I need help anyone please ?!!)::

Hello!

f(x) = x - 2

f(2) = 2 - 2 = 0

f(12) = 12 - 2 = 10

The measure of line MN in the secant line using the Intersecting theorem is approximately 19.5.

Intersecting secants theorem states that " If two secant line segments are drawn to a circle from an exterior point, then the product of the measures of one  of secant line segment and its external secant line segment is the same or equal to the product of the measures of the other secant line segment and its external line secant segment.

From the figure:

Sectant line segment QO = 48

internal line segement of QO = QP = 29

External line segement of QO =  PO = 48 - 29 = 19

Second sectant line segment MO = NO + MN = ( 22 + x )

External line segement of MO = NO = 22

Using the Intersecting secants theorem:

22( 22 + x ) = 19 × 48

Solve for x:

484 + 22x = 912

22x = 912 - 484

22x = 428

x = 428/22

x = 19.5

Therefore, line MN is approximately 19.5.

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[tex]\tan(x )=\cfrac{\stackrel{opposite}{18}}{\underset{adjacent}{11}} \implies \tan^{-1}(~~\tan( x )~~) =\tan^{-1}\left( \cfrac{18}{11} \right) \\\\\\ x =\tan^{-1}\left( \cfrac{18}{11} \right)\implies x \approx 58.6^o[/tex]

Make sure your calculator is in Degree mode.

Answer:

x =  58.6°

Step-by-step explanation:

Because this is a right triangle, we're able to find the measure of angle x using one of the trigonometric ratios.  

When angle x is the reference angle, the side that is 18 units long is the opposite side and the side that is 11 units long is the adjacent side.

Thus, we can use the tangent ratio, which is given by:

tan (θ) = opposite / adjacent, where

Thus, we have tan (θ) = 18 / 11

In order to find angle measures we use inverse trigonometry:

tan^-1 (18 / 11) = x

58.57043439 = x

58.6 = x

Thus, the measure of angle x is about 58.6°

We can conclude that points, planes, lines, and other undefinable terms are important concepts in geometry. They are essential building blocks of geometric shapes and are used in mathematical calculations and problem-solving.

Geometry is a field of mathematics that deals with the study of shapes, sizes, relative positions, and properties of space. It involves understanding the properties of lines, points, planes, and other shapes in space. Undefinable terms are important concepts in geometry that are not defined or are difficult to define. Some statements that are true regarding undefinable terms in geometry are as follows: A point has no length or width.

A point is one of the fundamental concepts of geometry, and it is an essential building block of other geometric shapes. A point has no length or width; instead, it indicates a specific location in space. Points are represented as dots in geometry.A plane has one dimension, length. A plane is a flat, two-dimensional surface that extends infinitely in all directions. It has only one dimension, length.

A plane is a surface that has no thickness or depth, but it has an infinite number of points.A plane consists of an infinite set of lines. A plane is made up of an infinite number of lines that are parallel to each other. All of these lines extend in both directions, so they never meet. When a plane is intersected by a line, it creates a point where the two meet.

A line has a definite beginning and end. A line is a geometric object that extends infinitely in both directions. It has no width or thickness, but it has a definite beginning and end. A line is usually represented as a straight line that extends infinitely in both directions. A line is made up of an infinite number of points.

A line consists of an infinite set of points. A line is an infinite set of points that are aligned in a straight line. A line has no thickness or width, but it is infinitely long. The points on a line have no beginning or end, but they are considered to be in a specific order.

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The equation of the line that goes through the point (-2, -2) with a slope of -4 is y = -4x - 10.

To find the equation of a line, we need to use the point-slope form of a linear equation:

y - y₁ = m(x - x₁)

Where (x₁, y₁) is the given point on the line, and m is the slope.

Given that the point is (-2, -2) and the slope is -4, we can substitute these values into the equation:

y - (-2) = -4(x - (-2))

Simplifying:

y + 2 = -4(x + 2)

Expanding the brackets:

y + 2 = -4x - 8

Now, let's rearrange the equation to get it into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept:

y = -4x - 8 - 2

y = -4x - 10

Therefore, the equation of the line that goes through the point (-2, -2) with a slope of -4 is y = -4x - 10.

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The probability that the student guesses all three compounds correctly is 1/1320.

To calculate the probability that the student guesses all three compounds correctly, we need to determine the number of favorable outcomes (correct guesses) and the total number of possible outcomes (all possible combinations).

Given that the student randomly chooses 3 compounds from a list of 12 possible compounds, the total number of possible outcomes is the number of ways to choose 3 compounds out of 12, which can be calculated using the combination formula:

Total number of possible outcomes = C(12, 3) = 12! / (3!(12-3)!) = 220

Now, let's consider the favorable outcomes, which are the cases where the student guesses all three compounds correctly. Since the student has no prior knowledge of the compounds, the probability of guessing each compound correctly is 1 out of 12.

For the first guess, there is a 1/12 probability of choosing the correct compound. Similarly, for the second guess, there is a 1/11 probability of choosing the correct compound (as one compound has already been chosen). Finally, for the third guess, there is a 1/10 probability of choosing the correct compound (as two compounds have already been chosen).

To find the probability of all three correct guesses, we multiply the probabilities of each independent event:

Probability of all three correct guesses = (1/12) * (1/11) * (1/10) = 1/1320

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Answer:

Step-by-step explanation:

if x = -1,

     a-b+c = 0 (eq1)

if x = 1,

    a+b+c = 0(eq2)

from eq 1 and 2;

a+c = 0;

so, a = -c,

if a+c = 0, b = 0

Ans : a=-c, b=0

The value of constants a and b are -2 and 0 respectively.

Given: x=-1 and x=1 are both the solution to equation ax²+bx+c=0.

To find: the constant a and b

Solution:

To obtain this, first, we have to simplify the equation by putting x=1 into the given equation, we get;

a+b=-2

afterward, we have to put x=-1 in the given equation, and we get;

a-b=-2

Now, we will add the two obtained equations, we get;

2a=-4 i.e., a=-2

Now, a+b=0 which means the value of b is 0.

Hence, the constants a and b are -2 and 0 respectively.

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(g∘f)(2) = 4.

To find (g∘f)(2), we need to substitute the value of f(x) into g(x) and evaluate the resulting expression at x = 2.

First, let's find f(2):

[tex]f(x) = -5 + 3[/tex]

[tex]f(2) = -5 + 3[/tex]

[tex]f(2) = -2[/tex]

Now, substitute f(2) into g(x):

[tex]g(x) = x^2[/tex]

[tex]g(f(2)) = (f(2))^2[/tex]

[tex]g(f(2)) = (-2)^2[/tex]

[tex]g(f(2)) = 4[/tex]

Therefore, (g∘f)(2) = 4.

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Answer:The equation that can be paired with x + 2y = 5 to create an inconsistent system is given by:

2x + 4y = 3.

Step-by-step explanation:

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

An inconsistent system is a system that has no solutions, and it happens when the coefficients of x and y are multiples, and the independent terms are not.

Hence:

x + 2y = 5.

2x + 4y = 3.

Is inconsistent, as the variables are each multiplied by 2, but the independent term is not.

Answer:

Step-by-step explanation:

Mario recibe Q40,000.00, Leticia recibe Q20,000.00, and Beatriz receives Q20,000.00. Therefore, Mario and Leticia receive a total of Q60,000.00.

Answer:

the amount of metal required to make the can is 352.8π square centimeters.

Step-by-step explanation:

To calculate the amount of metal required to make the can, we need to find the surface area of the can.

The can consists of two circular ends (top and bottom) and a cylindrical body.

1. Surface Area of the Circular Ends:

The circular ends can be considered as two circles. The surface area of each circular end can be calculated using the formula for the area of a circle:

A_end = πr^2

Given the diameter of the can is 14 cm, the radius (r) is half the diameter, so r = 14 cm / 2 = 7 cm.

A_end = π * 7^2 = 49π cm^2 (for each circular end)

2. Surface Area of the Cylindrical Body:

The cylindrical body of the can can be represented as a rectangle that is rolled into a cylinder. The surface area of the cylindrical body can be calculated using the formula for the lateral surface area of a cylinder:

A_body = 2πrh

Given the height (h) of the can is 18.2 cm and the radius (r) is 7 cm, we can calculate the surface area of the cylindrical body:

A_body = 2π * 7 * 18.2 = 254.8π cm^2

3. Total Surface Area:

To calculate the total surface area of the can, we add the surface areas of the circular ends and the cylindrical body:

Total Surface Area = 2 * A_end + A_body

                 = 2 * 49π + 254.8π

                 = 98π + 254.8π

                 = 352.8π cm^2

Therefore, the amount of metal required to make the can is 352.8π square centimeters.

An x-y coordinate table is the appropriate table to use when graphing a piece of a function. This table helps you to determine the corresponding y-values for different x-values and plot the points on a graph.

To graph a piece of a function, you would typically use an x-y coordinate table, also known as a Cartesian coordinate system. This table consists of two columns: one for the x-values (also called the input values) and one for the corresponding y-values (also called the output values). Each row in the table represents a point on the graph.
To graph a piece of a function, you would need to identify the domain (the set of possible x-values) for that specific piece. Once you have the domain, you can choose values from that domain and calculate the corresponding y-values using the function.
For example, if you have a piece of a linear function, such as y = 2x + 3, you could create a table by choosing various x-values and calculating the corresponding y-values. Let's say we choose x-values of -2, 0, and 2. Plugging these values into the equation, we find the corresponding y-values: -1, 3, and 7.
So the table for this piece of the linear function would look like this:
x    |   y
--------------
-2  |  -1
0    |   3
2    |   7
Once you have the x-y coordinate table, you can plot the points on a graph and connect them to create the graph of the piece of the function.

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The probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 8/25 or 0.32 (rounded to the nearest millionth).

1. Calculate the total number of students on the Student Government Board by summing up the numbers in the table:

  Total Students = 2 + 2 + 2 + 4 + 0 + 3 + 4 + 2 = 19

2. Calculate the total number of graduate students on the Student Government Board:

  Total Graduate Students = 2 + 0 = 2

3. Calculate the total number of students living in on-campus housing:

  Total On-Campus Housing = 2 + 2 + 0 + 4 + 2 = 10

4. Calculate the probability of selecting a graduate student from the Student Government Board by dividing the total number of graduate students by the total number of students:

  Probability of Graduate Student = Total Graduate Students / Total Students = 2 / 19

5. Calculate the probability of selecting a student living in on-campus housing by dividing the total number of students in on-campus housing by the total number of students:

  Probability of On-Campus Housing = Total On-Campus Housing / Total Students = 10 / 19

6. Calculate the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing by summing up the probabilities from steps 4 and 5:

  Probability = Probability of Graduate Student + Probability of On-Campus Housing = 2 / 19 + 10 / 19

7. Simplify the fraction if necessary. In this case, the fraction cannot be simplified further, so the final probability is 2 / 19 + 10 / 19 = 12 / 19.

8. Convert the fraction to a decimal by dividing the numerator by the denominator: 12 / 19 ≈ 0.631578947, which rounds to 0.632 (rounded to the nearest thousandth).

9. Finally, express the probability as a fraction in lowest terms: 12 / 19 is already in lowest terms.

Therefore, the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 12/19 or approximately 0.632 (rounded to the nearest thousandth).

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The surface area of the rectangular prism is 108 cm².

To calculate the surface area of an object, you need to measure the areas of all of its faces and then add them up.

The formula for the surface area of a rectangular prism is SA = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.

To calculate the surface area of a rectangular prism,

Measure the length, width, and height of the rectangular prism in centimeters.

Use the formula SA = 2lw + 2lh + 2wh to calculate the surface area. Plug in the values for l, w, and h, and perform the necessary calculations.

This will give you the surface area in square centimeters.

Round the answer to two decimal places to get the final answer.

The following example demonstrates how to calculate the surface area of a rectangular prism.

Example:

Calculate the surface area of a rectangular prism with a length of 6 cm, a width of 4 cm, and a height of 3 cm.

Measure the length, width, and height of the rectangular prism in centimeters.

l = 6 cmw = 4 cmh = 3 cm

Use the formula SA = 2lw + 2lh + 2wh

To calculate the surface area.

SA = 2lw + 2lh + 2whSA = 2(6 cm × 4 cm) + 2(6 cm × 3 cm) + 2(4 cm × 3 cm)SA

= 48 cm² + 36 cm² + 24 cm²

SA = 108 cm²

Round the answer to two decimal places to get the final answer.

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The rational expression that is undefined when x = 0 is (8x + 6)/(-x^2 + 1).

To determine which rational expression is undefined when x = 0, we need to find the values of x that make the denominator equal to zero. When the denominator of a rational expression is zero, the expression is undefined because division by zero is not possible.

Let's analyze each of the given expressions:

(5x^2 - 4)/(3x - 3):

To check if this expression is undefined when x = 0, we substitute x = 0 into the denominator:

3(0) - 3 = -3

Since the denominator is not zero, this expression is defined when x = 0.

(6x^2)/(9x - 3):

Similarly, we substitute x = 0 into the denominator:

9(0) - 3 = -3

Again, the denominator is not zero, so this expression is defined when x = 0.

(8x + 6)/(-x^2 + 1):

For this expression, we substitute x = 0 into the denominator:

-(0)^2 + 1 = -0 + 1 = 1

The denominator is not zero, indicating that this expression is defined when x = 0.

(4x - 8)/(-2x^2):

When we substitute x = 0 into the denominator:

-2(0)^2 = -2(0) = 0

The denominator becomes zero when x = 0. Therefore, this expression is undefined when x = 0.

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Answer:

12

Step-by-step explanation:

pitcher plant consumes one insect at a time so total number of pitcher plants used for insects consumption according to the given data set will be 12

In this triangle, the product of sin B and tan C is[tex]b^2/(ac)[/tex]  , and the product of sin C and tan B is [tex]c^2/(ab)[/tex].

In a right-angled triangle ABC, where angle A is 90 degrees, we have the following side lengths:

AB = c (base)

BC = a (hypotenuse)

AC = b (perpendicular)

We need to calculate the products of sin B and tan C, and sin C and tan B.

First, let's calculate sin B and tan C:

sin(B) = opposite/hypotenuse = AC/BC = b/a

tan(C) = opposite/adjacent = AC/AB = b/c

The product of sin B and tan C is sin(B) * tan(C) = (b/a) * (b/c) = [tex]b^2[/tex]/(ac).

Next, let's calculate sin C and tan B:

sin(C) = opposite/hypotenuse = AB/BC = c/a

tan(B) = opposite/adjacent = AB/AC = c/b

The product of sin C and tan B is sin(C) * tan(B) = (c/a) * (c/b) = [tex]c^2[/tex]/(ab).

Therefore, in the given right-angled triangle ABC, the product of sin B and tan C is[tex]b^2[/tex]/(ac), and the product of sin C and tan B is [tex]c^2[/tex]/(ab).

These formulas hold true for any right-angled triangle, where the base is AB, the hypotenuse is BC, and the perpendicular is AC.

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The question probable may be:

In this triangle, the product of sin B and tan C is _____ , and the product of sin C and tan B is _______.

The simplified form of 2i^68 is the value of 2^34.

To simplify 2i^68, we need to use the properties of imaginary numbers and the exponent rules. Here are the steps to simplify it:

Recall that i is defined as the square root of -1.

Since i^2 equals -1, we can rewrite the expression as (2i^2)^34.

Simplify the exponent by applying the rule that (a^m)^n equals a^(mn). In this case, we have (2i^2)^34 = 2^34 * (i^2)^34 = 2^34 * i^(234).

Simplify the terms. 2^34 is a large number, but we can still calculate it. i^(2*34) can be further simplified as i^68.

Determine the value of i^68 by noting that i follows a pattern: i^1 = i, i^2 = -1, i^3 = -i, i^4 = 1. The pattern repeats every four powers of i.

Since 68 is divisible by 4, i^68 equals 1.

Plug in the simplified values: 2^34 * i^(2*34) = 2^34 * i^68 = 2^34 * 1 = 2^34.

Calculate the value of 2^34 using a calculator or by applying exponent rules.

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By comparing the result obtained in Part B (6N) with the result obtained in Part A, we can see that the conjecture holds true. The result of the process is indeed related to the original number (N) by multiplying it by 6.

Part A:

Based on the given process, the conjecture that relates the result of the process to the original number (represented as N) is as follows:

Start with the original number N.

Multiply N by 4.

Add 12 to the product.

Divide the sum by 2.

Subtract 6 from the quotient.

The result of this process is the final number obtained.

Part B:

To prove the conjecture using deductive reasoning, we will follow the steps given in Part A:

Start with the original number N.

Multiply N by 12.

Add 4 to the product.

Divide the sum by 2.

Subtract 2 from the quotient.

We will simplify the steps using algebraic notation:

Step 1: N

Step 2: 12N

Step 3: 12N + 4

Step 4: (12N + 4) / 2

Step 5: [(12N + 4) / 2] - 2

Now, let's simplify Step 5:

Step 5: (12N + 4) / 2 - 2

      = (12N + 4 - 2*2) / 2

      = (12N + 4 - 4) / 2

      = 12N / 2

      = 6N

Therefore, the result of this process is 6N.

We may verify that the supposition is correct by comparing the result from Part B (6N) with the result from Part A. By multiplying the outcome by 6, the process does in fact relate to the original number (N).

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The complete question is:

Multiply the number by 4. Add 12 to the product. Divide this sum by 2. Subtract 6 from the quotient. 1st number is 3 and the results 2nd number is 6 and the results 3rd number is 8 and the results 4th number is 12 and the results part A. Write a conjecture that relates the result of the process to the original number selected. Represent the original number as N. What is the result part b Represent the original number as N, use deductive reasoning to prove the conjecture in part (a) multiply the number by 12 and the results add 4 to the product and the results divide the sum by 2 subtract 2 from the quotient

Algebra is introduced to primary school learners in a basic form to provide them with a foundation for mathematical thinking and problem-solving.

Here are some reasons why algebra is taught to primary school learners and the importance of teaching it at an early age:

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The correct answer is option e. The joint probability of two statistical dependent events Y and Z can be written as P(Y and Z) = P(Y) * P(Z|Y).

The concept of joint probability is utilized in probability theory, a statistical tool that investigates the probability of two events happening simultaneously. It is an estimation of the probability of two or more events occurring simultaneously. Joint probability is a method of defining the probability of two events happening at the same time.The joint probability of two statistical dependent events Y and Z can be written as P(Y and Z) = P(Y) * P(Z|Y).This implies that the possibility of Z happening given Y has happened multiplied by the probability of Y happening is the joint probability of Y and Z. P(Z|Y) refers to the probability of Z occurring when Y is true or has already occurred. It is conditional probability and is often used to calculate joint probabilities.The formula for conditional probability is P(A|B) = P(A and B)/P(B), which can be simplified to P(A and B) = P(A|B) * P(B). This formula is applicable to P(Y and Z), where P(Y and Z) = P(Z|Y) * P(Y).

The correct answer is option e.

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The most appropriate reason for Christie making changes to her budget at the end of every month in terms of smart financial planning is B. She is reviewing her goals and aligning the budget to work toward them.Option B is correct.

Smart financial planning involves regularly evaluating and adjusting one's budget to ensure that it reflects their financial goals and current circumstances. By reviewing her goals, Christie can assess if her budget is still aligned with those goals and make any necessary changes to stay on track.

Life circumstances, such as changes in income, expenses, or financial priorities, may warrant adjustments to the budget. Christie recognizes that her needs may change over time, and by modifying her monthly budget, she can ensure that her financial resources are allocated appropriately to meet her evolving goals.

Regularly revisiting and modifying the budget allows Christie to adapt her financial plans, optimize her spending, and make informed decisions to achieve her financial objectives. Option B is correct.

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Answer: 1105 grams of protein

Step-by-step explanation:

If the athlete eats 65 grams of protein per day, we multiply that by 17 for the amount of days.

1105x65=1105

These are the four solutions for each given equation within the range of -360 degrees to 360 degrees.

To find the solutions for the given equations involving tangent (tan) functions, we need to solve for the angle (x) that satisfies each equation. Keep in mind that angles in trigonometry are typically measured in degrees.

tan(x) = 0.781:

To find the angle x that satisfies this equation, we can use the inverse tangent function (arctan or tan^(-1)). Taking the inverse tangent of both sides, we have:

x = arctan(0.781)

Using a calculator or a trigonometric table, we find that:

x ≈ 38.08 degrees

Since tangent is a periodic function with a period of 180 degrees, we can add or subtract multiples of 180 to find the other solutions:

x ≈ 38.08 degrees + 180n, where n is an integer

So, the four solutions for tan(x) = 0.781 are approximately:

x ≈ 38.08 degrees, 218.08 degrees, 398.08 degrees, -141.92 degrees

tan(x) = -1.036:

Similarly, using the inverse tangent function, we have:

x = arctan(-1.036)

Using a calculator or a trigonometric table, we find that:

x ≈ -45.14 degrees

Again, considering the periodicity of tangent, we can add or subtract multiples of 180 to find the other solutions:

x ≈ -45.14 degrees + 180n, where n is an integer

The four solutions for tan(x) = -1.036 are approximately:

x ≈ -45.14 degrees, 134.86 degrees, 314.86 degrees, 494.86 degrees

tan(x) = 2.145:

Using the inverse tangent function, we have:

x = arctan(2.145)

Using a calculator or a trigonometric table, we find that:

x ≈ 65.64 degrees

Considering the periodicity of tangent, we can add or subtract multiples of 180 to find the other solutions:

x ≈ 65.64 degrees + 180n, where n is an integer

The four solutions for tan(x) = 2.145 are approximately:

x ≈ 65.64 degrees, 245.64 degrees, 425.64 degrees, -114.36 degrees

These are the four solutions for each given equation within the range of -360 degrees to 360 degrees.

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To calculate the present value of the cost savings, we can use the formula for the present value of a growing perpetuity. The formula is:

K = C / (r - g)

Where:

K = Present value of the growing perpetuity

C = Cash flow in the first year

r = Interest rate

g = Growth rate

In this case, C = $16,000, r = 8% (or 0.08), and g = -3% (or -0.03). We use a negative sign for the growth rate since the cost savings are decreasing each year.

Now we can substitute the values into the formula and calculate the present value:

K = 16000 / (0.08 - (-0.03))

K = 16000 / 0.11

K ≈ $145,454.55

Therefore, the present value of these cost savings is approximately $145,454.55.

Using the commutative property of addition, we can write the expression (3+7^) + (8-6^) as (8-6^) + (3+7^).

The property that allows you to write the expression (3+7^) + (8-6^) as (8-6^) + (3+7^) is the commutative property of addition.

The commutative property of addition states that changing the order of the addends does not affect the sum. In other words, when adding two numbers, you can rearrange the order of the numbers without changing the result.

Applying this property to the given expression, we can rearrange the order of the two addition operations:

(3+7^) + (8-6^) = (8-6^) + (3+7^)

So, using the commutative property of addition, we can write the expression (3+7^) + (8-6^) as (8-6^) + (3+7^).

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Step-by-step explanation:

To calculate the amount of air used to fill a spherical balloon, we need to determine its volume. The volume of a sphere can be calculated using the formula:

Volume = (4/3) × π × radius³

Given that the radius of the balloon is 165 mm, we can substitute this value into the formula:

Volume = (4/3) × π × (165 mm)³

Now, let's calculate the volume of the balloon:

Volume = (4/3) × 3.14159 × (165 mm)³

Volume ≈ 4.18879 × (165 mm)³

Evaluating this expression will give us the volume of the balloon in cubic millimeters. However, to express it in a more practical unit, such as liters, we need to convert the volume from cubic millimeters to liters.

1 liter = 1000 cubic centimeters (cc)

1 cubic centimeter (cc) = 1 milliliter (ml)

1 milliliter (ml) = 1 cubic millimeter (mm³)

To convert the volume from cubic millimeters to liters, we divide the volume by 1000:

Volume (liters) = Volume (cubic millimeters) / 1000

So, let's calculate the volume of the balloon in liters:

Volume (liters) = (4.18879 × (165 mm)³) / 1000

Using a calculator to evaluate this expression, we find:

Volume (liters) ≈ 7.976 liters

Therefore, approximately 7.976 liters of air were used to fill the spherical balloon.

The percent increase in enrollment from 1980 to 2004 is 125%.

To calculate the percent increase in enrollment from 1980 to 2004, we can use the following formula:

Percent Increase = ((Final Value - Initial Value) / Initial Value) * 100

Given that the number of students in 1980 was 4,000 and the number of students in 2004 was 9,000, we can substitute these values into the formula:

Percent Increase = ((9,000 - 4,000) / 4,000) * 100

Simplifying the numerator:

Percent Increase = (5,000 / 4,000) * 100

Performing the division:

Percent Increase = 1.25 * 100

Calculating the final result:

Percent Increase = 125%

Therefore, the percent increase in enrollment from 1980 to 2004 is 125%.

This means that the number of students increased by 125% over the 24-year period. In other words, the enrollment more than doubled during this time frame.

It is important to note that the percent increase indicates the relative change in enrollment from the initial value. In this case, the enrollment increased by 125% compared to the enrollment in 1980.

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