n n n prove this with induction

om command line arguments int N = atoi(argv[1]); int i; //Loop from 0 to N for (i= 0; i <= N; ++i) printf("%d ", i); //printing new line printf('\n'); return 0; }

ne the area of the triangle. (Include the diagram)

ring. a) Calculate the work done to compress the spring. (2 marks) b) What happens to the work done on the spring ? (1 mark) c) If the spring is released, what happens to the energy of the spring? (1 mark) d) Calculate the total mechanical energy of the ball at the instant it leaves the spring. (2 marks) e) What will be the speed of the ball at the instant it leaves the spring? (2 marks) f) If the ball is fired up into the air by the spring, how much gravitational potential energy will it gain? (1 mark) g) What will be the maximum height of the ball? (2 marks

to the right. Determine the work done by Glen on the sled. *

2,3,4,7). If it lands tails, a fair six-sided die is thrown (with values 3,4,5,6,7,9). Regardless of which die is used, Alice eats n grains of rice, where n is the largest prime factor of the die result (for example, the largest prime factor of 9 is 3). (a) What is the conditional probability that the coin lands heads, given that Alice eats three grains of rice? (b) Suppose that the entire experiment is conducted twice on the following day (starting with a new coin toss on the second run-through). What is the conditional probability that the coin lands heads on both run-throughs, given that Alice eats a total of five grains of rice during the two run-throughs? (Do not count the two grains from part (a) in part (b); we assume two brand new experiments, each with a new coin toss. Start your solution by defining a suitable partition of the sample space. Please use an appropriate notation and/or justification in words, for each value that you give as part of your solution.) Exercise 5) Alice and Bob throw an unfair coin repeatedly, with probability 2/5 of landing heads. Alice starts with £2 and Bob starts with £3 . Each time the unfair coin lands heads, Alice gives Bob £1 . Each time the unfair coin lands tails, Bob gives Alice £1 . The game ends when one player has £5 . (a) Draw a labelled Markov chain describing the problem, and write down a transition matrix P. Write down the communication classes, and classify them as either recurrent or transient. (b) Using the transition matrix, calculate the probability that Alice loses all of her money in exactly four tosses of the unfair coin. (c) Calculate the (total) probability that Alice loses all of her money (before Bob loses all of his). (d) Calculate the expected (mean) number of tosses of the unfair coin, for the game to end.

an arbitrary point (2 sin 2t, 2 cos 2t, 3t) on the helix. b) Compute the arc length from (0,2,0) to (0,-2,3π/2) c) Compute the vectors T, N and B at (0,-2,3π/2) d) Compute the curvature at (0,-2,3π/2) e) Find the angle between T and the z-axis at (0,-2,3π/2) to the nearest tenth of a degree.

a prize with probability p independently of the other curtains. The player chooses one curtain (a) The game host tells the contestant there's a prize hiding behind at least one of the other curtains, and offers the player a chance to change his choice. Should he? (b) The game host tells the player there's a prize hiding behind exactly one of the other curtains. Should the player change his choice? How does your answer depend on p (c) How would your answer to section (b) change if there are n curtains in total? (d) Bonus (4 points): How would your answer to section (a) change if there are 4 curtains in total?

Recursive Step: if (n,m,r) ∈ A then (n+1,m+2,m+r+2) ∈ A Prove, using structural induction, that for every .( n , m , r ) ∈ A , 0 ≤ n < m and n + m ≤ r .

a) A scientific theory must be able to be proven. b) A scientific theory has been derived from known facts and always applies. c) A scientific method should give different results depending on who performs the method. d) Knowledge of our surroundings usually emerges through an interplay between theory and experiment. 2) The sides of a straight block are measured to 3,202 cm; 0.0012 cm and 11.2 cm, respectively. Calculate the volume of the straightening block and enter it with the correct number of value digits. (2/0/0) Number of words: 0 3) A 9.2 dm long and evenly thick rod rests on a support. 0.55 dm from one end, a dynamometer is hung so that the rod will hang horizontally. Then the dynamometer shows 4.4 N. How much does the bar weigh? (1/1/0) Number of words: 0 4) A bar AB that is homogeneous and evenly thick has a length of 2.70 m and is rotatable about an axis at A. The bar weighs 25 kg and is kept in equilibrium by a force F which has its point of attack in B. is 45 degrees. How big is the force F? (1/1/0) Saved! 25 * 9.82 = 245.5 N Number of words: 6 5) A trolley rolls at a constant speed to the right. On the cart is an upward cannon that suddenly shoots a bullet. The carriage continues to the right with the same speed as before. Where does the bullet end up when it falls? For a detailed reasoning. (1/1/1) Number of words: 0 6) A river is 200 m wide. The water in the river flows at a speed of 2.5 m / s. A motorboat steers across the river at its maximum speed, which in stagnant water is 5.0 m / s. The boat is constantly heading perpendicular to the banks of the river. Where does the motorboat land on the other shore? (2/0/0) Number of words: 0 7) A ball with a mass of 2.0 hg moves at a constant speed in a circular path. The radius of the track is 1.5 m and it takes the ball 3.0 seconds to move one turn. How big is the centripetal force? (1/1/0) Number of words: 0 8) A bullet moves at a constant speed. Can we then safely say that the resultant of the forces acting on the bullet is zero? Motivate and discuss your answer. (0/1/1) Number of words: 0 9) A conductor is located between the poles of a permanent magnet. The current in the conductor goes in the direction of the plane of the paper (away from the reader). How is the force acting on the leader directed? (1/0/0) a) To the right of the figure b) To the left in the figure c) Downwards in the figure d) Upwards in the figure 10) Protons enter horizontally from the left between two large metal plates at a speed v = 0.80 Mm / s. The plates are connected to a voltage source with the pole voltage U. Between the plates there is a homogeneous magnetic field with a flux density of 38 mT directed perpendicular to the plane of the paper. The distance between the plates is 1.5 cm. They want the protons to continue with unchanged direction and speed between the plates. Which of the plates should be connected to the positive pole of the voltage source and how large should the voltage U be? (0/2/0) Number of words: 0 11) The magnetic flux Φ through a 700-speed coil decreases linearly with time according to the diagram below. Calculate the voltage across the coil at time t = 1.0 ms. 12) The current in a coil with an inductance of 35 mH has a growth rate of 6.2 A / s at a given moment. What is the instantaneous value of the ems induced in the coil?

be the cardinality of B, so m = |B|. As B is larger, n < m. What can we say about the cardinality of: _________ ≤ |A ∪ B| ≤ _________ _________ ≤ |A \ B| ≤ _________ _________ ≤ |A × B| ≤ _________ _________ ≤ |(A × B) \ (A × A)| ≤ _________ _________ ≤ |(A ∪ B) × (B \ A)| ≤ _________ _________ ≤ |(A ∪ B) × (A \ B)| ≤ _________

x+1, determine the numerical length of \overline{MO}. MO

Since he became the president, did President Trump act with the transparency and the integrity that you expect from a president?” 675 voters responded the poll and 351 responded “YES.” Assume that 40% of the U.S. population supports Trump. a. Define a binary random variable, Y, for supporting Trump (Y=1) vs. not (Y=0). Calculate the population mean (????????) and variance (???????? 2 ) for supporting Trump. b. Calculate the sample mean ????̅ and the sample standard deviation of ????̅ (????????̅ ) for the poll. c. Calculate the standard error of ????̅ and construct a 95% confidence interval from the poll using ????̅ and its sample standard error. d. Conduct a two-sided hypothesis test at 5% significance level to determine whether 40% of the U.S. population supports Trump. State the null and the alternative hypotheses, calculate the test statistics and the associated p-value, and conclude. Is the Fox News survey reliable? Why? Why Not? e. Suppose that you wanted to design a survey that had a margin of error of at most 1%. That is: the difference between the upper bound and the lower bound of the confidence interval should be a maximum of 2 percentage points. For example, for ????̅ = 0.52 you are aiming for the 95 % CI to be [0.51 0.53]. How large should n be if the survey uses simple random sampling?

kg. The plane has the capacity to carry 120 passengers, and when there are 40 passengers on the plane, the total mass of the plane and passengers is 7480kg. a) Calculate the mean mass of a passenger. b) Hence, write an expression for nu that gives the total mass of the plane and passengers when there are n passengers on board. c) State the values of n for which your model is valid.

34.0 N when it’s not in the water. When it’s submerged in water (the density of water is 1.00 x 103 kg/m3) the scale now reads 27.0 N. (a) What is the density of the block? (b) If you suspended another object from the block that has a density of 3.20 x 103 kg/m3, with both objects submerged, what would the object's mass need to be for the scale to once again read 34.0 N? Note: Part (a) is worth 7 points, and part (b) is worth 8 points.

of years it was purchased. How much will the antique be worth in 10 years

f the students make their choices independently and each is as likely to pick one integer as any other, what is the probability that 8 or more will select 4,5 or 6? b Having observed eight students who selected 4, 5, or 6, what conclusion do you draw based on your answer to part (a)?A missile protection system consists of n radar sets operating independently, each with a probability of .9 of detecting a missile entering a zone that is covered by all of the units. a If n = 5 and a missile enters the zone, what is the probability that exactly four sets detect the missile? At least one set? b How large must n be if we require that the probability of detecting a missile that enters the zone be .999?

S_n=(a_1 (1-r^n))/(1-r) b. S_n=(a_1 (1-r^n))/r c. S_n=(a_1 (r^n))/(1-r) d. S_n=(a_1 (1-r^n))/(1+r)

n = 65 California boys. It was used to predict 18-year old height from 6-year old height. - At age 6, the average height was 46 inches with a standard deviation of 1.7 inches - At age 18, the average height was 70 inches with a standard deviation of 2.5 inches - r = .80 use this information to determine the LSRL

ng n distinct integers in just his thoughts. He plays turns on the list. In each turn he does the following– He takes a number (in its index’s order ) and swap it with any number in the list including itself i.e. if it swap it with itself it doesn’t move at all (The selection of the number is completely random). He does the same for all the elements in their index’s order in that turn. If initially the list was unsorted, such that, no element was in sorted position, then find the probability that the list is sorted after m such turns. Note : Take the assumption that if an element is not in its sorted position then it can be in any other n − 1 positions equally likely.

and B where m is an integer such that m is congruent to 1 modulo b have the same cardinality. I need help with the process of finding a function to define the two sets to determine the bijection.

ng the snow. The first child exerts a force of F1 = 11 N at an angle θ1 = 45° counterclockwise from the positive x direction. The second child exerts a force of F2 = 6 N at an angle θ2 = 30° clockwise from the positive x direction. Find the magnitude (in N) and direction of the friction force acting on the sled if it moves with constant velocity. magnitude direction (counterclockwise from the +x-axis) What is the coefficient of kinetic friction between the sled and the ground? What is the magnitude of the acceleration (in m/s2) of the sled if F1 is doubled and F2 is halved in magnitude?

esis StartFraction 1 Over x cubed EndFraction right parenthesis Superscript n . Write a simplified expression that represents the amount of bacteria in an infection 2 hours after taking medication. The expression nothing represents the amount of bacteria in an infection 2 hours after taking medication. ​(Type your answer using exponential notation. Simplify your​ answer.)

/ SQRT(n) = 0.03 So, n = 1067 (approx.) Edit

+ Sqrt[2 - 2 y] - k)/((y + 1) Sqrt[1 - y^2]), Sqrt[2]/2/m == k/(k - Sqrt[2 - 2 y]), n == Sqrt[2 - 2 Sqrt[1 - m^2]], z == Sqrt[2 - 2 y]/f == Sqrt[(zn)^2 - 2 + 2 y]/ Sqrt[n^2 - f^2], t == (Sqrt[g^2 - 2 g^3 - g^4 + 2 g + 1] + Sqrt[2 - 2 g] - t)/((g + 1) Sqrt[1 - g^2]), Sqrt[2]/2/h == t/(t - Sqrt[2 - 2 g]), q == Sqrt[2 - 2 Sqrt[1 - h^2]], l == Sqrt[2 - 2 g]/p == Sqrt[(lq)^2 - 2 + 2 g]/ Sqrt[q^2 - p^2], (z + 1) x == (l + 1) 2 x == (y + 1) Sqrt[1 - y^2]/ Sqrt[2] == Pi/4, q == m and determine true it or false thank you

el tabletop. A child attempting to use the spring to pull the block directly horizontally from rest extends the spring by 30.0 cm a) Does the block slip? Explicitly state how you know. b) Calculate the magnitude of the acceleration if the block accelerates or, if it does not, calculate the magnitude of the static frictional force acting on the block.

he money in an e-account at 3.25%. This account pays interest (compounds) monthly. The monthly interest rate is (3.25/12)%. The algebraic model of his savings account is A = 500(1.002708)n, where A represents the account balance and n represents the number of times interest has been paid. Use Desmos to create the graphical model of David's earnings.

hey have the same remainder after division by n. Prove that a ≡ b (mod n) if and only if n|(a − b).

hey have the same remainder after division by n. Prove that a ≡ b (mod n) if and only if n|(a − b).

ite the formula for total amount A after t years. What is formula for interest when both A and P is known? A(t) = … … … I = … … …

ite the formula for total amount A after t years.

e investigations we determined that the program input size can be varied in a wide range and for N-bit input the program result is also always N – Bit long. Additionally we found that the program working time depends significantly on input length N, especially when N is greather than 10- 15 . Our test also revealed, that the program working time depends only on input length ,not the input itself. During our tests, we fixed the following working times (with an accuracy of one hundredth of a second) N = 2 – 16.38 seconds N = 5 – 16.38 seconds N = 10 – 16.44 seconds N = 15 – 18.39 seconds N = 20 – 1 minute 4.22 seconds We also planned to test the program for N = 25 and N = 30, but for both cases the program didn’t finish within half and hour was forced to terminate it. Finally, we decided for N = 30 to not terminate the program,but to wait a little bit longer.The result was 18 hours 16 minutes 14.62 seconds . We repeated the test for N = 30 and it gave us exactly the same result, more than 18 hours. Tasks: a) Find the program working times for the following three cases N = 25, N = 40 and N = 50. b) Explain your result and solution process.

by 5.00 cm and has a force constant of 8.00 N/m. When the cannon is fired, the ball moves 15.0 cm through the horizontal barrel of the cannon, and there is a constant friction force of 0.032 N b/t the barrel and the ball. (a) With what speed does the projectile leave the barrel of the cannon? (b) At what point does the ball have max speed? (c) What is this max speed?

ight of 5854 N through a distance of 2.5 meters. What is the mechanical efficiency of the lever? A 141.3 newton person climbs a set of stairs that is 25.2 meters long but only 8.8 meters high. The person only needs to exert 163.2 newtons of effort to climb the stairs. What is the mechanical efficiency of the this staircase?

5. Determine the probabilities below.

and how to solve: “A history lecture hall class has 15 students. There is a 15% absentee rate per class meeting. Find the probability that exactly one student will be absent from class.” I already know that: n = 15 p = 15% q = 1 - 15 = 1 - 0.15 = 0.85 ...and then you do: p (x = 1) = C 15 & 1 and then... (0.15)^1 (0.85)^14 Please help me understand the rest. Thank you!

SWER TO EACH QUESTION ON THE APPROPRIATE LINE ON THE ANSWER SHEET. FOR OTHER QUESTIONS, CLEARLY WRITE THE ANSWER, INCLUDING UNITS WHEN NECESSARY, ON THE ANSWER SHEET. SHOW ALL WORK ON A SEPARATE SHEET OF PAPER. HAND IN ASSIGNMENT, ANSWER SHEET, AND SCRAP WORK. 1. How many valence electrons are expected for an element that is in group 15/5A of the periodic table? A. two B. three C. five D. eight E. ten 2. Which of the following pairs of bonded atoms would be expected to have the longest bond length? A. C  N B. C  S C. C  B D. C  Fsdfasdfas

onnect a line between every two consecutive points (xi, yi) and (xi+1, yi+1), where 0 <= i <= n. xi = s * ((a + b) * cos (i * PI) - b * cos ((a + b) / b * i * PI)) yi = s * ((a + b) * sin (i * PI) - b * sin ((a + b) / b * i * PI)) Verify with s = 10, a = 19, b = 5, n = 1000 to get this displayed result. Note that the sin and cos trigonometry functions accept a radiant value not angle. For example, 30 degree should be replaced with PI/180*30 instead. Moreover, the divisions inside the functions need to be kept in double not int precision in order to render a correct result.

te data object as present inside each element of the array children . The output will be series of lines as follows: "data": {...} "data": {...} The contents between the curly braces will vary from one data object to another, and the subfields can be objects themselves (i.e., the subfields may have their values surrounded by curly braces). At the time of this writing, 26 such objects printed. It is critical to keep in mind that the order of the fields within the data objects is not important. The closest this can be described in C is as follows: struct data { char c; long n; }; The application code mustn't rely on the fact that field c was defined before the field n . In other words, a well written C application would work perfectly, without any code changes, even if the structure was redefined as follows: struct data { long n; char c; };