Fractional index
Without using mathematical table simplify the following
(16/81)^-3/4

Format in the example are Surds on the page above in own word is [tex]36z^{15} ,\ 100,\ 9^7,\ and \ 6r^3\\[/tex]

Surds are the root values for which there is no whole number representation. Indices represent the exponent or power of a value. For instance, the base is 3 and the index is 2 for the number 32. the index being 3/2.

These are the surds rules:

1) [tex](2z^3)^5=32^{15}[/tex]

2)  [tex]\sqrt[3]{1000*1000}=100[/tex]

3) [tex]\frac{9^{3} }{9^{-4} } = 9^7[/tex]

4) [tex](6r^{-3}) ^{-1} = 6r^3[/tex]

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Answer:

the aswer is A  i did this

Step-by-step explanation

1.  you are asked to find how many weeks it would take Alex to work 51 hours.

2. Alex  works  [tex]3\frac{1}{7}[/tex] weeks.

3. It makes sense in fractional from.

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction.

Alex works 3 hours a day and 4 days a week.

Alex works in a week = ( 3×4) hour = 12 hour

Alex  works = 51 hours = 48 hours + 3 hours = (48/12) weeks + 1 day

= 3 weeks and 1 day.

= [tex]3\frac{1}{7}[/tex] weeks.

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On solving the provided question we can say that - the increased value in fraction will be [tex]3\frac{1}{4}[/tex]

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

we have,

initial =  [tex]4\frac{5}{6}[/tex]

increased by =  [tex]4\frac{1}{4}[/tex]

son difference is = [tex]3\frac{1}{4}[/tex]

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Function: A function is a mathematical relationship between two sets of values, where each element in the first set (called the domain) is related to exactly one element in the second set (called the range). A function can be represented by a formula, equation, or graph, and it describes how one set of values is related to another.

Domain: In a function, the domain is the set of all possible values that can be used as input for the function. It is the set of values that the function operates on.

Range: In a function, the range is the set of all possible values that can be produced as output by the function. It is the set of values that the function produces as a result of operating on the domain.

Vertical line test: The vertical line test is a method used to determine whether a graph represents a function.

Hope This Helps You!

y2-y1/x2-x1

= (-1-3)/(5+1)

= -4/6

= -2/3

y = -(2/3)x + c

3 = (2/3) + c

c = -2/3 + 3

c = -2/3 + 9/3

c = -7/3

y = (2/3)x + (7/3)

Answer:

Eva has $127.31 after 2 years.

Step-by-step explanation:

Here is the formula for compound interest

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where [tex]A[/tex] is the final amount, [tex]P[/tex] is the initial amount, [tex]r[/tex] is the interest rate as a decimal, [tex]n[/tex] is the number of times the interest applied per time period, and [tex]t[/tex] is the number of time periods.

We are given

[tex]P=120\\r=0.03\\n=1\\t=2[/tex]

Substitute our numbers into the equation

[tex]A=120(1+\frac{0.03}{1})^{1*2}[/tex]

[tex]A=120(1.03)^{2}[/tex]

[tex]A=120*1.03^{2}[/tex]

[tex]A=120*1.0609[/tex]

[tex]A=127.308[/tex]

For the given line whose equation is [tex]y=x+3[/tex] :

x   y    (x,y)

0 3     (0,3)

1 4     (1,4)

2 5     (2,5)

3      6      (3,6)

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

A line in slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept .

Given the equation y = x + 3, the slope (m) is 1 and the y-intercept (b) is 3.

So, we can fill the table like this:

For the given line whose equation is [tex]y=x+3[/tex] :

x   y    (x,y)

0 3     (0,3)

1 4     (1,4)

2 5     (2,5)

3      6     (3,6)

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Answer:

10

Step-by-step explanation:

50 students.

20% = 20/100 = 1/5

50*1/5 = 10

There are 10 left-handers.

The possible roots of the cubic polynomial 9x³ + 14x² - x + 18 are 1, 2, and 3.

The rational root theorem explains how a polynomial's roots and coefficients are related. It explains the kind of rational roots that the polynomial might have in particular.

According to the rational root theorem, the possible roots of a polynomial of degree three and above are,

± (coefficient of the last term)/(coefficient of the first terms).

Given, A polynomial 9x³ + 14x² - x + 18 it is a cubic polynomial so it should have three roots they could be,

The factors of the constant term divided by the factors of the first terms,

So, 18 has factors ± (1, 2, 3, 6, 9, 18) and 9 has factors ± (1, 3, 9).

So, The possible roots are ± (1, 2, 3) and so on.

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Rewriting 6-6-6-6 in exponential notation is -1.2×10¹

Exponential notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, or standard form.

When writing in exponential notation, it must be in standard l i.e writing in this format 3.577× 10⁴ not 35.77× 10³.

Though both of the expression are literally correct but 3.577× 10⁴ is the acceptable way of writing a scientific notation.

similarly 6-6-6-6 will give -12

writing -12 in exponential notation is -1.2×10¹

Therefore the exponential notation of 6-6-6-6 is -1.2×10¹.

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Answer:

Step-by-step explanation:

To solve this system of equations, you can use the substitution method.

In this method, you solve one of the equations for one of the variables in terms of the other variable. Then you substitute this expression into the other equation. This will give you a single equation in one variable, which you can solve to find the value of that variable. Finally, you can substitute this value back into one of the original equations to find the value of the other variable.

To solve this system using substitution, we can solve the second equation for y:

y = x - 4

Then, we substitute this expression for y in the first equation:

x + (x - 4) = 8

Combining like terms, we get:

2x - 4 = 8

Adding 4 to both sides, we get:

2x = 12

Dividing both sides by 2, we find that:

x = 6

Now we can substitute this value back into one of the original equations to find the value of y. Let's substitute it into the second equation:

x - y = 4

Substituting 6 for x, we get:

6 - y = 4

Subtracting 6 from both sides, we find that:

y = 2

So the solution to the system of equations is x = 6 and y = 2.

Answer:

x=6, y = 2

Step-by-step explanation:

If you add 2 expressions, 2x = 12, so x = 6.

So the other one y = 2.

You can hire around 173 employees. Here's the calculation: $1,900 / ($11/hour * 40 hours/week) = 173.333..., which rounds down to 173.

a) The after-tax cost of the vehicle Rachel is buying is $29,368.70.

b) The part of the after-tax cost that Rachel will finance after making the down payment is $25,118.70.

c) The total payments after 5 years are $30,659.60.

d) The total interest Rachel paid is $1,290.90.

The interest payment represents the difference between the total monthly payments and the financing part of the after-tax cost of the vehicle.

The total monthly payments ($26,409.60) are obtained by multiplying the monthly payments ($440.16) by the number of payment periods (60).

Value of vehicle = $25,990

Harmonized sales tax (HST) = 13%

After-tax cost of the vehicle = $29,368.70 ($25,990 x 1.13)

Down payment = $4,250

Financing part = $25,118.70 ($29,368.70 - $4,250)

Monthly payments = $440.16

Financing period = 60 months (5 years x 12)

Total monthly payments = $26,409.60 ($440.16 x 60)

The total amount paid for the car = $30,659.60 ($26,409.60 + $4,250)

Total interest = $1,290.90 ($26,409.60 - $25,118.70)

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Answer:

If the pharmaceutical sales representative meets her target for Medication A, she will receive 60% of the $20,800 bonus, or $12,480. When added to her base salary of $68,400, her total compensation for the year would be $80,880.

Step-by-step explanation:

Answer:

The total would be 99,620

Step-by-step explanation:

29400*0.80=23520

Add the amount to the base salary

76100+23520=99,620

Study data: The 45 exercise sessions from study participants were all recorded.

Study Data includes all information created, obtained, or acquired during the conduct of the Study, including Samples 1 through 3 including databases, documents, reports, and other material.

Any information that has been gathered, noticed, produced, or made specifically to support initial study conclusions is referred to as research data. Research data can also be found in non-digital media like diary and lab notebooks, despite being mostly digital.

A. Study data: The 45 exercise sessions from study participants were all recorded.

B. Study parameter: The average weekly exercise time for all participants.

C. Study variable: The length of time that each individual fitness facility patron exercises.

D. Study participants: all patrons of the fitness club.

E. The 45 gym patrons who took part in the survey made up the study's sample.

F. Statistics of the study: The average amount of time that a sample of clients exercises in one week

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The amounts of goo after each hour are given as follows:

The time that it takes for the goo to return to original size is given as follows:

n hours, for which:

[tex](2)^n(0.25)^n = 1[/tex]

An increasing exponential function is defined as follows:

y = a(1 + r)^x.

For which the parameters are given as follows:

Her sample is of 10 grams, and the amopunt of goo increases by 100%, hence the parameter values' are given as follows:

a = 10, r = 1.

Thus the exponential function is defined as follows:

y = 10(2)^n.

Then the amounts are given as follows:

A decreasing exponential function is given as follows:

y = a(1 - r)^x.

The goo shrinks by 75% every hour, hence:

r = 0.75.

The amount after n hours is of 10(2)^n, hence the shrinking function is given as follows:

[tex]y = 10(2)^n(0.25)^n[/tex]

It returns to the original amount when:

y = 10.

Hence:

[tex]10 = 10(2)^n(0.25)^n[/tex]

[tex](2)^n(0.25)^n = 1[/tex]

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If it cost the shoe factory $26.47 to make a pair of Purple Pedi running shoes and the mall sells them for $128.98 then 3.87 is the percent mark-up.

The gross profit of a unit is determined by subtracting its cost to produce or acquire for resale from its sales price to determine the markup percentage. The markup percentage is computed as (12 - 8) / 8 and equals 50% if an item is priced at $12 but costs the manufacturer $8 to produce.

Some individuals will inform you that a 5% markup equates to a markup of 5% of the price your customer pays. In your illustration, this is stating that you add a specific amount to your cost, $62, to arrive at a price of $P for your customer, and the amount you added is 5% of $P. This means that your cost of $62 is 95% of the price of P.

($128.98 - $26.47)/ $26.47

= 3.87.

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Answer: The equation y = 53+2x relates the variables x and y, where x represents the number of days the crew has worked and y represents the total length of the road.

The change per day in the road's length is given by the coefficient of x in the equation, which is 2. Thus, the change per day in the road's length is 2 miles.

The road's length when the crew started working is given by the constant term in the equation, which is 53. Thus, the road's length when the crew started working was 53 miles.

Step-by-step explanation:

Answer:

(k+3)(k+3) + (k-9)(k-9), or p = (k+3)^2 + (k-9)^2, or p = 4k^2 - 24k + 180

Step-by-step explanation:

A rectangle has four sides, two sides both have equal width, while the other two have equal length. The perimiter is the total sum of these sides. We can use the following equation to represent the perimiter using the width and length:

p = 2w + 2l

We know that the width equals (k+3)(k+3), so 2w would equal 2(k+3)(k+3). In the form of a quadratic equation, this would equal 2k^2+12k+18.

We also know that the length equals (k-9)(k-9), so 2l would equal 2(k-9)(k-9). As a quadratic equation, this would equal 2k^2-36k+162.

Plugging these values into our equation we get:

p = (k+3)(k+3) + (k-9)(k-9), or p = (k+3)^2 + (k-9)^2.

Or in the form of a quadratic equation:

p = 2k^2 + 12k + 18 + 2k^2 - 36k + 162

=

p = 4k^2 - 24k + 180

Hope this helps!

The perimeter of the rectangle can be calculated using the formula 2(length + width). Substituting the given expressions for length and width, we get 2[(k+3)(k+3)+(k-9)(k−9)]. This simplifies to the expression 4k^2-24k+180.

The perimeter of a rectangle is calculated by adding the lengths of all its sides. With the width given as (k+3)(k+3) centimeters, and the length as (k-9)(k−9) centimeters, we can substitute these into the formula for the perimeter of a rectangle, which is 2(length + width).

Therefore, the expression representing the perimeter of the rectangle is 2[(k+3)(k+3)+(k-9)(k−9)]. This simplifies to 2[(k^2+6k+9)+(k^2-18k+81)], which further simplifies to 2[2k^2-12k+90], and ultimately simplifies to 4k^2-24k+180.

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Answer:

(-2,-6)

Step-by-step explanation:

we can solve this system of equations with the substitution method because y is already by itself.

since they are both equal to y, we can set both equations equal to each other.

4x+2=x-4

subtract 2 from both sides

4x=x-6

subtract x from both sides

3x=-6

divide both sides by 3

x = -2

now that we know x, we can plug this value into one of the original equations and solve for y.

y=-2-4

y=-6

so on a graph, these two equations will intersect at the point (-2,-6)

The population of North Carolina will reach 12 million in the year 2028.

Population growth is defined as the increase in the number of people which is calculated using population growth rate.

Given that,

Population in 2010 = 9.5 million

Population is increasing to 1.3% per year.

Annual growth rate = 1.3% = 1.3/100 = 0.013

We have the population growth formula,

P = P₀ e^(r t)

Here, P₀ = 9.5 million = 9,500,000

and P = 12 million = 12,000,000

r = 0.013

We have to find t.

12,000,000 = 9,500,000 e^(0.013t)

120 / 95 = e^(0.013t)

Taking natural logarithm on both sides and also ㏑(e^m) = m ㏑ e, we get,

㏑(12/9.5) = 0.013t × ㏑e

[㏑(12/9.5) ÷ 0.013] = t  [since ln e = 1]

t = 17.97 ≈ 18 years

The year is 2010 + 18 = 2028

Hence in the year 2028, the population will be 12 million.

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The integral ∫1/√1 +(lnx) 2dx is -x+2xln(x)+c

An integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data

The given integral is ∫1/√1 +(lnx) 2dx

= ∫1 +2(lnx)dx

Apply the sum rule

∫f(x)±g(x)=∫f(x)±∫g(x)

= ∫1dx +2∫(lnx)dx

=x+2(xln(x)-x)+c

=-x+2xln(x)+c

Hence, the integral ∫1/√1 +(lnx) 2dx is -x+2xln(x)+c

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Therefore, Mr. Tompkins lives 240 miles from the airport.

Acceleration is the rate of change of velocity of an object. It is a vector quantity that has both magnitude and direction. Mathematically, it is the derivative of velocity with respect to time. In simpler terms, it is the change in speed or direction of an object over time.

Velocity is a vector quantity that describes the rate of change of an object's position. It has both magnitude and direction. The magnitude of velocity is the speed of an object, which is the distance covered per unit of time.

We can start solving the problem by using the formula: distance = speed x time.

Let x be the distance from Mr. Tompkins' home to the airport in miles.

Therefore, the distance from the airport to the other city is (670 - x) miles

we know that the total traveling time is 4 hours

so we can set up two equations:

x/30 + (670 - x)/250 = 4

x + (670 - x)/8 = 120

we can solve for x

x = 240 miles

Therefore, Mr. Tompkins lives 240 miles from the airport.

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Answer:

Step-by-step explanation:

Certainly! To set up the problem, we can consider the owner-manager's utility as a function of two variables: income (profit) and charitable contributions or civic expenditures. Let's call these variables x and y, respectively.

The owner-manager utility is given by the function U(x,y), where x is the income (profit) and y is the charitable contributions or civic expenditures.

The cost of obtaining this utility is given by the function C(x,y), where x is the income (profit) and y is the charitable contributions or civic expenditures.

To find the lowest possible cost at which the owner-manager can obtain a specific level of utility, we can use the following optimization conditions:

The cost function C(x,y) should be minimized subject to the constraint U(x,y) = k, where k is the specific level of utility that the owner-manager wishes to achieve.

The first-order necessary conditions for a minimum are:

∂C/∂x = λ ∂U/∂x

∂C/∂y = λ ∂U/∂y

where λ is a Lagrange multiplier.

These conditions are known as the Karush-Kuhn-Tucker (KKT) conditions.

These optimization conditions differ from the utility-maximizing conditions in that we are minimizing the cost function instead of maximizing the utility function. In addition, we have the constraint U(x,y) = k, which means that we are trying to achieve a specific level of utility rather than trying to maximize it.

The average value of f is 16.25.

A contour line of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. It is a plane section of the three-dimensional graph of the function f parallel to the-plane.

Given that, a contour map is shown for a function f on the square R = [0, 8] [0, 8].

Since the given square is 8 by 8 and we are using m=n=2, then each sub-rectangle is 4 by 4. So, the area of the given rectangle is 64 and the area of each sub-rectangle is 16, that is, ΔA=16

Furthermore, the centers of the sub-rectangles are (2,2),(2,6),(6,2),(6,6).

a) The estimated value of [tex]\int\limits\int\limits_R f{x} \, dA[/tex]

=16⋅f(2,2)+16⋅f(2,6)+16⋅f(6,2)+16⋅f(6,6)

≈16⋅27+16⋅3+16⋅12+16⋅23

≈1040

b) The average value of f will be

[tex]f_{avg}=\frac{1}{A}.\int\limits\int\limits_R (x, y) \, dA[/tex]

≈ 1/64 ×1040

≈ 16.25

Therefore, the average value of f is 16.25.

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Answer:

3.95 + 0.50 + 4.50 × 2 = 13.45

13.45 × x = 124.70

x = 9

Therefore, she can make 9 shirts.

Answer:

Yes, Anna and Sharon both created triangles that are congruent. Their triangles are congruent because they have 2 corresponding, congruent side-lengths and an included angle that is congruent. Therefore, their triangles are congruent by SAS (Side-Angle-Side).