Molly has a rectangular piece of cardboard. If the length of the cardboard can be modeled by 3x - 1 and the width of the cardboard can be modeled by 2x + 5, which polynomial models the area of her piece of cardboard? *

Answer:

0.5

Step-by-step explanation:

7 1/2 • 2 = 15

7 times 2 is equal to 14

1/2 times 2 is equal to 1

14 plus 1 is equal to 15

Answer: all of them

Step-by-step explanation:

Rational numbers are represented as dividing two integers, which is a fraction or decimal. Therefore, the numbers stated (134, 49, 9, etc.) are rational numbers since they are all whole numbers.

The volume of the block of wood is 78 cubic inches.

What is cube?

A cube is a three-dimensional geometric shape that has six equal square faces, 12 equal edges, and eight vertices (corners). All the angles between the faces and edges of a cube are right angles (90 degrees), and all the edges are of equal length. A cube is a special type of rectangular prism where all the sides are equal in length, making it a regular polyhedron.

To find the volume of the block of wood, you need to multiply its length, width, and height together.

Volume = length x width x height

Volume = 6.5 inches x 1.5 inches x 8 inches

Volume = 78 cubic inches

Therefore, the volume of the block of wood is 78 cubic inches.

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Therefore, a central angle of the regular polygon with 27 diagonals measures 40 degrees.

To find the measure of a central angle of a regular polygon with 27 diagonals, we use the formula: Number of Diagonals = (Number of Sides * (Number of Sides - 3)) / 2. Setting the number of diagonals to 27, we solve for the number of sides.

By trying different values, we find that the regular polygon has 9 sides. Using the formula for the measure of a central angle in a regular polygon, Central Angle = 360 degrees / Number of Sides, we calculate that the measure of the central angle is 40 degrees.

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The date on which the loan amount is to be fully paid is called the maturity date.

The maturity date is an essential component of a loan agreement, particularly for loans with a fixed repayment schedule. It represents the deadline by which the borrower is required to repay the entire loan amount, including any interest and fees.

When a loan is taken out, the lender and borrower agree upon the terms and conditions, including the repayment schedule. The maturity date is determined based on these terms, specifying the duration over which the borrower is expected to make regular payments.

For example, in a mortgage loan, the maturity date could be set for 30 years from the loan origination date. This means that the borrower has 30 years to repay the loan in full, either through monthly installments or other agreed-upon payment arrangements.

The maturity date is important for both the lender and the borrower as it establishes a clear timeline for the loan repayment. It helps ensure that the borrower understands the duration of the financial obligation and allows the lender to plan their cash flows and monitor the progress of the loan repayment.

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In order to have independents events, we need to verify the following equation:

If event A is "the hot air balloon contains 1 passenger", the probability of this event is the sum of the number of balloons with 1 passenger divided by the total number of balloons:

If event B is "the hot air balloon is orange

The number of students who for between 4-8 hours and obtained an average above 80 expressed as a percentage is 11.7%.

Rather than expressing values in fractions. A certain portion of a whole lot or item can be multiplied by 100 to get its equivalent value expressed as a percentage .

From the table , the number of students who studied for 4-8 hours and also had a grade above 80 is 11.

Total number of students in the sample = 94

Expressing as a percentage;

(11/94) × 100%

= 0.117 × 100%

= 11.7%

Hence, the percentage value is 11.7%

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Answer:

power of ten

Step-by-step explanation:

A power of ten is an exponential expression with 10 as the base. The first few power of tens (nonnegative) are 1, 10, 100, 1,000, and so on.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

A) Function is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).

b)  The local minimum value of f is; 5608/2197 at x = -42/13, and the local maximum value of f is 139/8 at x = 7/2.

(a) To determine the intervals on which f is increasing or decreasing, we need to determine the critical points and then check the sign of the derivative on the intervals between them.

f(x)=8x³-42x-48x + 4

f'(x) = 24x² - 90

Setting f'(x) = 0, we get

24x² - 90 = 0

24x² = 90

x =±  √3.75

So, the critical points are;

x = -1 and x = 7/2.

We can test the sign of f'(x) on the intervals as; (-∞, -1), (-1, 7/2), and (7/2, ∞).

f'(-2) = 72 > 0, so f is increasing on (-∞, -1).

f'(-1/2) = -25 < 0, so f is decreasing on (-1, 7/2).

f'(4) = 72 > 0, so f is increasing on (7/2, ∞).

Therefore, f is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).

(b) To determine the local maximum and minimum values of f, we need to look at the critical points and the endpoints of the interval (-1, 7/2).

f(-1) = -49

f(7/2) = 139/8

f(-42/13) = 5608/2197

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The inputs and outputs match up with each other implying that they are inverses of each other.

To determine if the functions are inverses of each other, you need to check two conditions:

According to the previous information we can conclude that the inputs and outputs match up with each other implying that they are inverses of each other.

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a) The optimal size of the production run is approximately 39, units (rounded to the nearest whole number).

b) The average holding cost per year is approximately $1,755.00 (rounded to two decimal places).

c) The average setup cost per year is approximately $24,300.00 (rounded to two decimal places).

d) The total cost per year, including the cost of the lights, is approximately $43,071.00 (rounded to two decimal places).

a) To find the optimal size of the production run, we can use the economic order quantity (EOQ) formula. The EOQ formula is given by:

EOQ = √[(2 * D * S) / H]

Where:

D = Annual demand = 11,700 units

S = Setup cost per production run = $81

H = Holding cost per unit per year = $0.15

Plugging in the values, we have:

EOQ = √[(2 * 11,700 * 81) / 0.15]

= √(189,540,000 / 0.15)

= √1,263,600,000

≈ 39,878.69

Since the optimal size should be rounded to the nearest whole number, the optimal size of the production run is approximately 39, units.

b) The average holding cost per year can be calculated by multiplying the average inventory level by the holding cost per unit per year. The average inventory level can be calculated as half of the production run size (EOQ/2). Therefore:

Average holding cost per year = (EOQ/2) * H

= (39,878.69/2) * 0.15

≈ 2,981.43 * 0.15

≈ $447.22

So, the average holding cost per year is approximately $447.22 (rounded to two decimal places).

c) The average setup cost per year can be calculated by dividing the total setup cost per year by the number of production runs per year. The number of production runs per year is given by:

Number of production runs per year = D / EOQ

= 11,700 / 39,878.69

≈ 0.2935

Total setup cost per year = S * Number of production runs per year

= 81 * 0.2935

≈ $23.70

Therefore, the average setup cost per year is approximately $23.70 (rounded to two decimal places).

d) The total cost per year, including the cost of the lights, can be calculated by summing the annual production cost, annual holding cost, and annual setup cost. The annual production cost is given by:

Annual production cost = D * Cost per light

= 11,700 * 1

= $11,700

Total cost per year = Annual production cost + Average holding cost per year + Average setup cost per year

= $11,700 + $447.22 + $23.70

≈ $12,170.92

Therefore, the total cost per year, including the cost of the lights, is approximately $12,170.92 (rounded to two decimal places).

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Answer:

\(6x = 4x + 6 \\ 6x - 4x = 6 \\ 2x = 6 \\ x = \frac{6}{2} \\ \boxed{x = 3}\)

Answer:

x = 3

Step-by-step explanation:

In pic

(Credits: Symbolab)

(Hope this helps can I pls have brainlist (crown)☺️)

The measure of angle fge is 53.13°.

The equation used to find the measure of angle fge is the Law of Cosines. The Law of Cosines states that for any triangle, the square of the length of any side is equal to the sum of the squares of the other two sides, minus twice the product of those sides and the cosine of the angle opposite the side.

Using the Law of Cosines, we can solve for the measure of angle fge as follows:

\(fge = cos-1((a^2 + b^2 - c^2) / 2ab)\)

For example, if the length of side a is 3, the length of side b is 4, and the length of side c is 5, then the measure of angle fge can be calculated as follows:

fge =\(cos-1((3^2 + 4^2 - 5^2) / 2(3)(4))\)

fge = \(cos-1(1/6)\)

fge = 53.13°

Therefore, the measure of angle fge is 53.13°.

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Answer:

Number 3 does not have a solution

Step-by-step explanation:

Answer: I think it's 6

Step-by-step explanation: I'm not to good with linear equations, but if you substitute 6 in the place of x, you'll get 18.

Answer:

x=6

Step-by-step explanation:

7x-12-2x=18

+2. +2

7x-2x=30

5x=30

÷5. ÷5

x=6

Answer:

because, it will completely change the slope

Step-by-step explanation:

It does not matter which point you choose when writing the

equation of the line in point-slope form because the slope of the line remains same.

A slope can be thought of as rate of change of y axis with respect to x axis.

We have been asked in this statement that why it doesn't matter that which point we choose when writing the equation in point slope form.

Let us understand this with an example,Suppose we have two pair of points. (x₁,y₁) = (2,3) and (x₂,y₂) = (5,9).

We know slope(m) is = (y₂-y₁)/(x₂-x₁).

Slope(m₁) = (9-3)/(5-2)

               = 6/3

               = 2.

Now if interchange the points  (x₁,y₁) =  (5,9) and  (x₂,y₂) =  (2,3).

Slope(m₂) = (3-9)/(2-5)

                = -6/-3

                = 2.

So, even when interchanging the points the slope m₁ = m₂ this is the reason why it doesn't matter which point we choose.

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Answer:

\(f^{-1}(x)=\sqrt{x}+2\)

Step-by-step explanation:

Given function is,

f(x) = (x - 2)²

Step - 1

Rewrite the function in the form of a equation.

y = (x - 2)²

Step - 2

Interchange the variables 'x' and 'y',

x = (y - 2)²

Step - 3

Solve the equation for y,

x = (y - 2)²

y - 2 = √x

y = 2 + √x

Step - 4

Rewrite the equation in the form of a function,

\(f^{-1}(x)=\sqrt{x}+2\)

The correct answer will be option C Randomization of students in morning and afternoon classes.

Psychology is the scientific study of the mind and behavior, according to the American Psychological Association.

The only way to minimize this effect would be through randomization of students in morning and afternoon classes.

Doing so apply the factor of skill from an individual student to either time of day class greatly lessens the overall effect that it has on the results.

This therefore, minimizes the effect it has on the experiment itself, since the same students that have been studying in a certain time of day would be randomized and not have the same environment that they are used to.

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Answer:

Step-by-step explanation:

Direct control by requiring every class to take the same test

The given statement the purpose of process control to detect assignable causes of variation is true because helps improve efficiency, productivity, and customer satisfaction by managing and correcting such causes.

The purpose of a process control is to detect when assignable causes of variation are present. This is done through the use of control charts, which are used to monitor the process and identify any deviations from the expected process behavior.

When an assignable cause of variation is detected, it can be addressed and corrected, helping to ensure that the process remains stable and produces consistent, high-quality products or services.

By detecting and addressing assignable causes of variation, process control helps to prevent problems before they occur, leading to improved efficiency, productivity, and customer satisfaction.

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To solve this problem, we need to find the intersection of the circle with a 61-mile radius centered at the transmitter and the straight line connecting the two cities.

First, let's draw a diagram of the situation:

r

Copy code

T (transmitter)

|\

| \

|  \

|   \

|    \

|     \

|      \

|       \

C1      C2

Here, T represents the transmitter, C1 represents the city 68 miles north of the transmitter, and C2 represents the city 81 miles east of the transmitter. We want to find out how much of the straight line from C1 to C2 is within the range of the transmitter.

To solve this problem, we need to use the Pythagorean theorem to find the distance between the transmitter and the straight line connecting C1 and C2. Then we can compare this distance to the radius of the transmitter's range.

Let's call the distance between the transmitter and the straight line "d". We can find d using the formula for the distance between a point and a line:

scss

Copy code

d = |(y2-y1)x0 - (x2-x1)y0 + x2y1 - y2x1| / sqrt((y2-y1)^2 + (x2-x1)^2)

where (x1,y1) and (x2,y2) are the coordinates of C1 and C2, and (x0,y0) is the coordinate of the transmitter.

Plugging in the values, we get:

scss

Copy code

d = |(81-0)*(-68) - (0-61)*(-68) + 0*0 - 61*81| / sqrt((81-0)^2 + (0-61)^2)

 = 3324 / sqrt(6562)

 ≈ 41.09 miles

Therefore, the portion of the straight line from C1 to C2 that is within the range of the transmitter is the portion of the line that is within 61 miles of the transmitter, which is a circle centered at the transmitter with a radius of 61 miles. To find the length of this portion, we need to find the intersection points of the circle and the line and then calculate the distance between them.

To find the intersection points, we can solve the system of equations:

scss

Copy code

(x-0)^2 + (y-0)^2 = 61^2

y = (-61/68)x + 68

Substituting the second equation into the first equation, we get:

scss

Copy code

(x-0)^2 + (-61/68)x^2 + 68(-61/68)x + 68^2 = 61^2

Simplifying, we get:

scss

Copy code

(1 + (-61/68)^2)x^2 + (68*(-61/68))(x-0) + 68^2 - 61^2 = 0

Solving this quadratic equation, we get:

makefile

Copy code

x = 12.58 or -79.23

Substituting these values into the equation for the line, we get:

scss

Copy code

y = (-61/68)(12.58) + 68 ≈ 5.36

y = (-61/68)(-79.23) + 68 ≈ 148.17

Therefore, the intersection points are approximately (12.58, 5.36) and (-79.23, 148.17). The distance between these points is:

scss

Copy code

sqrt((12.58-(-79.23))^2 + (5.36-148.17)^2)

≈

To calculate the probability of drawing a red marble followed by a blue marble with replacement from the given bag containing 6 green marbles, 2 blue marbles, and 4 red marbles.

we need to consider the individual probabilities of each draw and multiply them together.

The first paragraph provides a concise summary of the answer, while the second paragraph explains the solution in more detail.

The probability of drawing a red marble followed by a blue marble with replacement can be calculated by multiplying the probability of drawing a red marble and the probability of drawing a blue marble.

The probability of drawing a red marble on the first draw is 4/(6+2+4) = 4/12 = 1/3, as there are 4 red marbles out of a total of 12 marbles. Since the draws are made with replacement, the probabilities remain the same for each draw.

Similarly, the probability of drawing a blue marble on the second draw is 2/12 = 1/6, as there are 2 blue marbles out of 12 marbles.

To calculate the probability of both events occurring consecutively, we multiply the probabilities together: (1/3) * (1/6) = 1/18.

Therefore, the probability of drawing a red marble followed by a blue marble with replacement from the given bag is 1/18.

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Answer: e + c ≤ 21, 225e + 275c ≤ 6000

Step-by-step explanation:

Maximum of 21 hours each semester between elective classes and core classes, the required inequality is:

e + c ≤ 21

Each elective class cost $225 per semester hour and each core class costs $275, the sum is 225e + 275c.

He cannot spend more than $6,000, the required inequality is:

225e + 275c ≤ 6000

Answer:

12.73

Step-by-step explanation:

The diagonal of the square forms the shape of a right angle with two adjacent sides of the square.

The diagonal is the hypotenuse.

Pythagoras theorem states that the square of the hypotenuse is equal to the sum of the square of the other two sides of the triangle:

\(d^2 = a^2 + b^2\)

where d = hypotenuse = diagonal.

Since the other two sides are equal, then:

\(d^2 = a^2 + a^2\\\\d^2 = 2a^2\)

The length of the side of the square is 9:

\(d^2 = 2 * 9^2 \\\\d^2 = 2 * 81\\\\d^2 = 162\\\\d = \sqrt{162}\\ \\d = 12.73\)

The length of the diagonal is 12.73

Answer:

12.73

Step-by-step explanation:

Therefore, the measure of angle x is approximately 59.04 degrees.

In geometry, a triangle is a three-sided polygon that is formed by connecting three non-collinear points with straight line segments. Each of the line segments is called a side of the triangle, and the point where two sides meet is called a vertex of the triangle. Triangles are one of the most basic and fundamental shapes in geometry, and they have many important properties and applications. The sum of the internal angles of a triangle is always 180 degrees, and there are several different types of triangles, including equilateral triangles (where all three sides are of equal length and all three internal angles are equal to 60 degrees), isosceles triangles (where two sides are of equal length and two internal angles are equal), and scalene triangles (where no sides or angles are equal). Triangles are used in a wide range of fields, from architecture and engineering to physics and computer graphics.

Here,

To find the measure of angle x, we can use the trigonometric function sine, which relates the opposite side (perpendicular) to the hypotenuse of a right triangle. Specifically, we can use the formula:

sin(x) = opposite/hypotenuse

Substituting the given values, we get:

sin(x) = 12/13

To find the value of x, we can take the inverse sine (or arcsine) of both sides of the equation, using a calculator:

x = sin⁻¹(12/13) ≈ 59.04 degrees

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Complete question:

Please help with this!!! Find the measure of angle x. Round your answer to the nearest hundredth.

To solve the equation 1/3x - 4 = 3/4x + 1, we need to simplify and rearrange the equation to isolate the variable x.

Let's start by eliminating the fractions by multiplying every term in the equation by the least common multiple (LCM) of the denominators, which in this case is 12. Multiply both sides of the equation by 12 to get rid of the fractions: 12 * (1/3x) - 12 * 4 = 12 * (3/4x) + 12 * 1.

Simplifying this equation, we have: 4x - 48 = 9x + 12.

Next, we want to isolate the variable x on one side of the equation. Let's move all terms containing x to one side and the constant terms to the other side: 4x - 9x = 12 + 48.

Combining like terms, we get: -5x = 60.

To solve for x, divide both sides of the equation by -5: x = -60 / 5 = -12.

Therefore, the solution to the equation is x = -12.

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Answer:

3 pounds

                                                    1p+1p+1p=3p

Step-by-step explanation: 4p +2j +2j +2j =10pounds which is more than 8p

Answer:

Step-by-step explanation:

5 + 11 = 16 for AC