which expression gives the area of the triangle shown below

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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Answer:

predict the impact of removing snakes from this food web

The major determinant of the permeability of a membrane to a specific ion is "the quantity of open ion channels that are specific to that ion."

Certain cells, known as excitable cells, are distinguished by their capacity to produce electrical signals.

Some key features regarding the open ion channels are-

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To determine the constant amount that can be withdrawn each year for 20 years, we need to calculate the annuity payment using the present value of an annuity formula.

Inherited amount: RM300,000

Interest rate: 7% per year

Number of years: 20

Using the present value of an annuity formula:

PV = P * [(1 - (1 + r)^(-n)) / r]

Where:

PV = Present value (inherited amount)

P = Annuity payment (constant amount to be withdrawn each year)

r = Interest rate per period (7% or 0.07)

n = Number of periods (20 years)

Plugging in the values:

300,000 = P * [(1 - (1 + 0.07)^(-20)) / 0.07]

Solving this equation, we find that the constant amount that can be withdrawn each year is approximately RM15,000.

Therefore, the correct answer is A. RM15,000.

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The pentagonal prism with volume 360 in³ and height of 3 inches have a base area of 120 in²

A pentagonal prism is a prism that has two pentagonal bases like top and bottom and five rectangular sides.

Given that, the volume of a pentagonal prism is 360 in³, with a height of 3 inches,

We need to find the area of the base,

We know that, the volume of a pentagonal prism is =

V = 1/4 √(5(5+2√5)·a²h

Where a is the base edge and h is the height,

360 = 1/4·3 √(5(5+2√5)·a²

1/4·√(5(5+2√5)·a² = 120

Since, the base of a pentagonal prism is a pentagon, and the area of a pentagon = 1/4 √(5(5+2√5)·a²

And we have,

1/4 √(5(5+2√5)·a² = 120

Therefore, the base area is 120 in²

Hence, the pentagonal prism with volume 360 in³ and height of 3 inches have a base area of 120 in²

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Project management services refer to the professional assistance and support provided to organizations to plan, execute, and manage projects effectively. These services may include a range of activities, such as project planning, scheduling, budgeting, risk management, stakeholder management, quality assurance, and project reporting.

Project management services can be provided by both internal and external professionals. Internal project managers are employees of the organization who are responsible for managing projects within the company.

External project management services can be hired from consulting firms, specialized project management companies, or freelance professionals who work independently.

Project management services can help ensure that projects are delivered on time, within budget, and to the required quality standards.

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Explain project Management Services

The correct answer is option A which is y = 25x + 100.

Given the following:

To join a local square dancing group, Jan has to pay a $100 sign-up fee plus $25 per month

We need to write an equation for the cost (y) based on the number of months.

To solve the above problem, the answer is;a. y = 25x + 100

Explanation; Let's break down the problem

The $100 sign-up fee is a fixed cost that is added only once to the monthly fee which is $25. Thus the equation for the cost (y) based on the number of months can be expressed as; y = 25x + 100 where:y is the cost for the number of monthsx is the number of months

Therefore the correct answer is option A which is;y = 25x + 100.

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To join a local square dancing group,

Jan has to pay a $100 sign-up fee plus $25 per month.

The equation for the cost (y) based on the number of months is

y = 25x + 100,

where x is the number of months.

Option A is the correct equation for the cost based on the number of months.

Writing the equation:

y = 25x + 100

Where:

y = Cost based on the number of months

x = Number of months

Therefore, when Jan has been part of the local square dancing group for 1 month, the total cost will be:

$25 * 1 + $100 = $125

And if Jan has been a part of the group for 4 months, then the total cost would be:

$25 * 4 + $100 = $200

Therefore, option A is the correct answer.

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2.5 cm, 6.5 cm, and 6 cm are the sides of a right triangle.

The sides of a triangle are 2.5 cm, 6.5 cm, and 6 cm in length.

The Pythagorean Theorem states that The sum of the squares representing the base and height equals the square of the hypotenuse.

\((Perpendicular)^{2}+(Base)^{2}=(Hypotenuse)^{2}\)

                        \((2.5)^{2}+(6)^{2}=(6.5)^{2}\)

                            6.25 + 36 = 42.25

                                  42.25 = 42.25

The sides offered satisfy the specifications for a right triangle.

Given that it satisfies the Pythagorean theorem, a right triangle with sides of 2.5 cm, 6.5 cm, and 6 cm can be built.

Hence, 2.5 cm 6.5 cm 6 cm can be the sides of a right triangle.

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Answer:

A B DE on ed 2021

Step-by-step explanation:

The first question was answered on another page.

As for your second question, you are unfortunately not correct.

We can check each possible answer by adding up the costs for each road. I recommend getting a marker out to trace the path, to help keep track of which roads were taken.

So we have...

We see that Circuit ACDBA is the cheaper route of the answer choices given, and it perfectly matches with choice 2.

This may or may not be the cheapest route. I'm not all that familiar with the Nearest Neighbor algorithm to properly find the cheapest route (the next best thing is brute force). Luckily we can just use the answer choices as shown above. Besides the question doesn't ask for the absolute cheapest, but instead, "one of the cheapest".

The limit is 1

To evaluate the limit, we first observe that it is of the form 1^infinity (since as x approaches infinity, the fraction inside the parentheses approaches 1). We can use the property that e^L = lim(x-> infinity) (1 + 1/x)^x for any L, to rewrite the limit as:

lim x → [infinity] e^[(ln(1+5/x)*x)/10]

Now we can use l'Hôpital's rule to evaluate the limit of the natural logarithm of the original expression, since it has the indeterminate form 0/0 as x approaches infinity:

ln(1+5/x) = (1/(1+5/x)) * (d/dx)(1+5/x) = -5/(x+5)^2

Thus, we have:

lim x → [infinity] e^[(ln(1+5/x)*x)/10] = lim x → [infinity] e^[-(5x)/(10(x+5)^2)]

= e^0 = 1

Therefore, the limit is 1

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The two numbers are 109 and 77.

Let's denote the two numbers as x and y. We are given two equations:

Equation 1: x + y = 186

Equation 2: x - y = 32

To solve the system of equations by graphing, we can plot the two equations on a graph and find their point of intersection, which represents the values of x and y that satisfy both equations.

For Equation 1, when x = 0, y = 186, and when y = 0, x = 186. Plotting these two points and connecting them gives us a straight line.

For Equation 2, when x = 0, y = -32, and when y = 0, x = 32. Plotting these two points and connecting them also gives us a straight line.

The point where these two lines intersect is the solution to the system of equations. In this case, the intersection point is (109, 77), indicating that x = 109 and y = 77.

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The difference quotient of f(x) is \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\) .

According to the given question.

We have a function

f(x) = -1/(5x -12)

As we know that, the difference quotient is a measure of the average rate of change of the function over and interval.

The difference quotient formula of the function y = f(x) is

[f(x + h) - f(x)]/h

Where,

f(x + h) is obtained by replacing x by x + h in f(x)

f(x) is a actual function.

Therefore, the difference quotient formual for the given function f(x)

= [f(x + h) - f(x)]/h

= \(\frac{\frac{-1}{5(x+h)-12} -\frac{-1}{5x-12} }{h}\)

= \(\frac{\frac{-1}{5x + 5h -12}+\frac{1}{5x-12} }{h}\)

= \(\frac{\frac{-1+5h}{5x + 5h-12} }{h}\)

= \(\frac{-1+5h}{(5x +h-12)(h)}\)

= \(\frac{-1+5h}{5xh + h^{2} -12h}\)

= \(\frac{h(-\frac{1}{h}+5) }{h(5x+h-12)}\)

= \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\)

Hence, the difference quotient of f(x) is \(\frac{-\frac{1}{h}+ 5}{5x+ h -12}\) .

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Answer:

It would be (1,-1)

Step-by-step explanation:

Answer:

6.75 grams

Step-by-step explanation:

Total amount of lemonade with Samantha =  4 1/2 gallons

         = (4*2 + 1)/2 gallons = 9/2 gallons = 4.5 gallons

Amount of fat in 1 gallon of lemonade = 1.5 grams

To find amount of fat in 4.5 gallons lemonade

we multiply both side of equation with 4.5

Amount of fat in 1*4.5 gallon of lemonade = 1.5*4.5  grams = 6.75 grams

Thus,

there is  6.75 grams of fat in  all the lemonade Samantha has for the party

Based on the fact that this is an equilateral triangle, the value of y can be found to be 5.

The figure given is an equilateral triangle which means that the lengths of all the sides are equal.

As DC is equal to 20, it means that all the other sides should be 20 as well.

This means that the value of y is:

20 = 15 + y

y = 20 - 15

y = 5

In conclusion, y is 5.

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Answer:

1) 1 ounce costs 46 cents. 2) 1 ounce  of cornflakes costs 19 cents ( 0.19125).

3) 1 once cornflakes is 16 cents (0.1608) ( 36-ounces). 4) The 36 ounce box is a better buy.

Step-by-step explanation:

Divide the cost by the number of x units to find the cost of one unit. You are welcome.

The yy-component of vector a a is -y-direction, which is equal to 0 m/s2.the product of the second term of the vector with unit vector j^j^, which is in the direction of the y-axis.

Given a vector, a⃗ a→ = (5.0 m/s2, −y−direction)Find the yy -component of the given vector a⃗ a→.Solution: The yy-component of the given vector a⃗ a→ = -y-directionTo find the yy-component of the given vector a⃗ a→, we have to take the product of the second term of the vector with unit vector j^j^, which is in the direction of the y-axis.Therefore, the yy-component of vector a⃗ a→ is :a_yy = -y-direction = (-1)(0) = 0 m/s²  Answer: 0 m/s².

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The yy-component of vector a⃗ a→ is -y-direction.

The yy-component of a vector represents the magnitude of the vector in the y-direction.

In this case, the vector a⃗ a→ is given as (5.0 m/s2, −y-direction).

Since the yy-component is the magnitude in the y-direction, the yy-component of the vector a⃗ a→ is -y-direction.

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The surface area of the square pyramid will be 105768.98 square meters.

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of anybody is called the surface area.

Given that:-

The surface area of the pyramid will be:-

\(SA\ = \ a^2+2a\sqrt{\dfrac{a^2}{4}+h^2}}\)

SA  =  48400 + 440 √17000

SA  =   48400  +  57368

SA  =   105768.98  square meters

Therefore the surface area of the square pyramid will be 105768.98 square meters.

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Answer:

Table 1: Non Linear Relationship

Table 2: Linear Relationship

Table 3: Linear Relationship

Hope this helps!

The price of carrots per ounce is $0.24 .

Ounce is an unit of mass in the Imperial System. It is widely used throughout the world and is one of the oldest units of measurement to still exist. The unit ounce is derived from uncia, a unit of measurement in roman times.

The ounce(abbreviated oz) is equal to approximately 28.35 grams and 16 ounces make up a pound.

Now it is given that a 2-pound bag of carrots cost $7.68 .

Therefore price per pound of carrots=$7.68÷2

Price per pound=$ 3.84 .

Now we know that 16 ounces make up a pound.

Price of carrots per ounce=  $3.84 ÷16

Price per ounce=  $ 0.24

Therefore the price of carrots per ounce is $0.24

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Answer:

$165

Step-by-step explanation:

120÷8=15

15×11=165

To calculate the probability of landing on a number less than 5 and then landing on a number less than 6, we need to determine the total number of favorable outcomes and the total number of possible outcomes.

Given the numbers 3, 4, 5, and 6, we have two favorable outcomes: landing on either 3 or 4 (both less than 5) and then landing on a number less than 6.

The total number of possible outcomes is 4 because we have four numbers in total (3, 4, 5, 6).

Therefore, the probability is given by:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 2 / 4

Probability = 1/2

So, the probability of landing on a number less than 5 and then landing on a number less than 6 is 1/2 or 0.5 (50%).

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A congruent polygon refers to two or more polygons that have the same shape and size. There must be an equal number of sides between two polygons for them to be congruent.

Congruent polygons have parallel sides of equal length and parallel angles of similar magnitude. When two polygons are congruent, they can be superimposed on one another using translations, rotations, and reflections without affecting their appearance or dimensions. Concluding about the matching sides, shapes, angles, and other geometric properties of congruent polygons allows us to draw conclusions about them.

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Answer:

6

Step-by-step explanation:

Answer:

Area = Width * Length

Step-by-step explanation:

This is the formula for a rectangle. If you plug in the values that were givin to you, the answer is 6 units^2.

The mean of the sample means will be 25

As Sample mean is an estimate of the population mean. If we increment the number of observations the precision of the sample means will be improved to get closer to the population mean and according to Central Limit Theorem, The sampling distribution of the sample statistic can be considered roughly if any of the below-mentioned criteria is satisfied :

We are provided with a sample size which is 100, a population mean which is 25, and a population standard deviation which is 20.

So , n =100

      μ= 25

      σ= 20

therefore, the mean of the sample means is

μₓ =μ

    =  25

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Answer:

A) The unit rate is 2 inches of snow per hour.

&

E) At the same rate 12 inches of snow will fall in 6 hours.

Step-by-step explanation:

Answer:

a and e

Step-by-step explanation:

did it on usatestprep

Answer: y=4

Step-by-step explanation:

9/4y-12=1/4y-4+12

+12. +12

9/4y=1/4y+8

-1/4y -1/4y

2y/2=8/2

y=4

Based on the given equality, we can determine that the equality is TRUE as the result is the same.

To find out if the equality is true, both sides of the equation need to add up to the same number.

The result of the first side of the equation is:

= 9 + (- 4)

= 9 - 4

= 5

The result of the second side of the equation:
= - 4 + 9

= 9 - 4

= 5

Both sides of the equation add up to 5 so the quality is TRUE.

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