490 as a product of its prime factors

The area A of the region between the two curves x = y^3–4y^2+3y and x+y=y^2 is 11.8334.

The graph of the question is given below:

We have to evaluate the integral needed to determine the area A of the region between the two curves x = y^3–4y^2+3y and x+y=y^2 i.e. x = y^2-y.

Now the area A of the given region is:

A = \(\int^1_{y=0}\left[g(y)-f(y)\right]dy+\int^4_{y=1}\left[g(y)-f(y)\right]dy\)

A = \(\int^1_{y=0}\left[(y^3-4y^2+3y)-(y^2-y)\right]dy+\int^4_{y=1}\left[(y^2-y)-(y^3-4y^2+3y)\right]dy\)

A = \(\int^1_{y=0}\left[y^3-4y^2+3y-y^2+y)\right]dy+\int^4_{y=1}\left[y^2-y-y^3+4y^2-3y)\right]dy\)

A = \(\int^1_{y=0}\left[y^3-5y^2+4y\right]dy+\int^4_{y=1}\left[5y^2-y^3-4y)\right]dy\)

Further simplification

A = \(\left[\frac{y^4}{4}-\frac{5y^3}{3}-\frac{4y^2}{2}\right]^1_{y=0}+\left[\frac{5y^3}{3}-\frac{y^4}{4}-\frac{4y^2}{2}\right]^4_{y=1}\)

A = \(\left[(\frac{1}{4}-\frac{5}{3}-2)\right-(0-0+0)]+\left[(\frac{320}{3}-64-32)\right-(\frac{5}{3}-\frac{1}{4}-2)]\)

A = (3-20+24)/12 + 320/3 - 96 - (20-3-24)/12

A = 7/12 + 32/3 + 7/12

A = (7+128+7)/12

A = 142/12

A = 11.8334

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The temperature on the second day is 11°.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Temperature is a unit used to express hotness or coldness on any of a number of scales, including Fahrenheit and Celsius. The direction that heat energy will spontaneously flow depending on temperature.

Let the temperature on the second day be x.

Based on the information, temperature cooled by 4° on the first day of the year together on the 1st 2 days of the year the temperature heated up.

-4 + x = 7

Collect the like terms

x = 7 + 4..

x = 11

The temperature is 11°

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The temperature cooled by 4° on the first day of the year together on the 1st 2 days of the year the temperature heated up 7°. What is the Temperature on tue second day?

We can substitute the number in the inequality to find if the inequality holds true. If the inequality holds true, it is a valid solution. This is very similar to substituting a number in an equation, in order to check if it holds.

The same holds true for others.

The length in centimeters of AB is 125/360 x 42cm.

What is the circumference of the circle?

The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter.

Here, we have

Given: The circumference of the circle is 42 centimeters

AB is an arc, the formula for calculating the length of an arc is given as

L = Ф/360 X 2πr

where Ф is the angle subtended by the arc, and 2πr is the circumference of the circle.

Substituting the given values into the formula, we have

L = 125/360 x 42

L = 14.5

Hence, the length in centimeters of AB is 125/360 x 42cm.

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Answer 40% passed

and 50% failed

Step-by-step explanation:

If the recycling center gives Marry $0.40 per pound money she will earn for both days of recycling is $11.20

What information is given in the question?

Marry collected 16.2 pounds of cans for the recycling center on Monday.

On Tuesday, she collected 11.8 pounds.

The recycling center gives her $0.40 per pound.

According to the given question:

To find how much money she will earn for both days of recycling, calculate money earned on Monday and Tuesday. Then add the amount to get the amount earned on both days.

Money earned by Marry on Monday = 16.2 x 0.40 = $6.48

Similarly, money earned by Marry on Tuesday = 11.8 x 0.40 = $4.72

Therefore, Total money earned by Marry for both days

= 6.48 + 4.72

= $11.20

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Answer:

2sqr3, the first option

Step-by-step explanation:

Answer:

f(-2)=(-11)

Step-by-step explanation:

f(-2)=5(-5)+14

=(-25)+14

=(-11)

Answer:

55?

Step-by-step explanation:

........................

Answer:

AB=55

Step-by-step explanation:

9x+1=7x+13

2x=12

x=6

9x+1=9(6)+1

55

Answer:

Step-by-step explanation:

the answer is 18 I think?

Answer:

18

Step-by-step explanation:

6 (legs) x 3 (ants) = 18 legs

It can also be represented as 6+6+6 (18)

hope this helps :)

Answer:

p

Step-by-step explanation:

Answer:

jsjsnnjs jsksi j sjsjsdjsis jsji

9514 1404 393

Answer:

  (a) A : B = $9000 : $6000

  (b) $1260

  (c) A : S : J = $1050 : $2250 : $1200 = 7 : 15 : 8

Step-by-step explanation:

(a) The investment ratio is ...

  Angela : Barbara = 24000 : 16000 = 3 : 2

The profit of 15,000 goes 3/(3+2) = 3/5 to Angela, and 2/5 to Barbara:

  Angela's share: (3/5)($15,000) = $9,000

  Barbara's share: (2/5)($15,000) = $6,000

__

(b) We can multiply the ratio by $140 to see the larger amount:

  4 : 9 = ($140)(4) : ($140)(9) = $560 : $1260

The larger share is $1260.

__

(c) Sian gets (1/2)($4500) = $2250. Anesha gets $1050. So  Joanne gets ...

  $2250 -1050 = $1200

Then the shares are ...

  i. Sian: $2250

  ii. Joanne: $1200

  iii. Ratios: A : S : J = 105 : 225 : 120 = 7 : 15 : 8

The electrical resistance varies directly as the square of the voltage and inversely as the electric power, and the equation that relates them isR ∝ V²/PR = kV²/PR = V²/P. This relationship can be used to calculate the electrical resistance of the wire or component for any given voltage and power.

The electrical resistance is the measure of the difficulty in passing electric current through a wire or an electrical component. It depends on various factors, such as the material, dimensions, and temperature of the wire.The given statement says that the electrical resistance varies directly as the square of the voltage and inversely as the electric power.

In mathematical terms, this relationship can be expressed as R ∝ V²/PR = kV²/P where R is the electrical resistance, V is the voltage, P is the electric power, and k is the constant of proportionality. The constant k depends on the material, dimensions, and temperature of the wire or component.

The given statement implies that the constant k is the same for the given wire or component, and it is not affected by the voltage or the power.To find the value of k, we can use the given values of V, P, and R.

According to the statement, if the voltage is 20 volts and the electric power is 5 watts, then the electrical resistance is 80 ohms. Therefore,R = kV²/PR = k(20²)/5R = 400k/5R = 80 ohms

Substituting the value of R in the equation, we get80 = 400k/5k = (80 x 5)/400k = 1. Therefore, the equation that relates the electrical resistance, voltage, and power isR = V²/PThe constant of proportionality k is 1 for the given wire or component.

Therefore, the electrical resistance varies directly as the square of the voltage and inversely as the electric power, and the equation that relates them isR ∝ V²/PR = kV²/PR = V²/P. This relationship can be used to calculate the electrical resistance of the wire or component for any given voltage and power.

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Answer:

.84

Step-by-step explanation:

geometcdf(.6,2) = .84

The equation 6( 3x + 4 ) + 2( 2x + 2 ) + 2 = 22x + 31 has no solution for the variable x.

Given the equation in the question:

6( 3x + 4 ) + 2( 2x + 2 ) + 2 = 22x + 31

To solve the equation 6(3x + 4) + 2(2x + 2) + 2 = 22x + 31 for the variable x, we will simplify and solve for x.

Apply distributive property:

6 × 3x + 6 × 4 + 2 × 2x + 2 × 2 + 2 = 22x + 31

18x + 24 + 4x + 4 + 2 = 22x + 31

Collect and combine like terms on both sides:

22x + 30 = 22x + 31

Next, we want to isolate the variable x on one side.

22x - 22x + 30 = 22x - 22x + 31

30 = 31

However, we notice that the x terms cancel out when subtracted:

30 ≠ 31

This means that there is no solution.

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Answer:

the answer is D

Step-by-step explanation:

A. √123 = 11.09

11.09-11 = 0.09

B. √115 = 10.72

11-10.72 = 0.28

C. √118 = 10.86

11-10.86 = 0.14

D. √120 = 10.95

11-10.95 = 0.05 ( the smallest difference )

Answer:

13) 6a + 2

14) 6x + 9h +3

15) 10y - 3

16) a) 12C + 7b + 24

b) 12(4) + 7(3) + 24=$93

The volume of the cuboid is 153000 \(cm^{3}\);

What is the volume of the cuboid?

In general, the volume of a cuboid is equal to the area that it takes up in space. It is dependent upon the cuboid's three dimensions, or its length, breadth, and height. Due to the fact that all of a cuboid's faces are rectangular, the term "Solid Rectangle" is also referred to as a cuboid. All of the angles and the opposite faces of a cuboid in a rectangular cuboid are at right angles. A cuboid's volume is determined by the product of its length, breadth, and height. Cubic units are used to measure cuboids' volume.

The product of a cuboid's base area and height determines its volume. We can therefore write;

Cuboid volume equals base area times height [in cubic units].

The cuboid's base is shaped like a rectangle. As a result, a cuboid's base area is determined by multiplying its length by its breadth. Hence,

A cuboid's volume is equal to its length, width, and height in cubic units, or

A cuboid's volume is equal to l b h [in cubic units].

l = length, b = width, and h = height.

In the given question, we have;

Length = 30 cm;

Breadth = 60 cm;

Height = 85 cm;

And,

we know that:

The volume of the cuboid = lbh

The volume of the cuboid  = 30×60×85 \(cm^{3}\)

The volume of the cuboid  = 1800 ×85 \(cm^{3}\);

The volume of the cuboid  = 153000 \(cm^{3}\);

Hence,

The volume of the cuboid  = 153000 \(cm^{3}\);

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If rectangle has an area of 114cm squared and a perimeter of 50 cm, the dimensions of the rectangle are approximately 5 cm by 22.8 cm.

Let's assume the length of the rectangle is "l" and the width is "w". We can start by using the formula for the area of a rectangle, which is A = lw. From the given information, we know that the area is 114cm².

So, we have:

lw = 114

Next, we can use the formula for the perimeter of a rectangle, which is P = 2l + 2w. From the given information, we know that the perimeter is 50cm.

So, we have:

2l + 2w = 50

We now have two equations with two variables, which we can solve using substitution or elimination. Let's use substitution by solving the first equation for l:

l = 114/w

We can then substitute this expression for l in the second equation:

2(114/w) + 2w = 50

Multiplying both sides by w to eliminate the fraction, we get:

228 + 2w² = 50w

Rearranging and simplifying, we get a quadratic equation:

2w² - 50w + 228 = 0

We can solve for w using the quadratic formula:

w = [50 ± √(50² - 4(2)(228))]/(2(2)) ≈ 11.4 or 5

Since the length and width must be positive, we can discard the solution w = 11.4. Therefore, the width of the rectangle is approximately 5 cm. We can then use the equation lw = 114 to solve for the length:

l(5) = 114

l ≈ 22.8

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Queremos maximizar el precio de tal forma que los ingresos no disminuyan.

Ese maximo precio es: $14,040.6

Sabemos que actualmente el precio es:

p = $6,000

El número de clientes es:

C = 120

Actualmente los ingresos son el producto de esos dos números, es decir:

ingresos = $6,000*120 = $720,000

Ahora sabemos que por cada incremento de $700 en el precio, el número de clientes decrece en 10.

Entonces podemos escribir el número de clientes como una ecuación lineal.

C(p) = a*p + b

tal que tenemos dos puntos en esa linea:

($6,000, 120)

($6,700, 110)

La pendiente es:

\(a = \frac{110 - 120}{\$6,700 - \$6,000} = \frac{-10}{\$ 700}\)

Entonces tenemos:

C(p) = (-10/$700)*p + b

Sabemos que:

C($6,000) = 120 = (-10/$700)*$6,000 + b

                     120 = -85.71 + b

                     120 + 85.71 = b =

Entonces la ecuación lineal es:

C(p) = (-10/$700)*p + 205.71

Los ingresos serán dados por:

ingresos = C(p)*p = (-10/$700)*p^2 + 205.71*p

Y queremos maximizar p de tal forma que esto sea igual a lo que obtuvimos antes:

(-10/$700)*p^2 + 205.71*p = $720,000

Entonces debemos resolver la ecuación cuadratica:

(-10/$700)*p^2 + 205.71*p - $720,000 = 0.

Las soluciones son dadas por la formula de Bhaskara.

\(p = \frac{-205.71 \pm \sqrt{(205.71)^2 - 4*(-10/\$ 700)*\$ 720,000} }{2*(-10/\$ 700)} \\\\p = \frac{-205.71 \pm 195.45}{(-20/\$ 700)}\)

La solución de maximo valor es:

p = (-205.71 - 195.45)/(-20/$700) = $14,040.6

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The answer to this question: B

Answer: Triangle C.

Step-by-Step Explanation:

To solve this problem, we need to understand what it means for a triangle to be a translation of another triangle. A translation for a triangle means that it is the same shape and size as the original triangle, but it has shifted (or moved) a specific number of units either up, down, left, or right.

In this problem, we have Triangle P, which has been shifted 5 units to the right and 7 units up to form Triangle C. To determine which triangle is a translation of Triangle P, we can look at the coordinates of the different triangles.

Triangle A: (1, 4), (3, 7), (5, 6)

Triangle B: (2, 3), (4, 6), (6, 5)

Triangle C: (6, 11), (8, 14), (10, 13)

Triangle D: (3, 5), (5, 8), (7, 7)

If we compare the coordinates of each triangle with those of Triangle P, we can see that Triangle C, with coordinates (6, 11), (8, 14) and (10, 13), is the translation of Triangle P because all of the coordinates of Triangle P have been shifted 5 units to the right, and 7 units up. Therefore, the answer is Triangle C.

Answer: D.

Step-by-step explanation: First you find the common factor, which is 5x³y. Then you write in parenthesis what's left over from each term. So  the answer should look like: 5x³y(-3x⁵-4z+9).

The equation of the function in the form y=mx+b is y = 110x-2020

The standard equation of a line is expressed as:

y = mx + b

where:

m is the rate of change or slope

b is the intecept

Using the coordinate points

Determine the slope

m = 550/5

m = 110

For the intercept

280 + 110(20) + b

280 = 2200 + b

b = 180 - 2200

b = -2020

Hence the equation of the function in the form y=mx+b is y = 110x-2020

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Answer:

im pretty sure its 2

Step-by-step explanation:

Answer:

2 3/4

Step-by-step explanation:

The sentence that contains filler is: D. This set also includes heroes like Obi-Wan Kenobi and Anakin Skywalker, both of whom come fully-equipped with their signature lightsabers and Jedi robes. Option D

In this sentence, the phrase "also includes heroes like Obi-Wan Kenobi and Anakin Skywalker" acts as a filler. The main purpose of this phrase is to provide additional information about the set and highlight the inclusion of popular characters from the Star Wars franchise. It doesn't directly contribute to the core information about the set's features or components.

The other sentences (A, B, and C) provide specific details and descriptions about the LEGO set, such as the number of pieces, minifigures, droids, and features like the opening top hatch and cockpit. They directly convey important information about the set itself without any filler or additional unnecessary information.

In marketing or promotional contexts, fillers are often used to enhance the appeal of a product or create excitement by mentioning well-known or desirable elements that may not be directly relevant to the core features. The filler in sentence D serves to attract fans of Obi-Wan Kenobi and Anakin Skywalker by emphasizing their presence in the set and the inclusion of their iconic weapons and attire.

Option D

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Answer:D

Step-by-step explanation:

Answer:

the answer is D. F(x) = 1/x(x-3)

Step-by-step explanation:

The given procedure results as not binomial and cannot be treated as binomial. It is not binomial because the probability of success does not remain the same in all trials. The correct answer is option B.

Binomial distribution compiles the number of trials, or observations when each trial has the same probability of attaining one particular value. Binomial distribution controls the probability of observing a specified number of successful outcomes in a specified number of trials.

In a binomial distribution, the probability of getting a success have to remain the same for the trials we are investigating. For example, when tossing a coin, the probability of flipping a coin is half or 0.5 for every trial we conduct, because there are only two possible outcomes.

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Answer:

Average time per day = 1.2 hours per day
Average time per day = 72 minutes per day

Step-by-step explanation:

To find Clarence's average time per day, we need to divide the total time he takes to walk the 15.5 miles by the number of days he walks, which is five.

Let's calculate his average time per day:

Average time per day = Total time / Number of days

Since Clarence takes a total of 6 hours to walk the 15.5 miles, we'll divide 6 by 5 to find his average time per day:

Average time per day = 6 hours / 5

Average time per day = 1.2 hours per day

To convert hours to minutes, we'll multiply the average time per day by 60:

Average time per day = 1.2 hours * 60 minutes

Average time per day = 72 minutes per day

Therefore, Clarence's average time per day is 72 minutes.

The radius of the gear should be approximately 2.8644 inches.It is important to note that when making calculations involving units, we need to make sure that all units are consistent and convert them when necessary. In this case, we converted the answer from feet to inches to match the given unit.

To find the radius of the gear that will pull a chain at 60 ft/min when rotating at 40 rev/min, we can use the formula:

chain speed = 2 x pi x radius x rotational speed

where pi is a mathematical constant approximately equal to 3.14.

We know that the chain speed is 60 ft/min and the rotational speed is 40 rev/min, so we can substitute those values into the formula:

60 = 2 x 3.14 x radius x 40

Simplifying the equation, we get:

radius = 60 / (2 x 3.14 x 40)

radius = 0.2387 ft

To convert feet to inches, we can multiply the answer by 12:

radius = 0.2387 x 12 = 2.8644 inches.

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