Simplify the expressions with rational exponents 25 1/2 / 27 1/3

Therefore, the area of the square with coordinates at (–5, 3), (1, 1), (–5, –1), and (–1,3) is 40 square units.

A coordinate is indeed a geometry technique that uses one or more quantities or coordinates to better be able to watch points as well as other geometrical items on a continuum, such as Ellipsoid. A point or object's coordinates on the double plane are indeed a combination of integers. The y and x dimensions of a point on a plane surface are two numbers that identify its location. a collection of numbers that represent exact coordinates.

Here,

To find the area of a square with these coordinates, we need to find the length of one of its sides first. We can use the distance formula to find the length of the side between two adjacent vertices:

Side AB: √((1-(-5))² + (1-3)²) = √(36 + 4) = √(40) = 2√(10)

Side BC: √((-5-1)² + (-1-1)²) = √(36 + 4) = √(40) = 2√(10)

Since the opposite sides of a square are equal, we know that the other two sides also have a length of 2sqrt(10).

Now we can use the formula for the area of a square, which is side squared. In this case, the area is:

Area = (2√(10))² = 4 × 10 = 40

Therefore, the area of the square with coordinates at (–5, 3), (1, 1), (–5, –1), and (–1,3) is 40 square units.

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Answer: a. The rate of change in this situation represents the average number of pages read per minute. From the table, it can be seen that the rate of change is constant, as the ratio of the change in y (pages) to the change in x (minutes) is always the same.

For example, when x increases from 0 to 5, y increases from 0 to 25, so the rate of change is 25/5 = 5 pages per minute.

b. To represent the total number of pages as it relates to the number of minutes read, a linear equation can be used. The slope of the line represents the rate of change, and the y-intercept represents the number of pages read when x is equal to 0 (minutes).

Using the rate of change from the above example (5 pages per minute), the equation can be written as y = 5x + 0, where x represents the number of minutes and y represents the total number of pages read.

Step-by-step explanation:

The median of this data set is 30. If the largest observation (50) were deleted, the median would become 25, which is a 5 unit change.

Here's a data set with five observations for which the median would change significantly if the largest observation were deleted:

Observation 1: 20

Observation 2: 25

Observation 3: 30

Observation 4: 35

Observation 5: 50

The median of this data set is 30. If the largest observation (50) were deleted, the median would become 25, which is a 5 unit change. This is a significant change because the median is a measure of central tendency that shows the midpoint of a set of data and is sensitive to outliers. By removing the largest observation, the data set is no longer skewed towards larger values, and the median changes to reflect this.

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The slope-intercept form of the lines are given below.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂),

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

Given:
A). Line 5 passes through (0, 5) and (10, 0),

then the equation of the line is,

y - 5 = -1/2(x)

y = -x/2 + 5

B). Line 6 passes through (0, 7) and (1, 7),

then the equation of the line is,

y = 7

C). Line 7 passes through (0, 0) and (9, 3),

then the equation of the line is,

y = 3x

D). Line 8 passes through (-1, 0) and (0, 1),

then the equation of the line is,

y = x + 1

E). Line 9 passes through (-1, 1) and (0, -1),

then the equation of the line is,

y = -2x - 3

F). Line 10 passes through (0, 2) and (-0.5, 8),

then the equation of the line is,

y = -12x + 24

G). Line 11 passes through (4, 0) and (4, 1),

then the equation of the line is,

x = 4

H). Line 12 passes through (0, 0) and (-3, 1),

then the equation of the line is,

y = (-1/3)x

Therefore, all the equations are given above.

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The point where the horizontal axis and the vertical axis intersect in a coordinate plane is called the ORIGIN.

Given the question below:

What is the intersection of the vertical and horizontal lines in a coordinate plane?

A coordinate plane is a plane formed by a horizontal number line (the x-axis) and a vertical number line (the y-axis) that intersect at a point called the origin.

The vertical intercept (y-intercept) is found by evaluating the function when the input variable, x, is 0 and is always the same as the constant b. It can be thought of as the original value of the function. The horizontal intercept (x-intercept) is the value of the variable x when the function value is 0.

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Step-by-step explanation:

a1) Through how many radians does Jamie turn in 99 minutes?

One revolution is equal to 2 * pi radians, so 1.08 revolutions is equal to 1.08 * 2 * pi radians.

In 99 minutes, the restaurant rotates for 99 / 60 = 1.65 hours.

Therefore, the angle Jamie turns through in 99 minutes is 1.65 * 1.08 * 2 * pi radians.

a2) Exact answer:

angle = 1.65 * 1.08 * 2 * pi radians

b1) Approximate answer (rounded to 3 decimal places):

angle = 11.045 radians

b2) How far does Jamie move in 99 minutes?

The distance Jamie moves can be calculated using the formula:

distance = angle * radius

where radius is Jamie's distance from the center of the restaurant, which is 22.2 meters.

b2) Exact answer:

distance = 11.045 * 22.2 meters

b2) Approximate answer (rounded to 1 decimal place):

distance = 245.3 meters

The equilibrium point for the market is (102.54, 351.81).

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

Given that, a group of retailers will buy 104 televisions from a wholesaler if the price is $350 and 144 if the price is $300.

Here, (104, 350) and (144, 300)

Now, slope (m)=(300-350)/(144-104)

= -50/40

= -1.25

Substitute m=-1.25 and (x, y)=(104, 350) in y=mx+c, we get

350=-1.25(104)+c

350=-130+c

c=480

Substitute m=-1.25 and c=480 in y=mx+c, we get

y= -1.25x+480

The wholesaler is willing to supply 68 if the price is $300 and 148 if the price is $390.

The coordinate points are (68, 300) and (148, 390)

Slope (m)= (390-300)/(148-68)

= 90/60

= 3/2

= 1.5

Substitute m=1.5 and (x, y)=(68, 300) in y=mx+c, we get

300=1.5×68+c

c=198

Substitute m=1.5 and c=198 in y=mx+c, we get

y=1.5x+198

So, the solution is (102.54, 351.81)

Therefore, the equilibrium point for the market is (102.54, 351.81).

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Answer:

Below

Step-by-step explanation:

The two angles labeled are alternate angles of a pair of parallel lines crossed by a transversal ( the diagonal) ....so they are equal

x+ 18 = 4x+15    Solve for x

3 = 3x   ====>    x = 1    

Now....x+18  angle and angle ABD are complementary....the add to 90 °

   so   x+18    + ABD   = 90°        x = 1 from above....so

            1 + 18 + ABD = 90

               19  + ABD = 90

                        ABD = 71 °

Step-by-step explanation:

Lance makes 8.5 an hour

He works for 40 hours

This means he earns 8.5 40 times

So 8.5 x 40

Which equals 340

This means lance earned $340.

The statement that correctly describes whether this is a theory or a law is C. It is a theory, because it explains the cause of the dinosaur extinction.

A law is a statement that describes a general observation or a relationship that has been consistently proven through experimentation and evidence.  A theory, on the other hand, is a more comprehensive explanation that helps to understand a wide range of observations and experimental results.

The excerpt spoke on how a meteorite hitting Earth led to the extinction of the dinosaurs. However, this is not a law as it aims to explain why dinosaurs died out.

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The full question is:

A meteorite hit Earth sixty five million years ago​. Scientists have found a high concentration of iridium in the sedimentary clay layer from this time period. Iridium is very rare in Earth’s crust, but it is abundant in meteorites. Scientists believe this impact caused the extinction of the dinosaurs. Which of these statements correctly describes whether this is a theory or a law and why?

A. It is a law, because it includes a numerical analysis.

B. It is a law, because it explains all causes of animal extinction.

C. It is a theory, because it explains the cause of the dinosaur extinction.

D. It is a theory, because it shows regular patterns from a generalization of the data.

Answer:

Below

Step-by-step explanation:

a vertical line is just  X = ......

So for this one through the point  7,-7     just      x = 7

(a) The zero vector in the space of degree three polynomials is the polynomial with zero coefficients, i.e., p(x) = 0 for all x.

In mathematics, a vector is an ordered collection of numbers, typically referred to as scalars.

(b) The zero vector in the space of matrices is the matrix with all elments equal to zero, i.e., A = [0, 0, ..., 0] where A is an m x n matrix.

(c) The zero vector in the space of continuous functions is the constant function with value zero, i.e., f(x) = 0 for all x.

(d) The zero vector in the space of real-valued functions of one natural number variable is the function that maps every natural number to zero, i.e., f(n) = 0 for all natural numbers n.

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Answer:

12

Step-by-step explanation:

there are 7 days in a week so just simply divide 84 by 7 :)

Answer:

two plus two equals five

Step-by-step explanation:

Answer:

1723.9 mb

Step-by-step explanation:

Essentially, the question is asking "281 is 16.3% of what number.

Thus, we can find the percentage of a number using the formula

[tex]Px=y[/tex], where P is the percentage.  In context of the question, x is how many megabytes have already downloaded and y is 281.

We simply need to solve for x and round to the nearest:

[tex]\frac{16.3}{100}x=281\\ \\0.163x=281\\x=1723.92638=1723.9[/tex]

There is a total of 120 workers at the company

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

Using the above as a guide, we have the following:

Number of workers = 96/80%

Evaluate the quotient

Number of workers = 120

Hence, the workers are 120

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Answer:

P = C(55,845, 40) / C(56,142, 40) = (55,845!) / (40! * (55,845 - 40)!) / (56,142!) / (40! * (56,142 - 40)!)

Step-by-step explanation:

To find the probability that none of the 40 subjects randomly selected left the treatment center against medical advice, we can use the formula for combinations. The number of ways to choose 40 subjects out of 55,845 that did not leave against medical advice is given by C(55,845, 40), which can be calculated as:

C(55,845, 40) = 55,845 choose 40 = (55,845!) / (40! * (55,845 - 40)!)

The probability that none of the 40 subjects randomly selected left the treatment center against medical advice is given by the number of ways to choose 40 subjects out of 55,845 that did not leave against medical advice, divided by the number of ways to choose 40 subjects out of 56,142 total subjects:

P = C(55,845, 40) / C(56,142, 40) = (55,845!) / (40! * (55,845 - 40)!) / (56,142!) / (40! * (56,142 - 40)!)

the value of a will be 17 for the given set of data.

The properties of the triangle are: The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is greater than the length of the third side. In the same way, the difference between the two sides of a triangle is less than the length of the third side.

Given, KLH is an equilateral triangle.

Since we all know that all angles of an equilateral triangle are equal.

Also From the property of  the triangles:

Sum of all angles = 180°

∠K + ∠L + ∠H = 180°

3 * (4a -8) = 180

4a -8 = 60

4a = 68

a = 17

Therefore, the value of a will be 17 for the given set of data.

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[tex]17\frac{1}{2}[/tex] cups of flour we need to make three of each cake.

A fraction represents a part of a whole.

Given that the first recipe calls for 2 1/2 cups of flour and the second one calls for 3 1/3 cups of flour.

We need to make three of each cakes.

[tex]2\frac{1}{2}[/tex] cups x 3 = [tex]7\frac{1}{2}[/tex] cups of flour for the first recipe.

And for the second recipe [tex]3\frac{1}{3}[/tex] cups x 3 = 10 cups of flour.

So in total  [tex]7\frac{1}{2}[/tex]  cups + 10 cups = [tex]17\frac{1}{2}[/tex] cups of flour.

Hence,  [tex]17\frac{1}{2}[/tex] cups of flour we need to make three of each cake.

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The equation [tex]\frac{x}{x+8} = -\frac{1}{6}[/tex] is not defined at x = - 8.

Suppose we have an ordered pair (x, y) then the domain of the function is the set of values of x and the range is the set of values of y for which x  is defined.

Given, An equation [tex]\frac{x}{x+8} = -\frac{1}{6}[/tex].

We know the denominator of a rational expression can not be equal to zero.

Therefore, x + 8 ≠ 0 ⇒ x ≠ - 8.

So, The restriction of the expression is at - 8 and it is undefined at - 8.

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The probability that a randomly selected Atlantic cod has a length of 53.68 cm or less is given by the equation P ( x > 38.68 ) = 0.99865

The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.

The Z-score is calculated using the formula:

z = (x - μ)/σ

where z: standard score

x: observed value

μ: mean of the sample

σ: standard deviation of the sample

Given data ,

Let the probability that a randomly selected Atlantic cod has a length of 53.68 cm or less be represented as P

Now , the equation will be

The observed value of x = 38.68 cm

The mean of the sample μ = 49.9 cm

The standard deviation of the sample σ = 3.74 cm

Now , z-score is calculated using the formula:

z = (x - μ)/σ

Substituting the values in the equation , we get

z = ( 38.68 - 49.9 ) / 3.74

z = -3

Now ,the p value from the z table is

P ( x > 38.68 ) = 1 - P ( x < 38.68 )

P ( x < 38.68 ) = 0.0013499

P ( x > 38.68 ) = 0.99865

And , the probability is P ( x > 38.68 ) = 0.99865 = 99.865 %

Hence , the probability is 84.392 %

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Note that the system of linear inequalities that match the graph is: Option D  . -x + y ≤ 2; x + y ≤ 2; x + y < 2-

A system of linear inequalities is similar to a system of linear equations, except that it is made up of inequalities rather than equations. To represent scenarios with various restrictions, systems of linear inequalities are utilized.

A system of linear equations is a group of two or more linear equations that include the same variables in mathematics. Linear equations are defined as first-order equations when the maximum power of the variable is 1. One, two, or three variables can be used in linear equations.

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The value of x in the given equation -3x+2=4x+2 is x=0.

Two or more expressions with an Equal sign is called as Equation.

The given equation is -3x+2=4x+2

Minus three times of x plus two equal to four times of x plus two.

-3x+2=4x+2

Add 3x on both the sides

2=4x+3x+2

x=0

Hence, the value of x in the given equation -3x+2=4x+2 is x=0.

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The measure of the angle m∠BDE obtained using the exterior angles theorem is 86°. The correct option is therefore;

86°

The exterior angle theorem states that the angle formed by two secants, a secant and a tangent or two tangents of a circle is equivalent to the half of the difference of the arcs intercepted.

The specified interior angle of the triangle ΔOBJ, ∠J = 47°

The segments OJ and BO are radial lengths of the circle, therefore;

JO ≅ BO

JO = BO (definition of congruency)

The triangle ΔOBJ is an isosceles triangle (definition of isosceles triangles)

∠J ≅ ∠B (Base angles of an isosceles triangle)

∠B = ∠J = 47°

m∠BOJ = 180°- 47° - 47° = 86° (angle sum property of a triangle)

Whereby EJ is a diameter of the circle, with center at O, we get;

∠BOJ and ∠BOE are linear pair angles, therefore;

m∠BOJ + m∠BOE = 180° (Linear pair angles are supplementary)

m∠BOE = 180° - m∠BOJ

m∠BOE = 180° - 86° = 94°

The exterior angle theorem indicates that we get;

m∠BDE = Half the difference of the intercepted arcs BJE and BE, found as follows;

[tex]m\widehat{BE}[/tex] = m∠BOE = 94°

[tex]m\widehat{BJE}[/tex] = 360° - m∠BOE = 360° - 94° = 266°

[tex]m\widehat{BJE}[/tex] = 266°

m∠BDE = ([tex]m\widehat{BJE}[/tex] - [tex]m\widehat{BE}[/tex])/2

m∠BDE = (266° - 94°)/2 = 86°

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Answer:

24

Step-by-step explanation:

The rate of change over a function f(x) is given by its first derivative
[tex]f'(x) = \dfrac{d}{dx} (f(x))[/tex]

[tex]\mathrm{Differentiating\; f(x) = 3x^2- 5 \;w.r.t \;x : }[/tex]

[tex]\dfrac{d}{dx}\left(3x^2-5\right) = \dfrac{d}{dx}\left(3x^2\right)-\dfrac{d}{dx}\left(5\right)\\\\= 6x - 0\\\\= 6x\\\\[/tex]

[tex]f'(x) = 6x\\\\[/tex]

Over the interval [2, 6] the average rate of change would be  [tex]f'(6) - f'(2)[/tex]
[tex]f'(6) = 6 \cdot 6 = 36\\\\f'(2) = 6\cdot 2 = 12\\\\f'(6) - f'(2) = 36 - 12 = 24\\\\[/tex]

Average rate of change of the function f(x)=3x²-5 over the interval [2,6]

= 24

The line tangent to the graphs are y = 77 and y = -74/49(x - 2) + [f(2)/g(2)].

Function (1)

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

y = 4x+ 3 and y = 6x - 5

At x = 2, we have

y = 4(2) + 3 and y = 6(2) - 5

So, we have

y = 11 and y = 7

So, we have:

Tangent line: y = 11 * 7

y = 77

Function 2

Here, we have

The derivative of the quotient of two functions:

(d/dx)(f(x)/g(x)) = (g(x) * df/dx - f(x) * dg/dx) / g(x)^2

Substituting the tangent lines for f and g, we get:

(d/dx)(f(x)/g(x)) = (6x - 5 * 4 - (4x + 3) * 6) / (6x - 5)^2

Evaluating at x = 2, we get:

(d/dx)(f(x)/g(x)) = (-16 - 18) / (-3)^2 = -74/49

Hence, the line tangent to the graph of y = f(x)/g(x) at x = 2 is y = -74/49(x - 2) + [f(2)/g(2)].

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It took the 26 offshore oil workers an average of 94.85 seconds to complete the simulated escape exercise, with a variance of 828.19 and a standard deviation of 28.79 seconds.

The data set consists of 26 offshore oil workers who took part in a simulated escape exercise. The data set measures the time (in seconds) it took for each worker to complete the escape. To analyze the data, we can calculate the mean, variance, and standard deviation.

The mean is calculated by adding up the time for each worker and dividing the sum by the total number of workers (26). This results in a mean of 94.85 seconds.

The variance is calculated by subtracting the mean from each individual time, squaring the results, adding the squared results together, and dividing the sum by the total number of workers (26). This results in a variance of 828.19.

The standard deviation is calculated by taking the square root of the variance. This results in a standard deviation of 28.79 seconds.

In conclusion, it took the 26 offshore oil workers an average of 94.85 seconds to complete the simulated escape exercise, with a variance of 828.19 and a standard deviation of 28.79 seconds.

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The measure of the smallest angle of the triangle would be = 33°

The total angle measurement of a triangle is a total of 180°.

That is ;

180° = 90 + (4x-7)° + (3x-15)°

180 = 90-7-15+4x+3x

180 = 90-22+7x

180 = 68+7x

180-68 = 7x

7x = 112

X= 112/7

X= 16

substitute X=16 into both angles (4x-7)° and (3x-15)° to know the smallest.

= 4(16)-7

= 64-7

= 57°

and;

= 3(16)-15

= 48-15

= 33°

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