Solving a Formula for a Variable
Solve for the width in the formula for the area of a rectangle.
Use the rewritten formula to find the width of a rectangle with an area of 42 square inches and a length of 16.8 inches.
I

The result of the each of the following set is

A ∪ B = {1, 3, 5, 6, 7, 9}

A ∩ B = {3, 9}

A ∪ C = {1, 2, 3, 4, 5, 6, 7, 8, 9}

A ∩ C = {∅}

A - B = {1, 5, 7}

B - A = {6}

B U C = {2, 3, 5, 6, 8, 9 }

B ∩ C = {6}

The given values are

A = {1, 3, 5, 7, 9}

B = {3, 6, 9}

C = {2, 4, 6, 8}

Then find the each given terms in set roaster notation

Union of the set, intersection of the set  and the difference of the set are the basic operations of set

A ∪ B = {1, 3, 5, 6, 7, 9}

A ∩ B = {3, 9}

A ∪ C = {1, 2, 3, 4, 5, 6, 7, 8, 9}

A ∩ C = {∅}

A - B = {1, 5, 7}

B - A = {6}

B U C = {2, 3, 5, 6, 8, 9 }

B ∩ C = {6}

Therefore, all the given terms has been found

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Answer: 3.675 seconds

Step-by-step explanation:

Hi, when the object hits the ground, h=0:

h=−16t^2+48.6t+37.5

0=−16t^2+48.6t+37.5

We have to apply the quadratic formula:  

For: ax2+ bx + c  

x =[ -b ± √b²-4ac] /2a  

Replacing with the values given:  

a=-16 ; b=48.6; c=37.5

x =[ -(48.6) ± √(-48.6)²-4(-16)37.5] /2(-16)  

x = [ -48.6 ± √ 4,761.96] /-32

x = [ -48.6 ± 69] /-32

Positive:  

x = [ -48.6 + 69] /-32 = -0.6375

Negative:  

x = [ -48.6 - 69] /-32 = 3.675 seconds (seconds can't be negative)

Feel free to ask for more if needed or if you did not understand something.  

If the price of rough rice increases from 12,000 to 20,000 rupees per ton, the supply curve of milled rice in India will decrease by 96 million tons per year.

To determine how the supply curve changes when the price of rough rice increases from 12,000 to 20,000 rupees per ton, we need to analyze the given supply function:

Q = 8 + 9p - 12p,

In the supply function, "p" represents the price of milled rice in thousands of rupees per ton. However, there is a typo in the equation provided for the supply function. It appears that the equation contains two terms with the variable "p," which should be corrected.

Assuming the corrected supply function is:

Q = 8 + 9p - 12p',

Where p' represents the price of rough rice in thousands of rupees per ton.

Now, let's calculate the initial supply quantity and then compare it with the new supply quantity after the increase in the price of rough rice.

For the initial price of rough rice (p') at 12,000 rupees per ton:

Q1 = 8 + 9p - 12(12)

Q1 = 8 + 9p - 144

For the new price of rough rice (p') at 20,000 rupees per ton:

Q2 = 8 + 9p - 12(20)

Q2 = 8 + 9p - 240

The change in supply can be calculated as the difference between Q2 and Q1:

Change in supply (ΔQ) = Q2 - Q1

= (8 + 9p - 240) - (8 + 9p - 144)

= -240 + 144

= -96

The change in supply (ΔQ) is -96 millions of tons of rice per year.

Therefore, if the price of rough rice increases from 12,000 to 20,000 rupees per ton, the supply curve of milled rice in India will decrease by 96 million tons per year.

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Answer:

0.83

Step-by-step explanation:

The number of push-ups did sara did during gym class if for every 7 push-ups Dulce can do, Sara can do 6 is 24 push ups.

Number of push ups Dulce can do : number of push ups Sara can do

Let

number of push ups Sara does = x

7 : 6 = 28 : x

7/6 = 28/x

cross product

7 × x = 28 × 6

7x = 168

divide both sides by 7

x = 168/7

x = 24

Therefore, Sara does 24 push ups during the gym class.

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Answer:

23x-40

Step-by-step explanation:

(-5x10) (-2x-5)

v

-5(3x+10)-2(4x-5)

v v v v

-15x -50 -8x 10

combine like terms

-15x-8x= 23x ( 2 negatives make a positive)

-50+10= -40

23x-40

Answer:

3 (or x > 2)

Step-by-step explanation:

If your answer is only taking integers, then the first integer that would make this statement true would be 3. If it's for any numerical value, then the inequality would be true for any value above 2.

Answer is x>2

Step-by-step explanation:

\(10x + 5 > 25\)

Bring 5 to the right side for easy calculation,

\(10x > 25 - 5\)

Now Solve directly.

\(→10x > 20\)

\(→x > \frac{20}{10} \)

\(→x > 2\)

Here, above, 20 and 10 has 0, so cancel it, giving you 2/1. It means 2

Therefore, final answer is x>2

Answer:

88

Step-by-step explanation:

Angles b and 88 are corresponding angles,

Corresponding angles are equal.

So,

b = 88

Answer No because it does not have a coefficient

Step-by-step explanation:

On average, it takes approximately 14 minutes for a plane to complete the entire arriving process, from radioing the control tower to landing on the runway, in the morning at Nogan Airport.

To determine the average time that elapses between a plane radioing the control tower and its completion of the entire arriving process in the morning, we need to consider the different steps involved in the process.

Radioing the control tower: The time between two consecutive arriving requests follows an exponential distribution with an average of 10 minutes. Hence, on average, it takes 10 minutes for a plane to radio the control tower after the previous plane.

Assigning position in queue: The air traffic controller assigns the plane a position in the queue on a first-come-first-serve basis, implying that there is no additional delay for this step.

Landing on the runway: Once the plane reaches the front of the queue, it lands on the runway. The time it takes for a plane to use a runway, either for landing or departing, follows an exponentially distributed process.

Since the runway dedicated to arrival can serve 15 flights per hour, the average time it takes for a plane to complete the landing process is 1/15 hour, or 4 minutes.

Considering these steps, the average time that elapses between a plane radioing the control tower and completing the entire arriving process in the morning can be calculated as follows:

Average time = Time to radio the control tower + Time to land on the runway

= 10 minutes + 4 minutes

= 14 minutes

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Okay we’re gonna do the order of PEMDAS.  Here is my work! I hope you have a great day or night or whate it is for you.

Answer:

Step-by-step explanation

Here is the solution of your question.

Hope it helps you!!

Option D is the correct answer. if the residuals from a fitted regression violate the assumption of homoscedasticity their variance is not constant.

Homoscedasticity: It is an assumption of equal or similar variances in different groups are being compared. It is a condition in which the variance of the residual, or error term, in a regression model, is constant.

This is one of the most important assumptions of parametric statistical tests because they are sensitive to any dissimilarities. It is valid when X and Y are independent.

To deal with this First, we have attempted to transform your target using square root, log, reciprocal square root, or reciprocal transformations.

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The solution for b is y-mx in the equation y=mx+b.

The given equation is y=mx+b

y equal r=to m times of x plus b

We need to solve for b in the equation

To solve we have to isolate b from the equation

Subtract mx from both sides

y-mx=b

Hence, the solution for b is y-mx in the equation y=mx+b.

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Answer:

A shipment of 150 bottles will weigh 120 pounds.

Step-by-step explanation:

Given that:

24 bottles of water weigh 30 pounds

Ratio of bottles to weight = 24 : 30

Number of bottles in shipment = 150

Weight of bottles = x

Ratio = x : 150

As the relation is proportional

24 : 30 :: x : 150

Product of mean = Product of extreme

30x = 24 * 150

30x = 3600

Dividing both sides by 30

\(\frac{30x}{30}=\frac{3600}{30}\\x= 120\)

Hence,

A shipment of 150 bottles will weigh 120 pounds.

Answer:

Step-by-step explanation:

5+4g+8=1

add like terms

(5+8)+4g=1

13+4g=1

subtract a -13 from both sides to get 4g by itself

4g=1-13

4g=-12

divide by 4 on each side to solve for g

g=-3

To minimize the cost of operating three different types of machines while meeting product demand, it's essential to choose the appropriate machine based on the cost and capacity.

There are certain numbers of machines available for each type. The information on machines Alpha-1000, Alpha-2000, and Alpha-3000 is given below:Alpha-1000 Alpha-2000 Alpha-3000Initial cost per day $200 $275 $325

Additional cost per product $1.50 $1.80 $1.90Products per day (Max) 40 60 85Number of machines 8 5 3Given that each machine type has a different cost and capacity, the goal is to find the minimum cost of production while maintaining the required product demand. A mathematical model can be developed to minimize the cost of operation of the machines, subject to the demand for products.

The mathematical model can be defined as follows:

Let xi represent the number of machines of type Alpha-i required (i = 1, 2, 3).

The objective function to be minimized is the total cost of production, which can be defined as follows:

Total Cost = (200 × x1) + (275 × x2) + (325 × x3) + (1.50 × x1 × 40) + (1.80 × x2 × 60) + (1.90 × x3 × 85)

Subject to: 40x1 + 60x2 + 85x3 >

= Product demandx1 <= 8, x2 <= 5,

x3 <= 3x1,

x2,

x3 >= 0

From the above model, we can see that the objective is to minimize the total cost of production while ensuring that the demand for products is met.

The model's constraints ensure that the maximum number of machines of each type is not exceeded and that there is enough capacity to meet the required product demand.

In conclusion, the above model can be solved using a linear programming algorithm to determine the optimal number of machines of each type that will minimize the cost of production.

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Answer:

x=9

Step-by-step explanation:

alright so first we eliminate the -15 and to do that we add 15 on both sides:

-3x-15+15=12+15

-3x=27

Now we divide 3 on both sides to make the equation equal to x

\( \frac{-3x}{-3} = \frac{27}{-3} \)

x=9

And that's your answer, you're welcome :)

Step-by-step explanation:

1/4096

0.000244140625

2^-12

1/(2^12)

All of the above expressions are equivalent to (12⁻₂)₈, which is a decimal representation of a number that is obtained by dividing 1 by 2 raised to the power of 12. The first and second expressions are decimal representation of the number, the third one is the representation of the number by using the base 2 logarithm, and the fourth one is the mathematical representation of the number by dividing 1 by 2 raised to the power of 12.

Answer:

Get the equation in the form y = ax2 + bx + c. Calculate -b / 2a. This is the x-coordinate of the vertex. To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y.

Step-by-step explanation:

The vertex formula to find the vertex coordinates (h,k)= (-b/2a, -D/4a) from the standard equation y = ax2 + bx + c, where D = b2 - 4ac.

or give your problem and i can solve it

Answer: 1371.57 calories

Step-by-step explanation:

Plug 150 in for m.

Cube it to cancel out the cube root on the right side:

\(150^{3}\) = 3375000

Find its 4th root to cancel out the exponent of 4 on the right side:

\(\sqrt[4]{3375000}\) = 42.861

Now multiply by 32 to find r:

42.861 * 32 = 1371.57 calories

The velocity of a particle = i + 2t j

The acceleration of a particle = 2 j

The speed of a particle = \(\sqrt{1 + 4t^{2} }\)

Here,

The position function is, \(r (t ) = ti + t^{2} j +2k\)

We have to find, the velocity, acceleration, and speed of a particle with the given position function.

What is Velocity of a particle with the given position function?

The instantaneous velocity v(t) of a particle is the derivative of the position with respect to time. That is, v(t)=dx/dt.

Now,

The position function is, \(r (t ) = ti + t^{2} j +2k\)

The velocity of a particle = \(\frac{d r(t)}{dt}\)

\(r (t ) = ti + t^{2} j +2k\)

\(\frac{d r(t)}{dt} = i + 2t j\)

The acceleration of a particle = \(\frac{d^{2} r(t)}{dt^{2} }\)

\(r (t ) = ti + t^{2} j +2k\)

\(\frac{d r(t)}{dt} = i + 2t j\)

\(\frac{d^{2} r(t)}{dt^{2} }= 2j\)

The speed of a particle = \(| \frac{d r(t)}{dt}| = |v(t)|\)

\(\frac{d r(t)}{dt} = i + 2t j\)

\(|v(t)|=\sqrt{1 + 4t^{2} }\)

Hence, The velocity of a particle = \(i + 2t j\)

The acceleration of a particle = \(2 j\)

The speed of a particle = \(\sqrt{1 + 4t^{2} }\)

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a. The price of the consol is approximately $133.33.

b. The new price of the consol would be $100. The price of the consol falls by 24.99% and the interest rate rises by 1%.

c. Your holding period return is approximately -49.99%.

a. The price of the consol can be calculated using the formula for the present value of a perpetuity:

Price = Annual Payment / Interest Rate

In this case, the annual payment is $4 and the interest rate is 3%. Substituting these values into the formula:

Price = $4 / 0.03 ≈ $133.33

Therefore, the price of the consol is approximately $133.33.

b. To calculate the new price of the consol if the interest rate rises to 4%, we use the same formula:

New Price = Annual Payment / New Interest Rate

Substituting the values, we get:

New Price = $4 / 0.04 = $100

The percentage change in the price of the consol can be calculated using the formula:

Percentage Change = (New Price - Old Price) / Old Price * 100

Substituting the values, we have:

Percentage Change in Price = ($100 - $133.33) / $133.33 * 100 ≈ -24.99%

The percentage change in the interest rate is simply the difference between the old and new interest rates:

Percentage Change in Interest Rate = (4% - 3%) = 1%

Comparing the two percentages, we can see that the price of the consol falls by approximately 24.99%, while the interest rate rises by 1%.

c. The holding period return can be calculated using the formula:

Holding Period Return = (Ending Value - Initial Value) / Initial Value * 100

The initial value is the purchase price of the consol, which is $133.33, and the ending value is the price of the consol after one year with an interest rate of 6%. Using the formula for the present value of a perpetuity, we can calculate the ending value:

Ending Value = Annual Payment / Interest Rate = $4 / 0.06 = $66.67

Substituting the values into the holding period return formula:

Holding Period Return = ($66.67 - $133.33) / $133.33 * 100 ≈ -49.99%

Therefore, the holding period return is approximately -49.99%.

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irrational numbers

Step-by-step explanation:

Because that are not rational numbers which cannot be represented as fraction

The width of the frame is 8 inches.

Now, According to the question:

The length of a rectangular frame is 15 inches

The diagonal length of the frame is 17 inches.

To find the width of the frame in inches.

Let's take the width of the frame is = w

Based on the information given, it should be noted that the diagonal will be the longest side. Therefore, we'll use the Pythagoras theorem to solve the question.

This will be:

17² = 15² + w²

289 = 225 + w²

289 - 225 =  w²

64 =  w²

w = \(\sqrt{64}\)

w = 8

Hence, The width of the frame is 8 inches.

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You should check the following options:

( ) PQ = 10

( ) QS = 12

( ) QS = 13

( ) SR = 5

( ) SR = 6

Let's calculate the distances between the given points using the distance formula and check which statements are true.

Distance between points P and Q (PQ):

PQ = sqrt((x2 - x1)^2 + (y2 - y1)^2)

= sqrt((4 - (-2))^2 + (11 - 3)^2)

= sqrt(6^2 + 8^2)

= sqrt(36 + 64)

= sqrt(100)

= 10

So, PQ = 10 is true.

Distance between points Q and S (QS):

QS = sqrt((x2 - x1)^2 + (y2 - y1)^2)

= sqrt((9 - 4)^2 + (-1 - 11)^2)

= sqrt(5^2 + (-12)^2)

= sqrt(25 + 144)

= sqrt(169)

= 13

So, QS = 13 is true.

Distance between points S and R (SR):

SR = sqrt((x2 - x1)^2 + (y2 - y1)^2)

= sqrt((12 - 9)^2 + (3 - (-1))^2)

= sqrt(3^2 + 4^2)

= sqrt(9 + 16)

= sqrt(25)

= 5

So, SR = 5 is true.

Based on our calculations, the following statements are true:

PQ = 10

QS = 13

SR = 5

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Answer:

verdical lines have an undefined slope so it might be 4