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Using Law of exponents, The value of [tex]5\sqrt{\frac{8xz^{2} }{y^{3} } }[/tex]   [tex](\frac{8xz^{2} }{y^{3} } )^{\frac{1}{5} }[/tex]

Exponent rules are the laws that are applied to simplify exponent-based expressions. The principles of exponents make it simple to carry out numerous arithmetic operations, such as addition, subtraction, multiplication, and division, in a short amount of time. Additionally, these rules aid in the simplification of numbers with complex powers incorporating roots, fractions, and decimals.

Exponent rules, commonly referred to as the "laws of exponents" or "properties of exponents," facilitate the task of simplifying exponent-based statements. These guidelines are useful for reducing the complexity of expressions whose exponents are decimals, fractions, irrational numbers, or negative integers.

Given,

[tex]5\sqrt{\frac{8xz^{2} }{y^{3} } }[/tex]

⇒ [tex](\frac{8xz^{2} }{y^{3} } )^{\frac{1}{5} }[/tex]

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The quadratic equation are y= 5x-3/2+x^2, y= x^2+5x-2 and y= x-1/x.

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

Here,

A. y= 5x-3/2+x^2

It has a degree is 2, So quadratic equation.

B. y= x^2+5x-2

It has a degree is 2, So quadratic equation.

C. y=-x+2

It has a degree is 1, So it's not quadratic equation.

Hence the value of k is 0.33.

D. y= x-1/x

y = x² -1/x

It has a degree is 1, So it's not quadratic equation.

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Answer:

x <= 1.

Step-by-step explanation:

Let x be the number of jeans Jordan can purchase.

We know that the total cost of the leather jacket, hat and jeans is $45 + $10 + $35x = $45 + $10 + $35x.

We also know that the total cost cannot exceed the amount of money Jordan has, which is $90.

So we can write the inequality: $45 + $10 + $35x <= $90

Solving for x, we get: $35x <= $35

x <= 1

So the number of jeans Jordan can purchase is x <= 1.

Therefore , the solution of the given problem of unitary method is Boat is travelling at a speed of 21.6 miles /hour.

The unit method is a way of problem-solving where you first calculate the worth of a single group, subsequently multiply that value to get the answer. Simply expression, a single system value is extracted from a specified multiple using the unit method. For illustration, 40 pens will set you back 400 rupees, or $1.01. The method used to accomplish this might be standardized. a solitary nation. anything has a distinctive component. (Mathematics, Algebra) Its adjoint or reciprocal are equivalent. (Linear Algebra, Mathematical Interpretation, Mathematics of Matrix or Operators)

Here,

A boat has a speed = 36 km/hour

a km is about 60% of a mile.

1 km = 60/100 mile = 0.6 mile

the boat has a speed = (0.6 × 36) mile/hour

                                   = 21.6 miles/ hour

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The x-intercepts of the graph of the equation are (8,0) and (-6,0).

What are intercepts?

A point on the y-axis known as an intercept is where the line's slope passes.

X-intercept and Y-intercept are the two main intercepts. The line's x-intercept and y-intercept are located where the line crosses the x and y axes, respectively.

Now, in order to find the x- intercepts, we need to put y=0 because at that point the line crosses the x- axis and therefore, y=0 at that point.

So,

x^2-2x+(0)^2-3(0)=48

⇒x^2-2x=48

⇒x^2-2x-48=0

⇒x^2+6x-8x-48=0

⇒x(x+6)-8(x+6)=0

⇒(x-8)(x+6)=0

So, x= 8,-6

Hence, the x-intercepts of the graph of the equation are (8,0) and (-6,0).

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Answer:

67,43/10 = 6.743

When dividing any number by 10, you just move the decimal to the left. When multiplying, you move it to the right.

Step-by-step explanation:

Hope it helps! =D

Answer: The solution to the expression is the result of the mathematical operations being performed in the correct order. The order of operations is: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

5/34 is a fraction, 22 2/3 is a mixed number, and 2 1/9 is also a mixed number. To perform the operations, we need to convert all these mixed numbers to fractions.

So, 22 2/3 is equal to (223+2)/3 = 68/3

and 2 1/9 is equal to (29+1)/9 = 19/9

Now the expression become 5/34 x 68/3 - 19/9

We can now perform the operations:

5/34 x 68/3 - 19/9

= (568)/(343) - 19/9

= 340/102 - 19/9

Now we have to perform subtraction, for this we need to have a common denominator:

= (3409 - 19102)/(102*9)

= 2861/918

The solution is 2861/918 which can be simplified to 3 3/34

Step-by-step explanation:

The amount of pints of punch that Jason served is; 52 pints

Algebraic word problems are defined as the questions that require translating sentences to equations, then solving those equations. and a single variable.

We are given that;

Amount of punch made = 8 gallons

Amount of punch left after serving = 12 pints

Now, conversion of pints to gallon is;

1 pint = 0.125 gallons

Thus;

12 pints = 1.5 gallons

Thus;

Amount of pints served = 8 - 1.5 gallons

= 6.5 gallons

Converting to pints gives 52 pints

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To determine the probability that the sample mean for French is greater than that of the Americans, we need to use the Central Limit Theorem, which states that as the sample size increases, the distribution of the sample means will become more and more normal, regardless of the distribution of the population from which the samples are drawn.

So, we can assume that the sample means of both American and French adults will be normally distributed with a mean of 43.5 hours/week and 36 hours/week respectively and a standard deviation of 4.6/sqrt(110) and 5.1/sqrt(135) respectively.

We can use these assumptions and the Z-score formula to find the probability that the sample mean for French is greater than that of Americans.

Z = (36 - 43.5) / (sqrt((4.6/sqrt(110))^2 + (5.1/sqrt(135))^2))

The resulting Z-score will be negative, meaning that the probability that French sample mean is greater than American sample mean is low and it's a rare event.

Using the substitution method, we know that the values of A is 19,200.

The substitution method is typically used in mathematics to solve an equation system.

In this approach, you solve the equation for one variable first, then you enter its value into the other equation.

So, we know that:

I = 240

W = I / 3

A = I * W

A = ?

Now, keep substituting the values to get A as follows:

I = 240

W = 240/3

W = 80

A = I * W

A = 240 * 80

A = 19,200

Therefore, using the substitution method, we know that the values of A is 19,200.

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Therefore , the solution of the given problem of unitary method comes out to be  56 tablespoons in 3 1/2 cups of vinegar .

The unit technique is a method for resolving variable problems that includes multiplying the value of a unit by the required number of units. A unified force number can be extracted from a given many using the unit function, to put it simply. The price of 40 needles is 400 rupees, or about $1.50. It might be possible to verify this using a regular procedure. simply one nation. Everything possesses a unique quality.

Here,

Given :

=> 3 1/2 cups or 7/2 cups or 3.5 cups

16 tablespoons in one cup ,

=> 16 * 3.5

=> 56 tablespoons

Therefore , the solution of the given problem of unitary method comes out to be  56 tablespoons in 3 1/2 cups of vinegar .

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The value of the function is 5.33

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

f(x) = 1/3 * 4^x

To find f(2), we need to substitute x = 2 into the function f(x) = 1/3 * 4^x

f(x) = 1/3 * 4^x

f(2) = 1/3 * 4^2

f(2) = 1/3 * 16

f(2) = (1/3) * 16

f(2) = 16/3

f(2) = 5.33

So the value is f(2) = 5.33

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The Perimeter of the space that is not filled with cheese tart is 44 cm.

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Answer:33

Step-by-step explanation:

49-16=33

Using Pythagoras theorem, the altitude a is √33.

The Pythagorean theorem, a cornerstone of Euclidean geometry, connects the side lengths of a right triangle via the straightforward formula a² + b² = c². Ancient scholars and architects from Babylon, Egypt, China, and India were aware of the connection.

While Pythagoras lived and wrote between 569 and 475 BCE, the work that bears his name first appeared on clay Babylonian tablets around 1800 BCE. Early Chinese scholars were also aware of the Pythagorean theorem, and it was mentioned in ancient Indian sacred texts that dealt with the construction of altars.

To solve a,

We can see a right triangle forming by those 3 squares

Lets take theirs sides as the base, altitude and hypotenuse

Hypotenuse = 7

Base = 4

Altitude = to find

Using Pythagoras theorem

[tex]a^2 + b^2 = c^2[/tex]

[tex]\Rightarrow a = \sqrt{c^2 - b^2 }[/tex]

[tex]\Rightarrow a = \sqrt{7^2 - 4^2 }[/tex]

[tex]\Rightarrow a = \sqrt{49 - 16 }[/tex]

[tex]\Rightarrow a = \sqrt{33 }[/tex]

Thus, Using Pythagoras theorem, the altitude a is √33.

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Answer:

Text are too tiny for me to see sorry

Answer:

2.5

Step-by-step explanation:

P=29

w+w=4+4=8(rule of perimeter is 2w+2L)

29-8=21

21-16=5(L+L=8+8=16)

5 will be over 2 since it's for the 2 sides so 5÷2=2.5

your welcome

a. The probability that X is less than 95 is approximately 0.0668

b. The probability that X is between 95 and 97.5 is approximately 0.1359

c. The probability that X is above 102.2 is approximately 0.0228

d. The value of X for 65% chance is 99.23

We know, z=(X-mean)/ (S.D./sqrt N)

Thus, putting in the values for the respective cases, we get

(a) z value corresponding to X=95 is,

z=(95-100)/(10/sqrt 25)= -2.5

Therefore, required probability= area under the standard normal curve left to

z= -2.5 = 0.5000- 0.4938= 0.0062

(b) z value corresponding to X=95 is -2.5 and X=97.5 is,

z=(97.5-100)/(10/sqrt 25)= -1.25

Therefore, required probability= area under the standard normal between

z= -2.5 and z= -1.25= 0.4938- 0.3944= 0.0994

(c) z=(102.2-100)/(10/sqrt 25)= 1.1

Therefore, required probability= area under the standard normal curve right to

z= -2.5 = 0.5000- 0.3643= 0.1357

(d) 65%= 0.6500 is an area on the left side of the z value.

Or, we can say 35%= 0.3500 is on the right side of the z value.

therefore, the corresponding z value is -0.385 approximately.

Thus, for X value,

-0.385= (X-100)/(10/sqrt 25)

-0.385= (X-100)/2

-0.77= X-100

X= 99.23

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The standard deviation of the data-set is given as follows:

2.24.

The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.

The sum of the differences squared between each observation and the mean is given as follows:

4 x (6 - 9.28)² + 5 x (7 - 9.28)² + (8 - 9.28)² + 4 x (9 - 9.28)² + 5 x (10 - 9.28)² + 4 x (11 - 9.28)² + 6 x (12 - 9.28)² = 144.75.

Dividing by the number of values, we have that:

144.75/(4 + 5 + 1 + 4 + 5 + 4 + 6) = 5.

Taking the square root, the standard deviation is given as follows:

2.24.

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The expression is equal to f(x) g(x) is 77x⁷ + 78x⁶ - 27x⁵

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

In order to find which expression is equal to f(x) g(x), multiply (11x³ - 3x²) by (7x⁴ + 9x³). That is:

f(x) g(x) = (11x³ - 3x²)(7x⁴ + 9x³)

Expand the expression:

f(x) g(x) = 11x³ × 7x⁴ + 11x³ × 9x³ - 3x² × 7x⁴ - 3x² × 9x³

f(x) g(x) = 77x⁷ + 99x⁶ - 21x⁶ - 27x⁵

Combine like terms:

f(x) g(x) = 77x⁷ + 78x⁶ - 27x⁵

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Complete Question

Select the correct answer.

Consider functions f and g.

f(x) = 11x³ - 3x²

g(x) = 7x² + 9x³

Which expression is equal to f (x) g(x)?

A. 7x⁴ + 99x³ -3x²

B.77x¹² +99x⁹- 21x⁸ - 27x⁶

C. 18x⁷ + 10x⁶ + 6x⁵

D. 77x⁷ + 78x⁶ - 27x⁵

To calculate the average (mean) value of a function, you need to find the area under the curve of the function, divide it by the interval over which the function is defined, and then find the value of the function at the midpoint of the interval.

In this case, the function is 3t³ - t² and we need to find an interval to calculate the average (mean) value. A common interval used for this calculation is from 0 to 1.

The area under the curve of the function from 0 to 1 can be found by integrating the function from 0 to 1. However, to keep it simple, we can also use the definite integral of the function from 0 to 1, which is:

∫ (3t³ - t²) dt = 3t⁴/4 - t³/3 | from 0 to 1

= (3/4) - (1/3) = 1/4

So, the average (mean) value of the function 3t³ - t² over the interval 0 to 1 is: 1/4 ÷ 1 = 1/4

And the value of the function at the midpoint of the interval, which is 0.5, is: 3(0.5) ³ - (0.5) ² = 3/8 - 1/4 = -1/32

So, the average (mean) value of the function 3t³ - t² over the interval 0 to 1 is -1/32.

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Expressions → Type of factoring

3x³ + 15x² + 2x + 10 → Grouping

x³ + 27 → Sum of cubes

2x² + 6x → Greatest common factor

x² - 25 → Difference of squares

x² + 6x + 8 → Unfoil

x³ - 1 → Difference of cubes

'Factor' is a term used to express a number as a product of any two numbers. Factorization is a method of finding factors for any mathematical object, be it a number, a polynomial or any algebraic expression. Thus, factorization of an algebraic expression refers to finding out the factors of the given algebraic expression.

Given expressions

Using grouping method

= (3x³ + 15x²) + (2x + 10)

= 3x²(x + 5) + 2(x + 5)

Factoring out common term

= (x+5)(3x² + 2)

It can be written as

= x³ + 3³

Which is sum of cubes

it can be written as

= 2x.x + 2x.3

GCF (greatest common factor) = 2x

= 2x (x + 3)

It can be written as

= x² - 5²

which is difference of squares

= x² + 4x + 2x + 8

= x(x + 4) + 2(x + 4)

= (x + 4) (x + 2)

Which is unfoil.

it can be written as

= x³ - 1³

which is difference of cubes.

Hence, the factoring of expressions 3x³ + 15x² + 2x + 10, x³ + 27,  2x² + 6x, x² - 25, x² + 6x + 8, x³ - 1 refers to grouping, sum of cubes, greatest common factor, difference of squares, unfoil and difference of cubes respectively.

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Price of gasoline is with Time:

The term "rate of change" (ROC) describes the rate which something alters over time.

For the stated graph.

Price of gasoline is fixed for Time: A , C, E, and G.

Price of gasoline is increasing rate for Time: D

Price of gasoline is decreasing rate for Time: B, and F

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The slope of the linear equation perpendicular to:

x - 6y = 24

is a = -6.

A general line can be written in the slope-intercept form as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Particularly, two lines are perpendicular if the product between their slopes is equal to -1.

Here we want to find a line perpendicular to:

x - 6y = 24

First, we need to find the slope of this line.

x - 6y = 24

-6y = -x + 24

y = (-1/6)*-x - 24/6

y = (1/6)*x - 3

The slope is 1/6, then if the slope of the perpendicular line is a, the slope must be a solution of:

a*(1/6) = -1

a = -6

The slope of the perpendicular line is -6.

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The Gold Standard was a system under which nearly all countries fixed the value of their currencies in terms of a specified amount of gold, or linked their currency to that of a country which did so.

Step-by-step explanation:

Answer:

No longer used.

Step-by-step explanation:

Due to too much paper money being printed, some countries did not have enough gold reserves to exchange for the excessive amounts of paper promissory notes. (China's overprinting of printed money during the 9th and 15th centuries foreshadowed England's overprinting during WWI some 200 years later.) This rendered the paper money worthless. (One of the causes of the Great Depression.)

The gold standard is no longer used now, but the system it inspired is currently used between nations.

The errors of quadratic equation is [tex]x=4 \pm \sqrt{24} &[/tex].

The given quadratic equation is [tex]8x^{2}-x-1=0[/tex]

The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of:

where x is the unknown variable and a, b and c are the constant terms.

Standard Form of Quadratic Equation is [tex]ax^{2} + bx + c = 0[/tex] where a,b,c are real number and a≠0

Therefore the roots of the given equation can be found by:

[tex]x=\frac{-b\±\sqrt{b^{2}-4ac } }{2a}[/tex]

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

⇒[tex]$$8 x^2-x-1=0$$[/tex]

Multiply both sides by 8.

⇒[tex]8\left(8 x^2-x=1\right)[/tex]

[tex]x^2-8 x=8 & \\x^2-8 x+16=8+16 & \\(x-4)^2=24 & \\x-4=\pm \sqrt{24} & \\x=4 \pm \sqrt{24} &[/tex]

Therefore, the x is [tex]x=4 \pm \sqrt{24} &[/tex].

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A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution.

Tables of the standard normal distribution are frequently used to show different regions of the normal distribution. A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.

Tables of the standard normal distribution are frequently used to show different regions of the normal distribution.The standard deviation reveals the degree of data skewedness. It gauges how far away from the mean each observed value is. Approximately 95% of values in any distribution will be within two standard deviations of the mean.

A sigma value, typically represented by the Greek letter or lower case s, is a measure of how far a sample or point of data is from its mean. It is given in standard deviations.

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Answer:

a = 15 , b = [tex]\frac{2}{9}[/tex]

Step-by-step explanation:

the equation of proportion is

y = kx ← k is the constant of proportion

to find k substitute x = 0.7, y = 2.1 , values from the table into the equation

2.1 = 0.7k ( divide both sides by 0.7 )

3 = k

y = 3x ← equation of proportionality

then using x = 5

a = 3 × 5 = 15

using y = [tex]\frac{2}{3}[/tex]

[tex]\frac{2}{3}[/tex] = 3b ( multiply both sides by 3 to clear the fraction )

2 = 9b ( divide both sides by 9 )

[tex]\frac{2}{9}[/tex] = b

Sally put in 36 hours, Harold put in 30 hours, and Nora put in 15 hours.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Here,

Let x be the work hours of Sally, y be the work hours of Harold and z be the work hours of Nora.

x+y+z=81

x=y+6

y=2z

x=2z+6

2z+6+2z+z=81

6+5z=81

5z=75

z=15

y=2z

=30

x=y+6

=30+6

=36

Sally worked for 36 hours while Harold worked for 30 hours and Nora worked for 15 hours.

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The comparison that can be be made between population of city A and B is City A < City B

The population of city A is eighty-four thousand two hundred-six

This is written in numerals as : 84,206

For Population B the size is said to be:

80,000 + 4000 + 200 + 10 +6

we would have to add this up

= 84216

Now we are to compare the value that is greater

84216 is greater than 84206

hence we would say that City A has a less population compared to City B which is greater

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