Given that g and h are both positive, which of the following is equivalent to the
expression √gh³27g¹h³?
A) gh√/g² - 27
B) ghg³-27g
C) g²h-3gh3√g
D) g²h-33/g

∫(f(x) + g(x)) dx = ∫f(x) dx + ∫g(x) dx is the sum rule in integration.

The sum rule in integration states that if f(x) and g(x) are two functions that are both integrable over a given interval, then the integral of the sum of these functions over that interval is equal to the sum of the integrals of the individual functions over that interval. Mathematically, this can be expressed as:

∫(f(x) + g(x)) dx = ∫f(x) dx + ∫g(x) dx

The sum rule of integration is: Integral of the sum of two functions is equal to the sum of integration of individual functions.

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Answer: 30+1+.002

Step-by-step explanation:

Just break it up into number groups. Like tens, ones, or hundreds

95% of toy eskimo dogs have weight between 6.04 and 9.96 pounds assuming normal distribution.

What is weight ?

Weight is a measure of the force exerted on an object due to gravity. It is typically measured in units of mass such as kilograms (kg) or pounds (lbs). The weight of an object can be determined by multiplying its mass by the acceleration due to gravity.

Assuming the weights of toy eskimo dogs are normally distributed, we can use the standard normal distribution table to find the range of weights that would include 95% of the dogs.

The standard normal distribution table gives the proportion of data within a given number of standard deviations from the mean. Since the standard deviation of the toy eskimo dog's weight is 1 pound, we can use this table to find the range of weights that are within 1.96 standard deviations from the mean.

Using this method, we can find that 95% of the toy eskimo dogs will have a weight that is between 6.04 pounds (8 - 1.96) and 9.96 pounds (8 + 1.96).

95% of toy eskimo dogs have weight between 6.04 and 9.96 pounds assuming normal distribution.

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The 2 real solutions are rational and irrational solutions.

Quadratic Formula is the simplest method to find the roots of a quadratic equation. There are particular quadratic equations that cannot be easily factorized, and here we use this quadratic formula to find the roots in the quickest possible way.

Quadratic Formula: The roots of a quadratic equation ax² + bx + c = 0 are given by x = [-b ± √(b² - 4ac)]/2a.

The value b² - 4ac is called the discriminant of a quadratic equation and is represented as 'D'. The nature of the roots of the quadratic equation can be predicted based on the discriminant value.

If D > 0, the roots are real and distinct (two real solutions).

If D = 0, the roots are real and equal (one real solution).

If D < 0, the roots do not exist, or they are imaginary (two imaginary solutions).

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Quadratic equations' solutions are  x=0, x=32 , y=3, y=-2 , [tex]y=-\frac{5}{2}, y=4$$[/tex] , z=0, z=-10 , and x=0, x=3

[tex]$$x(x-32)=0 \quad: \quad x=0, x=32$$[/tex]

Steps

x(x-32)=0

If a b=0, then either a=0 or b=0, according to the Zero Factor Principle.x=0 or x-32=0

Solve x-32=0:  x=32

The following are the quadratic equation's solutions:

x=0, x=32

2 . [tex]$$(y-3)(y+2)=0 \quad: \quad y=3, y=-2$$[/tex]

Steps

(y-3)(y+2)=0

If a b=0, then either a=0 or b=0, according to the Zero Factor Principle. y-3=0 or y+2=0

Solve y-3=0 :  y=3

Solve y+2=0 :  y=-2

The following are the quadratic equation's solutions:

y=3, y=-2

3. [tex](2 y+5)(y-4)=0 \quad: \quad y=-\frac{5}{2}, y=4$$[/tex]

Steps

(2 y+5)(y-4)=0

If a b=0, then either a=0 or b=0, according to the Zero Factor Principle. 2 y+5=0 or        y-4=0

Solve 2 y+5=0:  y=-[tex]\frac{5}{2}[/tex]

Solve y-4=0 :  y=4

The following are the quadratic equation's solutions:

[tex]y=-\frac{5}{2}, y=4$$[/tex]

4.[tex]$$2 z^2+20 z=0 \quad: \quad z=0, z=-10$$[/tex]

steps

[tex]$$2 z^2+20 z=0$$[/tex]

The following are the quadratic equation's solutions:

[tex]$$z_{1,2}=\frac{-20 \pm \sqrt{20^2-4 \cdot 2 \cdot 0}}{2 \cdot 2}$$$$\sqrt{20^2-4 \cdot 2 \cdot 0}=20$$$$z_{1,2}=\frac{-20 \pm 20}{2 \cdot 2}$$[/tex]

Distinguish the answers

[tex]$$\begin{aligned}& z_1=\frac{-20+20}{2 \cdot 2}, z_2=\frac{-20-20}{2 \cdot 2} \\& z=\frac{-20+20}{2 \cdot 2}: 0 \\& z=\frac{-20-20}{2 \cdot 2}:-10\end{aligned}$$[/tex]

The following are the quadratic equation's solutions:

z=0, z=-10

5 .

[tex]$$\begin{aligned}& 9 x^2=27 x: x=0, x=3 \\& \text { Steps } \\& 9 x^2=27 x\end{aligned}$$[/tex]

Move 27 x to the left side

[tex]$$9 x^2-27 x=0$$[/tex]

[tex]$$\begin{aligned}& \text { Factor } 9 x^2-27 x: \quad 9 x(x-3) \\& 9 x(x-3)=0\end{aligned}$$[/tex]

If a b=0, then either a=0 or b=0, according to the Zero Factor Principle. x=0 or x-3=0

Solve x-3=0: x=3

The following are the quadratic equation's solutions

x=0, x=3

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Samuel needs a total of 6 containers for his plan

The complete question is added as an attachment

From the question, we have the following parameters that can be used in our computation:

1 cup of rubbing alcohol = 1/(1/2) = 2 shares

Also, we have

1 cup of rubbing alcohol contains = 1 + 1/2 + 16 = 17.5

For the 2 shares calculated above, we have

2 shares = 17.5 * 2

Evaluate

2 shares = 35

Given that each can hold a maximum of 6 cups, the number of containers needed is

Container = 35/6

This gives

Container = 5.83

Round up

Container = 6

Hence, he needs 6 containers

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The given expression is expressed in an algebraic expression as: y^5 + 11

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

In mathematics, when we express “sum” we mean an addition. So the expression "the sum of y... and eleven"  is represented by:

y + 11

When we refer "fifth power" we mean an exponent equal to five. So the expression “y to the fifth power” is represented by:

y^5

The complete expression "the sum of y to the fifth power and eleven" in an algebraic expression represented by: y^5 + 11

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Correctly written question:

Write an algebraic expression that represent the sum of y to the fifth power and eleven

Correct option is A,  f(x) -2 has changed the parent function f(x) = (0.5)x to its new appearance.

The parent function f(x) = log5x has been modified by reflecting it over the x-axis, extending it vertically by a factor of three, and moving it down by three units.

In the picture below you can see the blue line is the graph of the function

f(x) = log(5x) and the green line is the graph of the function

g(x) = log[5(x + 4)] - 2

Since the function f passes at point (2, 1), we must reduce it by 2 units to ensure that it also passes at position (-2, -1). To do this, we add 2 to the function f.

We only need to add 4 to the variable x to have the function go left when we obtain log(5x) - 2.

The function shifts to the left when you add a number to x;

The function moves to the right when you remove a number from x;

The function increases when you add a number to it;

The function decreases when you take a number away from it.

Then we get a function g(x) = log[5 (x + 4)] - 2.

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By using the multiplication formula, the number of apples in all 4 boxes are 40.

Aside from addition, subtraction, and division, multiplication is also considered to be one of the four fundamental mathematical operations. Multiplying in mathematics refers to the process of repeatedly adding together groups of the same size.

The multiplication formula is expressed as:

Multiplicand × Multiplier = Product

Where:

Multiplicand: The first number (factor)

Multiplier: The second number (factor)

Product: The final result after multiplying the multiplicand and multiplier

In this case, we are given that:

Multiplicand = 4 boxes

Multiplier = 10 apples

Thus, the number of apples in 4 boxes are:

Product = 4 x 10

Product = 40

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320 peoples are fishing for their peir.

A statement that demonstrates the link between various variables using mathematical processes is called an equation. It is applied to problem-solving and forecasting. The same relationship can be expressed in an equation in a number of ways, and it can be used to obtain the value of an unknown variable by setting it to a known value.

length of fishing pier 3200 feet

Requirement of one person = 10 feet

so the let x person can accomodate in the given length

so 10 * x =3200

so , x = 3200/10

=> x =320

so 320 are fishing for their pier.

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When you solve an equation for one variable and then substitute the resulting expression in for that variable in the other equation its is known as Substitution method.

I will demonstrate how the substitution method works. Suppose we have the following systems of linear equations with two variables:

Equation 1:  3x + 2y = 11

Equation 2:  -x + y = 3

By solving these two equations we get x=1 and y=4.

Equation 2:  -x + y = 3

-x + x + y = x + 3

y = x + 3

Next, substitute the value of y in Equation 2 (from the previous step), and substitute its value into Equation 1 to solve for x:

Equation 1:  3x + 2y = 11

Substitute y = x + 3 into Equation 1:

3x + 2(x + 3) = 11

3x + 2x + 6 = 11

Combine like terms:

5x + 6 = 11

5x + 6 - 6 = 11 - 6

5x = 5

Divide both sides by 5 to solve for x:

[tex]\frac{5x}{5} = \frac{5}{5}[/tex]

x = 1

Substitute the value of x into Equation 2 to solve for y:

Equation 2:  -x + y = 3

-1 + y = 3

y = 3 + 1

y = 4

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The coordinates of the vertex of the function y = -3x² -12x + 3 is (-2,15) and the graph of the function is attached below.

Vertex in math is known as a point on a polygon where the sides or edges of the object meet or where two rays or line segments meet.

Here we have given that the function y = -3x² - 12x + 3 and we have to find the coordinates of the vertex.

As we all know that for any equation of the type y = ax² + bx + c the vertex is given by (h, k)

And the value of the vertex is calculated by using the formula  h = -b/2a and k = (4ac - b2)/4a.

From the given question we have identified the value of  a = -3, b = -12 and c = 3

Then the value of h is calculated as,

=> h = -(-12)/2(-3)

When we simplify this one then we get the value of h as -2

Similarly the value of k is calculated as,

=> 4ac = 4(-3)(3) = -36

Then the equation is written as,

=> k = [-36 - (-12)2]/4(-3)

When we simplify this one then we get

=> k = -180/-12

Therefore, the value of k is 15

Hence the coordinates of the vertex is (h, k) = (-2, 15).

Complete Question:

What are the coordinates of the vertex of the graph of the function y = -3x² -12x + 3?

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The solution is,  A’B’ =  12 units, when AB = 12.

A transformation is a dramatic change in form or appearance. An important event like getting your driver's license, going to college, or getting married can cause a transformation in your life. A transformation is an extreme, radical change.

here, we have,

Given

Line segment AB = 12 units

Translation of AB → A'B' by the rule T(x +0, y+5)

This translation won't change the length of A'B' as the difference in (x2-x1) and (y2-y1) stays same

because x-coordinate stays as is and y-coordinate's change cancelled when subtracting.

So,  A'B' = 12 units.

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The number in question is 4*20 = 80.

The factors of 80 are:

1, 2, 4, 5, 8, 10, 16, 20, 40 and 80

A factor of a number is an integer that divides the number completely without leaving a remainder. To find the factors of 80, we can start with 1 and divide 80 by each number up to 80. Any number that divides 80 without leaving a remainder is a factor of 80.

1, 2, 4, 5, 8, 10, 16, 20, 40 and 80 are the factors of 80.

The difference between the largest 5-digit number and the smallest 6-digit number is 1.

The aim is to find the largest 5-digit and the smallest 6-digit numbers, and then we need to identify the difference between these two values.

Let's start by finding the smallest 6-digit number.

We know that 0 is the smallest digit that can not be used in the highest place value, so we will consider the next smallest digit; that is, 1 and 1 can be used in the highest place value.

Thus, we can create the required 6-digit smallest number with 0 and 1.

Hence, the smallest 6-digit number is 100000.

Now, we will discover the largest 5-digit number.

As we know, the largest digit is 9, which can be used anywhere. So, we will form the largest 5-digit number with the digit 9.

Thus, the largest 5-digit number is 99999.

Next, we need to find the difference between these two values.

So, we can determine the difference between the smallest 6-digit number and the largest 5-digit number by subtracting the smallest from the largest.

Thus, we get,

⇒100000 - 999999

⇒1

Hence, 1 is the difference between the smallest 6-digit and the largest 5-digit numbers.

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Answer:

use symbolab it will give you the answer

Step-by-step explanation:

Answer:

The given expression is -7xy^3z^2

The degree of x is 1

The degree of -7 is 0

The degree of y^3 is 3

The degree of z^2 is 2

The degree of a polynomial is the highest exponent of its variables. In the case of the polynomial -7xy^3z^2, the degree is the highest exponent among x, y, and z.

The highest exponent is 3, which is the exponent of y. So the degree of the polynomial -7xy^3z^2 is 3.

It's worth noting that the coefficient -7 has no effect on the degree of the polynomial. The degree of a polynomial is determined by the exponents of its variables, not its coefficients.

The experimental probability of getting a cinnamon jelly bean is P = 2/11

Suppose that we have an experiment with some given number of outputs, and we perform that experiment N times.

The experimental probability of a given outcome is equal to the quotient between the number of times that we got that outcome and the total number of times we performed the experiment.

Here we have the data:

root beer = 5

licorice = 22

cinnamon = 6

For a total of 5 + 22 + 6 = 33 tries.

Then the probability of getting a cinnamon jelly bean is:

P = 6/33 = 2/11

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Answer:

23.6 units.

Step-by-step explanation:

Since quadrilateral DEFG is similar to quadrilateral HIJK, the ratios of corresponding sides are equal. We can use this information to find the measure of IJ.

We know that:

DF/HJ = EF/IJ = 6/23.6 = 2/8 = 1/4

So we can set up the proportion:

IJ/EF = HJ/DF

IJ/6 = 23.6/6

IJ = 23.6/6 * 6 = 23.6

All questions are solved using BODMAS rule.

BODMAS stands for Brackets, Orders (of operations), Division, Multiplication, Addition, and Subtraction. It is a commonly used acronym in mathematics to remember the order in which mathematical operations should be performed. When solving mathematical expressions, operations within brackets should be done first, followed by any exponents or roots.

Next, perform any divisions or multiplications from left to right, followed by any additions or subtractions from left to right. This order ensures that the expression is evaluated correctly and avoids confusion or errors.

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The pair of linear equations 3x + 5y = 20 and 6x + 10y = 40 have infinitely many solutions.

The given pair of linear equations can be represented in the form of Ax + By = C and Dx + Ey = F, where A = 3, B = 5, C = 20, D = 6, E = 10, and F = 40.

To find the number of solutions for the given pair of linear equations, we can use the following method:

So, the pair of linear equations 3x + 5y = 20 and 6x + 10y = 40 have infinitely many solutions.

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The tan function is referred to as the ratio of a right-angled triangle's opposite side to its neighbouring side.

The length of the neighbouring side to the angle and the opposite side to the angle are compared using the Tan formula. If we know the angle and either side of the triangle.

The six inverse trigonometric ratios are as follows: sin-1 (opposite)/(hypotenuse) = cos-1 (base)/(hypotenuse) = tan-1 (opposite)/(hypotenuse)=θ

we can also use the tan formula to determine the lengths of the triangle's sides. Tan Formula is formally defined as

tan⁡Ф = Opposite SideAdjacent Side

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The two boys are far away from the resort and distance measured about 35.81m.

The Pythagoras theorem equation is written as c² = a² + b², with c denoting the hypotenuse of the right triangle and a and b denoting the other two legs. So, any triangle that has a 90° angle creates a Pythagoras triangle, which can then be solved using the Pythagoras equation.

We must first use the Pythagoras theorem to determine how far the resort is from Manuel's home.

S₁ = √50²+20²

S₁ = √2500+400

S₁ = √2900

S₁ = 53.85m.

The distance between Manuel's house and his friend's house must then be calculated.

S₂ = √15²+10²

S₂ = √225+100

S₂ = √325

S₂ = 18.03m.

The displacement of the two boys will be,

∆S = S₁-S₂

∆S =  53.84-18.03

∆S = 35.81m.

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The two boys are far away from the resort and the distance measured about 35.81 m.

The Pythagoras theorem equation is written as c² = a² + b², with c denoting the hypotenuse of the right triangle and a and b denoting the other two legs. So, any triangle that has a 90° angle creates a Pythagoras triangle, which can then be solved using the Pythagoras equation.

We must first use the Pythagoras theorem to determine how far the resort is from Manuel's home.

S₁ = √50²+20²

S₁ = √2500+400

S₁ = √2900

S₁ = 53.85m.

The distance between Manuel's house and his friend's house must then be calculated.

S₂ = √15²+10²

S₂ = √225+100

S₂ = √325

S₂ = 18.03m.

The displacement of the two boys will be,

∆S = S₁-S₂

∆S =  53.84-18.03

∆S = 35.81m.

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It would take the automated car wash 20 hours to wash 120 cars.

What is rate ?

In general, a rate is a measure of how much of something happens within a certain period of time. It can be thought of as a ratio that compares two different units of measurement.

In the context of the problem, the rate at which the automated car wash can wash cars is the number of cars that it can wash per unit of time.

The rate at which the automated car wash can wash cars is 30 cars per 5 hours. To find out how long it would take to wash 120 cars, we can use the formula:

Time = (Number of cars / Rate)

Time = (120 cars / 30 cars per 5 hours)

Time = (120/30) * 5 hours

Time = 20 hours

So it would take the automated car wash 20 hours to wash 120 cars.

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The rate at which the automated car wash can wash cars is 30 cars per 5 hours. To find out how long it would take to wash 120 cars, we can use the formula:

Time = (Number of cars / Rate)

Time = (120 cars / 30 cars per 5 hours)

Time = (120/30) * 5 hours

Time = 20 hours

So it would take the automated car wash 20 hours to wash 120 cars.

Step-by-step explanation:

[tex]volume \: of \: cyinder = \pi{r}^{2}h \\ \pi {r}^{2} \times 120cm = 2880\pi {cm}^{3} \\ {r}^{2} = 24 \: {cm}^{2} \\ r = \sqrt{24} \: = 4.899 \: cm[/tex]

To find the sine of an angle in a right triangle, we can use the following relationship:

[tex]sin(angle) = opposite side / hypotenuse\\[/tex]

What is right triangle?

A right triangle is a type of triangle that has one angle that measures exactly 90 degrees (also known as a right angle). This angle is formed by the intersection of two legs of the triangle, which are not the hypotenuse of the triangle. The side opposite the right angle is called the hypotenuse and it is always the longest side of the triangle.

To find the sine of an angle in a right triangle, you can use the following relationship:

[tex]sin(angle) = opposite side / hypotenuse\\[/tex]

This relationship holds true for any angle in a right triangle, not just the acute angles.

For example, if you have a right triangle with an angle of 30 degrees and the opposite side is 5 units and the hypotenuse is 12 units, you can find the sine of the angle by dividing the opposite side by the hypotenuse:

[tex]sin(30) = 5/12 = 0.4166\\[/tex]

It's also important to note that the sine of an angle is always between -1 and 1, and the sine of an acute angle is always positive.

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To find the sine of an angle in a right triangle, we can use the following relationship:

sine = opposite side / hypotenuse side

What is right triangle?

A right triangle is a type of triangle that has one angle that measures exactly 90 degrees (also known as a right angle). This angle is formed by the intersection of two legs of the triangle, which are not the hypotenuse of the triangle. The side opposite the right angle is called the hypotenuse and it is always the longest side of the triangle.

To find the sine of an angle in a right triangle, you can use the following relationship:

sine = opposite side / hypotenuse side

This relationship holds true for any angle in a right triangle, not just the acute angles.

For example, if you have a right triangle with an angle of 30 degrees and the opposite side is 5 units and the hypotenuse is 12 units, you can find the sine of the angle by dividing the opposite side by the hypotenuse:

sin(30) = 5/12 = 0.4166

It's also important to note that the sine of an angle is always between -1 and 1, and the sine of an acute angle is always positive.

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Answer: Yes, it does.

Step-by-step explanation: Let x represent the price of gas today. 200% of x=200/100*x, which can be written as 2x because 200/100=2. 2x is x doubled, and therefore, it does mean the price has doubled.

Answer:

yes, the price has doubled

The area of the carpeted part of the patio is 1 [tex]\frac{11}{16}[/tex] square yards.

Mixed fractions are type of fractions which consist of a whole number part and a fractional part.

Mixed fractions are of the form a b/c where a is the whole number part and b/c is the fractional part.

Given that,

Area of the patio = 2 1/4 square yards

                             = (2 × 4 + 1) / 4 square yards

                             = 9/4 square yards

Also given that, 3/4 of the patio is carpeted.

Area of the carpeted part of the patio = 3/4 (9/4)

                                                               = 27/16 square yards

                                                               = 1 11/16 square yards

Hence the area of the carpeted part is 1 [tex]\frac{11}{16}[/tex] square yards.

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The complete question is as follows :

A patio has an area of 2 1/4 square yards. 3/4 of the patio is carpeted. What is the area of the carpeted part of the patio?