65 points im desparate dont worry about the name i will give brainlest helppppppp

1. Answer the following questions.
Questions
What is an amount between $2 and $10? (A) __________
What is an amount between $10 and $20? (B) __________
What is an amount greater than $50? (C) __________
What is your name? (D) ____________________
What is the name of an item that you will buy only once? (E) ____________________
What is the name of an item that you will buy more than once? (F) ____________________

2. Create a word problem that leads to an inequality by filling in the blanks with your corresponding answers.
Word Problem
(D) ____________________ is going shopping for (E) ____________________ and (F) ____________________. The cost of (E) ____________________ is (B) __________ and the cost of each (F) ____________________ is (A) __________.
If (D) ____________________ can spend at most (C) __________, how many (F) ____________________ can be purchased?

3. Write an inequality of the form Ax + B ≤ C to represent the word problem using your answers for A, B, and C. Solve the inequality and show your work.


4. Graph the solution to your inequality on a number line or describe, in words, how to graph the inequality on a number line.


5. Explain what the solution means in the context of the word problem.

The explicit formula for an, the nth term of the sequence 28,14,7,.... is

[tex]a_n = 28 / 2^{(n-1)}[/tex]

What is a sequence?

A Sequence is a set of things (usually numbers) that are in order. Each number in the sequence is called a term (or sometimes "element" or "member"), read Sequences and Series for a more in-depth discussion.

To find the explicit formula for the sequence 28, 14, 7, ... we can observe that each term in the sequence is half of the previous term.

Specifically, we can see that the first term is 28, the second term is 14, which is half of 28, the third term is 7, which is half of 14, and so on.

Therefore, we can express the nth term of the sequence as:

[tex]a_n = 28 / 2^{(n-1)}[/tex]

where n is the position of the term in the sequence.

For example, the fourth term of the sequence would be:

a4 = 28 / 2⁽⁴⁻¹⁾ = 28 / 2³ = 28 / 8 = 3.5

Note that this formula is based on the observation that each term is half of the previous term.

If this pattern does not continue indefinitely, the formula may not accurately represent the sequence beyond a certain point.

Therefore, the explicit formula for an, the nth term of the sequence 28,14,7,.... is

[tex]a_n = 28 / 2^{(n-1)}[/tex]

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The interval for the graphed function that contains the local maximum is from (negative 0.5, negative 7) to (1.5, 1).

To find the interval for the graphed function that contains the local maximum, we need to use the given minimum and maximum values. The minimum values are (negative 0.5, negative 7) and (2.5, negative 1), and the maximum value is (1.5, 1). We need to determine the x-axis and y-axis crossings. The x-axis crossings are (negative 1, 0), (1, 0), and (3, 0), and the y-axis crossing is (0, negative 6). To find the interval, we need to find the lowest x-coordinate and the highest y-coordinate of the given values. The lowest x-coordinate is (negative 0.5, negative 7) and the highest y-coordinate is (1.5, 1). Thus, the interval for the graphed function that contains the local maximum is from (negative 0.5, negative 7) to (1.5, 1).

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The volume of the solid obtained by rotating the region bounded by the curves x=y and x=y² about the y-axis is π/6 cubic units. We can find the solution in the following manner.

To find the volume of the solid obtained by rotating the region bounded by the curves x=y and x=y² about the y-axis, we can use the method of cylindrical shells.

First, we need to determine the limits of integration. The curves x=y and x=y² intersect at y=0 and y=1. Therefore, the limits of integration will be from y=0 to y=1.

Next, we need to express the equation x=y in terms of y. This gives us x=y.

Then, we need to express the equation x=y² in terms of y. This gives us x=y².

Now, we can set up the integral for the volume of the solid using the formula for cylindrical shells:

V = 2π∫[y=0 to y=1] y(x=y² - x=y) dy

Simplifying the expression inside the integral, we get:

V = 2π∫[y=0 to y=1] y(y² - y) dy

V = 2π∫[y=0 to y=1] (y³ - y²) dy

V = 2π [ 1/4 y⁴ - 1/3 y³ ] [y=0 to y=1]

V = 2π (1/12)

V = π/6

Therefore, the volume of the solid obtained by rotating the region bounded by the curves x=y and x=y² about the y-axis is π/6 cubic units.

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Answer:

Slope:3x

Y-intercept: 4

Step-by-step explanation:

You can rearrange this equation to be to see it easier:

y=3x+4

Then, the slope always shows how many units you need to move up/down/left/right and always has an "x" next to it.

The y-intercept is the last number in the equation, which represents where the line intercepts the y-axis.

Answer:

slope is 3

y intercept is 4

Step-by-step explanation:

The equation of the line is in slope intercept form y = mx + b, where m is the slope and b is the y intercept. Judging by this information, we can analyze the line and see which is the slope and which is the y intercept.

[tex]y=3x+4[/tex]

The slope is 3, since it is m in the equation, and the y intercept is 4, since it is b in the equation.

The simple interest fοr 2 years is $318.

The cοst οf bοrrοwing mοney is knοwn as simple interest because cοmpοunding effects are nοt taken intο cοnsideratiοn. Simply said, simple interest sοlely affects the principal sum. When mοney is bοrrοwed fοr a specific periοd οf time at a specific rate, a tiny sum οf mοney knοwn as simple interest is levied.

Here the given ,

Principal P = $3000

Rate of interest = 5.3%

Number of years = 2

Now simple interest = [tex]\frac{PNR}{100}[/tex]

=> I = [tex]\frac{3000\times5.3\times2}{100}[/tex]

=> I = $318

Hence the simple interest for 2 years is $318.

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Calculate the simple interest for the following data:

​Principal ​= $3000​;

Annual interest​ rate =5.3​%;

​time 2 years.

Let's assume that the job requires x workers to complete it in 12 hours.

We can use the following formula:

workers × time = constant

Therefore, for 3 workers to complete the job in 28 hours, we have:

3 × 28 = 84

For x workers to complete the same job in 12 hours, we have:

x × 12 = 84

Solving for x, we get:

x = 7

Therefore, we need 7 workers to complete the job in 12 hours, which is 4 more workers than the initial 3.

We have shown that the first difference system with scaled feedback by a is equal to the summation formula.

The first difference system with scaled feedback by a is given by:

We can rewrite this equation in terms of summation notation:

By substituting k = i - 1, we can rewrite the summation as:

Now, we can use the property of summation that states that ∑ a[i]b[i] = a ∑ b[i], where a is a constant, to rewrite the equation as:

Since [] is a constant, we can divide both sides of the equation by [] to get:

Finally, we can simplify the left-hand side of the equation to get:

This equation is equivalent to the summation formula given in the question:

Therefore, we have shown that the first difference system with scaled feedback by a is equal to the summation formula.

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The correct response is C. 3.75 hats per game. The graph of the function 3.75 hats per game.

A collection of dots, lines, line segments, curves, or areas that show how one variable changes in connection to one or more other variables a grouping of all points whose coordinates meet a certain relation (such as a function)

According to the graph of the function, we know that the fitting line goes through points (3, 25) and (7, 40).

So, the rate of change is equal to 40-25/7-3=15/4=3.75

So choose A. 3.75 hats per game.

(If line goes through point [tex](x_{0}, y_{0})[/tex] and point [tex](x_{1}, y_{1})[/tex] Hence, its rate of change equals [tex]\frac{y_{1}-y_{0}}{x_{1}-x_{0}}[/tex] ([tex]x_{1}[/tex] is not equal to [tex]x_{0}[/tex]))

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The approximate radius of curvature of the function f(t) matches None of the options.

To find the approximate radius of curvature of the function f(t) at the point (x, y) = (8, 16), we need to first find the first and second derivatives of the function. The first derivative of f(x) is f'(x) = 6 and the second derivative is f''(x) = 0.

Next, we can use the formula for the radius of curvature,

R = [(1 + (f'(x))^2)^(3/2)] / |f''(x)|.

Plugging in the values of f'(x) and f''(x) into the formula, we get:

R = [(1 + (6)^2)^(3/2)] / |0|

Since the denominator is 0, the radius of curvature is undefined. The answer is none of the options given.

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The values οf A and B1 are ±2√3 and 3, respectively.

An equatiοn is a mathematical statement that shοws the equality οf twο expressiοns οr values, typically represented by the use οf an equals sign (=) between them.

Given equatiοns are:

B1 = -A²  + 15 ...(i)

-B1 = -A²  + 9 ...(ii)

Multiplying equatiοn (ii) by -1, we get:

B1 = A²  - 9

Nοw, equating equatiοns (i) and (iii), we get:

-A^2 + 15 = A²  - 9

2A²  = 24

A²  = 12

A = ±√12

A = ±2√3

Putting A = 2√3 in equatiοn (i), we get:

B1 = - (2√3)²  + 15

B1 = -12 + 15

B1 = 3

Sο, the values οf A and B1 are:

A = ±2√3

B1 = 3

Similarly, putting A = -2√3 in equatiοn (i), we get:

B1 = - (-2√3)² + 15

B1 = -12 + 15

B1 = 3

Sο, the values οf A and B1 are:

A = ±2√3

B1 = 3

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The probability that you receive a hand with at least 3 suits if you are dealt 5 cards from a well-shuffled deck of cards is 0.45.

A standard deck of cards has 52 cards.

Each card belongs to one of four suits: diamonds, hearts, clubs, and spades.

There are thirteen cards in each suit:  ace, two, three, four, five, six, seven, eight, nine, ten, jack, queen, and king.

Calculation:

The total number of hands that can be drawn from a deck of 52 cards is given by 52C5 or (52 × 51 × 50 × 49 × 48) / (5 × 4 × 3 × 2 × 1) = 2,598,960.

There are 4 ways to choose 3 suits out of 4.

If we select 3 suits, each suit is represented by 13 cards, so the number of ways to select 3 suits is

[tex]13C_5 × 13C_5 × 13C_5 = 5,531,120.[/tex]

Ways to select 4 suits:

There are 4 ways to select 4 suits, each with 13 cards, so the number of ways to select 4 suits is

[tex]13C_5 × 13C_5 × 13C_5 × 13C_5 = 13,842,900.[/tex]

Total ways of selecting a hand of 5 cards with at least 3 suits = 5,531,120 + 13,842,900 = 19,374,020

Therefore, the probability of getting a hand with at least 3 suits is 19,374,020 / 2,598,960 = 0.45.

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In terms of sin t and cos t, (f g)(t) equals (5cos t - 1)/sin t.

To find (f ∘ g)(t), we need to substitute g(t) into f(x): (f ∘ g)(t) = f(g(t)) = f(cot t)

Now we can substitute cot t into the equation for f(x):

f(cot t) = 5(cot t) - (cot t)^2 - 1

Next, we can simplify by using the identities cot t = 1/tan t and tan t = sin t/cos t:

f(cot t) = 5(1/tan t) - (1/tan t)^2 - 1

f(cot t) = 5(cos t/sin t) - (cos t/sin t)^2 - 1

Finally, we can simplify further by multiplying by the common denominator of sin t:

f(cot t) = (5cos t - cos^2 t - sin^2 t)/sin t

Using the identity sin^2 t + cos^2 t = 1, we can simplify the numerator:

f(cot t) = (5cos t - 1)/sin t

Therefore, (f ∘ g)(t) = (5cos t - 1)/sin t.

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Answer:

yes

Step-by-step explanation:

This is an isosceles triangle.  The base (4) just needs to be less than 32 (16+16), which it is!

Answer:

2 and 25

Step-by-step explanation:

(i)

to find g(g(0)) , evaluate g(0) , then substitute the value obtained into g(x)

g(0) = 0² + 1 = 0 + 1 = 1 , then

g(1) = 1² + 1 = 1 + 1 = 2

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

(ii)

to find f(g(2)), evaluate g(2) , then substitute the value obtained into f(x)

g(2) = 2² + 1 = 4 + 1 = 5 , then

f(5) = 5² = 25

Answer:

89.375m of wire

Step-by-step explanation:

0.325 times 275 is equal to 89.375 meters of wire in about 79 seconds.

c = 6t this equation states that the number of chairs is equal to 6 times the number of tables.

An equation is a mathematical statement that shows that two expressions are equal. It usually contains one or more variables, which are represented by letters, and one or more constants, which are represented by numbers.

Based on the given information, we can see that the number of chairs is directly proportional to the number of tables.

When the number of tables increases, the number of chairs also increases, and vice versa.

The constant of proportionality is 6, since each table has 6 chairs. Therefore, the equation that represents the relationship between the number of chairs, c, and the number of tables, t, is:

c = 6t

This equation states that the number of chairs is equal to 6 times the number of tables.

For example, the equation 2x + 5 = 13 is an equation that contains the variable x, and states that the expression 2x + 5 is equal to 13. In this case, the goal is to find the value of x that makes the equation true, which is x = 4.

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A homogeneous equation.

Yes, the following are linear equations:
(A) Ut = (xux)2 + (yuy)y + xy
This equation can be put in the form Lu linear operator L as follows: LAUt = 0, which is a homogeneous equation.

(B) uux + Uxxx = Ut
This equation can be put in the form Lu linear operator L as follows: LBu = Ut, which is an inhomogeneous equation.

(C) Utt = Uxxxx + Uyyyy
This equation can be put in the form Lu linear operator L as follows: LCT = 0, which is a homogeneous equation.

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The answer isarc sin(x/a) * a^2/2 + C.

∫ √ a^2 - x^2 dx = arc sin(x/a) * a^2/2 + C. To evaluate the given integral, we need to use trigonometric substitution. Let's substitute x = a sin θ.Then, dx = a cos θ dθNow, the limits will change as below.

When x = 0, θ = 0When x = a, θ = π/2∫ √ a^2 - x^2 dx = ∫ √ a^2 - a^2 sin^2 θ a cos θ dθ= a^2 ∫ cos^2 θ dθ= a^2/2 ∫ (1 + cos 2θ) dθ= a^2/2 [θ + sin 2θ/2] + C Putting the limits, we get;∫ √ a^2 - x^2 dx = arc sin(x/a) * a^2/2 + C Therefore, the answer isarc sin(x/a) * a^2/2 + C.

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The probability of the third card being the same suit as the first two is 11/50, since there are only 11 cards of that suit remaining in the deck. Thus, the probability of all three cards having the same suit is:4 x (1 x 12/51 x 11/50) = 0.0588, which is approximately 5.88%.

The standard deck of 52 cards includes four suits, each containing 13 cards. These suits are hearts, diamonds, clubs, and spades.Each of the 13 cards in a suit includes an ace, 2 through 10, a jack, a queen, and a king. Thus, the total number of aces in a standard deck of cards is 4. Similarly, the total number of cards in a standard deck of cards is 52.

The solution to the problem are as follows:a) Probability of getting three acesThe probability of getting an ace on the first draw is 4/52. The probability of getting another ace on the second draw is 3/51, since there are only three aces remaining in the deck.

The probability of getting the third ace on the third draw is 2/50, since there are only two aces remaining in the deck. Thus, the probability of getting three aces is:4/52 x 3/51 x 2/50 = 0.00018, which is approximately 0.02%b) Probability of getting a pairThe probability of getting a pair is the probability of getting two cards of the same rank, regardless of the suit.

There are 13 possible ranks to choose from. The probability of getting the first card is 52/52, since all 52 cards are available. The probability of getting the second card of the same rank is 3/51, since there are only three cards of that rank remaining in the deck.

The probability of getting the third card is 48/50, since two cards of that rank have already been drawn. Thus, the probability of getting a pair is:13 x (52/52 x 3/51 x 48/50) = 0.2353, which is approximately 23.5%.c) Probability of all three cards having the same suitThe probability of the first card being any suit is 1. The probability of the second card being the same suit as the first is 12/51, since there are 12 cards of that suit remaining in the deck.

The probability of the third card being the same suit as the first two is 11/50, since there are only 11 cards of that suit remaining in the deck. Thus, the probability of all three cards having the same suit is:4 x (1 x 12/51 x 11/50) = 0.0588, which is approximately 5.88%.

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Start with the element in the first row and column and add it to the sum. Then, recursively call the same function on the remaining elements in the same row, until all elements in the row are summed. Once the row is complete, start with the next row and add it to the sum.

Recursion is a powerful technique for computing the sum of elements in an n × n (two-dimensional) array of integers. To do this, start with the element in the first row and column and add it to the sum. Then, recursively call the same function on the remaining elements in the same row, until all elements in the row are summed. Once the row is complete, start with the next row and add it to the sum. This process should be repeated until all rows and columns have been processed. By using recursion, you can compute the sum of all the elements in the array in an efficient manner.

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The area of the shaded portion is 7.7 units²

What is the area of a square?

A square is a 2D figure in which all the sides are of equal measure. Since all the sides are equal, the area would be length times width, which is equal to side × side. Hence, the area of a square is a side square.

In the figure, the side  length of the square = 6 units

And the also sector of the circle lies inside the square.

To find the area of the shaded portion.

So, the area of the shaded portion= ( area of the square - area of the sector)

The area of the square = ( side)²

                                     = (6)²

                                      = 36 units

And the area of the sector = ( θ°/360°) ×πr²

                                           = ( 90°/360°) ×(22/7)×(6)²

                                           = (1/4)×(22/7)×(36)

                                           = 28.3 units²

So, the area of the shaded portion = ( 36 - 28.3 ) units²

                                                        = 7.7 units²

Hence,  the area of the shaded portion is 7.7 units²

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Answer:

the answer to y is 92

Step-by-step explanation:

if x=25 and y=23 if we multiply x by 4 to get 100 and did the same with y it will get 92

y + 1 = 3(x-6) in Ax + By = C form is 3x - y = 19. A quadratic function's standard form is written as f(x) = ax2 + bx + c, where c is the y-intercept of the function's graph.

A quadratic function is the polynomial function that a quadratic polynomial defines. f(x) = ax2 + bx + c, where a, b, and c are constants and a = 0 represents a quadratic function. The quadratic term, abbreviated as ax2, the linear term, abbreviated as bx, and the constant term are all names for the function (abbreviated as c). Three points produce a quadratic function of the formula f(x) = ax2 + bx + c. A quadratic function can be determined by finding a, b, and c algebraically given three locations on the graph.

The y-intercept is the location on a graph where the y-axis crosses. To get 3x - 18 on the right side, we shall first distribute the 3 through the parenthesis. Bring down your y + 1 to the left to obtain y + 1 = 3x - 18. Subtract 1 from both sides to get y = 3x - 19, then transfer the 1 to the right side. To get -3x + y = -19, subtract 3x from both sides now. The x term's coefficient in standard form must be positive. Thus, subtract -1 from both sides to get 3x - y = 19.

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∫xdy1−x2y2 dx = - ydx xdy1−x2y2 + c

To solve the differential equation ydx xdy1−x2y2 xdx=0, start by integrating both sides with respect to x. This yields:

∫ydx xdy1−x2y2 xdx = ∫0 dx

Next, solve the integrals on the left side of the equation by applying the following formula:

∫u dv = uv - ∫v du

This gives us:

ydx xdy1−x2y2 = 0 - ∫xdy1−x2y2 dx

Finally, integrate both sides with respect to x. This will yield the solution to the differential equation:

∫xdy1−x2y2 dx = - ydx xdy1−x2y2 + c

Where c is the constant of integration.

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[0,∞)

Given f(x) = x, g(x) = √x.

To find (f + g)(x), first, add f(x) and g(x) to get the result.

(f + g)(x) = f(x) + g(x) = x + √x

(f + g)(x) = x + √x.

For the domain of (f + g)(x), we need to consider the values that are acceptable for both x and √x. x can be any real number, but √x is only defined for x ≥ 0. Therefore, the domain of (f + g)(x) is [0,∞).

Domain of (f + g)(x) = [0,∞)

Now, let us find the other results.

(f - g)(x) = f(x) - g(x) = x - √x

(fg)(x) = f(x)·g(x) = x·√x = x^(3/2)

(f/g)(x) = f(x) / g(x) = x / √x = √x

(f - g)(x) = x - √x

The domain of (f - g)(x) is also [0,∞) as √x is defined for x ≥ 0.

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When f(x) = x, g(x) =√x

(f + g)(x) = x + √x, Domain: [0, +∞)

(f - g)(x) = x - √x, Domain: [0, +∞)

fg(x) = x√x = x^(3/2), Domain: [0, +∞)

f/g(x) = x/√x = √x, Domain: [0, +∞)

To find (f + g)(x), we add the two functions together:

(f + g)(x) = f(x) + g(x) = x + √x. The domain of this function is restricted by the domain of g(x), which is a non-negative value, hence the domain of (f + g)(x) is [0, +∞).

To find (f - g)(x), we subtract g(x) from f(x): (f - g)(x) = f(x) - g(x) = x - √x. The domain of this function is also [0, +∞).

To find fg(x), we multiply f(x) and g(x): fg(x) = f(x)g(x) = x√x = x^(3/2). The domain of this function is again [0, +∞).

To find f/g(x), we divide f(x) by g(x): f/g(x) = f(x) / g(x) = x / √x = √x. The domain of this function is the same as the domain of g(x), which is [0, +∞]

Therefore, we have found the functions (f + g)(x) = x + √x, (f - g)(x) = x - √x, fg(x) = x^(3/2), and f/g(x) = √x, along with their corresponding domains [0, +∞).

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The triangle is an οbtuse triangle.

Tο determine if the triangle is acute, οbtuse, οr right, we need tο check if it satisfies the Pythagοrean theοrem. Accοrding tο the Pythagοrean theοrem, in a right triangle, the sum οf the squares οf the lengths οf the legs (the shοrter sides) is equal tο the square οf the length οf the hypοtenuse (the lοngest side). Sο, if the sum οf the squares οf the twο shοrter sides is equal tο the square οf the lοngest side, then the triangle is a right triangle.

Let's calculate the squares οf the three sides:

The square οf the first side (18 cm) is 324.

The square οf the secοnd side (80 cm) is 6400.

The square οf the third side (81 cm) is 6561.

Nοw, we need tο determine if the sum οf the squares οf the twο shοrter sides is greater than οr less than the square οf the lοngest side. Sο, we have:

324 + 6400 = 6724

Since 6724 is less than 6561, the triangle dοes nοt satisfy the Pythagοrean theοrem and it is nοt a right triangle. Therefοre, the triangle is either an acute οr οbtuse triangle.

Tο determine if the triangle is acute οr οbtuse, we need tο find the largest angle οf the triangle. We can use the Law οf Cοsines tο find the largest angle οf the triangle, which is οppοsite the lοngest side. The Law οf Cοsines states that in any triangle:

[tex]c^2 = a^2 + b^2[/tex] - 2ab cοs(C)

where a, b, and c are the lengths οf the sides οf the triangle, and C is the angle οppοsite the side c.

In οur case, a = 18 cm, b = 80 cm, and c = 81 cm. Sο, we have:

[tex]81^2 = 18^2 + 80^2 - 2(18)(80) cos(C)[/tex]

6561 = 324 + 6400 - 2880 cοs(C)

Nοw, we can sοlve fοr cοs(C):

cοs(C) = (6400 + 324 - 6561) / (2(18)(80))

cοs(C) = -0.2216

Since cοsine is negative, the angle C is οbtuse.

Therefοre, the triangle is an οbtuse triangle.

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You want to know the classification of a triangle with side lengths 18 cm, 80 cm, and 81 cm. A triangle can be classified by looking at the measure of its largest angle. The classification of the triangle is the same as the classification of that angle: obtuse if > 90°, right if = 90°, and acute if < 90°.

The largest angle is always opposite the longest side. In a triangle with angles A, B, C and their opposite sides a, b, c, we can call the largest angle C. Its measure can be computed using the Law of Cosines, which tells you ...

  C = arccos((a² +b² -c²) / (2ab))

  C = arccos((18² + 80² - 81²) / (2×18×80)) = arccos(163/2880) ≈ 86.8°

The largest angle is less than 90°, so the triangle is an acute triangle.

The numerical value of the expression tanh(0) is 0.

The hyperbolic tangent function, tanh(x), is defined as:

tanh(x) = (e^x - e^(-x)) / (e^x + e^(-x))

When x = 0, the function simplifies to:

tanh(0) = (e^0 - e^(-0)) / (e^0 + e^(-0))

Since e^0 = 1, the expression becomes:

tanh(0) = (1 - 1) / (1 + 1) = 0 / 2 = 0

Therefore, the hyperbolic tangent function tanh(x) equals (e^x - e^(-x)) / (e^x + e^(-x)). When x = 0, tanh(0) simplifies to 0.

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As per the concept of integral, the solution of the equation has the value of $2,777,200.00

The definite integral of R(t) over the interval [61, 62] can be written as:

∫[61,62] (900t² + 300) dt

To calculate this integral, we need to first find its antiderivative, which is the function that, when differentiated, gives us R(t). The antiderivative of 900t² + 300 is 300t³ + 300t + C, where C is the constant of integration.

To evaluate the definite integral over the interval [61, 62], we can plug in the upper limit 62 into the antiderivative and subtract it from the antiderivative evaluated at the lower limit 61. This gives us:

(300(62)³ + 300(62)) - (300(61)³ + 300(61)) = $2,777,200.00

Simplifying this expression gives us the amount of money PayBuddy loses during the one-second downtime, which is approximately equal to $2,777,200.00 (rounded to two decimal places).

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Discrete random variables take on a countable number of distinct values. Therefore, the random variables that are discrete from the given set are:

The number of people riding on a bus: This is a discrete random variable as it can only take on integer values. The number of people on the bus can be 0, 1, 2, 3, and so on, but cannot take on fractional or continuous values.

The number of concert tickets sold: This is also a discrete random variable as the number of tickets sold can only take on integer values. The number of tickets sold can be 0, 1, 2, 3, and so on, but cannot take on fractional or continuous values.

The life span of a parakeet: This is a continuous random variable, as the life span of a parakeet can take on any value within a range of possible values, such as 2.5 years, 3.2 years, or 4.8 years.

The height of a person from a class of eight: This is a continuous random variable, as height can take on any value within a range of possible values, such as 5'7.5", 5'10", or 6'2".

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