Write two different expressions you could use to represent the
combined area of the Activities and Quotations sections. What
information about the sections does each expression show?

The limit in question is

[tex]$$\lim_{n\to \infty} \frac{1^3 + 2^3 + 3^3 + \dots + n^3}{n^4}$$[/tex]

This limit can be interpreted as the Riemann sum of a function defined on the interval [0, 16]. To calculate the sum, we need to first find the function that is being approximated. To do this, we can use the fact that the numerator of the limit can be rewritten as a single summation:

[tex]$$\sum_{k=1}^n k^3 = \frac{n^2 (n+1)^2}{4}$$[/tex]

This means that the function we are approximating is [tex]$f(x) = \frac{x^2 (x+1)^2}{4}$[/tex]

Now, to calculate the Riemann sum, we need to divide the interval [0, 16] into $n$ equal subintervals. The width of each subinterval is given by [tex]$\Delta x = \frac{16}{n}$\\The Riemann sum is given by $$\sum_{i=1}^n f\left(x_i\right) \Delta x = \sum_{i=1}^n \frac{\left(x_i\right)^2 \left(x_i+1\right)^2}{4} \cdot \frac{16}{n}$$[/tex]

where [tex]$x_i = \frac{16i}{n}$[/tex]

Plugging this into the limit, we get

[tex]$$\lim_{n\to \infty} \frac{1^3 + 2^3 + 3^3 + \dots + n^3}{n^4}\\ = \lim_{n\to \infty} \frac{\sum_{i=1}^n \frac{\left(x_i\right)^2 \left(x_i+1\right)^2}{4} \cdot \frac{16}{n}}{n^4} = \\frac{16}{4} \lim_{n\to \infty} \frac{\sum_{i=1}^n \frac{\left(x_i\right)^2 \left(x_i+1\right)^2}{n}}{n^3}$$[/tex]

Finally, we can take the limit of the above expression to get

[tex]$$\lim_{n\to \infty} \frac{1^3 + 2^3 + 3^3 + \dots + n^3}{n^4} = \frac{16}{4} \cdot \frac{f(16)}{16^3} = \frac{1}{4}$$[/tex]

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The complete function tables are written above.

A function describes a relationship between a dependent and independent variable. Example -

y = f(x) = 5x + 9

A quadratic function is of the form -

f(x) = ax² + bx + c

Given are the function tables as shown in the image attached.

{ 4 } -

Rule : h = 8c

{c}    2    3    4     5    6    7

{h}   16   24  32  45  48  56

{5} -

Rule : k = 2r

{r}    6     7    8    9    12    11    14

{k}   12   14   16   18   24   22  28

{6} -

Rule : k = 2r

{r}    6     7    8    9    12    11    14

{k}   12   14   16   18   24   22  28

Therefore, the complete function tables are written above.

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Since the mid-points of opposite sides of a square are equal, the quadrilateral formed will also be a square.

A four-sided polygon whose all sides are equal is a square. This means that the opposite sides of a square are equal in length and the opposite angles are also equal. Furthermore, the diagonals of a square bisect each other at their mid-points. Therefore, if the mid-points of opposite sides of a square are joined, a quadrilateral is formed. Since the opposite sides and angles are equal, the quadrilateral formed is also a square. To prove this, we can draw a line from the mid-point of one side of the square to the mid-point of the opposite side. We can then draw a line from the mid-point of the other side of the square to the mid-point of the opposite side. This will form a quadrilateral, and due to the equal sides and equal angles, it will be a square.

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Part A: The teacher's method is partially fair.

Part B: She can set up a fair way to make the decision that includes everyone by making it an open tournament for all such that all can participate.

Part A: The teacher's method is fair in terms of giving all students an equal opportunity to win the tickets by playing chess matches and having their names put into the hat.

However, it does not take into account the skill level of the students, which could result in a less skilled student winning the tickets over a more skilled student. To make the method more fair, the teacher could use a combination of wins and chess ratings to determine which students have the best chance to win the tickets.

Part B: To include the new students in the chance to win the tickets, the teacher could have them play chess matches against the current club members and use a combination of wins and chess ratings to determine the two students who will win the tickets.

This method is fair because it gives all students, including the new ones, the opportunity to compete and be recognized for their chess skills, rather than simply giving the tickets to the two students who have been in the club the longest. Additionally, using a combination of wins and ratings ensures that the most skilled players have a better chance of winning the tickets.

Therefore, the correct answer is as given above

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Answer:

{x | x is a real number}

Step-by-step explanation:

x can have any real number value.

Answer: $385.50

Step-by-step explanation: 25,700x1.5% = 385.50

The domain for 'n' will be all integers where n ≥ 1. Then the correct option is A.

A series of non-zero integers where every term after the first is obtained by increasing the one before it by a constant, non-zero value known as the scale factor.

Let a₁ be the first term and r be the common ratio. Then the nth term of the geometric sequence is given as,

aₙ = a₁ · (r)ⁿ⁻¹

The geometric sequence where a₁ = 7 and the common ratio is 3. Then the formula is given as,

aₙ = 7 · (3)ⁿ⁻¹

In the geometric sequence, the value of the exponent should be greater than or equal to zero. Then we have

n - 1 ≥ 0

n ≥ 1

The domain for 'n' will be all integers where n ≥ 1. Then the correct option is A.

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All u have to do is use the Traingle Inequality theorem, which states that the sum of two sides lenghts of a triangle is always greater than the third side. if this is true for all three combinations of added side lengths then you will have a triangle

Hope this helps :>

Answer:

3, 5, 7

Step-by-step explanation:

given 3 sides, for a triangle to be formed, then the sum of any 2 sides must be greater than the third side.

4 , 4 , 8

4 + 4 = 8 , not greater than 8, so does not form a triangle

1 , 2 , 3

1 + 2 = 3 , not greater than 3, so does not form a triangle

3 , 9 , 14

3 + 9 = 12 < 14 , so does not form a triangle

3 , 5 , 7

3 + 5 = 8 > 7

3 + 7 = 10 > 5

5 + 7 = 12 > 3

condition is satisfied , so will form a triangle

When an occurrence is so common that it shouldn't be the result of chance or external influences on the study, it is said to be "statistically significant."

Different clinical significance exists. It alludes to tangible results. It frequently refers to the actual impact of a medical problem (or medical treatment) on a patient's health. The effects of a medicine are clinically meaningful if they provide alleviation. A medical problem is also considered clinically significant if it affects a patient's quality of life or expected lifespan.

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The significantly low values are:

Lower than 871.6 cm³.

The significantly high values are:

Higher than 1369.6 cm³.

Hence a volume of 1389.6 cm³ is significantly high, as it is more than 2 standard deviations from the mean.

The range rule of thumb states that measures that are more than two standard deviations from the mean in a data-set are considered unusual.

Considering the mean and the standard deviation for this problem, the bounds are given as follows:

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The time(s) that the projectile will​ (a) reach a height of 192 ft is 4 seconds  and (b) return to the ground when is 8 seconds

Time is the continued sequence of existence and event that can occur in an apparently inevitable succession from the past through the present

The set height, s=192

(a) 192=-16t²+112t

-16t^2+112t-192=0

-t^2+8t-16=0

t^2-8t+16=0

(t-4)(t-4)=0

t=4 twice

The projectile will reach a height of 192ft after 4 sec on the way up and after 4 sec again  on the way down

..

Also, set height, s=0

(b) -16t^2+128t=0

-t^2+8t=0

-t(t-8)=0

t=0 (reject)

or

t=8

The projectile will return to the ground after 8 sec

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Correct question:

A projectile is launched from the ground with an initial velocity of V0 feet per second. Neglecting air resistance, its height in feet per seconds after launch is given by s = -16t^2 +V0t. Find the time(s) that the projectile will

(a) reach a height of 192ft and

(b) return to the ground when V0= 112 feet per second.

The recursive formula that represents the number of sequences in this sequence is n(n-1)(n-2)/6, where n is the number of terms in the sequence.

This recursive formula is based on the pattern of the sequence. The sequence has three terms, a, b and c, and then three combinations of two terms, ab, ac and bc, and then one combination of all three terms, abc. This pattern of three terms, then three combinations of two terms, then one combination of all three terms continues as the sequence increases.

The recursive formula represents this pattern in a mathematical equation. The formula is n(n-1)(n-2)/6, where n is the number of terms in the sequence. This formula is derived from the fact that for each term there are two other terms that can combine with it to form a two-term combination, and one combination of all three terms. Therefore, for n terms, there are n(n-1)/2 two-term combinations and one combination of all three terms, for a total of n(n-1)(n-2)/6 sequences.

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The complete question is

if the pattern below contiunues which equation(s) is a recursive formula that reprsents the number of sequences in this sequence 5, 10, 20, 40.

Answer:

[tex]\underline{x\quad \:\:\:\:\:\:-8\quad\quad\;\;-6\quad\quad0\quad\quad\quad\;\; \;\;2}\\y\quad\quad\;\;\;\boxed{\dfrac{1}{3}}\quad\quad\quad \boxed{0} \quad\;\boxed{-1} \quad\quad \boxed{\dfrac{4}{3}}[/tex]

Step-by-step explanation:

The strategy is to substitute the value of each of the given x values into the equation
[tex]y = -\dfrac{x}{6} - 1[/tex]
and find the corresponding value for [tex]y[/tex]

[tex]x\quad\quad\quad\quad\quad\quad\quad\quad\quad y = -\dfrac{x}{6} - 1\\\line(1,0){180}\\\\[/tex]

[tex]-8\quad\quad\quad\quad\quad\quad\quad\quad\quad y = -\dfrac{-8}{6} - 1 = \bf{{\dfrac{1}{3}[/tex]
[tex]-6\quad\quad\quad\quad\quad\quad\quad\quad\quad y = -\dfrac{-6}{6}-1 = \bf{0}[/tex]
[tex]0\quad\quad\quad\quad\quad\quad\quad\quad\quad y = -\dfrac{0}{6}-1 = \bf{-1}[/tex]
[tex]2\quad\quad\quad\quad\quad\quad\quad\quad\quad y = -\dfrac{2}{6} -1 =\bf{-}\dfrac{4}{3}[/tex]

[tex]\line(1,0){180}\\\\[/tex][tex]\line(1,0){180}\\\\[/tex]

In 50! will have 12 leading zeroes so the power of 10 will be 12 And for 1000! will have 249 Zeroes so here the power of 10 will be 249.

We calculate the leading zeroes by knowing the numbers 2 And 5 So

This number must end with 249 zeroes since there are 249 fives (and more than 249 twos) in its prime factorization. Thus 10 249 is the highest power of 10 that divides 1000!

To see why we have 249 powers of five:

200 + 48 + 8 + 1 = 249

And also we can do this with a formula n−σp(n)/(p−1) where σp(n)  is the sum of the digits of n written in base-p

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.

When the domain of x is restricted, the function x2 becomes one-to-one, and the inverse function is x.

It is true that limiting a function's domain might cause it to become invertible. Because it is not one-to-one in the example, the function x2 is not invertible across its complete domain of real numbers (i.e., it assigns multiple outputs to some inputs). However, x2 becomes one-to-one and invertible when the domain of x is constrained to or any subset of that interval. The range of x2, which is, is used to define the inverse function in this situation, which is

The function x2 becomes one-to-one when the domain of x is constrained, and the inverse function is

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Because x is 6, points A, B, and C are collinear.

The intersection of two lines in Euclidean geometry can be the empty set, a point, or another line. Distinguishing these cases and locating the intersection have applications in computer graphics, motion planning, and collision detection, among others. The intersecting lines are two lines that share exactly one common point. The intersecting lines have a point in common. The point of intersection is the common point that exists on all intersecting lines. When two or more lines intersect in a plane, they are referred to as intersecting lines. The intersecting lines share a common point, which exists on all of them and is known as the point of intersection.

Here,

Since the opposite angle are equal in intersecting lines,

42=7x

x=6

The value of x is 6 so that points A, B, and C are collinear.

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A). The first term represents the total cost of the waffle irons and the second term represents the expenses.

B). The algebraic expression represents if the company sells 350 waffle irons per day will be 350x - 1500

C). The company's profit for a 5-day week is $250.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the algebraic expression 25x - 1,500 can be used to describe the daily profit of a company that makes waffle irons.

A). The first term represents the total cost of the waffle irons and the second term represents the expenses. Here 25 is the number of the waffle iron and the x is the number of days.

B). The algebraic expression represents if the company sells 350 waffle irons per day will be written as:-

350x - 1500

C). The company's profit for a 5-day week will be;-

Profit = 350x - 1500

Profit = ( 350 x 5 ) + 1500

Profit = 1750 - 1500

Profit = 250

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The volume of his large vase is 2,373.84cm^3 (option A)

The is 4 times the volume of the small verse. (option A)

A cylinder is a three-dimensional object. It is a prism with a circular base.

volume of a cylinder = nr^2h

Where:

Radius of the small verse = 6/2 = 3 cm

Volume of the small verse = 3.14 x 3² x 21 = 593.46 cm³

Radius of the large verse = (2 x 6) / 2 = 6cm

Volume of the large verse = 3.14 x 6² x 21 = 2,373.84 cm³

Difference in volumes =  2,373.84 cm³/  593.46 cm³ = 4

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The concept of linear pairs from the given diagram shows that; GKH =  90°

A linear pair is formed when two straight lines intersect to form two angles that are adjacent to each other and are on a straight line.

Now, what this means is that ∠F KG and ∠GKH will sum up to 180 degrees because they are linear pairs from the question.

Due to the fact that ∠F KG = 90°, then we can say that;

∠F KG + ∠GKH = 180°

90° + ∠GKH = 180°

∠GKH = 180° - 90°

∠GKH =  90°

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The simplified form of the first expression is -37 + 6i and the second expression is -16 - 14i.

What is the arithmetic operations?

Arithmetic operations are basic mathematical operations that can be performed on numbers, such as addition, subtraction, multiplication, and division.

The first expression is 7 - (3 + 41) + 6i. To simplify this expression, we need to first simplify the parentheses. Inside the parentheses, we have 3 + 41 = 44. So the expression becomes:

7 - 44 + 6i

Next, we can simplify the arithmetic operations by combining like terms:

7 - 44 + 6i = -37 + 6i

The second expression is -10 + (6 - 5i) - 9i. Similar to the first expression, we need to simplify the parentheses first. Inside the parentheses, we have 6 - 5i = 6 - 5i. So the expression becomes:

-10 + 6 - 5i - 9i

Next, we can simplify the arithmetic operations by combining like terms:

-10 + 6 - 5i - 9i = -16 - 14i

Hence, the simplified form of the first expression is -37 + 6i and the second expression is -16 - 14i.

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Answer:

B 6

Step-by-step explanation:

Answer:

B. 6

Step-by-step explanation:

6 x -14 = 3x + 4

3x = 18

X = [tex]\frac{18}{3}[/tex] Which equals =

6

There a rule for logarithms:

         [tex]\log_n(a^m) = m \cdot \log_n(a)[/tex]

So when you're working with [tex]\log_5(a^3)[/tex], we can use that rule to rewrite this as
        [tex]\log_5(a^3) = 3 \cdot \log_5(a)[/tex]

And since the first part tells us (on paper) that [tex]\log_5(a) = 2[/tex], then we can say
        [tex]\log_5(a^3) = 3 \cdot \log_5(a) = 3 \cdot 2 = 6[/tex]

Answer:

x

=

0

,

x

=

1

,

x

=

2

,

x

=

−

1

, and

x

=

−

2

Explanation:

Start off by factoring out an

x

as follows

x

(

x

4

−

5

x

2

+

4

)

=

0

We can factor

x

4

−

5

x

2

+

4

Doing so we have

x

(

x

2

−

4

)

(

x

2

−

1

)

=

0

So in order for this to be equal to zero

x

=

0

OR

x

2

−

4

=

0

OR

x

2

−

1

=

0

Well

x

=

0

x

2

=

4

x

=

±

√

4

=

±

2

x

2

=

1

x

=

±

√

1

=

±

1

Answer:x=4, y=5

Step-by-step explanation:

Step-by-step explanation:

Money she makes=$140

since she saves 4/5 of the money she earns that means that: 4/5×140 = $32

This means that she saves $32 out of $140 she makes or earn

The Rate of plane in still air and rate of wind is 738 , 100 respectively .

What is Linear equation ?

Linear equation can be defined as the equation in which the highest degree is one

Given ,

An airplane travels 4466 kilometers against the wind in 7 hours and 5866 kilometers with the wind in the same amount of time.

Let speed of plane be Vp and Va

Now,

Vp - Va  = 4466 / 7

Vp+Va = 5866 / 7

So, Evaluating the equations,

we get,

2Vp = (4466+5866) / 7

Vp = 1476 / 2

Vp = 738

So substitute Vp =738 in Vp-Va = 4466/7

738 - Va = 638

Va = 738 - 638

Va = 100.

Hence, The Rate of plane in still air and rate of wind is 738 , 100 respectively .

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Answer:

The function's minimal value is m = A |B|. When either sin x or cos x is equal to 1, this minimum is reached. Create a graph for the first example, y = 1 + 2 sin x.

Step-by-step explanation:

70 + 2x > 100 is an inequality to represent this situation.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given, At a local pizza shop, the delivery person earns $2 for every pizza delivered, plus $70 per day.

Let "x" be the number of pizzas he delivers

Thus, the Total money he earns by delivering pizza = 70 + 2x

To earn more than 100$ inequality represents

70 + 2x > 100

So,

2x > 30

x > 15

Therefore, to earn more than 100$ every day he needs to deliver at least 15 pizzas.

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