plane is V = xyz, where x, y, and z are the lengths of the sides of the rectangular box.

To find the largest volume, we need to maximize x, y, and z. Since we have three faces in the coordinate planes, one vertex will be at the origin (0, 0, 0). The other two vertices will lie on the coordinate axes.

Let's assume the vertex on the x-axis is (x, 0, 0), and the vertex on the y-axis is (0, y, 0). The third vertex on the z-axis will be (0, 0, z). Since the box is in the first octant, all the coordinates must be positive.

To maximize the volume, we need to find the maximum values for x, y, and z within the constraints. The maximum values occur when the box touches the coordinate planes. Therefore, the maximum values are x = y = z.

Substituting these values into the volume formula, we get V = xyz = x³. Therefore, the volume of the largest rectangular box is V = x³.

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What is the maximum volume of a rectangular box situated in the first octant, with three of its faces lying on the coordinate planes, and one of its vertices located in the plane?

1. (ℓ2, ∥⋅∥2) is a normed vector space over R. 2. (ℓ2, ∥⋅∥2) is complete. 3. The closed unit ball B(0,1) is not compact.

To show that (ℓ2, ∥⋅∥2) is a normed vector space over R, we need to verify the following properties:

a) Non-negativity: \(||a||_2 \geq 0\) for all a ∈ ℓ2.

b) Definiteness: \(||a||_2 = 0\) if and only if a = 0.

c) Homogeneity: \(||c. a||_2 = |c| . ||a||_2\) for all c ∈ R and a ∈ ℓ2.

d) Triangle inequality: \(||a+b||_2 \leq ||a||_2 + ||b||_2\) for all a, b ∈ ℓ2.

These properties can be easily verified using the definition of the norm \(|| \,||_2\) as the square root of the sum of the squares of the elements in the sequence.

To show that (ℓ2, ∥⋅∥2) is complete, we need to demonstrate that every Cauchy sequence in ℓ2 converges to a limit that is also in ℓ2. Let {an} be a Cauchy sequence in ℓ2, meaning that for any ε > 0, there exists N such that for all m, n ≥ N, we have \(||a_m - a_n||_2 < \epsilon\).

To show completeness, we need to find a limit point a ∈ ℓ2 such that \(\lim_{n \to \infty} ||an - a||_2\). We can construct this limit point by taking the limit of each component of the sequence. Since each component is a real number and the real numbers are complete, the limit exists for each component. Thus, the limit point a will also be in ℓ2, satisfying the completeness property.

To show that the closed unit ball B(0,1) = {a ∈ ℓ2 : ∥a∥2 ≤ 1} is not compact, we need to demonstrate that there exists an open cover of B(0,1) that does not have a finite sub-cover.

Consider the sequence {en}, where en is the sequence with a 1 in the nth position and 0s elsewhere. Each en is in B(0,1) since ∥en∥2 = 1. Now, for each n, consider the open ball B(en, 1/2). It can be shown that the intersection of any two of these open balls is empty, and hence, no finite sub-cover can cover B(0,1).

Therefore, B(0,1) is not compact.

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Answer:

2.08

Step-by-step explanation:

99/7.8=13.56

13.56/3.14=4.32

the square root of 4.32 is 2.08

(i)  It will take Evelyne approximately 63 months (or 5 years and 3 months) to repay the loan after increasing her repayments to $3000 per month. (ii) Interest saved = $642,064.

Interest can be simple or compound. Simple interest is calculated based only on the principal amount borrowed or invested. Compound interest, on the other hand, is calculated based on both the principal and the accumulated interest. In other words, the interest earned is reinvested back into the principal, which then earns additional interest. Compound interest results in a higher return compared to simple interest, as the interest earned is compounded over time.

Interest is an important concept in personal finance, business, and economics. It plays a key role in determining the cost of borrowing money and the return on investment, and affects the overall economy through its impact on consumption, investment, and savings.

c. After 10 years, Evelyne is able to increase her repayments to $3000 per month.

i. To determine how long it will take Evelyne to repay the loan after increasing her repayments to $3000 per month, we need to first calculate the remaining loan balance at that time. Since Evelyne has been repaying the loan for 10 years, the number of monthly payments remaining is:

20 years x 12 months/year - 10 years x 12 months/year = 120 months

Using the formula for the present value of an annuity, we can calculate the remaining loan balance after 120 months of monthly payments of $X:

\(PV=X*[1-\frac{(1+\frac{r}{12} )^{n} }{\frac{r}{12} } ]\)

where PV is the present value of the annuity (i.e., the remaining loan balance), X is the monthly payment, r is the monthly interest rate, and n is the number of months.

Substituting the given values, we get:

PV = $350,000 * [(0.0054167 - (1 + 0.0054167)⁻¹²⁰)/(0.0054167)] = $178,432.76

Therefore, the remaining loan balance after 10 years of repayments is $178,432.76.

To determine how long it will take Evelyne to repay the loan after increasing her repayments to $3000 per month, we can use the formula for the present value of a lump sum:

PV = FV / (1 + r/12)ⁿ

where FV is the future value (i.e., the remaining loan balance), r is the monthly interest rate, and n is the number of months.

Substituting the values, we get:

$178,432.76 = FV / (1 + 0.065/12)ⁿ

Solving for n, we get:

n = ln(\(\frac{FV}{PV}\)) / ln(1 + \(\frac{r}{12}\)) = ln( \(\frac{178432.76}{0}\)) / ln(1 + \(\frac{0.065}{12}\)) = 62.45

Therefore, it will take Evelyne approximately 63 months (or 5 years and 3 months) to repay the loan after increasing her repayments to $3000 per month.

ii. To calculate the interest that Evelyne will save by increasing her repayments to $3000 per month, we need to first calculate the total interest that she would have paid if she had continued with her original repayment schedule. Using the formula for the future value of an annuity, we can calculate the total amount that Evelyne would have paid over 20 years:

\(FV=X*[\frac{(1+\frac{r}{12} )^{n-1} }{\frac{r}{12} } ]\)

where FV is the future value of the annuity (i.e., the total amount paid), X is the monthly payment, r is the monthly interest rate, and n is the number of months.

Substituting the given values, we get:

FV = $1,176.42 * \([\frac{(1 + 0.0054167)^{240}-1 }{0.0054167} ]\)  = $842,064.88

Therefore, the total amount that Evelyne would have paid over 20 years is $842,064.88.

To calculate the interest that Evelyne will save by increasing her repayments to $3000 per month, we can subtract the total amount that she will pay with the increased repayments from the total amount that she would have paid with her original repayment schedule:

Interest saved = $842,064.88 - ($3000 * 63) = $642,064.

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Answer: 10

Step-by-step explanation:

Total number of students = 113

we require to find the number of students who like both hockey and rugby.

number of students who like game = total number of students - students who doesn't like either one

= 113 - 18 = 95 = A ∪ B

So equation become

A ∪ B = A + B - A ∩ B

95 = 60 + 45 - A ∩ B

A ∩ B = 105-95 = 10.

A circle is a curve sketched out by a point moving in a plane. The area of the circular paper is more than the area of the square.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

The arc length of radius 6 inches is equal to,

Length of the Arc of a quarter = 2πr×(1/4) = 2×π×6×0.25 =0.9448 inches

The area of the circular paper = πr² = π×6×6 = 113.097²

The area of the square with a side of 6 inches = 36 in²

Therefore, the area of the circular paper is more than the area of the square.

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Answer:

96/120 = 4/5

4/5 × 425 = 340 students

The complete table is

Sulfur atoms         6     9     12   27

Oxygen atoms     12    18    24   54    

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other.

A ratio can be compared by the division of two numbers. For example, the ratio of a and b can be represented as a: b and read as a is to b. Here a: b can be written as a/b

Here we have  

The ratio of oxygen atoms to sulfur atoms in sulfur dioxide is always the same. The table shows the number of atoms in different quantities of sulfur dioxide.  

The given table is

Sulfur atoms         6     9     12   ___

Oxygen atoms     12    __   ___   54      

Let x, y, and z be the missing values in the table

Given that ratio of oxygen atoms to sulfur atoms in sulfur dioxide is always the same.  

=> 12/6 = x/9 = y/12 = 54/z    

Now the x, y, and z values can be calculated as follows

Take 12/6 = x/9  

=> 2 = x/9    

=> x = 18  

Take 12/6 = y/12  

=> 2 = y/12

=> y = 24

Take 12/6 = 54/z  

=> 2 = 54/z

=> z = 54/2

=> z = 27    

Therefore,

The complete table is

Sulfur atoms         6     9     12   27

Oxygen atoms     12    18    24   54      

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The complete Question is given in the picture

The value of a = -2 and b = 3.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

Here, we have

Given: 3a - 5b = -26, a + 2b = 6

We have to solve this equation.

3a - 5b = -26...(1)

a + 2b = 6...(2)

Now we multiply equation (1) by 2 and equation (2) by 5 and we get

6a - 10b = -52....(3)

5a + 10b = 30....(4)

After solving equations (3) and (4), we get

11a = -22

a = -2

Now we put the value of 'a' in equation(3) and we get

6(-2) - 10b = -52

-10b = -52 + 12

-10b =  -30

b = 3

Hence, the value of a = -2 and b = 3.

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We may infer after addressing the stated question that As a result, ten expressions erasers set end to end would measure 25 inches in length.

You can add, subtract, divide, and multiply. This is how an expression is put together: Expression, number, and mathematical operator Numbers, variables, and operations (such as addition, subtraction, multiplication, and division, etc.) are all components of a mathematical expression. Expressions and phrases can be contrasted. Any mathematical statement with variables, integers, and an arithmetic operation between them is referred to as an expression or algebraic expression. For instance, the phrases 4m and 5 as well as the variable m from the given statement are all separated by the arithmetic symbol + in the phrase 4m + 5.

If an eraser is 2.5 inches long, then 10 erasers placed end to end equal:

25 inches = 10 erasers x 2.5 inches/eraser

As a result, ten erasers set end to end would measure 25 inches in length.

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Complete question:

Date Name Unit 4.7 LS² Day 3 Homework An Eraser Is 2(1)/(2) Inches Long. How Long Are 10 Erasers Placed End To End?

The answers have been shown below.

Questions regarding the time spent by Jack jogging and bike riding are needed to be answered.

(A) The equations are \(x+y=75, y=15+x\)

Time spent jogging is 30 minutes

The total time would be \(45+60=105\) minutes which is not equal to 75 minutes.

(B) Let \(x\) be the time spent jogging.

\(y\) be the time spent bike riding.

\(x+y=75\\y=15+x\\x+15+x=75\\2x+15=75\\x=\frac{75-15}{2} =30\)

Time spent jogging is 30 minutes.

\(y=60\\x+y=75\)

(C) If he rides his bike 15 minutes longer than he jogs then he would have to jog \(60-15 = 45\) minutes.

Therefore, the total time would be \(45+60=105\) minutes which is not equal to 75 minutes.

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Answer:

11

Step-by-step explanation:

17+9+11+7 divided by 4

because the mean= sum of the terms divided by the number of terms

the sum= 17+9+11+7=44

the number of terms= 4

44 divided by 4= 11

Answer:

(17+9+11+7) / 4 mean is an average

it is equal to the sum of the elements divided by the number of elements

the sum is 44

the number of elements is 4

the mean is the average= 44/4=11

Step-by-step explanation: i dont know why they would ask that

Step-by-step explanation:

1. k = 32

k + 19 = 51

32 + 19 = 51

51 = 51

correct, so, k=32 is a valid solution.

2. x = 43

16 = x - 27

16 = 43 - 27

16 = 16

correct, so, x = 43 is a valid solution.

3. m = 9

28 - m = 17

28 - 9 = 17

19 = 17

wrong. so, m = 9 is NOT a valid solution.

4. y = 8

y + 19 = 27

8 + 19 = 27

27 = 27

correct, so, y = 8 is a valid solution.

5. p = 22

19 = p + 3

19 = 22 + 3

19 = 25

wrong. so, p = 22 is NOT a valid solution.

6. r = 11

4 + r = 15

4 + 11 = 15

15 = 15

correct, so, r = 11 is a valid solution.

7.

a - 8 = 9 adding 8 to both sides

a = 17

8.

v + 13 = 15 subtracting 13 from both sides

v = 2

9.

16 = n - 24 adding 24 to both sides

40 = n or n = 40, of course

10.

c - 9 = 16 adding 9 to both sides

c = 25

11.

11 + k = 18 subtracting 11 from both sides

k = 7

12.

15 = w - 7 adding 7 to both sides

22 = w or w = 22, of course

Answer:

its D because they all match the sides

(L2) An inscribed circle is one that encompasses a polygon so that it passes by each of the polygon's vertices.

A circumcircle, not an inscribed circle, is a circle that encircles a polygon at each vertex. A circle that is enclosed within a polygon and intersects each side of the polygon exactly once is said to be inscribed. A circumcircle, on the other hand, is a circle that goes through every vertex of the polygon, with its center located at the point where the perpendicular bisectors of the polygon's sides converge. The greatest circle that can be drawn within a polygon is the circumcircle, while the largest circle that can be drawn inside a triangle is the inscribed circle.

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Answer:

Falso.

Step-by-step explanation:

Sea \(d = \frac{a}{b}\) un número racional, donde \(a, b \in \mathbb{R}\) y \(b \neq 0\), su opuesto es un número real \(c = -\left(\frac{a}{b} \right)\). En el caso de elevarse a un exponente dado, hay que comprobar cinco casos:

(a) El exponente es cero.

(b) El exponente es un negativo impar.

(c) El exponente es un negativo par.

(d) El exponente es un positivo impar.

(e) El exponente es un positivo par.

(a) El exponente es cero:

Toda potencia elevada a la cero es igual a uno. En consecuencia, \(c = d = 1\). La proposición es verdadera.

(b) El exponente es un negativo impar:

Considérese las siguientes expresiones:

\(d' = d^{-n}\) y \(c' = c^{-n}\)

Al aplicar las definiciones anteriores y las operaciones del Álgebra de los números reales tenemos el siguiente desarrollo:

\(d' = \left(\frac{a}{b} \right)^{-n}\) y \(c' = \left[-\left(\frac{a}{b} \right)\right]^{-n}\)

\(d' = \left(\frac{a}{b} \right)^{(-1)\cdot n}\) y \(c' = \left[(-1)\cdot \left(\frac{a}{b} \right)\right]^{(-1)\cdot n}\)

\(d' = \left[\left(\frac{a}{b} \right)^{-1}\right]^{n}\)y \(c' = \left[(-1)^{-1}\cdot \left(\frac{a}{b} \right)^{-1}\right]^{n}\)

\(d' = \left(\frac{b}{a} \right)^{n}\) y \(c = (-1)^{n}\cdot \left(\frac{b}{a} \right)^{n}\)

\(d' = \left(\frac{b}{a} \right)^{n}\) y \(c' = \left[(-1)\cdot \left(\frac{b}{a} \right)\right]^{n}\)

\(d' = \left(\frac{b}{a} \right)^{n}\) y \(c' = \left[-\left(\frac{b}{a} \right)\right]^{n}\)

Si \(n\) es impar, entonces:

\(d' = \left(\frac{b}{a} \right)^{n}\) y \(c' = - \left(\frac{b}{a} \right)^{n}\)

Puesto que \(d' \neq c'\), la proposición es falsa.

(c) El exponente es un negativo par.

Si \(n\) es par, entonces:

\(d' = \left(\frac{b}{a} \right)^{n}\) y \(c' = \left(\frac{b}{a} \right)^{n}\)

Puesto que \(d' = c'\), la proposición es verdadera.

(d) El exponente es un positivo impar.

Considérese las siguientes expresiones:

\(d' = d^{n}\) y \(c' = c^{n}\)

\(d' = \left(\frac{a}{b}\right)^{n}\) y \(c' = \left[-\left(\frac{a}{b} \right)\right]^{n}\)

\(d' = \left(\frac{a}{b} \right)^{n}\) y \(c' = \left[(-1)\cdot \left(\frac{a}{b} \right)\right]^{n}\)

\(d' = \left(\frac{a}{b} \right)^{n}\) y \(c' = (-1)^{n}\cdot \left(\frac{a}{b} \right)^{n}\)

Si \(n\) es impar, entonces:

\(d' = \left(\frac{a}{b} \right)^{n}\) y \(c' = - \left(\frac{a}{b} \right)^{n}\)

(e) El exponente es un positivo par.

Considérese las siguientes expresiones:

\(d' = \left(\frac{a}{b} \right)^{n}\) y \(c' = \left(\frac{a}{b} \right)^{n}\)

Si \(n\) es par, entonces \(d' = c'\) y la proposición es verdadera.

Por tanto, se concluye que es falso que toda potencia que se obtiene de elevar a un mismo exponente un número racional y su opuesto es la misma.

Answer:

Step-by-step explanation:

Answer: 1,820 Pushups

Step-by-step explanation: 29+36=65

65 x 7 (days in a week)=455

455 x 4(as in the 4 weeks)=1,820 Pushups total

I hope this helped! let me know if you need more help! :)