For a square ABCD, the side BC = 13 units.
A is at (.x, 8) and B is at (-7,3)
Also, x > 0.
Find.x​

The time complexity of the given code is O(n^3) or cubic complexity. This is because there are three nested loops that iterate over the range from 1 to n, resulting in a cubic relationship between the input size and the number of operations.

The code contains three nested loops. The outermost loop iterates from 1 to n, resulting in n iterations. The second loop is nested inside the outermost loop and also iterates from i to n, resulting in an average of n/2 iterations. The innermost loop is nested inside both the outermost and second loops and iterates from j+1 to n, resulting in an average of (n-j) iterations.

Considering all three loops together, the total number of iterations can be calculated as the product of the number of iterations in each loop. Thus, the time complexity is given by:

n * (n/2) * (n-j)

Simplifying this expression, we get:

(n^3)/2 - (n^2)/2

However, when analyzing time complexity, we focus on the dominant term, which is the term with the highest power of n. In this case, it is (n^3). Therefore, we can conclude that the time complexity of the code is O(n^3), or cubic complexity.

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Answer:

Correct V100 is right

Step-by-step explanation:

Answer:

A=-3

Step-by-step explanation:

To begin, a parabola of form a(x-h)² +k opens upward when a is positive. Similarly, when a is negative, the parabola opens downward. Therefore, a must be negative here, as our expression for the parabola is a(x-0)²+0 = ax², with (0,0) being (h,k) and the vertex.

To determine whether a should be -3 or -0.6, we can think about the values on the graph that correspond to these values. A narrower graph would have a steeper slope. A narrower graph would have a large change in y with little change in x. Therefore, as ax² = y is our equation, and when a=-3, y changes more rapidly relative to when a = -0.6, A=-3 is our answer

Answer:

i think the answer is C. 1.5w^2 + 7.5w + 9

To find a quadratic equation with the y-intercept and vertex, follow these steps: identify the coordinates of the y-intercept and vertex, substitute them into the general form of the quadratic equation, solve for the coefficients, and substitute the coefficients back into the equation. For example, if the y-intercept is (0, 3) and the vertex is (-2, 1), the quadratic equation would be y = x^2 + x + 3.

To find a quadratic equation with the y-intercept and vertex, we can follow these steps:

For example, let's say the y-intercept is (0, 3) and the vertex is (-2, 1). We can substitute these coordinates into the general form of the quadratic equation:

3 = a(0)^2 + b(0) + c

1 = a(-2)^2 + b(-2) + c

Simplifying these equations, we get:

c = 3

4a - 2b + c = 1

By substituting c = 3 into the second equation, we can solve for a and b:

4a - 2b + 3 = 1

4a - 2b = -2

2a - b = -1

By solving this system of equations, we find a = 1 and b = 1. Substituting these values back into the general form of the quadratic equation, we obtain the final equation:

y = x^2 + x + 3

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To find a quadratic equation with a given y-intercept and vertex, you need the coordinates of the vertex and one additional point on the curve.

Example:

Suppose we want to find a quadratic equation with a y-intercept of (0, 4) and a vertex at (2, -1).

To find a quadratic equation with a given y-intercept and vertex, you can use the vertex form of a quadratic equation and substitute the coordinates to obtain the equation. Then, use the y-intercept to find an additional point on the curve and solve a system of equations to determine the coefficients. Finally, substitute the coefficients into the standard form of the quadratic equation to get the final equation.

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The given line is

We need two points to graph a line. Let's find the axis intercepts with x=0 and y=0.

The y-intercept: x=0

The y-intercept is (0,-5).

The x-intercept: y=0

The x-intercept is (-5,0).

Now, we graph these points and draw a straight line.

4 houses have 0 bicycles

4 x 0 = 0

2 houses have 1 bicycle

2 x 1 = 2

3 houses have 2 bicycles

3 x 2 = 6

5 houses have 3 bicycles

5 x 3 = 15

6 houses have 4 bicycles

6 x 4 = 24

2 houses have 5 bicycles

2 x 5 = 10

0 + 2 + 6 + 15 + 24 + 10

2 + 21 + 34

23 + 34

57

There are 57 bicycles altogether on merton street.

Hope this helps!

Answer:

-1/3

Step-by-step explanation:

Multiply by root 3 on the top and bottom. Root 3 times root 3 is 3. 2-3 is -1.

a) The feasible set can be represented as a straight line with a negative slope on a graph.

b) The preferred choice point is (15, 15).

c)  With an entrance fee of $9, the new feasible set shifts vertically upwards.

d)  The change in entrance fee reduced the amount of leftover cash in the feasible set.

a) The x-axis represents the number of pizza slices, and the y-axis represents the leftover cash. The line starts at the point (0, 60) and intersects the x-axis at (20, 0). This means that you can buy a maximum of 20 pizza slices with $60, and if you don't buy any pizza, you will have $60 left.

b) This point represents buying 15 slices of pizza, which costs $45, and having $15 left. It is the preferred choice because it allows for a balance between enjoying pizza and not exhausting all the cash. It provides both a substantial amount of pizza and a reasonable amount of leftover cash.

c) The line now starts at (0, 51) and intersects the x-axis at (20, 9). This means that with the entrance fee, you can buy a maximum of 20 pizza slices and have $9 left.

d) It means that you have less cash available after buying pizza slices. The new preferred choice would likely shift downwards to a point that allows for a reasonable number of pizza slices while still leaving enough money to cover the entrance fee.

The change in entrance fee makes it necessary to consider the balance between the number of pizza slices and the available cash more carefully to ensure you can afford the entrance fee and still enjoy a satisfying amount of pizza.

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Answer:

y = - 1/2x + 5

Step-by-step explanation:

the slope is -1/2 because the line is declining two units to the right for every one unit down. and the "b" is 5 because the line hits the y-axis at +5

Answer:

Step-by-step explanation:

0.6 add thatby 3.8 and the answer is 5

Answer:

y= 3/4x+17/4

Step-by-step explanation:

You're welcome :)

Answer:

DE = 6 cm

Step-by-step explanation:

The concept behind this question is the Chord-Chord Power Theorem. This product states that "if two chords intersect in a circle, then the products of the lengths of the chords segments are equal". In this case:

CE × DE = AE × BE

4 × DE = 8 × 3

4 × DE = 24
DE = 6 cm

Hope this helps!

a) The average annual sales of bottled water over the period 2000-2010 is estimated to be 10200 million gallons per year to the nearest 100 million gallons.

b) The two-year moving average of s(t) for each value of t within the range [0, 10] is: (7650, 8012.5, 7650, 7410, 6300, 6600, 4800, 4050, 1200, -150, -3900)

(a) To estimate the average annual sales of bottled water over the period 2000-2010, we need to calculate the average value of the function s(t) = -45\(t^2\) + 900t + 4200 over the interval [0, 10].

The average value of a function f(x) over an interval [a, b] is given by the expression:

Average value = (1 / (b - a)) * ∫[a, b] f(x) dx

In this case, the interval is [0, 10] and the function is s(t) = -45\(t^2\) + 900t + 4200.

Therefore, the average annual sales can be estimated by:

Average annual sales = (1 / (10 - 0)) * ∫[0, 10] (-45\(t^2\) + 900t + 4200) dt

Evaluating the integral:

Average annual sales = (1 / 10) * [-15\(t^3\) + 450\(t^2\) + 4200t] evaluated from t = 0 to t = 10

Average annual sales = (1 / 10) * [(0 - 0) - (-15000 + 45000 + 42000)]

Average annual sales = (1 / 10) * [102000]

Average annual sales = 10200 million gallons per year

Therefore, the average annual sales of bottled water over the period 2000-2010 is estimated to be 10200 million gallons per year to the nearest 100 million gallons.

(b) To compute the two-year moving average of s, we need to find the average of s(t) over each two-year interval.

We can calculate this by taking the average of s(t) at each point t and its neighboring point t + 2.

Two-year moving average of s(t) = (s(t) + s(t + 2)) / 2

To apply the formula for the two-year moving average of s(t), we need to calculate the average of s(t) and s(t + 2) for each value of t within the range [0, 10].

For t = 0:

Two-year moving average at t = 0: (s(0) + s(2)) / 2 = (-45(0)^2 + 900(0) + 4200 + (-45(2)^2 + 900(2) + 4200)) / 2 = (8400 + 6900) / 2 = 7650

For t = 1:

Two-year moving average at t = 1: (s(1) + s(3)) / 2 = (-45(1)^2 + 900(1) + 4200 + (-45(3)^2 + 900(3) + 4200)) / 2 = (8555 + 7470) / 2 = 8012.5

For t = 2:

Two-year moving average at t = 2: (s(2) + s(4)) / 2 = (-45(2)^2 + 900(2) + 4200 + (-45(4)^2 + 900(4) + 4200)) / 2 = (8400 + 6900) / 2 = 7650

For t = 3:

Two-year moving average at t = 3: (s(3) + s(5)) / 2 = (-45(3)^2 + 900(3) + 4200 + (-45(5)^2 + 900(5) + 4200)) / 2 = (7470 + 7350) / 2 = 7410

For t = 4:

Two-year moving average at t = 4: (s(4) + s(6)) / 2 = (-45(4)^2 + 900(4) + 4200 + (-45(6)^2 + 900(6) + 4200)) / 2 = (6900 + 5700) / 2 = 6300

For t = 5:

Two-year moving average at t = 5: (s(5) + s(7)) / 2 = (-45(5)^2 + 900(5) + 4200 + (-45(7)^2 + 900(7) + 4200)) / 2 = (7350 + 5850) / 2 = 6600

For t = 6:

Two-year moving average at t = 6: (s(6) + s(8)) / 2 = (-45(6)^2 + 900(6) + 4200 + (-45(8)^2 + 900(8) + 4200)) / 2 = (5700 + 3900) / 2 = 4800

For t = 7:

Two-year moving average at t = 7: (s(7) + s(9)) / 2 = (-45(7)^2 + 900(7) + 4200 + (-45(9)^2 + 900(9) + 4200)) / 2 = (5850 + 2250) / 2 = 4050

For t = 8:

Two-year moving average at t = 8: (s(8) + s(10)) / 2 = (-45(8)^2 + 900(8) + 4200 + (-45(10)^2 + 900(10) + 4200)) / 2 = (3900 + (-1500)) / 2 = 1200

For t = 9:

Two-year moving average at t = 9: (s(9) + s(11)) / 2 = (-45(9)^2 + 900(9) + 4200 + (-45(11)^2 + 900(11) + 4200)) / 2 = (2250 + (-2850)) / 2 = (-300) / 2 = -150

For t = 10:

Two-year moving average at t = 10: (s(10) + s(12)) / 2 = (-45(10)^2 + 900(10) + 4200 + (-45(12)^2 + 900(12) + 4200)) / 2 = ((-1500) + (-6300)) / 2 = (-7800) / 2 = -3900

Therefore, the two-year moving average of s(t) for each value of t within the range [0, 10] is as follows:

(7650, 8012.5, 7650, 7410, 6300, 6600, 4800, 4050, 1200, -150, -3900)

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Answer:

-7y^2-x+11y

Step-by-step explanation:

Answer:

where is the equal to sign????

A. Manager A wants the decision to be 0.4, so they would recommend a decision of 0.4 to the principal.

B. The recommendations in the Nash equilibrium would be rA = 0.4 and rB = 0.7.

(a) If Manager B always truthfully reports the state of the economy (s = 0.7), Manager A would send a recommendation that minimizes their disutility Ua. In this case, Manager A wants the decision to be 0.4, so they would recommend a decision of 0.4 to the principal.

(b) In a Nash equilibrium, both managers strategically make their recommendations based on their own utility. Manager A wants to minimize their disutility Ua, which increases as the decision deviates from 0.4. Manager B wants to minimize their disutility UB, which increases as the decision deviates from 0.7.

To find the Nash equilibrium, we need to consider the recommendations made by both managers simultaneously. Let's denote the recommendations as rA (from Manager A) and rB (from Manager B). The principal's decision, d, would be the average of the recommendations, so d = (rA + rB) / 2.

Given that both managers strategically choose their recommendations, they will aim to minimize their disutility. In this case, Manager A would recommend a decision of 0.4 (as it minimizes Ua), and Manager B would recommend a decision of 0.7 (as it minimizes UB). Therefore, the recommendations in the Nash equilibrium would be rA = 0.4 and rB = 0.7.

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The equation of the tangent line to the curve \(\(f(x) = \cos\left(\frac{2x}{\pi} - 1\right)\) at \(x = \frac{\pi}{2}\) is \(x = \frac{\pi}{2}\).\)

What are Tangent lines?

Lines that touch a curve at a certain location and have the same slope as the curve are known as tangent lines. In other words, the slope or instantaneous rate of change of a curve at a specific point is represented by a tangent line to a curve. The curve near that point is approximated linearly by it. Calculus frequently makes use of tangent lines to analyze the behavior of functions and pinpoint crucial elements like derivatives, rates of change, and local linearity.

Let's find the equation of the tangent line to the curve \(\(f(x) = \cos\left(\frac{2x}{\pi} - 1\right)\) at \(x = \frac{\pi}{2}\).\)

The equation of a tangent line to a curve can be written in the form \(\(y = mx + b\),\) where \(\(m\)\) is the slope of the tangent line and b is the y-intercept.

To find the slope of the tangent line, we take the derivative of \(\(f(x)\)\) with respect to x:

\(\[f'(x) = -\frac{2}{\pi} \sin\left(\frac{2x}{\pi} - 1\right)\]\)

Substituting \(\(x = \frac{\pi}{2}\) into \(f'(x)\),\) we have:

\(\[f'\left(\frac{\pi}{2}\right) = -\frac{2}{\pi} \sin\left(\frac{2}{\pi} \cdot \frac{\pi}{2} - 1\right) = -\frac{2}{\pi} \sin(0) = 0\]\)

Since the slope of the tangent line is 0, the equation of the tangent line is simply the vertical line \(\(x = \frac{\pi}{2}\).\)

Therefore, the equation of the tangent line to the curve \(\(f(x) = \cos\left(\frac{2x}{\pi} - 1\right)\) at \(x = \frac{\pi}{2}\) is \(x = \frac{\pi}{2}\).\)

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a. The median number of calls = 55

b. The first and third quartiles, Q1 = 48 and Q3 = 66

c. The first decile and the ninth decile, D1 = 45 and D9 = 71.

d. The 33rd percentile = 52.5

To answer the questions, let's first organize the data in ascending order:

38 40 41 45 48 48 50 50 51 51 52 52 53 54 55 55 55 56 56 57 59 59 59 62 62 62 63 64 65 66 66 67 67 69 69 71 77 78 79 79

(a) The median is the middle value of a dataset when arranged in ascending order.

Since we have 40 observations, the median is the value at the 20th position.

In this case, the median is the 55th visit.

(b) The quartiles divide the data into four equal parts.

To find the first quartile (Q1), we need to locate the position of the 25th percentile, which is 40 * (25/100) = 10.

The first quartile is the value at the 10th position, which is 48.

To find the third quartile (Q3), we need to locate the position of the 75th percentile, which is 40 * (75/100) = 30.

The third quartile is the value at the 30th position, which is 66.

Therefore, Q1 = 48 and Q3 = 66.

(c) The deciles divide the data into ten equal parts.

To find the first decile (D1), we need to locate the position of the 10th percentile, which is 40 * (10/100) = 4.

The first decile is the value at the 4th position, which is 45.

To find the ninth decile (D9), we need to locate the position of the 90th percentile, which is 40 * (90/100) = 36.

The ninth decile is the value at the 36th position, which is 71.

Therefore, D1 = 45 and D9 = 71.

(d) To find the 33rd percentile, we need to locate the position of the 33rd percentile, which is 40 * (33/100) = 13.2 (rounded to 13). The 33rd percentile is the value at the 13th position.

Since the value at the 13th position is between 52 and 53, we can calculate the percentile using interpolation:

Lower value: 52

Upper value: 53

Position: 13

Percentage: (13 - 12) / (13 - 12 + 1) = 1 / 2 = 0.5

33rd percentile = Lower value + (Percentage * (Upper value - Lower value))

                = 52 + (0.5 * (53 - 52))

                = 52.5

Therefore, the 33rd percentile is 52.5.

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Answer:

D. 5

Step-by-step explanation:

We can triangle JHK is isosceles because two of its sides are radii, and radii of the same circle are always equal. Let the radius equal r. We can say that both JH and HK equal r because the extend from the center to the circle. We can set up the equation:

PJHK = JK + JH + HK

18 = 8 + r + r

10 = 2r

r = 5

Since HK equals r, it equals 5.

(f - g)(x) = f(x) - g(x)

… = (3x² - 4) - (4x + 1)

… = 3x² - 4x - 5

The given data is,A matched pairs experiment compares the taste of instant with fresh-brewed coffee. Each subject tastes two unmarked cups of coffee, one of each type, in random order and states which he or she prefers.

Of the 60 subjects who participate in the study, 21 prefer the instant coffee. We need to find the probability that a randomly chosen subject prefers fresh-brewed coffee to instant coffee, let's say p. The formula to calculate the proportion of the population is:

p = (n1 + n2) / (x1 + x2)n1 and n2 are the sample sizes of two categories and x1 and x2 are the number of favorable outcomes from the respective categories. Here, n1 = n2 = 60 and x1 = 39 (since 21 out of 60 prefer instant coffee, the remaining 39 must prefer fresh-brewed coffee).Now, p = (60 + 60) / (39 + 21) = 1.2. Since p is a probability, it must be between 0 and 1. But here, p is greater than 1, which is not possible. Therefore, there is an error in the given data and we cannot proceed with the calculation.

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It will cost you $48 to rent the moving truck from True Value Rentals for 5 hours.

The cost to rent a moving truck from True Value Rentals for 5 hours, considering their rental rates. Let's break down the costs step-by-step:

1. For the first 3 hours, the rental fee is $16.
2. We need to calculate the additional time beyond the initial 3 hours. In this case, you want to rent the truck for 5 hours, which is 2 hours longer than the initial period.
3. The additional charge is $4 for every 15 minutes. To find out how many 15-minute intervals are in the extra 2 hours, we'll convert 2 hours to minutes (2 hours * 60 minutes/hour = 120 minutes) and then divide by 15 minutes/interval:
  120 minutes / 15 minutes/interval = 8 intervals
4. Now that we know there are 8 additional 15-minute intervals, we'll multiply the number of intervals by the extra charge per interval ($4):
  8 intervals * $4/interval = $32
5. Finally, to find the total cost of renting the truck for 5 hours, we'll add the initial rental fee of $16 to the additional charge of $32:
  $16 + $32 = $48

In conclusion, it will cost you $48 to rent the moving truck from True Value Rentals for 5 hours.

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Answer:

Step-by-step explanation:

Circle centre: (4,7)

Radius: 3

Equation is:

  \((x-h)^2+(y-k)^2=r^2\)   (where (h,k) is center, r is radius)

  \((x-4)^2+(y-7)^2=3^2\)

  \((x-4)^2+(y-7)^2=9\)     (This is the general standard form )

in expanded form,

  \((x^2-8x+16)+(y^2-14y+49)=9\)

  \(x^2+y^2-8x-14y+56=0\)

Note: Unless stated either form is an acceptable answer.

Answer:

For the given information, let's solve the following:

a. Do you know that the period of a function is the time taken for one complete cycle of the function? In this case, the Ferris wheel takes one rotation every 80 seconds, which means it completes one cycle in 80 seconds. Therefore, the period of the function is 80 seconds.

b. To write f(t) in the form of f(t) = a sin b(t-h) + k, we first need to determine the amplitude, period, and phase shift of the function. The amplitude is half the distance between the highest and lowest points of the function, which is (102-94)/2 = 4 feet. The period is 80 seconds, which we found in part a. The phase shift is 0 since the ride starts at the highest point. Therefore, the function can be written as f(t) = 4 sin (2π/80)t + 102.

c. To graph the function, we can plot the height of the car (y-axis) against time (x-axis), using the function obtained in part b.

d. To find the value of f(15), we simply substitute t = 15 in the function obtained in part b. f(15) = 4 sin (2π/80)(15) + 102 = 98.28 feet. This makes sense because after 15 seconds, the car would have traveled a quarter of a cycle and would be descending from the highest point.

e. To find f(180), we can use the fact that the Ferris wheel takes one rotation every 80 seconds. Therefore, after 180 seconds, the wheel would have completed two full cycles and would be back at the highest point. Therefore, f(180) = 102 feet.

I hope this helps! Let me know if you have any further questions or if there's anything else I can assist you with.

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