Which of the following is the product of the rational expressions shown below?

The solution to the fractions are;

7. 5/6

8. 6/5

A fraction can be described as the part of a whole variable, number or element.

There are several types of fractions, which includes;

From the information given, we have that;

1 1/3 × 5/12

convert to improper fraction

4/3 × 5/12

Multiply the values

5/6

(7/10 + 1/5) ÷ ( 6/4 - 3/4)

find the lowest common denominators

( 7 + 2 /10) ÷ (6 - 3 /4)

subtract or add the numerators

9/10 ÷ 3/4

take inverse of the divisor and multiply

9/10 × 4/3

6/5

Hence, the values are 5/6 and 6/5 respectively.

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The volume of empty space in the box will be 220cm³

The diameter of the candle is equal to the width of the box (the length of the side of the square base of the box), and the height of the box is equal to the height of the candle, assuming that the candle fits tightly inside the box without wasting any room.

You may compute the prism's volume by multiplying it by the square base's area (height).

The area of the circular base can be used to compute the volume of the candle's cylinder (height).

The square box base's side measures 8 cm long, hence its area is equal to that measurement= 8cm²=64cm²

The candle's diameter is two times its radius, hence the radius is 8cm/2=4cm

area of the circular base thus Equals (A = π r²).

=πx4²

=16π²

Since the height of the candle and of the box is 16cm, the difference in volume is 1024-256π

=220cm³

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The number of cards were sold for mother's day is 900 cards.

To calculate a total number using a percentage, first identify the percentage and the total number. Then divide the percentage by 100 to convert it to a decimal fraction. Finally, multiply the total number by the decimal fraction to calculate the total number.

For example, if the percentage is 10% and the total number is 200, first divide 10% by 100 to get 0.1. Then multiply 0.1 by 200 to get 20. The total number is 20.

In another example, if the percentage is 25% and the total number is 500, divide 25% by 100 to get 0.25. Then multiply 0.25 by 500 to get 125. The total number is 125.

It is important to remember that percentages are based on a whole, which is usually 100. Therefore, to use percentages to calculate a total number, it is necessary to first convert the percentage to a decimal fraction by dividing it by 100. Then, multiply the total number by the decimal fraction to calculate the total number.

36 cards is 4% of the total cards sold for Mother's Day.

Total number of cards = 36 / 4%

Total number of cards = 36 x 100/4

Total number of cards = 900 cards.

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Answer:

Step-by-step explanation:

I don't know I'm just asking the question

The value of n=36 months.

It is given that the population is predicted to increase by 0.5%. To know the value after the increment, 215 has to be multiplied by (1 + 0.005) or 1.005.

In the equation P  =  215(1.005)t/3, the value of t/3 has to be equal to 1 for a 0.5% increase.

The population increases by 0.5 % every n month.

Initial Population = 215

Final Population:

=215+215*0.5/100

=215.1.074

=216.074

Substituting the value of, Initial and final Population

[tex]216.075=215*(1.005)^\frac{t}{3} \\\\(1.005)^\frac{t}{3} =\frac{216.075}{215}\\ \\(1.005)^\frac{t}{3}(1.005)^1\\\\\\frac{t}{3} =1[/tex]

t=3 years=>36 months.

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Answer:4√81=±3

Step-by-step explanation:

If (x+5)^4 = 81,

then (x+5)^2 = ± sqrt(81), so

        (x+5)^2 = ±9

Focusing on (x+5)^2 = 9 for the two real roots, we have

 (x+5)^2 = 9

       x+5 = ± sqrt(9)

       x+5 = ± 3

       x+5 = 3 gives you x = -2

       x+5 = -3 gives you x = -8

There are two complex roots too, but I'm not sure if you're studying that too.   If so, then you'd solve (x+5)^2 = -9:

       x+5 = ± sqrt(-9)

       x+5 = ±3i

       x = 5 ± 3i as the two complex roots.

The next time they will flash together will be at 4:00 AM.If they flash together at 1:00 AM.

According to the given information we are trying to find the smallest time interval at which both the lighthouses will flash together.The first lighthouse flashes every 15 minutes, and the second lighthouse flashes every 18 minutes.

To find the LCM of 15 and 18, we can list out the multiples of each number and find the smallest multiple that is common to both.
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, ...
Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, ...

As we can see, the smallest multiple that is common to both lists is 90. This means that the two lighthouses will flash together every 90 minutes.Since they both flash at 1:00 AM, we can add 90 minutes to 1:00 AM to find the next time they will flash together:
1:00 AM + 90 minutes = 4:00 AM

So, the next time they will flash together will be at 4:00 AM.

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As per the unitary method, the charge for each job in order to break even at the end of the third job is $3,000

In math the term unitary method is known as a single unit and then multiply the value of a single unit to the number of units to get the necessary value.

Here we have given that John is starting a roofing business. He will need to buy a truck and some supplies to get his business going.

And here we we have also known as the truck costs $13000 used.

The value of truck is 13000 and material for all 3 jobs is 3000

Here we have also know that each job takes 5 days for a total of 15 days

workers get paid 125 dollars a day.

As we all know that each worker gets 125 a day.

Then here we have also know that each job requires 5 days so he pays each worker 625 per job.

Then he has them work on 3 jobs, and then he pays each worker 1875 for all 3 jobs.

Where here he has 2 workers so he pays out 3750 in total to the workers for all 3 jobs.

Then the total cost is calculated as,

=> $13,000 for the truck

=> $3,000 for the material

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The distance PR across the river is 177 feet

The complete question is added as an attachment

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

The equivalent ratio represented as

PR : 125 = PR + 170 : 245

Express the ratio as a fraction

So, we have the following representation

PR/125 = (PR + 170)/245

Cross multiply

This gives

245PR = 125PR + 21250

Evaluate the like terms

120PR = 21250

Divide both sides by 120

PR = 177

Hence, the distance is 177 feet

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A horizontal parabola with a right-facing opening and a vertex at (1,1) is we have positive direction.

In order to make the coefficients of either the variable x or the variable y numerically equal, first multiply both of the following equations by any suitable non-zero constants.

Finding the single equation of a curve in standard form with only the variables xs and ys constitutes the cartesian equation of that curve. You must simultaneously solve the parametric equations in order to arrive to this equation.

X and Y both

are t-related functions.

We have t=y1 after solving y=t+1 to get t as a function of y.

Thus, given x=t2+1, we have x=(y1)2+1x1=(y1) by substituting t=(y1).

A horizontal parabola with a right-facing opening and a vertex at (1,1) is what we have positive direction.

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A function g that determine the point's x-coordinate in terms t.

g(t) = r .cos (2.t).

Now, According to the question:

The input variable and output variable are also called the domain and the range. The domain of a function is the set of all values that will work in the function, which are the inputs. The range of a function is the set of all possible outputs produced by the function. In the example above, the 3 would be part of the range and the 8 would be part of the domain.

Input data

A point started at the location (-4, 0)

and, moves CCW along a circle centered at (0, 0)

angular speed = 2 rad/s

Procedure

The value of x is equal to the cosine of the swept angle time radius.

We can calculate the swept angle as 2×t

g(t) = r .cos (2.t).

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The given question is incomplete.

For the complete question, To see the attachment.

Answer: c=√202

Step-by-step explanation:

c = √(9² + 11²)

which also simplifies to 23.769729

I hope this helps!

Answer:

Step-by-step explanation:

If the four players choose their numbers independently and uniformly at random from [0,1], then the expected value of the sum of the two middle numbers is 1/2, and the expected value of the sum of the two extreme numbers is 1/2. Therefore, in order to minimize the expected

One of the most straightforward methods for gathering information from the entire population is random sampling. Every member of the subset has an equal chance of being chosen as part of the sampling process when using random sampling. For instance, if an organization employs 300 people overall, a sample group of 30 workers will be chosen to participate in the survey. In this instance, the population is the entire workforce of the organization, and the sample is 30 employees. Since all of the employees who were picked to participate in the survey were chosen at random, every worker has an equal chance of getting chosen.

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To find the y intercept of a polynomial function solve the function for the input value of zero.

We know that a polynomial function is a function that contains only positive integer exponents of a variable.  

The highest power of a polynomial function is the degree of polynomial function.

A polynomial is generally represented as P(x).

The domain of a polynomial function is entire real numbers (R).

We know that the y-intercept is the value of the function for which the function has an input value of zero.

To find the y intercept of a polynomial function P(x) we substitute x = 0 and solve the polynomial function.

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The solution of the inequality is x < 60 and graph is shown in the image attached

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.

Let x represent the number of days.

Since 25 tables is being shipped daily and we want to find how many days will there be fewer than 1500 tables, we can write:

25x < 1500

x < 1500/25

x < 60

Note: fewer than means less than i.e. <

The graph is shown in the image attached

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The function to find the amount in dollars spent on monthly activities can be represented as: A(x) = (x - 500) * 1/4

Let x be the total monthly budget in dollars and A(x) be the function of x that determines the amount in dollars spent on monthly activities.

To find the value of A(x), we follow the steps:

First, we subtract the fixed monthly transportation cost of $500 from the total budget.

The remaining budget is then divided by 4 to find the amount spent on monthly activities.

Therefore, the function A(x) can be written as: A(x)= (x-500)/4

Thus, the function (x - 500) * 1/4 can be used to find the amount in dollars spent on monthly activities.

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The approximate area (shaded region) of the remaining portion of the circle in square feet is 55.94 ft².

We know that,

the side of square=2*[r*√2/2]=r*√2 that is being taken out.

diameter = 14 ft and radius , r = 7 ft.

the side of square=7*√2=9.89 ft

[area of the remaining portion of the circle]=[ area of a circle]-[area of a square]

[area of a square] = (7√2)²=98 ft²

[ area of a circle] = π*r²= π x 7^2 = 153.94 ft²

therefore,

[area of the remaining portion of the circle]=153.94 - 98=55.94 ft²

the answer is 55.94 ft².

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Answer: Use cross product property

Step-by-step explanation:

I solved it out for you below! I hope it helps! If you need a better explanation maybe ask your teacher? :)

The perimeter of the entire figure is 40 inches

It is important to note that the formula for area of a figure is expressed as;

A = a²

Where;

A + A = 100

a² = 100

Take the square root of both sides

a = √100

a = 10 inches

The formula for calculating the perimeter of a square is expressed as;

Perimeter = 4a

Substitute the value of a, we have;

Perimeter = 4(10)

expand the bracket

Perimeter = 40 Inches

Hence, the perimeter is 40 Inches

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The option that is a statistical question is how many miles do the students in your class run each week? (option b)

A statistical question is a question that can be answered by collecting data that have varying values.

For example, the number of miles that the students in your class run each week is statistical question because each student would run. This is because data would be collected from more than one student and the students would have varying miles that they run.

The number of pets your grandparents have is not a statistical questions because they can only have a set number of pets.

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Answer:

B. How many miles do the students in your class run each 

Step-by-step explanation:

When a  transformation is applied to a figure to create a new figure then Dilation do not preserve congruence but do preserve orientations.

Rotations, reflections, translations, and dilation are only a few of the many transformations. Dilation do not preserve congruence but do preserve orientations. Rotations, reflections, and translations all preserve congruence and are referred to as isometries.

Maintaining congruence refers to a transformation where the side lengths and angle measurements of the Image and Pre-Image are the same.

An object's orientation refers to how its related parts are ordered. As long as the components of an item remain in the same sequence, rotation and translation retain orientation. Orientation is not maintained by reflection.

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The measure of {x} equals to 8 and ∠WYZ is 32°.

The radian is the unit of angle in the International System of Units and is the standard unit of angular measure used in many areas of mathematics

Given is the figure as shown in the image.

It is given that ∠XYZ = 106°. We can write -

∠XYZ = ∠XYW + ∠WYZ

106 = 70 + 5x - 4

5x + 66 = 106

5x = 40

x = 8

∠WYZ = 5x - 8 = 5 x 8 - 8 = 32°.

Therefore, the measure of {x} equals to 8 and ∠WYZ is 32°.

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The solution of the system is x = 60 and y = 28.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

An algebraic equation,

[tex]a^{x} a^{y} = a^{88}[/tex]

When the base value is the same, we can add the exponents.

x + y = 88

And x - y = 32

Now, we have the system of equations,

Adding both the equations,

2x = 120

x = 60

And y = 28.

Therefore, the values are x = 60 and y = 28.

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S + R represents the total trips done by these trucks.

Volume is defined as the amount of space occupied by an object that is bound by a boundary. It must be noted that the volume is a mathematical term that is only applicable to 3D (three-dimensional) objects or spaces. As such, the units commonly used for volume are cubic units, that is, m3, cm3, in3, etc.

Two dump trucks hauling rock to a construction site is given by the expression. xS + yR

S +R

Truck 1 can haul x cubic yards

Truck 2 can haul y cubic yards.

Truck 1 makes P trips to the construction site, while truck 2 makes R trips.

Hence the trips made by truck 1 and truck 2 should be the addition of the trips made by the trucks individually.

So the total trips is represented by S + R

Therefore, S + R represents the total trips done by these trucks.

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Answer

see attached

Step-by-step explanation:

x-2y = 8 means x = 8+2y.  so when y =0, x = 8; when y=1, x =10. draw a line with these 2 points.

Same with x - 2y = 4 ==> x = 4+2y.  so when y=0, x = 4, when y=1, x=6, draw a line with these 2 points.

The value of x in the triangle is 8 units.

The midsegment of a triangle is a line connecting the midpoints between two sides of a triangle.

It is parallel to the third side and it is half the length of the third side.

Therefore, DE is the mid segment of the triangle ABC. The value of x can be found as follows:

Using the mid segment rule,

BE = EC

BD = DA

Therefore,

x = 8 units

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2 packs include 12 baseball cards, and there are 6 baseball cards per pack.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

given, There are 24 baseball cards In 4 packs complete the table to find the rate that gives the number of cards in 2 packs.

Since

There are baseball cards in 4 packs = 24

Thus,

Baseball cards in 1 pack = 24 / 4

Baseball cards in a pack = 6

Baseball cards in 2 packs = 12

therefore, there are 12 baseball cards in 2 packs also the rate of baseball cards per pack is 6.

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Complete question:

Answer: 0.2m/h

Step-by-step explanation: We can say when the turtle travels 1/10 of a mile in 1/2 of an hour, he's traveled 0.1 miles in 30 minutes.

If you're looking for the turtle's rate in miles per hour, just double both the time and the distance traveled.

You will end up with 0.2 miles per hour or 2/10 of a mile per hour.

Knowing that digital camera merchants typically mark up their products by 40%, even when a camera's actual cost is $175.50 The price of one rupee is $438.75.

Your boss has chosen to give old models of digital cameras a discount in order to make place for new ones. She wants to offer them for sale at the store's original price, without a markup, in order to move them quickly. You are requested by her to alter the price tags and create signage indicating the percentage of the reduction. A digital camera costs $175.50 at the manufacturer's suggested retail price, with shops adding 40% to that figure.

cost = ($175.50 / 40 ) × 100 = $438.75

In mathematics, the cost price formula, often known as C.P., is used to determine an object's exact price.The price that a buyer pays for a good, service, or commodity, according to the definition of C. P.In the estimation of profit and loss calculations for a specific purchase, it is frequently utilized.

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