Evaluate 0.5^3 and 0.5^-3 as fraction

The fastest way to find the distance between two points in a plane is to use the distance formula.

The distance formula is a mathematical expression that gives the distance between two points in a plane, given their coordinates. The distance formula is:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points, and d is the distance between them.

This formula uses the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

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Answer:

Yes

Step-by-step explanation:

y = 110 + 32x

Let x = each value in the table and calculate the corresponding value of y.

You get the following.

x = 0; y = 110

x = 2; y = 174

x = 4; y = 238

x = 6; y = 302

x = 8l y = 366

Since every value from evaluating the function gives the same value as the table, then the answer is yes, the table and the equation represent the same function.

Answer:

yes it is in simpleat form

Answer:

5%

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I = Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

Substitute the given values into the simple interest formula and solve for r:

[tex]\implies 500=5000 \cdot r \cdot 2[/tex]

[tex]\implies 500=10000r[/tex]

[tex]\implies r=\dfrac{500}{10000}[/tex]

[tex]\implies r=0.05[/tex]

[tex]\implies r=5\%[/tex]

Therefore, the interest rate is 5%.

Answer:

Interest rate = 5% (or) 0.05

Step-by-step explanation:

Now we have to,

→ find the required interest rate.

Formula we use,

→ I = P × R × T

→ PRT = I

→ R = I/PT

Then the interest rate will be,

→ R = I/PT

→ R = $500 ÷ ($5000 × 2 years)

→ R = 500/(5000 × 2)

→ R = 500/10000

→ R = 0.05 × (100)

→ [ R = 5% ]

Hence, the interest rate is 5%.

Miles per hour and meters per second are formally known as mph and m/s, respectively.

Kilometers per hour 28 km/h

Miles per hour 62.6342  

Let's first review the metric conversions for a mile and an hour. Speed is the distance traveled in a given amount of time.

Miles per hour and meters per second are formally known as mph and m/s, respectively. If so, converting mph to m/s will be simple. We are cognizant of:

A mile is equal to 1.60934 kilometers or 1609.34 meters.

3600 seconds make up 1 hour, which is equal to 60 minutes, 60 minutes, and 60 seconds.

With the help of these conversions, let's create the mph to m/s formula.

mph to m/s Formula

1 mph = 1 mile per hour

=1 mile / 1 hour

=1609.34 meters/3600 seconds

0.447 meter / seconds

=0.447 m/s

So, multiplying by 0.447 is required to change mph to m/s.

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99.9% of the population is within 4 standard deviations of the mean.

In information, the standard deviation is a degree of the quantity of variation or dispersion of a fixed of values. A low standard deviation indicates that the values tend to be near the implied (additionally called the predicted price) of the set, whilst an excessive preferred deviation suggests that the values are spread out over a wider variety.

Popular deviation can be abbreviated SD, and is maximum commonly represented in mathematical texts and equations by means of the decrease case Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample general deviation.

The standard deviation of a random variable, pattern, statistical population, statistics set, or possibility distribution is the square root of its variance. it's miles algebraically easier, even though in exercise less sturdy, than the common absolute deviation.

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The inequality form of the statement is: |4x - 2| ≤ 2. And the lowest value of x that makes this inequality true is x = -1.

To solve for the lowest value of x that makes this inequality true, we need to consider two cases:

If 4x - 2 ≥ 0, then |4x - 2| = 4x - 2, so the equation becomes:

4x - 2 ≤ 2

Adding 2 to both sides, we get:

4x ≤ 4

Dividing both sides by 4, we get:

x ≤ 1

If 4x - 2 < 0, then |4x - 2| = -(4x - 2), so the equation becomes:

-(4x - 2) ≤ 2

Adding 2 to both sides, we get:

-4x + 4 ≤ 4

Dividing both sides by -4, we get:

x ≥ -1

So, the solution to the inequality is -1 ≤ x ≤ 1. This means that any value of x that lies between -1 and 1, inclusive, satisfies the inequality.

So, the lowest value of x that makes this inequality true is x = -1.

"

Complete question

The absolute value of the difference between 4x and 2 is less than or equal to 2.

Write the statement as an inequality, then solve for the lowest value of  x that makes this inequality true. Lowest  value _____

"

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The cost of each cup of coffee at a kiosk is $ 4.

Let the cost of each cup of coffee is $ x.

A person buys 5 cup of coffee at a kiosk in the mall.

This question is related to unitary method problems.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Then, the cost of 5 cup of coffee is 5x.

Given that bill is under $20.

So the cost of 5 cup of coffee will be $20.

5x=20

x=20/5

x=4

Therefore,  the cost of each cup of coffee is $4.

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(5a - 6)(5a + 6)

The correct answer is D

There are four types of division are:

Now, According to the question:

Division is one of the four basic math operations with addition, subtraction, and multiplication. Division is an important operation because it is common in everyday life and helps people understand multiplication better. Division is splitting a group into equal parts. Division is used to split up a class into equal groups for a game or activity or even split a pizza into equal portions between a group of friends.

Dividend: The dividend is the number that is being divided in the division process. Divisor: The number by which the dividend is being divided by is called the divisor. Quotient: The quotient is a result obtained in the division process. Remainder: Sometimes, we cannot divide things exactly.

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Answer:

The 1 in the hundredths place is ten times bigger in value than the 1 in the thousandths place. They are also both behind the decimals.

Step-by-step explanation:

1/100 = 1/1000 x 10

The hip breadth of 95% of all male is 16.2 inches, which is greater than the mean of 14.8 inches with a standard deviation of 0.9 inches.

1. Calculate the Z-score for 95th percentile:

Z = (P95 - mean)/standard deviation

= (16.2 - 14.8)/0.9

= 2.44

2. Look up the Z-score in a Z-table to find the corresponding percentile:

95th percentile = 2.44

The hip breadth of 95% of all male can be calculated using the normal distribution. First, we must find the Z-score for the 95th percentile, which is calculated by subtracting the mean (14.8 inches) from the desired percentile (16.2 inches) and dividing by the standard deviation (0.9 inches). This gives us a Z-score of 2.44. We can then look this up in a Z-table to find the corresponding percentile, which is 95th percentile. Therefore, the hip breadth of 95% of all male is 16.2 inches.

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Answer:

The solution is: (-1,4)

Step-by-step explanation:

I used an online graph but you can replicate it onto paper

Purple is Y=-x+3

Black is Y=x+5

From 8 apples and 5 peaches, the probability for the first apple then peach fruit is 40/156.

What is probability?

Probability is defined as a number between zero to one for the analysis of random phenomena.

Given that there are 8 apples and 5 peaches in a basket.

Total Fruits = 13

For the first event, the probability of getting an apple is,

p1=8/13

Now, Total Fruits = 12

For the second event, the probability of getting peach is,

p2=5/12

The probability for both events is given below.

p=p1*p2 = (8/13)*(5/12) = 40/156

Hence we can conclude that the probability for the first apple then peach fruit is 40/156.

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The graph transformations are discussed below.

Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.

Given is the transformation of a graph.

A function transformation either "moves" or "resizes" or "reflects" the graph of the parent function. There are mainly three types of function transformations:

Transformation                Function                  Changes in Position/Size

Translation                 moves the curve                     Change in position

Dilation                Stretches or shrinks the curve     Change in the size

Reflection                   Flips the curve                      Change in position

                           and produces the mirror image.

Therefore, the graph transformations are discussed above.

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The minimum number of pears that each must pack is x = 12 pears.

We can start by using algebra to represent the problem.

Let x be the number of pears that Kendrick and Nick must pack.

We know that the total number of pear that Kendrick packs is 8 pear per crate * the number of crates he packs = 8x. Similarly, the total number of pears that Nick packs is 4 pears per crate * the number of crates he packs = 4x.

Therefore, the total number of pears that Kendrick and Nick must pack is 8x + 4x = 12x. We are given that they must pack the same total number of pears, so we can set this equal to x. Therefore, we have:

12x = x

So the minimum number of pears that each must pack is x = 12 pears. This means that Kendrick must pack 12 pears in 8 crates and Nick must pack 12 pears in 4 crates.

It could be also represented as:

Kendrick: 8 pear/crate * C crates = 12 pear

Nick: 4 pear/crate * C crates = 12 pear

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Given that f(x) is the square of x, there are no negative values in its range, which ranges from 0 to.

The answer to a polynomial equation with polynomial coefficients is a function, and that function is an algebraic function.

Linear, quadratic, cubic, polynomial, rational, and radical algebraic functions are some examples of the several types of algebraic functions.

The range of the function f(x) = x2 is higher than or equal to zero, and the domain of the function is the set of all real numbers (x can be anything).

A function that represents an upward-facing parabola is f(x) = x2.

Its range from - to - is its domain.

Given that f(x) is the square of x, there are no negative values in its range, which ranges from 0 to.

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The area of the front side of the fifty-cent piece is 48.06 mm².

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

Given, The front side of a circular area fifty-cent piece has a diameter of 30.61 mm.

We know, Radius is half of the diameter which is, (30.61/2) mm.

= 15.305 mm.

We also know the area of a circle is πr².

Therefore, The area of the front side of the fifty-cent piece is,

= π(15.305)² mm².

= 48.0577 mm².

= 48.06 mm².

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The roots of the quadratic equation 9 x 2 - 3 k x + k = 0 are equivalent. As a result, the needed values of k are 0 and 4.

Any equation featuring one condition that involves the unknown is cubed and no term in which it has been increased to a greater number is a quadratic equation.

This has the equation ax2 + bx + c = 0, where a = 9, b = -3k, and c = k.

If D=0, the solution will be implemented and will have real and equivalent roots.

Most typically, the quadratic equation is represented as ax2 + bx + c = 0. The coefficients are the recognized numbers a, b, and c, while x represents the undetermined.

Quadratic equations must be employed whether directly or indirectly in any field where speed, area, or profit must be calculated.

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The coordinate plane's formula is (x, y), where x denotes the x-axis and y denotes the y-axis.

A linear equation is a two-variable equation with a line as the graph.

A collection of points in the coordinate plane that are all solutions to the equation make up the graph of the linear equation.

If every variable has a real value, the equation can be graphed by placing enough points on the graph to identify a pattern, then connecting those points to include all of the points.

A linear equation must have at least two points in order to be graphed, however it's usually a good idea to utilize more.

Try to include zero as well as both positive and negative numbers when selecting your points.

The term "x-intercept" refers to the point where the graph crosses the x-axis, and the term "y-intercept" refers to the point where the graph crosses the y-axis.

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The total problems assigned over the weekend are 15.

In mathematics, a fraction is used to denote a portion or component of the total. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, while the denominator is the number at the bottom. The denominator specifies the total number of equal parts in the whole, whereas the numerator specifies the number of equal parts that were taken.

Let us suppose the total number of problems assigned = x.

Given that the problems solved on Saturday is 3/5 of her total questions. This is represented as:

(3/5) x

The remaining problems are:

1 - (3/5) x = (2/5) x

On, Sunday the problems solved are 1/3 of the remaining. This is represented as:

(1/3) (2/5) x

(2/15) x

The remaining problems are:

(1 - 1/3)(2/5 x) = (2/3) * (2/5) x = 4/15 x

Given that the final number of problems remaining are 4, that is:

(4/15) x = 4

x = 4 (15/4)

x = 15

Hence, the total problems assigned over the weekend are 15.

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Answer:

y=-2x+5

Step-by-step explanation:

To find the radius of the circular area, the organizers must divide 50,000 by pi and then multiply by 5. The result of this calculation is the amount of area needed, which can then be divided by pi to find the radius of the circular region, rounding to the nearest foot.

To find the radius of the circular area, the organizers should first calculate the amount of area needed to accommodate each person in the field. This is done by dividing the total number of people (50,000) by pi and then multiplying by 5, which represents the 5 square feet of space allotted to each person. The result of this calculation is the amount of area needed to fit all 50,000 people. Next, the organizers should divide this area by pi to calculate the radius of the circular region. Finally, they should round the result to the nearest foot. This will give them the radius of the circular area that is needed to fit all 50,000 people in the field.

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Step-by-step explanation:

(f○g)(x) = f(g(x))

it simply means that we put the expression of g(x) into ask places of x in f(x).

(f○g)(x) = g(x)² + 3

therefore,

g(x)² + 3 = 9x² - 12x + 7

g(x)² = 9x² - 12x + 4 = (a + b)² = a² + 2ab + b²

9x² = a² tells us that a = ±3x

4 = b² tells us that b = ±2

which signs of a and b do we need ?

-12x = 2ab gives us the answer

-6x = ab

that means the signs need to be opposite and we have 2 possible solutions

g(x) = 3x - 2

or

g(x) = -3x + 2

The types of solutions for an equation depend on the type of equation, but in general, the most common types of solutions are: single solution, no solution and infinite solutions.

In mathematics, particularly in algebra, a solution of an equation is a value or a set of values that, when substituted into the equation, makes it a true statement.

Single solution: An equation has a single solution when it has exactly one value that satisfies the equation. This solution is unique and it can be found by solving the equation for the variable.

No solution: An equation has no solution when it is impossible to find a value that satisfies the equation. This happens when the equation is contradictory or inconsistent. For example, the equation "2x = 5x + 1" has no solution because no value of x can make the equation true.

Infinite solutions: An equation has infinite solutions when any value of the variable satisfies the equation. This happens when the equation is an identity, meaning it is true for all values of the variable. For example, the equation "2x + 0 = 2x" has infinite solutions because any value of x will make the equation true.

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The round plate in the problem has a surface area of 63.754 square inches.

The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

Given, A circular plate has a circumference of 28.3 inches.

Since circumference of a circle = 2*3.14 * r

Where r is the radius

Thus,

circumference  = 28.3

6.28 * r = 28.3

r = 4.506

Radius of circle = 4.506

Since the area of the circle = 3.14 * r * r

Thus,

Area of given circle = 3.14 * 4.506 * 4.506

Therefore, the Area of the given Circular plate is 63.754 square inches.

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Answer:

$633.36

Step-by-step explanation:

10 2/5 % = 10.4% = 0.104

10 2/5 % of $6090 = 0.104 × $6090 = $633.36

Answer:

A = 28.8cm²

Step-by-step explanation:

multiply 9.6 by 6.0

= 57.6

divide 57.6 by 2

= 28.8