Simplify rational expressi

Simplify the following rational expression.

11k

55k^2+ 22k

Part A - The area of the deck is approximately equal to 691.150 square feet.

Part B - The deck requires 3.379 gallons of weather treatment.

Part C - The weather treatment have a cost of $ 121.48.

In this problem we must find the area of the deck around the pool, how many gallons of weather treatment are required and how much is needed to.

Part A - The area of the deck is a circular corona, whose formula is:

A = π · (R² - r²)

Where:

If we know that r = 6 ft and R = 16 ft, then the area of the deck is:

A = π · [(16 ft)² - (6 ft)²]

A = 220π ft²

A ≈ 691.150 ft²

Part B - If we know that a gallon is effective for an area of 204.5 square feet, the number of gallons can be determined by cross multiplication:

x = (691.150 ft² / 204.5 ft²) × 1

x = 3.379

A number of 3.379 gallons are required for weather treatment.

Part C - The cost of the number of gallons (C), in monetary units, is equal to the product of the number of gallons (n), in gallons, and unit cost (c), in monetary units per gallon:

C = n · c

If we know that n = 3.379 gal and c = $ 35.95 / gal, then the cost of the number of gallons is:

C = (3.379 gal) · ($ 35.95 / gal)

C = $ 121.48

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A parallel gateway with three sequence flows would have three tokens leaving the gateway - True.

Reason: Each path has a token.

A parallel gateway can synchronize or merge the parallel flows once more, or split the sequence flow into two or more parallel flows. Awaiting the arrival of all incoming sequence flows is synchronization. After that, the flow resumes.

Instead, two concurrent jobs in a business flow are represented by a parallel gateway. In a UML activity diagram, it is equivalent to a fork. The business process in the example below uses a parallel gateway because the company is trying to have its cake and eat it too. With Lucid chart, diagramming is quick and simple.

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The smallest integer that satisfies the inequality is 110

The least number is calculated by first generation g the inequality equation

The statement "A number increased by 15 is greater than 124" is written in an equation form, assuming the number is x

x + 15 > 124

Solving for x with the generated expression

x + 15 > 124

isolating x

x + 15 - 15 > 124 - 15

x > 124 - 15

x > 109

since x is greater than 109 the least integer greater than 109 is 110

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Yes, this relationship is a Funtion.

The relationship between the no of gallons of milk purchased and the total cost can be represented by this equation:
y = 3.5x

where y is the total cost  and x represents the number of gallons of milk purchased. A function is a collection of ordered pairs (x, y) with exactly one value of y for each value of x. for each input (x), just one output (y) is created.

In this situation, there is only one equivalent value of y for each value of x .We may see this by putting different value of x into the equation and get ing a different result for y.
For example, when x = 1, y = 3.5 ×1 = 3.5
when x = 2, y = 3.5 × 2 = 7
when x = 3, y = 3.5 × 3 = 10.5
and so on.

So, the relationship between the number of gallons of milk purchased and the total cost is a Funtion.

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The average velocity is 94.6km / hour

Average velocity is defined as the change in position or displacement (∆x) divided by the time intervals (∆t) in which the displacement occurs. The average velocity can be positive or negative depending upon the sign of the displacement. The SI unit of average velocity is meters per second (m/s or ms-1).

therefore average velocity = change in displacement / change in time

change in displacement = 485 - 154 = 331 km

change in time = 4:30-1:00 = 3 hours 30minutes = 3½ hrs

average velocity = 331/3.5

= 94.6km/hour

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No, we cannot conclude that studying longer hours leads to higher GPAs based on this survey.

This survey only provides us with the average GPAs and average hours per week spent studying for a sample of 218 undergraduates from Duke University who took an introductory statistics course in spring 2012. This is not enough information to draw a conclusion about the correlation between hours of study and GPA. To do this, we would need to look at the correlation between the two variables. To calculate the correlation, we would need the individual data points of the GPAs and hours of study for each respondent. We could then calculate the Pearson correlation coefficient and the significance of the correlation. This would provide us with a more definitive answer to our question.

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1. The equation when Buggo crawls did 28 minutes at a rate of -2 centimeters per minute will be x = -2 × 28

2. The equation when Buggy slides for 3.2 seconds at -8.1 millimeters per second will be: y = -8.1 × 3.2

3. The equation when Buggum creeps for 3.5 seconds and finishes at -28.5 centimeters will be 3.5x = -28.5

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

The equation when Buggo crawls did 28 minutes at a rate of -2 centimeters per minute will be:

Let x = total centimeters

x = -2 × 28

The equation when Buggy slides for 3.2 seconds at -8.1 millimeters per second will be:

Let y = ital millimeters

y = -8.1 × 3.2

The equation when Buggum creeps for 3.5 seconds and finishes at -28.5 centimeters will be 3.5x = -28.5

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Answer:

see explanation

Step-by-step explanation:

the total cost is dependent on the number of rides she takes, then

the number of rides is the independent variable and the total cost is the dependent variable.

----------------------------------------------------------------------------

(2)

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given m = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (- 4, 2 ) into the partial equation

2 = - 2(- 4) + c = 8 + c ( subtract 8 from both sides )

- 6 = c

y = - 2x - 6 ← equation of line

--------------------------------------------------------------------------

(3)

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, 6 ) and (x₂, y₂ ) = (9, - 2 )

m = [tex]\frac{-2-6}{9-(-3)}[/tex] = [tex]\frac{-8}{9+3}[/tex] = [tex]\frac{-8}{12}[/tex] = - [tex]\frac{2}{3}[/tex] , then

y = - [tex]\frac{2}{3}[/tex] x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (9, - 2 )

- 2 = - [tex]\frac{2}{3}[/tex] (9) + c = - 6 + c ( add 6 to both sides )

4 = c

y = - [tex]\frac{2}{3}[/tex] x + 4 ← in slope- intercept form

multiply through by 3 to clear the fraction

3y = - 2x + 12 ( add 2x to both sides )

2x + 3y = 12 ← equation in standard form

----------------------------------------------------------------------------

(4)

linear function has the form

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 200) and (x₂, y₂ ) = (2, 500) ← 2 ordered pairs from the table

m = [tex]\frac{500-200}{2-0}[/tex] = [tex]\frac{300}{2}[/tex] = 150

the ordered pair (0, 200 ) indicates that c = 200

y = 150x + 200 ← linear equation

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(5)

money left over f(x) is

f(x) = initial amount - expenses

    = 125 - (15 + 40 + 5x)

    = 125 - (55 + 5x)

    = 125 - 55 - 5x

    = 70 - 5x

that is

f(x) = - 5x + 70

The ratio table is presented below and a total of 4 cases of possible.

Given that,

s: the number of cans of soup concentrate

w: the number of cans of water

Ratio: 1:5

so w = 5s

Therefore,

s        w            Total cans of heated soup to serve

1          5                          6

2         10                         12

3         15                          18

4         20                         24

Therefore, a total of four cases are possible to make up to 24 total cans of heated soup to serve at the party.

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1 quart equals 2 pints, which equals 4 cups, so 3 quarts equals 12 cups. Dividing the ice cream among 15 people means each gets 1 3/12 cup(s).

Nick has 3 quarts of ice and he wants to split it with 15 members of the team.

To solve this, we have to convert quarts to cups. We have that:

1 quart = 2 pints

and 1 pint = 2 cups

This means that:

1 quart = 2 × 2 cups

1 quart = 4 cups

So, 3 quarts will be:

3 quarts=3 × 4

3 quarts =12

Therefore, dividing the ice cream among 15 people would mean that we have to divide 12 cups by 15 people.

That is:

= 15/12

= [tex]1\frac{3}{12}[/tex]

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The complete question is:

Nick is splitting 3 quarts of ice cream with 15 members of the team. If the ice cream is split evenly, how many cups will each person get?

Explain 1 quart equals _ pints, which equals _ cups, so 3 quarts equals _ cups. Dividing the ice cream among _ people means each gets _ cup(s).

Answer:

  (x, y) = (0.5, -3)  or  (8, 12)

Step-by-step explanation:

You want x and y such that 8, 2x, 2y is an arithmetic sequence and 2x, 2y, 36 is a geometric sequence.

The difference of successive terms is a constant for an arithmetic sequence.

  2x -8 = 2y -2x

  2x -4 = y . . . . . . . . divide by 2, add x

The ratio of successive terms is a constant for a geometric sequence.

  2y/2x = 36/2y

  y² = 18x . . . . . . . . . simplify and cross multiply

We can substitute the expression for y from the arithmetic sequence into the expression for y² in the geometric sequence:

  (2x -4)² = 18x

  4x² -16x +16 = 18x . . . . . expand

  2x² -17x +8 = 0 . . . . . . . divide by 2, subtract 9x

  (2x -1)(x -8) = 0 . . . . . . . factor

The values of x that make the factors zero are x = 1/2 and x = 8. The corresponding values of y are 2{1/2, 8} -4 = {1, 16} -4 = {-3, 12}.

The values of x and y are (1/2 and -3) or (8 and 12).

__

Additional comment

The two sequences are ...

  8, 1, -6  and  1, -6, 36 — difference of -7, ratio of -6

or

  8, 16, 24  and  16, 24, 36 — difference of 8, ratio of 3/2

Answer: I think x=22.

Step-by-step explanation:

If you look at half of the circle you can see a line in it right? This line measures to 180 degrees. This is a right triangle. Usually triangles have a little box in the corner to tell you that is it indeed a right triangle. I don't know why this one doesn't. anyways, if you add 90+68, you get 158. Now you need to get to 180 by simply adding 22. Thats why i think the answer is 22. Sorry if im wrong.

The final sales price is equal to $200.

In Mathematics, a percentage simply refers to any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.

In order to decrease 250 dollars by 20 percent (20%), we would have to multiply the given amount of money by 80 percent (80%) because it denotes a percentage decrease:

Percentage decrease = 250 × 80/100

Percentage decrease = 250 × 0.8

Percentage decrease = $200.

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The probability for the question as per the information that has been provided, can be solved in the following manner:

a) Probability for picking an all men committee

P = picking a Male probability

= 99/1715

Now, P = picking a female probability

= 1616/1715

The number of 77-member committee is Binomial [1715,77]

The number of 77-member committee being male is Binomial [99,77]

The probability of 77 men committee is Binomial [1715,77] / Binomial [99,77] or 99C77/1715C77

b) Probability for picking an all women committee

P = picking a Male probability

= 99/1715

Now, P = picking a female probability

= 1616/1715

The number of 77-member committee is Binomial [1715,77]

The number of 77-member committee being women is Binomial [1616,77]

The probability of 77 men committee is Binomial [1715,77] / Binomial [1616,77] or 1616C77/1715C77

c) Probability for picking 44 men and 33 women

Desired set is 44 men and 33 women, which can be done in 99C44 and 1616C33 ways.

So, P(44 men and 33 women) = 99C44 × 1616C33 / 1715C77

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The side length that could be a right triangle are

Applying Pythagoras theorem, for each side length we solve for the longest side in each case assuming the longest side is x

Using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

checking for 4 7 8

let x be the required distance

x² = 4² + 7²

x² = 16 + 49

x² =  65

x = √65

this is not a right triangle

checking for 6 8 10

let x be the required distance

x² = 6² + 8²

x² = 36 + 64

x² =  100

x = √100

x = 10

this is a right triangle

checking for 5 12 13

let x be the required distance

x² = 5² + 12²

x² = 25 + 144

x² =  169

x = √169

x = 13

this is a right triangle

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The amount of trace element collected by Owen is 59.3 g.

To calculate the amount of trace element collected by Owen, we first need to find the volume of the container. Given the radius of 6.7 cm and the height of 13.3 cm, the volume of the cylinder is given by:

V = π * r^2 * h = π * (6.7)^2 * 13.3 = 615.96 cm^3

Since there are 0.097 grams of the trace element per cubic centimeter of water, the amount of trace element in the container can be calculated as:

m = V * 0.097 g/cm^3 = 615.96 cm^3 * 0.097 g/cm^3 = 59.32 g

Rounding to the nearest tenth, the answer is 59.3 g.

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If U and V are orthogonal then the magnitude of U times V will be U.V = 0 or |UxV| = uv.

U and V are two orthogonal vectors.

since the angle between them is θ = 90⁰

let u and v be the magnitudes of the vectors U and V respectively.

so first dot-product: If two non-zero vectors are orthogonal than the dot product of these vectors will be zero. Dot product of two vectors is expressed by:

U.V = uv cosθ

since these vectors are orthogonal so,

U.V = uv cos90⁰ = 0

And Cross-product: Magnitude Cross product of two orthogonal vectors will be equal to product of magnitude of these vectors.

|UxV| = uv sin θ

|UxV| = uv sin 90⁰ = uv

Therefore, U.V = 0, |UxV| = uv.

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The points (2,2) and (-2,2) are both solutions to the equation y=2.

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The solutions to the x and y intercepts are;

1) The slope will be positive.

2) The student is incorrect because (0, 5) is not the x-intercept.

3) The point at which the graph crosses the x axis is; x = 2

4) The point at which the graph crosses the y axis is; y = 6

5) x-intercept is x = 4 and the y-intercept is; y = 2

6) The x-intercept is x = 6 and the y-intercept is; y = 2

7) The x-intercept is x = 2 and the y-intercept is; y = 10

1) The formula for the slope of a graph is;

Slope = Change in y value/change in x value

Thus, if both x and y intercepts are negative, then the slope will be positive.

2) The equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

The equation can be rewritten as;

y = -¹/₂x + 5

At y =0,

0 = -¹/₂(x) + 5

x = 8

Thus, (0, 5) is not the x-intercept.

3) The point at which the graph crosses the x axis is the x-intercept which is when y = 0. Thus;

2x + 0 = 4

2x = 4

x = 2

4) The point at which the graph crosses the y axis is the y-intercept which is when x = 0. Thus;

3(0) + y = 6

y = 6

5) 2x + 4y = 8

x-intercept; 2x + 4(0) = 8

x = 4

y-intercept; 2(0) + 4y = 8

y = 2

6) x + 3y = 6

x-intercept; x + 3(0) = 6

x = 6

y-intercept; 0 + 3y = 6

y = 2

7) 5x + y = 10

x-intercept; 5x + 0 = 10

x = 2

y-intercept; 5(0) + y = 10

y = 10

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Cross multiplying will help us identify the variable if it is the same variable that is present on both sides of the equation. Let's explain with the use of examples. Solve X/5 = 5/X, for instance.

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Answer by solving the expression 35 /2 using different methods are:

a. Area model : 35 /2  can be expressed as 17. 5 + 17.5 .(attached figure)

b. Long division method : 35 /2 = 17 + 1/2

c. Distributive property expressed as 35/2 = ( 34 + 1 ) × 1/ 2.

a. Area model.

Expression 35 /2 solved by area model is attached in the figure.

One part of 35 is divided into two parts each of 17.5 .

17.5 + 17.5 = 35

b. Long division.

How many 2's are there in 3

Answer is 1.

3−1⋅2=3−2=1

Write down the next digit of the dividend.

How many 2's are there in 15

Answer is 7

15−7⋅2=15−14=1.

( 35 /2 ) = 17 + ( 1/2)

c. Distributive property

35 /2

= ( 34 + 1 ) × 1/ 2

= 34 /2 + 1 /2

= 17  + 1 /2

= 17 + 0.5

= 17.5

Therefore, the solution of 35/2 using different methods are:

a. Using area model : 17.5 + 17.5  represent 35/2.

b. long division : 35 /2 = 17 + 1/2

c. Distributive property: 35/2 = ( 34 + 1 ) / 2

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Since John cannot make a negative number of pies or cobblers, the additional constraints that exist on the variables include the following:

B. x ≥ 0.

   y ≥ 0.

In order to write an equation that model this situation, we would assign a variable to the number of pies John makes and the total number of cobblers John makes respectively, and then translate the word problem into algebraic equation as follows:

However, it should be noted that John cannot make a negative number of pies or cobblers and as such, the number of pies he makes must be greater than or equal to zero (0) such as 0 pies, 1 pies, 2 pies, 3 pies, 4 pies, etc. Similarly, the aforementioned constrain applies to the number of cobblers John makes.

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The width of rectangular prism shaped Brandon's flower bed is 9 meters.

As per the known information, the formula to calculate volume of rectangular prism is -

Volume of rectangular prism = length × width × height

Keep the values in formula to find the volume of rectangular prism

405 = 15 × 3 × width of rectangular prism

Performing multiplication on Right Hand Side of the equation

405 = 45 × width of rectangular prism

Rewriting the equation

Width of rectangular prism = 405/45

Performing division

Width of rectangular prism = 9 meters

Thus, the width is 9 meters.

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Partial products can be used to multiply two or more numbers.

6 bags × cat food cost

The area of the circular figure which is the top of a can drink with a diameter of 3 inches is about 7.065 square inches

A circular figure is one that has no edges or sharp corners, and which is essentially round (in the form of a disc or the path described by rotary motion) in shape.

A circular object occupies the largest area per diagonal compared to other regular shapes, as the circular inscribes other regular shapes within its circumference.

The shape in the figure is a circle

The diameter of the circle, D = 3 in.

The formula for finding the area of a circle, A, for which the diameter is presented as follows;

Area of the circle, A = π·D²/4

The approximation of the value of π to be used are 3.14 or 22/7

The area is obtained by plugging in the values of D and π in the formula for the area of a circle as follows;

The area of the figure is; A = 3.14 × 3²/4 = 7.065

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Answer:

[tex]\displaystyle{(-1)^aa^{2a} b^a}[/tex]

Step-by-step explanation:

The following expression can be rewritten as:

[tex]\displaystyle{\left((-1)\cdot a^2 \cdot b\right)^a}[/tex]

In this case, we have to separate -1 out of a² since if a becomes even, the value of (-a)ª will become positive while (-a)ª becomes negative when a is odd.

We can apply the law of exponent when:

[tex]\displaystyle{\left(a \cdot b \cdot c \right)^m = a^m \cdot b^m \cdot c^m}[/tex]

Therefore:

[tex]\displaystyle{\left((-1)\cdot a^2 \cdot b\right)^a = (-1)^a\cdot a^{2a}\cdot b^a}\\\\\displaystyle{\left((-1)\cdot a^2 \cdot b\right)^a = (-1)^aa^{2a} b^a}[/tex]

This will make when a = even numbers, the expression is positive while negative when a is odd.

And no, the answer is not [tex]-a^{2a} b^a[/tex] since this will make the expression negative only but the problem can be positive when a = even number which is why we have to separate -1 out of -a² so that it meets the condition.

Hence, the answer is [tex]\displaystyle{(-1)^aa^{2a} b^a}[/tex]

The discount was 17 dollars and 87 cents.

What is a discount?

A discount is a reduction in the price of a product or service. It can be offered for a variety of reasons, such as to encourage sales or to reward loyal customers.

We have,

price of pair of sunglasses for $66,

coupon code discount of 30%,

15% processing fee to the price.

The final price is:

$66 * (1 - 30%) * (1 + 15%)

$66 * 0.7 * 1.15

$53.13

So, the actual discount is,

$(71 - 53.13)

= $17.87

Hence, the discount was 17 dollars and 87 cents.

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a) Upwards

b) x = -1

c) (-1,-9) (-1,-9)

d) Intercepts of x; and (2, 0) (-4,0)

is y intercept (0,-8)

a) The parabola, as seen, faces upward.

b) To identify the point through the parabola's vertex that precisely divides the parabola into two equal sections, we look at the plot of the graph.

The place where the line has an x-value of -1 is where the axis of symmetry's equation is located.

d) In this case, the vertex marks the circle's lowest point.

As we can see, this is the location where the axis of symmetry passes to divide the parabola symmetrically.

The location's coordinates are as follows:

(-1,-9)

The intercepts (d)

The parabola crosses the x-axis at two places, which are known as the x-intercept.

We have 2 and -4 for this point.

the coordinates of the x-intercepts are (2,0) and

In terms of the y-intercept, it is the y-coordinate of the location where the parabola crosses the y-axis.

The Complete Question.

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The probability that this song will be played on at least 2 days out of 4 days is 40.71%.

To calculate the probability that a song will be played on at least two days, you would need to find the probability that it is not played on any of the days (the complement) and then subtract that from 1.

The probability that a song is not played on a given day is 1 - 0.23 = 0.77. To find the probability that it is not played on at least two days, you would raise that probability to the power of the number of days, in this case 2.

So, 0.77^2 = 0.5929. To find the probability that it is played on at least two days, you would subtract that from 1: = 1 - 0.5929

= 0.4071

=40.71%.

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