Which of the following measurements could be the side lengths of a right triangle? A. 42 in, 63 in, 70 in B. 35 in, 56 in, 70 in C. 42 in, 56 in, 84 in D. 42 in, 56 in, 70 in

Final answer:

To determine if there's an arbitrage opportunity, convert an amount through various currencies in the table and see if you end with more than you started. If more is ended up with, there's an opportunity, specifying the currencies and transactions. If not, the market is in equilibrium, and rates will adjust to prevent arbitrage.

Explanation:

To identify an arbitrage opportunity within the given spot currency rates, one must find a sequence of exchanges that results in more currency than initially started with, after accounting for the currency exchange rates in table 1. The decision model for discovering an arbitrage opportunity typically involves converting an amount from one currency to another across several pairs and ending up with more than one started with in the original currency. The following steps outline the process to determine if arbitrage is possible:

Start with a denomination of one currency (e.g., $1).

Convert this amount into another currency using the provided spot rates.

Repeat the conversion process for subsequent currencies.

Finally, convert back to the original currency.

If the final amount is greater than the starting amount, an arbitrage opportunity exists. In such a scenario, the model should indicate the currencies involved and the specific transactions to execute the arbitrage. However, if no sequence of transactions results in profit, then no arbitrage opportunity is present given the rates provided. The absence of arbitrage ensures that the markets are in equilibrium, and the exchange rates will adjust to eliminate any potential for arbitrage as per the efficient market hypothesis.

The rate of change of volume of the sphere is [tex]56520\;\rm{mm/sec}[/tex].

According to the question, the radius of a sphere is increasing at a rate of [tex]5 mm/s[/tex] and the diameter is [tex]60 mm[/tex].

The volume of the sphere is, [tex]V=\dfrac{4}{3}\pi r^3[/tex] where, [tex]r[/tex] is the radius of the sphere.

Differentiate the volume of the sphere both sides with respect to [tex]t[/tex] as-

[tex]\dfrac{dV}{dt}=\dfrac{4\pi}{3}\dfrac{dr^3}{dt}\\\dfrac{dV}{dt}=\dfrac{4\pi}{3}\times 3r^2\dfrac{dr}{dt}\\\dfrac{dV}{dt}=4\pi r^2\dfrac{dr}{dt}[/tex]

The radius of the sphere is-

[tex]r=\dfrac{60}{2}\\r=30mm[/tex]

Substitute the value of the parameter as-

[tex]\dfrac{dV}{dt}=4\pi\times (30)^2\times 5\\\dfrac{dV}{dt}=62.8\times 900\\\dfrac{dV}{dt}=56520\;\rm{mm/sec}[/tex]

Hence, the rate of change of volume of the sphere is [tex]56520\;\rm{mm/sec}[/tex].

Learn more about volume of the sphere here:

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Answer:

  B.  no solution

Step-by-step explanation:

Multiplying the first equation by 4 gives ...

  4y = 12x -32

This is inconsistent with the second equation, ...

  4y = 12x -5

There can be no common point on these parallel lines, hence no solution.

Answer:

You will revise your narrative, indicating four instances in which you have added adjectives and/or adverbs.

You will also submit a reflection paragraph.

View the grading rubric as you complete your assignment. This is your guide to a super submission.

Add adjectives and adverbs. Mark your new additions with an (Adj) or (Adv).

Make other revisions suggested in your Discussion-Based Assessment.

Write a reflection paragraph discussing changes you made during the revision process. Explain how you feel these changes improved your narrative.

Submit your (1) final draft and your (2) reflection paragraph.

Save your work to your computer or drive.

Submit your work in 03.10 Kick It Up a Notch.

Step-by-step explanation:

Answer: Option 'C' is correct.

Step-by-step explanation:

Since we know that

[tex]f(x)=\sin x[/tex]

It is an odd function.

It has a period of 2π because the sine wave repeats after every 2π units.

It value lies between -1 and 1.

And we know that

[tex]\sin 0^\circ=0^\circ[/tex]

And 0 occurs exactly middle of -1 and 1.

So, the zeroes can be found in the middle, beginning and at the end.

But at maximum point, there will be no zero.

As when it attains its maximum point, it won't touch x-axis.

Hence, Option 'C' is correct.

Answer:

5 roots

Step-by-step explanation:

just did it on edge

The product of 3√24 and 3√45 is approximately 295.77.

To find the product, we can first simplify the individual square roots.

√24 = √(4 * 6) = 2√6

√45 = √(9 * 5) = 3√5

Substitute the simplified terms: 3 * 2√6 * 3 * 3√5 = 18√30

Factor out a 9: 18√30 = 9 * 2√(10 * 3)

Simplify the remaining square root: 9 * 2√30 ≈ 9 * 2 * 5.477 = 295.77 (rounded to two decimal places).

Therefore, the product of 3√24 and 3√45 is approximately 295.77.

The rate of change of the area when the radius is 35 centimeters is 420π cm2/min.

To find the rate of change of the area, we can use the formula for the area of a circle: A = πr2. We are given that the radius (r) is increasing at a rate of 6 centimeters per minute. We need to find the rate of change of the area when r = 35 centimeters.

First, differentiate the area formula with respect to time (t) using the chain rule:

dA/dt = 2πr(dr/dt)

Substitute the given values into the formula: dA/dt = 2π35(6) = 420π cm2/min.

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The rate of change of the circle's area when the radius is 35 cm is 420π cm²/min.

The subject of this question is related to the rate of change in the context of a circle's area, which is a topic in calculus. Given that the radius r of a circle is increasing at a rate of 6 centimeters per minute, we are to find the rate of change of the area when r = 35 centimeters.

The area A of a circle is given by the equation A = πr². If we differentiate this equation with respect to time t, we get dA/dt = 2πr(dr/dt). We know that dr/dt, the rate of change of the radius, is 6 cm/min. Substituting r = 35 cm and dr/dt = 6 cm/min into the derivative equation, we get dA/dt = 2π*35*6 = 420π cm²/min.

So, the rate of change of the circle's area when the radius is 35 cm is 420π cm²/min.

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To solve percent problems, we can use equivalent fractions, cross-multiply, solve for the unknown, or convert percent to a fraction and simplify. In context, a 24% positive rate among students indicates that 24 out of every 100 students are positive.

In mathematics, specifically in percentage calculation, there are several methodologies to solve problems. One very common way, as mentioned in the reference material, is by setting up equivalent fractions with 100 as the denominator, and cross-multiplying. For example, if you have the fraction 9/37 representing some scenario (like 9 successful attempts out of 37), you can set up an equation like 9/37 = x/100, where 'x' is the equivalent percentage. Cross-multiply and solve for 'x' to get x = (9/37) * 100, giving you the percentage.

Also, note that a percent can be converted to a fraction by writing the value of the percent as a fraction with a denominator of 100. Simplify the fraction, if possible.

In context, if 24% of students are positive, that means for every 100 students, 24 would be positive. If only 70 are surveyed, then (24/100)*70 = 16.8 students, but since we can't have a part of a student, we would round it to 17 students are positive for this sample size.

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Answer:

month 6

Step-by-step explanation:

khan academy

Answer:

20 KM

Step-by-step explanation:

God bless!!!

Answer: 20 Km

Step-by-step explanation: I did the assignment (Similar Polygons)

Answer:c 0.00463

Step-by-step explanation:

1/6×1/6×1/6=1/216

Answer:

Since the given problem statement and data is

Manicipal bond with par value=$500

commission rate =3.1%

charges of broker B=$24

bond market rate=$88.754

hence from the given data  Broker A charges a 3.1% commission on the market value of each bond sold is a better deal.

Solution:

we are given with a graph and we have been asked to find Which of the given options best describes the graph ?

As we know from the vertical line test of a function that a curve reprsents a function , if we draw a vertical line and that line intersect that curve only once.

If that vertical line interscet the given curve more than once it mean that curve does not represent a function.

Here for the given curve if we will draw any vertical line, that line will intersect it  more than once.

Hence the given curve does not represent a fimction.

Hence the correct option is D.

Answer:

5in and 9in

Step-by-step explanation:

The width of the porch is 5 feet and the length is 10 feet. The perimeter of the porch is 30 feet.

To find the perimeter of the porch, we first need to find the dimensions of the porch. Let's assume the width of the porch is x feet. According to the problem, the length of the porch is two times the width, so the length would be 2x feet. Since the area of the porch is 50 square feet, we can set up the equation: x * 2x = 50. Simplifying this equation, we get 2x^2 = 50. Divide both sides by 2 to isolate x^2: x^2 = 25. Taking the square root of both sides, we find that x = 5. Therefore, the width of the porch is 5 feet and the length is 2 * 5 = 10 feet.

To find the perimeter, we use the formula: perimeter = 2 * (length + width). Substituting the values, we get perimeter = 2 * (10 + 5) = 2 * 15 = 30 feet. So, the perimeter of the porch is 30 feet.

Answer:

4/14 = 2/7

15/20 = 3/4

 21/35 = 3/5

Step-by-step explanation:

Final answer:

18 people can eat 3/5 of a pizza, with a little pizza left over.

Explanation:

To find out how many people can eat 3/5 of a pizza at the party, we need to divide the total number of pizzas by the fraction each person can eat.

Therefore, approximately 18 people can eat 3/5 of a pizza at the party.

Assuming that the attached file is the lake which you are mentioning in the question.

The perimeter is the distance around the lake, we need to set up an equation based on the statement "When Amanda jogged twice around the lake she jogged a distance of 2,700 meters" as below:

[tex] 2(Perimeter \; of\; the\; lake) =2700\\ \\ 2(x+140+x+x+250+x+x+3x)=2700\\ Group \; Like\; Terms\\ \\ 2(x+x+x+x+x+3x+140+250)=2700\\ Combine \; Like\; Terms\\ \\ 2(8x+390)=2700\\ Distribute\; 2\; in\; left\; side\; of\; the\; equation\\ \\ 16x+780=2700\\ Subtract \; 780\; on\; both\; sides\\ \\ 16x+780-780=2700-780\\ Combine \; like\; terms\\\\16x=1920 \\ Divide\; 16 \; on\; both\; sides\\ \\ \frac{16x}{16}=\frac{1920}{16}\\ Simplify\; fraction\; on\; both\; sides\\ \\ x=120 [/tex]

Conclusion:

The value of x is 120 meters