1) 27/36 + 64/72 - 34/20 =
2) 77/66 + 33/22 + 44/55 =
3) 63/81 - 34/16 + 27 / 36 =
4) 60/15 + 26/14 - 18/20 =
5) 70/60 + 35/70 - 6/8 =
6) 2 + 3 + 4 + 3 1/8 =

The range of the inverse of g(x) = √(x³ - 1) is [0, ∞).

The range of a function's inverse is the set of all possible values that the inverse function can take. To find the range of the inverse of a function, we need to find the inverse function first and then determine the set of all possible values it can take.

For the function g(x) = √(x³ - 1), we first need to find its inverse. To do this, we need to switch the roles of x and y in the original function and solve for x.

g(x) = y

y = √(x³ - 1)

x³ - 1 = y²

x³ = y² + 1

x = ∛(y² + 1)

since x = g⁻¹(y)  = ∛(y² + 1)

Thus, g⁻¹(x) =  ∛(x² + 1)    (Replace y with x)

This is the inverse of g(x). To find the range of g⁻¹(x) we need to find the set of all possible values of x that the inverse function can take. Since the square root of a real number is always non-negative, the range of the inverse function will be all non-negative real numbers.

So, the range of the inverse of g(x) = √(x³ - 1) is [0, ∞).

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The math equation for this example would be 12 courses divided by 4 courses = 3 semesters.

The formula for computing the minimum number of semesters it would take a student to take all of the courses is calculated by dividing the total number of courses by the number of courses that can be taken in a semester. For example, if a student needs to take 12 courses, and the maximum number of courses that can be taken in a semester is 4, then the minimum number of semesters it would take the student to take all of the courses is 3 semesters. The math equation for this example would be 12 courses divided by 4 courses = 3 semesters. In order to determine the exact number of semesters it would take a student to take all of the courses, the total number of courses must be divided by the number of courses that can be taken in a semester.

The formula for calculating the minimum number of semesters it would take a student to take all of the courses is Total Number of Courses divided by Number of Courses that can be taken in a semester. For example, if a student needs to take 12 courses, and the maximum number of courses that can be taken in a semester is 4, then the minimum number of semesters it would take the student to take all of the courses is 3 semesters. The math equation for this example would be 12 courses divided by 4 courses = 3 semesters.

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To find the missing coordinates of the points A and B, you can use the equation c -3/7x + 3 = y. Plugging in the given x-coordinates for A and B, you can solve for their y-coordinates.

A: x = -2, y = -3 B: x = 9, y = 6

To find the slope of the line, you can use the formula m = (y2 - y1)/(x2 - x1). Plugging in the coordinates for A and B, you can calculate the slope as m = (6 - (-3))/(9 - (-2)) = 9/11.

To further explore the topic, you can look into how to graph equations in slope-intercept form, as well as how to find equations of parallel and perpendicular lines. You can also learn how to use the equation of a line to calculate distances between points, and how to calculate the midpoint of a line segment.

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The domain and the range of function f are given as follows:

The domain of a function is the set that contains all the input values that can be assumed by the function.

The function in this problem is a fraction, meaning that the denominator must assume values different of zero, hence the values outside the domain are:

x² - 3x - 18 = 0.

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

Hence:

Hence the domain is:

(-∞, -3) U (-3, 6) U (6, ∞).

The range of a function is the set that contains all the output values that can be assumed by the function.

The x - 6 term can be canceled, hence the output value that the function will never assume is of:

1/(6 + 3) = 1/9.

And also y = 0, as it would assume a value of zero at x = 6 but the denominator would also be zero.

Hence the range is of:

(-∞, 0) U (0, 1/9) U (1/9, ∞).

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Answer:

x [tex]\geq[/tex] 7

Explanation:

4x + 5 [tex]\geq[/tex] 33

4x + 5-5 [tex]\geq[/tex] 33 - 5

4x [tex]\geq[/tex] 28

[tex]\frac{4x}{4} \geq \frac{28}{4}[/tex]

x [tex]\geq[/tex] 7

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Answer: A

Step-by-step explanation: I just did 3.14x4

Answer:

Step-by-step explanation:

Area of a circle = πr²

r = radius and it is half of the diameter.

Diameter = 4 so radius = 2

Area = 3.14 (2)²

Area = 3.14(4)

Area = 12.56 yd²

Choice A

Answer:

C. [tex]40.6m^{2}[/tex]

Step-by-step explanation:

=  [tex]\frac{1}{2}[/tex] x ( 11 + 3 ) x 5.8

= [tex]\frac{1}{2}[/tex] x 7 x 5.8 =

[tex]40.6m^{2}[/tex]

We can then plug this value into the given for XZ, which is 3x, to solve for the length of XZ. This comes out to be 18. Therefore, the value of x is 6, and the length of XZ is 18.

x = 6, XZ = 18

To solve for x, we can use the formula for the midpoint of a segment, which is (x + z)/2.

Plugging in the given values, we get (x + 13)/2 = 6.

Simplifying, we get x = 6.

To solve for XZ, we can simply plug in the given value for x, which is 6.

Therefore, XZ = 3(6) = 18.

Given three values related to a line segment, XZ, XT, and TZ, we can solve for both the value of x and the length of XZ. To do this, we can use the formula for the midpoint of a segment, which is (x + z)/2. Plugging in the given values for XT and TZ, we can solve for x, which comes out to be 6. We can then plug this value into the given for XZ, which is 3x, to solve for the length of XZ. This comes out to be 18. Therefore, the value of x is 6, and the length of XZ is 18.

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Answer:

Question 1:

i) A pair of disjoint sets from the given sets are P and Q. Since there are no common elements between the sets P and Q, they are disjoint.

ii) A pair of equivalent sets from the given sets is Q and {0,1,2,3}. They contain the same elements and have the same number of elements.

Question 2:

The number of girls in the class is 3/7 * number of students in the class. Let's say there are n students in the class. Then, 3/7 * n = 3/7 * (24 + n) = 3 girls.

Solving for n, we get n = 84, which is the total number of students in the class.

Step-by-step explanation:

Comparing the articles I, II, and III of the constitution, in the descending order of length and detail, the articles are ranked as I, II, and III. Article I is the longest.

Article I of the constitution created the legislative branch, article II of the constitution created an executive branch, and article III of the constitution created a judicial constitution. Article I is the longest and more detailed part of the constitution as the powers and the duties of the legislative branch are much more varied than the executive branch. Additionally, the legislative branch is composed of more individuals than the executive branch.

Article 1 is the longest as founding fathers believed that a legislative branch is very important in a government that represents the citizens. Article 3 is the shortest part of the constitution as the founding fathers did not expect the judiciary to play a large role.

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Answer:

C and D

Step-by-step explanation:

Answer:(iii) To find the maximum area of the rectangle, we can use the formula for the area of a rectangle, A = lw, where l is the length and w is the width. Since the wire is 40 cm long, we have l = 40 cm - x cm = 40 - x cm. The maximum area occurs when the length and width are equal, so we set l = w and solve for x:

40 - x = x

2x = 40

x = 20

So, the maximum area of the rectangle is A = lw = (40 - x)x = (40 - 20) * 20 = 20 * 20 = 400 cm².

(iv) To show that the maximum area is only possible if the shape formed is a square, we use the result from part (iii) that the maximum area occurs when the width x = 20 cm. If the width is less than 20 cm, the length will be greater than 40 - x, and the area will be smaller. If the width is greater than 20 cm, the length will be less than 40 - x, and the area will be smaller. So, the maximum area is only possible if x = 20 cm, which means the rectangle is a square.

Step-by-step explanation:

Answer:

x = -6

Step-by-step explanation:

                   x + 4 = -2

Subtract 4 from both sides,

                x + 4 - 4 = -2 - 4

                         x = -6

                     [tex]\boxed{\bf x = -6}[/tex]

Check: Substitute x = -6 in the LHS of the equation,

      LHS = x +4

              = -6 + 4

              = -2 = RHS

Answer:about 3

Step-by-step explanation:

Step-by-step explanation:

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After 7 years, the balance of the savings account will be $1069.39.

An account balance is the amount of money in a financial repository at any particular time, such as a savings or checking account. The account balance is always the net amount after all debits and credits are subtracted.

The formula to calculate the balance after t years is A = P(1 + r/n)^(nt), where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.

In this case, P = 700.00, r = 0.07, n = 1 (since the interest is compounded annually), and t = 7. Plugging these values into the formula, we get:

A = 700.00 * (1 + 0.07/1)^(1 * 7)

A = 700.00 * (1.07)^7

A = 700.00 * 1.527674

A = $1069.39

So, after 7 years, the balance of the savings account will be $1069.39.

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The population is increasing at a constant rate, which can be represented by a simple exponential function.

Madison's expression: 1,000(3ℎ)

1,000 - This represents the starting population of amoebas, which is 1,000.

3 - This represents the rate of increase in size, which is a tripling of the original size every hour.

ℎ - This represents the number of hours for which the population is increasing.

So, the entire expression 1,000(3ℎ) means the number of amoebas after ℎ hours, where the population is tripling every hour.

Tyler's expression: (1+0.3)ℎ

1 - This represents the starting population of amoebas, which is 1.

0.3 - This represents the rate of increase in size, which is a 30% increase in size every hour.

ℎ - This represents the number of hours for which the population is increasing.

So, the entire expression (1+0.3)ℎ means the number of amoebas after ℎ hours, where the population is increasing by 30% every hour.

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The probability that one or more of the servers is operational is 0.898994.

The probability that one or more of the servers is operational is calculated as the complement of the probability that all servers fail. If the failure of each server is independent and has a probability of 0.1, the probability that all servers fail is 0.1 * 0.1 * ... (10 times) = 0.1^10 = 1e-10. The probability that one or more servers is operational is calculated as 1 - 1e-10 = 0.9999999999, which can be rounded to 0.898994. In other words, the probability of at least one server being operational is almost 90%.

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Three- Dimensional figures- Cube and Cylinder

Let a be the length of sides of cube and r and h be the radius and height of cylinder respectively.

Cube -  All sides are of same dimensions.

             Let a be the length of the dimensions

             The top, bottom and side view are squares each of length a units.

             The diagonal view is basically a three dimensional right angled   triangle.

Cylinder- h be the length/ height of cylinder and r be the radius of the cylinder.

The top view of cylinder is basically a circle of radius.

The side view is basically curved surface of the cylinder of length h.

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To determine the probability that no two red marbles are adjacent, we can calculate the number of arrangements of the 12 marbles such that no two red marbles are next to each other, and divide that by the total number of arrangements of the 12 marbles.

One way to do this is to place the red marbles first, and then the blue marbles. If we place the red marbles randomly, there are 5 gaps between the red marbles where we can insert the blue marbles. Thus, there are 5! = 120 ways to arrange the blue marbles.

Next, we need to determine the number of ways to arrange the red marbles. If we think of the red marbles as a sequence of R's and B's (where B represents a gap between red marbles), we have 4 R's and 5 B's. To avoid adjacent R's, we need to arrange the R's and B's such that no two R's are next to each other. One way to do this is to use the concept of combinations.

There are C(9,4) ways to arrange 4 R's and 5 B's in a sequence of 9 elements. This number can be calculated using the formula for combinations: C(n,k) = n! / (k! (n-k)!). In this case, C(9,4) = 126.

Finally, we divide the number of arrangements of the red marbles by the total number of arrangements of the 12 marbles to obtain the desired probability. The total number of arrangements of the 12 marbles is 12!. Thus, the desired probability is:

P = 126 / (120 * 12!) =

126 / (120 * 479001600)

= approximately 0.0000026

So, the probability that no two red marbles are adjacent is approximately 0.0000026.

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The fast-food worker receives 3 hours of break time per day.

This breaks down to a one-hour break in the morning, one hour for lunch, and one hour in the afternoon.

Mathematically, this can be expressed as

Additionally, the worker works 8 hours per day, Monday through Friday. This can be expressed as 5 days x 8 hours = 40 hours per week. The worker then receives 3 hours of break per day, which can be expressed as 40 hours - (5 days x 3 hours of break) = 25 hours of work per week.

Therefore, the fast-food worker receives three hours of break time per day and 25 hours of work time per week.

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The equivalent expressions are;

The correct answer choice is option B, C and E

-2/5(15 - 20d + 5c)

open parenthesis

= -30/5 + 40/5d - 10/5c

= - 6 + 8d - 2c

Check:

-6+8d-2c

True

-2c+8d-6

rearrange

= -6 + 8d - 2c

-2(3-4d+c)

open parenthesis

= -6 + 8d - 2c

Hence, the equivalent expression to -2/5(15 - 20d + 5c) are -6+8d-2c, -2c+8d-6 and -2(3-4d+c)

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The factor of its radius reduced is 3. The result is obtained by comparing the spherical volumes.

The volume of a spherical can be calculated by

V = 4/3 πr³

Where

A spherical balloon has volume v and radius r. Its volume is reduced by a factor of 27.0.

Find the factor of its radius reduced!

The factor of its volume is

V₁/V₂ = 27

We use the formula for spherical volume to find r₁/r₂.

V₁/V₂ = (4/3 πr₁³)/(4/3 πr₂³)

27 = (r₁/r₂)³

r₁/r₂ = ∛27

r₁/r₂ = 3

Hence, the radius is reduced by a factor of 3.

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The rate of change of the area of the rectangle as required in the task content is; 87 in²/sec.

It follows from the task content; The length is increasing by 9 in/sec which represents 75% of the initial length and the width is growing at 2 in/sec which represents 40% of the initial width.

Since the area of a rectangle is; A = l × w

A (initial) = 60in².

Therefore, the new area of the rectangle after every second is;

Area (new) = 1.75l × 1.4w

Area (new) = 2.45 lw

This therefore translates to the fact that the area of the rectangle is increasing by a factor of 1.45 which is equivalent to 145% of initial Area.

Therefore, the area is increasing by 1.45 × 60 = 87in²/sec.

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Answer:

  x ∈ {−2.18723​509003, 1.687​23509003}

Step-by-step explanation:

You want the value of x that satisfies the equation (4x +2)(x -1)(3x)(2x +3) = 194.

The fact that 194 is not divisible by 3 means the real solutions will not be integer values, likely irrational. A graphical solution and some iterations tell us the solutions are ...

  x = −2.18723​509003

or

  x = 1.687​23509003

__

Additional comment

The product has units of square meters, so we presume these dimensions come in pairs of factors. It appears that both the positive and negative values of x will give factors pairs that have a positive product.

Any rational solutions would be multiples of 1/24. These solutions are not rational.

The probability that I get a head in the coin toss and a letter card is 2/ 13.

Therefore the answer is 2/ 13.

There are 4 As, 4Qs, 4Ks and 4 Js, so there are 16 choices. The probability of getting a head in a coin toss is 1/2, and the probability of picking a letter card is 16/ 52 = 4/ 13. So

P(heads) = 1/ 2

P(letter card) = 4/ 13

To find the joint probability of both events happening (getting a head and picking a letter card), you multiply the individual probabilities:

P(heads and letter card) = P(heads) * P(letter card)

= (1/ 2) * (4/ 13)

= 2/ 13

So the probability of getting a head and picking a letter card is 2/13.

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The number of months for which the company made no profit is 18 months.

Generally speaking, a product's profit is defined as the sum received from sales, which should exceed the product's cost price. It is the gain from any type of commercial activity. In other words, if a product's selling price (SP) is higher than its cost price (CP), there has been a gain or profit. It explains the monetary gain realised if the revenue from the company activity is greater than the costs, such as taxes and expenses, involved in maintaining the business activity.

The cost function is given as: C(x) = 17- 8x - 2x²

The revenue function is given as: R(x) = 5 - 3x

Profit = Revenue - Cost

For no profit the equation becomes:

5 - 3x - 17 + 8x + 2x² = 0

2x² + 5x - 12 = 0

2x² + 8x - 3x - 12 = 0

2x(x + 4) - 3(x + 4) = 0

2x - 3 = 0 and x + 4 = 0

x = 3/2 and x = -4

Since, month cannot be a negative quantity we have x = 3/2.

That is 3/2 (12) = 18 months.

The number of months for which the company made no profit is 18 months.

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Answer:

The value of x for each triangle are:

Please note that I only answer the circled number and please refer to the attached picture for any additional annotations.

Note that each triangles are a right angled triangle. We use phytagoras theorem to find any unknown side of a triangle.

x² = 14² + y²

a² = y² + 4²

x² + a² = 18²

x² + a² = 18²

(14² + y²) + (y² + 4²) = 18²

14² + 2y² + 4² = 18²

196 + 2y² + 16 = 324

2y² = 112

y² = 56

x² = 14² + y²

x² = 196 + 26

x² = 252

x = 6√7

(x + 28)² = a² + b²

a² = 28² + 18²

b² = x² + 18²

(x + 28)² = a² + b²

(x + 28)² = (28² + 18²) + (x² + 18²)

x² + 56x + 784 = 1432 + x²

56x = 648

x = 11.6

a² = b² + (x - 12)²

b² = 16² - 12²

x² = 16² + a²

x² = 16² + a²

x² = 16² + (b² + (x - 12)²)

x² = 16² + [(16² - 12²) + (x - 12)²]

x² = 256 + 112 + (x - 12)²

x² = 368 + x² - 24x + 144

24x = 512

x = 21.3

x² = 15² + 6²

x² = 261

x = 3√29

(15 + z)² = x² + y²

y² = z² + 6²

(15 + z)² = x² + y²

(15 + z)² = 261 + (z² + 6²)

225 + 30z + z² = 261 + z² + 36

225 + 30z + z² = 297 + z²

30z = 72

z = 2.4

y² = z² + 6²

y² = 36 + 5.76

y² = 41.76

y = 6.46

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By applying permutation formula, it can be concluded that the probability that x₂ lies between x₁ and x₃ is 1/3

Permutation is rearranging a collection of objects in a different order from the original order.

P(n,r) = n! / (n-r)!    where

n = number of objects

r = number of object selected

We have three points x₁, x₂, and x₃ are selected at random on line L.

Number of points = 3.

Now we can calculate the number of ways of arranging 3 points:

P(3,3) = 3! / (3 - 3)!

         = 3!

         = 6

There are two arrangements that x₂ lies between x₁ and x₃.

Thus, the probability that X₂ lies between X₁ and X₃ = 2 / 6 = 1/3

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