Visitors to the library restroom used up 3/4 of a bottle of soap in 1/2 of a day. At that rate, how much soap would they use up in 1 full day?

For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

To determine the value of n₀ for which Algorithm A is better than Algorithm B when B uses n√n operations, we need to find the point at which the number of operations for Algorithm A is less than the number of operations for Algorithm B.

Algorithm A: 10n log n operations

Algorithm B: n√n operations

Let's set up the inequality and solve for n₀:

10n log n < n√n

Dividing both sides by n gives:

10 log n < √n

Squaring both sides to eliminate the square root gives:

100 (log n)² < n

To solve this inequality, we can use trial and error or graph the functions to find the intersection point. After calculating, we find that n₀ is approximately 459. Therefore, For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

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R-1.3: For \($n \geq 14$\), Algorithm A is better than Algorithm B when B uses \($n^2$\) operations.

R-1.4: Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

R-1.3:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n^2$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n^2$\)

\($10 \log n < n$\)

\($\log n < \frac{n}{10}$\)

To solve this inequality, we can plot the graphs of \($y = \log n$\) and \($y = \frac{n}{10}$\) and find the point of intersection.

By observing the graphs, we can see that the two functions intersect at \($n \approx 14$\). Therefore, for \($n \geq 14$\), Algorithm A is better than Algorithm B.

R-1.4:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n\sqrt{n}$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n\sqrt{n}$\)

\($10 \log n < \sqrt{n}$\)

\($(10 \log n)^2 < n$\)

\($100 \log^2 n < n$\)

To solve this inequality, we can use numerical methods or make an approximation. By observing the inequality, we can see that the left-hand side \($(100 \log^2 n)$\) grows much slower than the right-hand side \($(n)$\) for large values of \($n$\).

Therefore, we can approximate that:

\($100 \log^2 n < n$\)

For large values of \($n$\), the left-hand side is negligible compared to the right-hand side. Hence, for \($n \geq 1$\), Algorithm A is better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

So, for R-1.4, the value of \($n_0$\) is 1, meaning Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

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So, the simpler form of the radical expression 4 sqrt 1296 x^16y^12 is 144x^14y^14 sqrt (x) sqrt (y).

To simplify the radical expression 4 sqrt 1296 x^16y^12, we need to first factor the number inside the radical. 1296 can be factored into 36 x 36, which simplifies to 6^4. So, the expression becomes 4 sqrt (6^4 x^16y^12).
Next, we can simplify the expression further by using the property of exponents that says a^m x a^n = a^(m+n). This means that we can combine the exponents of x and y, which gives us 4 sqrt (6^4 x^(16+12) y^(12+16)). Simplifying this, we get 4 sqrt (6^4 x^28 y^28).
Now, we can simplify the radical expression even further by using the property that says sqrt (a x b) = sqrt (a) x sqrt (b). Applying this to our expression, we get 4 x 6^2 x sqrt (x^28) x sqrt (y^28). Simplifying this further, we get 144x^14y^14 sqrt (x) sqrt (y).
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The height of the cylinder is \(3 inch\)

Based on the attached figure,

Volume of the cylinder = 282.7 square inches

Radius of the cylinder =5 inches.

The height of the cylinder = ?

The volume of the cylinder  can be found with the formula as :

\(V=pi r^{2} h\)

\(h=\frac{V}{pi r^{2} } \\\\h = \frac{282.7}{3.142 * 5^{2} } \\\\=3 inch\)

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Answer:

\(\frac{2}{9}\)

Step-by-step explanation:

there is a four out of nine change to get a green marble

there is a 1/2 change to get heads

\(\frac{4}{9}\)×\(\frac{1}{2} =\frac{2}{9}\)

The only sort of proof among the following options in the question that is frequently employed in geometry is the 'two-column' proof.

Geometry is the area of mathematics that deals with the characteristics of space and the shapes of particular things as well as the interactions between them in space.

A two-column geometric proof consists of a list of assertions and the justifications for each one's truth.

The statements are listed in a left-hand column, while the justifications for the statements are listed in a right-hand column.

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Step-by-step explanation:

the notation f(-2) indicates that you will substitute x for the value -2.

f(-2) = 6 ( 8 - (-2) ) +5 = 65

Answer:

4+(8-2)=(4+8)+2

does not show associative property.

If for her party, Carla bought a 5-pound bag of candy to give as party treats. She invited 15 people. The amount of candy that each of the 15 people get is: A) 15 ÷ 5 = 15/5 = 3 pounds.

Given data:

Candy bought = 5

Number of people invited = 15

Now let find the amount of candy to gives as party treats

Number of candy = Number of people invited / Candy bought

Number of candy = 15/5

Number of candy = 3 pounds

Therefore we can conclude that the correct option is A.

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The trace of a matrix is the sum of the diagonal elements of a square matrix. It is not related to the determinant or the inverse of the matrix, and remains the same even when we take the transpose of the matrix.

The correct definition of the trace of a matrix is that it is the sum of the diagonal elements of a square matrix. In other words, if we have a square matrix, the trace is obtained by summing the elements on the main diagonal from the top-left to the bottom-right.

The trace of a matrix does not relate to the determinant or the inverse of the matrix. It is a separate concept that specifically refers to the sum of the diagonal elements.

Additionally, the trace of a matrix remains the same even when we take the transpose of the matrix.

This means that the trace of the transpose of a matrix is equal to the trace of the original matrix.

To summarize, the trace of a matrix is the sum of the diagonal elements of a square matrix, and it is unaffected by the matrix's inverse or transpose.

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Answer:

A

Step-by-step explanation:

since the slope (2) is positive the graph is similar to y=x, so graphs B and D are eliminated

so when x=1 we have

y=2(1)-3

y=2-3

y=-1

so the point is (1,-1), graph C eliminated

so it's A

The standard equation for finding the equation of a line is expressed as

y = mx + b

m is the slope of the line

b is the y-intercept

Before we can plot the equation of a line, we must know the slope and the y-intercept of such line.

Given the equation of a line to be plotted expressed as y = 2x - 3

Compared with the standard equation;

mx = 2x

m = 2

Hence the slope of the line is 2

Similarly;

b = -3

Hence the y-intercept is 3.

Find the required graph attached below:

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Answer:

y=-1/2 x-4

Step-by-step explanation:

y=mx+c

c is -4

m is rise/run so -1/2

Answer:

  circumcenter

Step-by-step explanation:

You want to know the name of the point equidistant from the vertices of a triangle.

The circle that passes through the vertices of a triangle is called a "circumcircle". It circumscribes the triangle. Its center is equidistant from all points on the circle, so is equidistant from the triangle's vertices.

The point equidistant from the vertices of a triangle is the circumcenter.

__

Additional comment

The circumcenter is at the intersection of the perpendicular bisectors of the sides of the triangle.

Answer:

I think the final cost would be:

562.86

Step-by-step explanation:

:))

Answer:

Step-by-step explanation:

11:30-9:30=2

so Danielle starts 2 hrs late.

let Danielle catches them after x hrs.

x×60=(x+2)×20

divide by 20

3x=x+2

3x-x=2

2x=2

x=1

so Danielle takes 1 hour to catches them.

Answer:

first option

Step-by-step explanation:

Using the rule of exponents

\((\frac{a^{m} }{a^{n} }) ^{p}\) = \(\frac{a^{mp} }{a^{np} }\) , then

\((\frac{2^{5} }{^{2} } )^{4}\)

= \(\frac{2^{5(4)} }{3^{2(4)} }\)

= \(\frac{2^{20} }{3^{8} }\)

Answer:

X=4 would be right above the 4 on the x axis.

Step-by-step explanation:

So you see where it says x? Graph it on the 4 on that line.

Answer:

Graph it on the 4 on line X

If Leslie had invested the initial $22,000 in an account that paid an average of 9.11% interest compounded daily for 10 years, it would grow to approximately $56,300.

b. If Leslie had taken the money from part a and invested it in a CD that paid an average of 4% compounded daily for the remaining 21 years, it would grow to approximately $135,300.

c. If Leslie deposited $750 each year into an account that paid 4.09% compounded annually for 31 years, he would have approximately $49,600.

d. The total gain from the three accounts would be approximately $158,200.

e. Leslie invested $22,000 in the Nomad.

f. Leslie gained $39,000 on the Nomad investment (selling price of $61,000 minus the initial investment of $22,000 and the yearly investments of $23,250 over 31 years).

g. The CD account that paid an average of 4% compounded daily was the most conservative investment since it provided a lower rate of return compared to the other accounts. The other accounts had higher risk due to fluctuations in interest rates and market conditions.

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Answer:

the answer is 3  

Step-by-step explanation:

The value of the product and the ratio of the variables is a constant in an

inverse and direct variation respectively.

Responses:

1. y·x is a constant, therefore, the relationship is an inverse variation

2. Neither y·x or \(\dfrac{y}{x}\) is constant, therefore, the relationship is neither direct or inverse variation

3. \(\mathbf{\dfrac{y}{x}}\) is constant, therefore, the relationship is a direct variation

4. \(\dfrac{y}{x}\) is constant, therefore, the relationship is a direct variation

5. Neither y·x or \(\dfrac{y}{x}\) is constant, therefore, the relationship is neither direct or inverse variation

6. y·x is a constant, therefore, the relationship is an inverse variation

7. C = 7 × 2 = 14

The function is therefore;

When x = 10, we have;

8. C = 0.2 × 4 = 0.8

The function is therefore;

When x = 10, we have;

\(y = \dfrac{0.8}{10} = \underline{0.08}\)

9. C = \(\frac{9}{10} \times \frac{1}{3} = \frac{3}{10}\) = 0.3

The function is therefore;

When x = 10, we have;

Please find attached the required graphs created with MS Excel

10. a. From the given table, we have;

C = p × h = 360 (constant)

Which gives;

b. If they charge p = $7.50 per hat, we have;

13. The constant is the product of the ordered pair;

\(C = 3 \times \dfrac{1}{3} =\underline{ 1}\)

14. The constant, C = 0.6 × 6 = 1.2

15. The constant C = 10 × 5 = 50

16. C = \(\dfrac{5}{7} \times \dfrac{2}{5}\) = \(\underline{\dfrac{2}{7}}\)

17. C = -13 × 22 = -286

18. \(C = \dfrac{1}{2} \times 10\) = 5

19. C = \(\dfrac{1}{3} \times \dfrac{6}{7}\) = \(\underline{\dfrac{2}{7}}\)

20. C = 4.8 × 2.9 = 13.92

21. C = \(\dfrac{5}{8} \times -\dfrac{2}{5}\) = \(\underline{-\dfrac{1}{4}}\)

22. 4.75 × 4 = 19

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3/10 (option B)

fraction that chose vanilla ice cream = 2/5

fraction that chose chocolate ice cream = 3/10

let the fraction that chose strawberry ice cream = y

Total fraction = 1

fraction that chose vanilla ice cream + fraction that chose chocolate ice cream + fraction that chose strawberry ice cream = 1

2/5 + 3/10 + y = 1

Fraction of the class chose strawberry ice cream is 3/10 (option B)

Answer: ( g+G) (x) =12+2x

Step-by-step explanation:

i used an math ap it is  an app you can get on your phone

The concept that can explain this is called "Survivorship Bias". Survivorship bias occurs when we focus on those who "survived" or made it through a particular event or process, and overlook those who did not. In the case of marriage, those who have divorced are not included in the statistics on happy marriages, so the overall rate of happy marriages appears to be higher than it actually is.

In other words, the statistics on divorce rates only take into account marriages that have ended in divorce, but not the marriages that have remained intact. Therefore, the majority of spouses who report being very happy in their marriage are likely the ones who have successfully stayed married and are still together. The statistics only reflect those who have not been able to maintain a happy marriage.

It's also important to note that happiness is subjective and can vary from person to person. Some individuals may find happiness in their marriage despite facing challenges, while others may not. Therefore, even if a marriage does end in divorce, it does not necessarily mean that it was unhappy throughout its duration.

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Answer:

x = 6.9168 or x = 7

Step-by-step explanation:

Hope that helps :)

The first model of inequality satisfy the problem i.e 2w + 2* 4w ≤ 106

A rectangle is a four-sided, two-dimensional flat shape. The opposite sides of a rectangle's four sides are parallel and equal to one another. It belongs to a category of quadrilaterals where each of the four angles is a straight angle or measures 90 degrees. A particular kind of parallelogram that has all of its angles equal is the rectangle. A square is a rectangle with four equally sized sides. Let's now explore the characteristics of the rectangle in this essay.

Rectangles' essential characteristics are as follows:

A rectangle is a parallelogram.

The Perimeter of the rectangle is 2a + 2b where a and b are the two sides

Now , if w is the width of the rectangle then, the length is 4w given in problem.

Perimeter,

2w + 2* 4w

As it is given in the problem

2w + 2* 4w ≤ 106

The first model of inequality satisfy the problem.

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Answer:

24

Step-by-step explanation:

Answer:

I think option no B is the correct answer wer.

Answer:

infinite number of solutions

Step-by-step explanation:

x + y = 1 → (1)

3y = - 3x + 3 ( add 3x to both sides )

3x + 3y = 3 ( divide through by 3 )

x + y = 1 → (2)

since the 2 equations are the same, this indicates the system has an infinite number of solutions

Answer:

Step-by-step explanation:

19?

Answer:

5 km

Step-by-step explanation:

I realize that the equation is different, but do it in the same way, it'll help! It is given that the water​ taxi's path can be modeled by the equation y =0.5(x - 14)^2. ​Therefore, this is one of the equations in this system. Find a linear equation that will model the path of the water​ skier, which begins at the point (6,6) and ends at the point (8,-4). The slope is (-5). Use the slope and one point on the line to find the​ y-intercept of the line.  The​ y-intercept of the line that passes through the points (6,6) and (8,-4) is (0,36). Thus, the equation is y=-5x+36. Now, to determine if it is possible for the water skier to collide with the​ taxi, we have to determine if there is a solution to the system of equations. To determine if there is a solution to the system of​ equations, solve the system using substitution.​ First, write the equation that models the water​ taxi's path in standard form. y=0.5(x - 14)^2-->0.5x^2-14x+98. Use substitution. Substitute for  y in the equation and then solve for  x. As the expression on the left side of the equation cannot easily be​ factored, use the Quadratic Formula to solve for x. Do x=-b(plusorminus)sqrrtb^2-4ac/2a. Identify a, b, and c. a=0.5, b=-9, and c=62. Substitute into the Quadratic Formula. If there is a negative number under the radical, there are NO solutions. Thus, the path of the water skier will never cross the path of the taxi.

In conclusion: It is not possible that the water skier could collide with the taxi as the two paths never cross.