The numerator and denominator of a fraction are in the ratio of one to two. When the numerator is decreased by two and
the denominator is multiplied by two, the simplified value of the new fraction is 3/8. Find the original fraction.

No, rectangle DABC is not the result of a dilation of rectangle HEFG with a center of dilation at the origin.

Dilation is a geometrical transformation that changes the size of a shape or figure. It is one of the four basic transformations of geometry alongside translation, rotation, and reflection. Dilation involves resizing a shape by a scale factor and keeping its overall shape intact. The scale factor is the ratio of the size of the image to the size of the original figure.

Dilation involves a scaling of a shape, where each point on the shape is moved away from or closer to the center of dilation, proportional to its distance from the center. In this case, the angles of rectangle DABC are different from the angles of rectangle HEFG, so it is not the result of a dilation. The angles of rectangle HEFG are ∠2, ∠33, ∠EDC, whereas the angles of rectangle DABC are ∠ADB, ∠BDC, and ∠CDB.

To learn more about dilation
https://brainly.com/question/26855848
#SPJ1

The inventory management model that should be used to solve this problem is the Model Economic Quantity to Order (EOQ) model. The optimal number of notebooks to make in each order is 590 units. The annual ordering cost (AOC) is approximately $892.20. The Annual Holding Cost (AHC) is $3540. The annual product cost (APC) is $233,460. The annual total cost of managing inventory (ATC) is approximately $237,892.20. The total number of orders in the year (N) is 33. The estimated time between each order (T) is approximately 7.58 days. The daily demand is approximately 77.82 units. The reorder point (ROP) is approximately 311 units.

The inventory management model that should be used to solve this problem is the Model Economic Quantity to Order (EOQ) model.

To find the optimal number of notebooks to make in each order, we can use the EOQ formula:

EOQ = √[(2 * Demand * Ordering Cost) / Holding Cost]

EOQ = √[(2 * 19455 * 27) / 6]

EOQ ≈ 589.96

Since the number of notebooks must be a whole number, the optimal number to order would be 590 notebooks.

The annual ordering cost (AOC) can be calculated by dividing the annual demand by the EOQ and multiplying it by the ordering cost:

AOC = (Demand / EOQ) * Ordering Cost

AOC = (19455 / 590) * 27

AOC ≈ $892.20

The Annual Holding Cost (AHC) is calculated by multiplying the EOQ by the holding cost per unit:

AHC = EOQ * Holding Cost

AHC = 590 * 6

AHC = $3540

The annual product cost (APC) is calculated by multiplying the annual demand by the cost per unit:

APC = Demand * Cost per unit

APC = 19455 * 12

APC = $233,460

The annual total cost of managing inventory (ATC) is the sum of the annual ordering cost, annual holding cost, and annual product cost:

ATC = AOC + AHC + APC

ATC = 892.20 + 3540 + 233460

ATC ≈ $237,892.20

The total number of orders in the year (N) can be calculated by dividing the annual demand by the EOQ:

N = Demand / EOQ

N = 19455 / 590

N ≈ 33

The estimated time between each order (T) can be calculated by dividing the number of working days in a year by the total number of orders:

T = Number of working days / N

T = 250 / 33

T ≈ 7.58 days

The daily demand is calculated by dividing the annual demand by the number of working days in a year:

Daily Demand = Demand / Number of working days

Daily Demand = 19455 / 250

Daily Demand ≈ 77.82 units/day

The reorder point (ROP) is the number of units at which a new order should be placed. It can be calculated by multiplying the daily demand by the lead time (time taken for the supplier to deliver the order):

ROP = Daily Demand * Lead Time

ROP = 77.82 * 4

ROP ≈ 311.28 units

Therefore, the reorder point would be approximately 311 units.

To know more about Model Economic Quantity,

https://brainly.com/question/29489377

#SPJ11

Answer:

4th option

Step-by-step explanation:

let f(x) = y , then rearrange making x the subject

y = 4x ( divide both sides by 4 )

\(\frac{1}{4}\) y = x

change y back into terms of x with x = h(x) , then

h(x) = \(\frac{1}{4}\) x

Answer:

3x^2 + 28x + 61

Step-by-step explanation:

I used MathPapa Algebra Calculator

Answer:

It is profit.

Step-by-step explanation:

Cp (Cost price) - Rs.12

Sp (Sold price) - Rs.576

Profit- Rs.564

Rs. 576

Rs. - 12

564

Answer:

Step-by-step explanation:

Given:

4 dozens erasers for Rs. 12 per piece

We know,

1 dozen =12 pieces

So,4 dozens= 4*12= 48 pieces

So, Total cost price =48*12=576

Here, by question sold price of erasers =576

So, There is no profit or loss for the buyer.

The average value of function f(x) over [a,b] = 1/(b-a) × definite integral of f(x) over [a,b]

To find the average value of a function f(x) over an interval [a,b], you need to follow these steps:

Calculate the definite integral of the function f(x) over the interval [a,b]. The definite integral will give you the total area under the curve of the function over the interval.

Find the length of the interval [a,b] by subtracting the lower bound a from the upper bound b. The length of the interval will be (b-a).

Divide the value of the definite integral by the length of the interval to get the average value of the function over the interval [a,b]. That is:

Average value of f(x) over [a,b] = 1/(b-a) × definite integral of f(x) over [a,b]

So, the average value of a function over an interval is simply the total area under the curve of the function over that interval divided by the length of the interval.

Learn more about average value here

brainly.com/question/22847740

#SPJ4

Answer:

45*x-10

Step-by-step explanation:

10 less than a number would give you

x - 10

and the product of a number means your multiplying and your multiplying 45 so you would get

45*x

add them together and you get

45*x-10

Answer: 1,004.8 cubic meters (choice D)

Work Shown:

V = (1/3)*pi*r^2*h

V = (1/3)*3.14*8^2*15

V = 1,004.8

The data distribution is skewed to the right. This is because the bars are clustered towards the left side of the histogram and taper off towards the right side.

The histogram of distances students live from school provided in the question shows that the majority of students in Tuan's homeroom live within a short distance of the school, with only a few students living farther away. The distribution is skewed to the right because the bars are clustered towards the left side of the histogram and taper off towards the right side. This indicates that there are fewer students who live farther away from school. A skewed distribution means that the data is not evenly distributed and tends to cluster towards one end. In this case, the distribution is skewed to the right because there are fewer students living farther away from school.

Learn more about histogram here: brainly.com/question/30354484

#SPJ4

Complete question is in the image attached below

Answer:

B. skewed.

Step-by-step explanation:

and then the next part is

1

hope this helps :)

Answer:

\((3,29)\)

Step-by-step explanation:

There is a formula that can be used to find the x-value of the vertex of the parabola. This formula is \(x=\frac{-b}{2a}\)

We have the function \(g(x)=-3x^2+18x+2\)

From this function, we can find that

\(a=-3\\b=18\\c=2\)

We can plug in our know values into the formula to get

\(x=\frac{-18}{2(-3)\\} \\x=\frac{-18}{-6} \\\\x=3\)

Then we can plug in our x-value to find the y-value of the vertex

\(g(3)=-3(3)^2+18(3)+2\\\\g(3)=-3(9)+54+2\\\\g(3)=-27+54+2\\\\g(3)=29\)

This means that the vertex would be \((3,29)\)

Answer:

C. (3,29)

Step-by-step explanation:

Edge 2020

Answer:

Step-by-step explanation:

The sum of the measures of the angles of a triangle is 180°.

m<D + m<E + m<F = 180°

4x + 2x + m<F = 180

What is the measure of <F? It's not clear in the post.

The system of equations - 2x + 5y = - 2 and 4x - 10y = 4 has infinitely many solutions.

Graphical solutions of a system of equations are way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

Given, A system of equations - 2x + 5y = - 2...(i) and 4x - 10y = 4...(ii).

Now, multiplying eqn(i) by 2 it becomes - 4x + 10y = - 4...(iii).

Now, by Adding (ii) and (iii) we get,

0x + 0y = 0.

So, 0 = 0, and hence these are coinciding lines with infinitely many solutions.

learn more about the system of equations here :

https://brainly.com/question/24065247

#SPJ1

Answer:

23

Step-by-step explanation:

Remember Order of Operations (PEMDAS):

12 - (9 - 2) + 3 · 6

12 - 7 + 3 · 6

12 - 7 + 18

5 + 18

23

The evaluated value of the expression 12 - (9 - 2) + 3 * 6 is 23.

Given expression 12 - (9 - 2) + 3 * 6,

Use the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

First, simplify the parentheses:

9 - 2 = 7

Now, substitute the simplified value back into the original expression:

12 - 7 + 3 * 6

Next, perform the multiplication:

3 * 6 = 18

Now, continue evaluating the expression:

12 - 7 + 18

Finally, perform the addition and subtraction from left to right:

12 - 7 + 18 = 5 + 18 = 23

Therefore, the expression 12 - (9 - 2) + 3 * 6 is 23.

Learn more about PEDMAS here:

https://brainly.com/question/24086845

#SPJ4

A mathematical expression is neither true nor false; it is evaluated rather than being assigned a truth value.

A mathematical expression, by itself, is not considered true or false because it does not make a specific claim or statement. An expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division. It represents a computation or evaluation, but it does not assert any truth value.

For example, the expression "2 + 3" is simply a calculation that evaluates to the value 5. It does not make a claim or statement that can be determined as true or false. Similarly, expressions like "\(x^2 + 4\)" or "sin(θ) + cos(θ)" represent mathematical computations but do not have a truth value.

To determine the truth value of a mathematical statement, you need an equation or inequality that makes a specific claim or relationship between mathematical expressions. For instance, the equation "2 + 3 = 5" is a mathematical statement that can be determined as true, while the inequality "x > 5" depends on the value of x and can be evaluated as true or false.

To know more about expression, refer here:

https://brainly.com/question/15994491

#SPJ4

based on the given information, we can definitively conclude that PV- is closer to 0 than to 1. The option (b) "PV- is closer to 0 than to 1" is the correct answer.

The present value (PV) represents the current value of a future cash flow or investment. If PV is approximately 1, it means that the value of the future cash flow or investment is close to its full value in the present.

When we subtract a value from PV to get PV-, the resulting value will be smaller than PV. Since PV is approximately 1, it implies that PV- is closer to 0 than to 1. This conclusion holds because subtracting a value from 1 will always yield a smaller value.

For example, if PV is exactly 1 and we subtract 0.5 from it, the resulting PV- will be 0.5, which is closer to 0 than to 1.

Learn more about present value here:

https://brainly.com/question/28304447

#SPJ11

Alicia's estimate of the surface area of the rectangular prism is not reasonable based on her miscalculation of the volume.

To determine whether Alicia's estimate of the surface area of the rectangular prism is reasonable, we first need to check if her calculation of the volume of the rectangular prism is correct.

The formula for calculating the volume of a rectangular prism is:

Volume = length x width x height

Substituting the given values in the formula, we get:

Volume = 11 meters x 5.6 meters x 7.2 meters

Volume = 449.28 cubic meters

As we can see, Alicia's estimate of 334 cubic meters is significantly lower than the actual volume of the rectangular prism, which is 449.28 cubic meters. Therefore, her estimate of the surface area is likely to be incorrect as well.

It is also important to note that the problem statement asks about the estimate of the surface area, not the volume. However, since the formula for calculating the surface area of a rectangular prism also involves the dimensions of length, width, and height, it is highly likely that Alicia's estimate of the surface area would also be incorrect given her miscalculation of the volume.

In conclusion, Alicia's estimate of the surface area of the rectangular prism is not reasonable based on her miscalculation of the volume.

Learn more about  volume from

https://brainly.com/question/27710307

#SPJ11

Answer:

The correct choice is D.

Answer:

Step-by-step explanation:

1/5 + 1/5 = 2/5

1/7 + 1/7 = 2/7

1/3 + 1/3 = 2/3

There are an infinite number of these fractions. They must be 1 and 1 in the numerator, and the denominator must be relatively prime  to 2. The examples I have picked are prime in the denominator, but the rule is not without many exceptions. For example

1/9 + 1/9 = 2/9

I don't think you can pick an even denominator because it will reduce when put with two.  Oh wait 2/18 + 2/18 = 4/18 = 2/9 But these could be reduced before adding. Still, it might count. It depends on who is marking the question.

What about an odd and even denominator?

1/9 + 1/18 = 3/18 = 1/6  There must be something that works, but I can't come up with an example.

Answer:

Q1: 3/72

Q2: 6 inches

Step-by-step explanation:

What is the unit rate for inches per yard on this blueprint?

First convert 1 1/5 yards to inches, so that becomes 216/5 inches.

To keep things consistent, let's convert the 1 4/5 inches to an improper fraction: 9/5 inches.

The question asks for inches per yard, so we substitute in the values:

\(\frac{\frac{9}{5} }{\frac{216}{5} }\)

and simplify: 3/72

If fence B is 4 yards long, how long is fence B on the blueprint?

Convert 4 yards to inches (to comply to the ratio above): 144 inches

The ratio is inches to yards, so substitute in the value:

\(\frac{3}{72} = \frac{x}{144}\)

and solve: 6 inches

Answer:

Option D

AC , CB , AB

Step-by-step explanation:

The shortest side is opposite to the small angle

58 < 59 < 63

AC < CB <AB

The volume of the cube expressed as a fraction will be 27x³y³ / 64.

Given that:

Volume, V = (0.75xy)³

It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.

The volume of the cube expressed as a fraction is calculated as,

V = (0.75xy)³

V = (3xy/4)³

V = 27x³y³ / 64

More about the volume link is given below.

https://brainly.com/question/1578538

#SPJ1

Answer:

10

20

Step-by-step explanation:

correct c=3 x 10

incorrect i=-1

-------

incorrect= 10

number of questions= 10+10= 20

Answer:

13.4

Step-by-step explanation:

1/3 * 3x + 5.2y

1/3 * 3(3)  + 5.2(2)

1/27  + 10.4

Answer:

B. 13.4

Step-by-step explanation:

We have the fraction, .It is required to find the value of the fraction when

x = 3 and y = 2.So, on substituting these values,

we get,i.e. i.e. i.e.

 So, the value of the fraction is 13.4

Hence, option B is correct.

Answer:

B

Step-by-step explanation:

The real zeros of the polynomial function P(x) = x⁵ − 50x³ + 49x are -1, 0, and 1.

To find the zeros of this function, we can factor it by first factoring out an x to get P(x) = x(x⁴ − 50x² + 49). Then, we can factor the quadratic expression inside the parentheses using the difference of squares formula, which gives us P(x) = x(x² − 1)(x² − 49). Simplifying further, we have P(x) = x(x − 1)(x + 1)(x - 7)(x + 7).

Therefore, the zeros of P(x) are the values of x that make each factor equal to zero. This gives us x = -7, -1, 0, 1, and 7. Since all of these values are real, we conclude that the number of real zeros of P(x) is 5.

learn more about polynomial function here:

https://brainly.com/question/30474881

#SPJ4

The  equation of best fit is ŷ = 2.69152X + 3.45818.

From the data we cab write,

Sum of X = 45

Sum of Y = 155.7

Mean X = 4.5

Mean Y = 15.57

Sum of squares (SSX) = 82.5

Sum of products (SP) = 222.05

So, Regression Equation = ŷ = bX + a

Now, b = SP/SSX = 222.05/82.5 = 2.69152

and, a = MY - bMX = 15.57 - (2.69*4.5) = 3.45818

Thus, the equation of best fit is ŷ = 2.69152X + 3.45818.

Learn more about Regression line here:

https://brainly.com/question/7656407

#SPJ1