¾ (x - 13) = -2 (9 + x)

Answer:

8( 3x+2y) ( 9x^2 -6xy +4y^2)

Step-by-step explanation:

216x^3 + 64y^3

Factor out the greatest common factor of 8

8( 27x^3 +8y^3)

Rewriting

8 ( (3x)^3 + (2y)^2))

Recognizing this as the difference of cubes)

a^3 + b^3 = (a+b) (a^2-ab+b^2)

8 ( (3x)^3 + (2y)^2)) = 8( 3x+2y) ( 9x^2 -(3x)(2y) +4y^2)

                                 =8( 3x+2y) ( 9x^2 -6xy +4y^2)

Answer:

5, 100, 10, 105, 15, 110,20}

Step-by-step explanation:

The range of the function is {100, 105, 110, 115, 120, 125, 130}. The correct answer is D.

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

We are given that;

The table

Now,

we can find the range of the function based on the input-output table:

The output values in the table are 100, 105, 110, 115, 120, 125, and 130. These are the possible pay per month that the function can produce for different hours of training.

To write the range as a set, we use curly braces {} and separate the elements by commas. We do not need to repeat any values that appear more than once in the table.

Therefore, by range of the function the answer will be {100, 105, 110, 115, 120, 125, 130}.

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Answer:

n = -4

Step-by-step explanation:

Notice how in the previous examples they all divide by 2? It is the same case here. So now the question is... "what" divided by "2" is "-2".

Let me show you:

n ÷ 2 = -2

if you know your integer math, you should know that...

-4 ÷2 = -2 (this is the correct equation)

Answer: Time taken by Ximena to paint the fence alone  = 24 hours

Time taken by Candice to paint the fence alone = 12 hours

Step-by-step explanation:

Let x= Time taken by Ximena to paint the fence alone .

Time taken by Candice to paint the fence alone = x-12

As per given , we have

\(\dfrac{1}{x}+\dfrac{1}{x-12}=\dfrac{1}{8}\\\\\Rightarrow\ \dfrac{x-12+x}{x(x-12)}=\dfrac{1}{8}\\\\\Rightarrow\ 8(2x-12)=x^2-12x\\\\\Rightarrow\ 16x-96=x^2-12x\\\\\Rightarrow\ x^2-12x-16x+96=0\\\\\Rightarrow\ x^2-28x+96=0\\\\\Rightarrow\ x^2-4x-24x+96=0\\\\\Rightarrow\ x(x-4)-24(x-4)=0\\\\\Rightarrow\ (x-4)(x-24)=0\\\\\Rightarrow x=4, 24\)

if x= 4

Time taken by Ximena = 4 hours

Time taken by Candice = 4-12 hours =-8 hours which is not possible. (time cannot be negative)

Therefore, x= 24

Such that

Time taken by Ximena to paint the fence alone  = 24 hours

Time taken by Candice to paint the fence alone = 24-12=12 hours

The first derivatives for the given functions are:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For  \(y = 100200x + 7x,\) the first derivative is dy/dx = 100207.

For \(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

To find the first derivative for each of the given functions, we'll use the power rule, constant rule, and chain rule as needed.

For the function\(y = 3x^2 + 5x + 10:\)

Taking the derivative term by term:

\(d/dx (3x^2) = 6x\)

d/dx (5x) = 5

d/dx (10) = 0

Therefore, the first derivative is:

dy/dx = 6x + 5

For the function y = 100200x + 7x:

Taking the derivative term by term:

d/dx (100200x) = 100200

d/dx (7x) = 7

Therefore, the first derivative is:

dy/dx = 100200 + 7 = 100207

For the function \(y = ln(9x^4):\)

Using the chain rule, the derivative of ln(u) is du/dx divided by u:

dy/dx = (1/u) \(\times\) du/dx

Let's differentiate the function using the chain rule:

\(u = 9x^4\)

\(du/dx = d/dx (9x^4) = 36x^3\)

Now, substitute the values back into the derivative formula:

\(dy/dx = (1/u) \times du/dx = (1/(9x^4)) \times (36x^3) = 36x^3 / (9x^4) = 4/x\)

Therefore, the first derivative is:

dy/dx = 4/x

To summarize:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For y = 100200x + 7x, the first derivative is dy/dx = 100207.

For\(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

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The quantities do not have a proportional relationship because the ratio of the cost to shirts is not equivalent.

The two quantities would have a proportional relationship if the constant of proportionality are equal. The constant of proportionality would be equivalent to the cost of one shirt.

The equation that can be used to determine the constant of proportionality is:

k = y / x

Where:

k = 25 / 2

k = 12.60

k = $36 / 3

k = $12

The quantities are not proportional because the constant of proportionality are different.

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Answer:

acute

Step-by-step explanation:

they are less than 90%

Answer:

C. Vertical / B. Acute

Step-by-step explanation:

Vertical angles are angles opposite each other where two lines cross.

The angles shown are displaying this. They are also under 90 degrees, so are acute too.

Answer:

Shirts : $24

Pants : $23.80

Shoes : $21

Ties : $30.60

Step-by-step explanation:

For the shirt : Price = $15 Discount = 20% 2 shirts are bought

Price after the discount = (100% - 20%) x (2 x $15) = $24

For the pair of pants : Price = $28 ; Discount = 15% ; 1 pair of pants is bought

Price after the discount = (100% - 15%) x $28 = $23.80

For the shoes : Price = $35 Discount = 40% 1 pair of shoes are bought

Price after the discount = (100% - 40%) x $35 = $21

For the tie: Price = $12 Discount = 15% 3 ties are bought

Price after the discount = (100% - 15%) x ( 3 x $12) = $30.60

Answer:

Shirts : $24

Pants : $23.80

Shoes : $21

Ties : $30.60

Step-by-step explanation:

For the shirt : Price = $15 Discount = 20% 2 shirts are bought

Price after the discount = (100% - 20%) x (2 x $15) = $24

For the pair of pants : Price = $28 ; Discount = 15% ; 1 pair of pants is bought

Price after the discount = (100% - 15%) x $28 = $23.80

For the shoes : Price = $35 Discount = 40% 1 pair of shoes are bought

Price after the discount = (100% - 40%) x $35 = $21

For the tie: Price = $12 Discount = 15% 3 ties are bought

Price after the discount = (100% - 15%) x ( 3 x $12) = $30.60

The candidate key for the relation schema R(A,B,C,D,E): A→B, C→B, D→A, D→B, D→C, C→D, D→E.

Candidate key for the given relation: To find the candidate key for the relation schema R(A,B,C,D,E), we need to follow the below steps:

Here, we have the following functional dependencies: A→B, C→B, D→ABC, AC→D, D→E.

Step 1: To normalize the given dependencies, we have the following dependencies:

A→B, C→B, D→ABC, AC→D, D→E becomes

A→B, C→B, D→A, D→B, D→C, D→E.

Step 2: To check for the minimal dependency, we can eliminate the redundancy by eliminating D→ABC. Therefore, we have the following dependency:

A→B, C→B, D→A, D→B, D→C, D→E.

Step 3: Find the closure on each attribute, which is as follows:

1. A+ = {A,B}

2. B+ = {B}

3. C+ = {B}

4. D+ = {A,B,C,D,E}

5. E+ = {E}

Step 4: The combination of attributes that have all attributes of the relation schema, and it will be a candidate key is AD. Therefore, the candidate key is AD.

Compute the minimal cover of F:

Minimal Cover: The minimal set of dependencies that is equivalent to the given set of dependencies is the minimal cover.

We have the following functional dependencies:

A→B, C→B, D→ABC, AC→D, D→E.

The process to compute the minimal cover of F is as follows:

Step 1: To find the redundant dependencies, we need to split the dependencies. We have the following dependencies:

A→B, C→B, D→ABC, AC→D, D→E  becomes

A→B, C→B, D→A, D→B, D→C, D→E.

Step 2: To eliminate the dependencies with three attributes, we can use the following steps:

If X→YZ, then X→Y and X→Z.

Therefore, we have the following dependency:

D→A, D→B, D→C.

Step 3: To eliminate the dependency with two attributes, we can use the following steps:

If X→Y and Y→Z, then X→Z.

We have the following dependency: AC→D, C→D.

Step 4: Therefore, the minimal cover of F is A→B, C→B, D→A, D→B, D→C, C→D, D→E.

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The Frances gets £135.

Given that :-

David, Egil, and Frances share money in the ratio 2:7:9, and David gets £75 more, and the same has E gil, we are to find out how much Frances gets.

The ratio of the amount of money that David, E gil, and Frances share is:

David : Egil : Frances = 2 : 7 : 9Let the constant of proportionality be k. So, David gets 2k.Egil gets 7k.And Frances gets 9k.Now, David gets £75 more than what he gets initially. This means that his amount increases to 2k + £75.So, E gil's amount must also be 7k + £75.Hence, 2k + £75 = 7k + £75 - - - - - - - - - - - - - - - - - - - - (1)Solving the above equation gives:k = 15Substituting the value of k in the three expressions gives: David = 2k = 2 × 15 = £30.E gil = 7k + £75 = 7 × 15 + £75 = £180.Frances = 9k = 9 × 15 = £135.

Therefore, Frances gets £135.

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The probability that I, Sharon, and Robert are chosen is 0.0012

What is the formula for calculating combinations?

The equation  \(^{n}C_{r}=\frac{n!}{(n-r)! r!}\) will be used to calculate combinations, where n is the overall number of things and r is the number of items that are being chosen at a time.

The total number of employees=18

The Boss must choose 3 employees to attend the conference.

The number of possible ways to choose 3 employees from the total of 18 employees is \(^{18}C_{3}\) .

The equation  \(^{n}C_{r}=\frac{n!}{(n-r)! r!}\) will be used to calculate combinations,.

So, \(^{18}C_{3}=\frac{18!}{(18-3)! 3!}\)

    \(^{18}C_{3}=\frac{18!}{(15)! 3!}\)  

    \(^{18}C_{3}=\frac{18 \times 17 \times 16 \times 15}{3 \times 2}\)

     \(^{18}C_{3} =816\)

The probability that I, Sharon, and Robert are chosen is  \(\frac{1}{816}\) = 0.0012

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The probability that I, Sharon, and Robert are chosen is 0.0012

What is the formula for calculating combinations?

The equation   \(^{n}C_{r}=\frac{n!}{(n-r)! r!}\)    will be used to calculate combinations, where n is the overall number of things and r is the number of items that are being chosen at a time.

The total number of employees=18

The Boss must choose 3 employees to attend the conference.

The number of possible ways to choose 3 employees from the total of 18 employees is \(^{18}C_{3}\)   .

The equation  \(^{n}C_{r}=\frac{n!}{(n-r)! r!}\)    will be used to calculate combinations,.

So,

\(^{18}C_{3}=\frac{18!}{(18-3)! 3!}^{18}C_{3}=\frac{18!}{(15)! 3!}^{18}C_{3}=\frac{18 \times 17 \times 16 \times 15}{3 \times 2}\)

\(^{18}C_{3}=816\)

The probability that I, Sharon, and Robert are chosen is  = 0.0012

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Answer:

The system of inequalities to represent this situation is \(x+y \leq 8\)

Step-by-step explanation:

Let the amount of fruits be x pounds

Let the amount of vegetables be y pounds

We are given that There are at most 8 pounds of fruits and vegetables in the salad.

This means that there are less than or equal to 8 pounds of fruits and vegetables in the salad.

So,\(x+y \leq 8\)

Hence the system of inequalities to represent this situation is \(x+y \leq 8\)

The correct alternative, based on the parallel, triangle sum, and isosceles triangle criteria, is 2.

Alternative 1

Since the base angle of an isosceles triangle is 52 degrees, let's say the third angle is x, and according to the triangle sum property,

x + 2 * 52 = 180,

x = 76.

triangle at the base

32 + 2x = 180 (triangle sum property for isosceles triangle)

x = 74

In accordance with the triangle sum property for isosceles triangles, the figure demonstrates that the base angle of the triangle at its base is also equal to 76.

False choice: Angles 74 and 76 are not equal.

Alternative 2:

x + 2 * 76 = 180 (triangle sum property for isosceles triangle)

x = 28

The diagram demonstrates that the triangle at the base angle has angle = 28.

124 + 2x = 180 (triangle sum property for isosceles triangle)

x = 28

Since the two angles 28 and 28 are equivalent, the choice is correct.

Alternative 3

wood you believe it, I past plain geometry -  wrong

would you believe it, I passed plain geometry - correct

Alternative 4

The parallelogram's isosceles triangle, with a base angle of 27,

Using the alternate internal angle theorem, 29's base angle is displayed.

at same point as 27 and both angles are not being equal.

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Answer:

love how all our accounts got deleted. smh

Step-by-step explanation:

When employing the slope intercept equation format, the answer to the equation of the linear function y-2x+5.

In algebra, the term "corresponds" refers to two different but related ideas. In calculus and related fields, a linear form of degree either 0 or 1 is a linear function if its graph is a continuous. A linear equation on a plane is a representation of a linear function. For instance, the linear function y = 3x - 2 is a straight line on the coordinate plane, hence it is a linear function. Since f(x) may be connected to y, the function can be expressed by f(x) = 3x - 2.

given

Y reduces by 2 for every increase in x.

hence, the slope is -2.

The y-intercept can be found by traveling backward, 1-1=0, 3+2=5

it is the y-intercept (0,5)

when employing the slope intercept equation format, the answer to the equation of the linear function y-2x+5.

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When all possible arrangements can be considered, there are 12 different programs (in terms of order) that can be arranged. When the comics must perform between bands, there are only 2 different programs that can be arranged.

Three bands and two comics are performing for a student talent show. We want to find out how many different programs (in terms of order) can be arranged.

Therefore the required answer is When all possible arrangements can be considered, there are 12 different programs (in terms of order) that can be arranged. When the comics must perform between bands, there are only 2 different programs that can be arranged.

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Answer:

105

Step-by-step explanation:

LN = 6x

LN = LM + MN ➡ LN = 4x + 8 + 27 so 6x = 4x + 8 + 27

2x = 35 and x = 17.5

6 × 17.5 = 105

Answer:

105

Step-by-step explanation:

4x+8+27=6x

subtract 4x from both sides you get 35 = 2x

divide and get x= 17.5

you know LN = 6(x), so substitute 17.5 in for x and you get 6(17.5)= 105

(1) The Lieutenant commander data should order 20 chips,

(2) The most number of chips that he will ever have to order is 20 chips.

To determine the number of chips Lieutenant Commander Data should order and maximum amount he will ever have to order, we use inventory control formula for a continuous review system with normal distribution demand:

Part (1) : To calculate the number of chips he should order, we find safety stock, which is buffer-stock kept to meet unexpected demand. The safety stock can be determined using formula,

Safety stock = Z × σ × √L,

Where : Z = Z-score representing desired service probability (in this case, 98% corresponds to a Z-score of approximately 2.33)

σ = Standard-deviation of daily demand (given as 3 chips per day)

L = Lead time (in this case, 2 days)

Safety stock = 2.33 × 3 × √2 ≈ 9.84

To calculate "order-quantity", we consider expected demand during  lead time and the safety stock:

Expected demand during lead time = (Average daily demand × Lead time) + Safety stock,

Expected demand during lead time = (5 × 2) + 9.84 ≈ 19.84

So, Commander Data should order 20 chips,

Part (2) : The maximum amount he will ever have to order is determined by sum of safety-stock and maximum expected demand during lead time:

Maximum order quantity = Safety stock + (Average daily demand × Lead time)

Maximum order quantity = 9.84 + (5 × 2) = 9.84 + 10 = 19.84

Therefore, the maximum amount he will ever have to order is 20 chips.

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Answer:

12 Hotdogs & 10 Hamburgers

Step-by-step explanation:

H - Hamburgers ; D - Hot Dogs

First make two equations :

H+D=22 ; since we sold 22 of both in total

4H+2D=64 ; since the total amount of money raised was $64

Now, use elimination to solve

-4(H+D=22) ; multiplying the first equation by -4 so that the H cancels out

-4H-4D=-88 + 4H+2D=64

4H   +2D      =64

-4H    -4D      =-88

-2D=-24

D=12

Then substitute D into an equation

H+12=22

H=10

Checking

4(10)+2(12)=64

40+24=64

64=64

So, the yearbook club sold 12 hot dogs and 10 hamburgers

10 Hamburgers

12 Hot Dogs

The ways I showed are not the only ways you could do this, the most important parts are getting the right equations and checking your work

The Laplace transform of f(t), with the period 3, is \(L{f(t)} = \frac{2}{s^2} \left(1 - e^{-3s} + e^{-3s} - e^{-6s} + e^{-6s} - e^{-9s} + \ldots\right)\)

The Laplace transform of a periodic function can be determined using the properties of the Laplace transform and the fact that the Laplace transform of a periodic function is also periodic.

In this case, we are given that the function f(t) has a period of 3 and is defined as f(t) = 2t for 0 < t < 3.

To find the Laplace transform of f(t), we can write it as a sum of scaled unit step functions, where each step function covers one period of the function. Since the function f(t) has a period of 3, we can write:

f(t) = 2t = 2t(u(t) - u(t-3)) + 2t(u(t-3) - u(t-6)) + 2t(u(t-6) - u(t-9)) + ...

Using the linearity property of the Laplace transform, we can take the Laplace transform of each term separately. The Laplace transform of 2t is 2/\(s^2\), and the Laplace transform of a unit step function u(t-a) is \(e^{(-as)}/s\).

Therefore, the Laplace transform of f(t) is:

\(L{f(t)} = \frac{2}{s^2} \left(e^{-0s} - e^{-3s}\right) + \frac{2}{s^2} \left(e^{-3s} - e^{-6s}\right) + \frac{2}{s^2} \left(e^{-6s} - e^{-9s}\right) + \ldots\)

Simplifying this expression further, we can combine the terms:

\(L{f(t)} = \frac{2}{s^2} \left(1 - e^{-3s} + e^{-3s} - e^{-6s} + e^{-6s} - e^{-9s} + \ldots\right)\)

The resulting Laplace transform is a sum of terms with exponential functions and can be expressed using the geometric series formula.

However, since the Laplace transform of f(t) is not directly related to its periodicity, a specific expression for the Laplace transform of f(t) cannot be determined without further information.

To graph f(t), plot the function f(t) = 2t for the interval 0 < t < 3, and then repeat this graph periodically every 3 units on the x-axis. This will result in a graph that shows the periodic nature of f(t) with a period of 3.

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Answer:

B.

Step-by-step explanation:

Answer:

try D

I got it wrong it’s B not D

Step-by-step explanation:

I’m not 100%p sure

Answer: slope= -3

Step-by-step explanation: use the slope intercept form to find slope

The relative price of x to y (Px / Py). If MUx / Px = MUy / Py, the consumer is in equilibrium.

(a) If 30% of the labor is allocated to x production and the rest to y production, we can calculate the resulting output pair as follows:

Lx = 0.3 * 10 = 3 units of labor allocated to x

Ly = 0.7 * 10 = 7 units of labor allocated to y

Using the production functions, we can calculate the corresponding outputs:

x = 10(Lx)^0.5 = 10(3)^0.5 = 10√3 ≈ 17.32

y = 5(Ly)^0.5 = 5(7)^0.5 = 5√7 ≈ 13.23

So the resulting output pair is approximately (17.32, 13.23).

(b) The equation for the Production Possibility Frontier (PPF) represents the maximum combination of outputs that can be produced given the available resources (labor endowment). In this case, the PPF can be obtained by varying the allocation of labor between x and y while keeping the total labor endowment constant.

Let's solve for the PPF by equating the total labor endowment to the labor allocated to each sector:

Lx + Ly = 10

Now we can express one variable (Ly) in terms of the other (Lx) to obtain the equation for the PPF:

Ly = 10 - Lx

Substituting this value into the production function for y:

y = 5(Ly)^0.5 = 5(10 - Lx)^0.5

This equation represents the PPF for this economy.

(c) If labor is equally split between sector x and y, then Lx = Ly = 5. We can calculate the opportunity cost of x by comparing the change in output of y when one unit of labor is shifted from x to y.

Opportunity cost of x = Δy / Δx

To find Δy, we calculate the output of y when Lx = 4 (one unit less than the initial allocation of labor to x):

Δy = y(Lx = 4) - y(Lx = 5)

Substituting the values into the production function:

Δy = 5(10 - 4)^0.5 - 5(10 - 5)^0.5 ≈ 2.74

To find Δx, we calculate the output of x when Lx = 5:

Δx = x(Lx = 5) - x(Lx = 4)

Substituting the values into the production function:

Δx = 10(5)^0.5 - 10(4)^0.5 ≈ 2.89

Now we can calculate the opportunity cost of x:

Opportunity cost of x = Δy / Δx = 2.74 / 2.89 ≈ 0.95

So the opportunity cost of producing an additional unit of x is approximately 0.95 units of y.

(d) To find the optimal basket (x*, y*) in a closed economy, we need to maximize the consumer's utility function u(x, y) subject to the production constraint. Since the utility function is defined as the minimum of 0.5x and y, the consumer's optimal choice will depend on the relative prices of x and y.

To find the optimal basket, we need to compare the marginal utility of x (MUx) and the marginal utility of y (MUy) with the relative price of x to y (Px / Py). If MUx / Px = MUy / Py, the consumer is in equilibrium.

However, without information about the relative prices or a  budget constraint, we cannot determine the specific optimal basket (x*, y*) in this closed economy.

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Answer: x=y=z=88

Step-by-step explanation:

All sides of a rhombus are congruent.

Answer:

Answer and steps in attachment

Step-by-step explanation:

Answer: 24

Step-by-step explanation:

1*4=4

2*4=8

3*4=12

6*4=24

9*4=36

Answer:

Here are the answers:

Step-by-step explanation:

1. t=1

2.m=2

3.n=2

4.a=2

5.x=1/3 or 0.3

6.x=15

7.s=4

8.t=2

9.s=1

10.s=3/28, or 0.10714285

11.x=1/3, or 0.3

12.r=2

13.c=-1

14. \(m= \frac{2}{n} \), n ≠ 0

n=\(\frac{2}{m} \), m ≠ 0

15. j= -2

Hope this helps! Brainliest would be much appreciated! Have a great day! :)

Answer:

here is some

Step-by-step explanation:

1. t=1

2.m=2

3.n=2

4.a=2