Suppose that the number of grams of a certain radioactive substance present after t seconds is given by the equation

esent the cost would be y=46+0.25x , where x is the number of miles traveled. a. What is your cost if you travel 59 mi? The cost is $ 43.26 . b. If your cost was $66.25 , how many miles were you charged for traveling? You were charged for traveling 66.51 miles. c. Suppose you have a maximum of $100 to spend for the car rental. What would be the maximum number of miles you could travel? The maximum number of miles you could travel is Number

xt 4 tests are performed, find P(x=0), P(x=1), P(x=2),P(x=3) and P(x=4). SHOW ALL WORK TO GET CREDIT) 4) Use the confidence interval (99%) to solve the following question. A company is trying to establish the number of average amount of funds that are owed by its employees. They collect 1,000 accounts and found the sample average owed is $250 with a standard deviation of 10. Calculate the confidence interval (MUST SHOW ALL WORK TO GET CREDIT) 5) Use the t distribution formula and table to solve the following question. A random sample of 91 with a sample average of 90 and a standard deviation of 4.2 hours, calculate the confidence interval at 98% (MUST SHOW ALL WORK TO GET CREDIT) 6) A poll of 3,000 adults out of 5,500 was collected to found that they did not get a master’s degree. Calculate the confidence interval at 95%. (MUST SHOW ALL WORK TO GET CREDIT)

hour. Let N(t) be the number of custoer arrivals up to time t, with hour as the unit. There are two types of soft drinks, type A and B, stored in the machine. Suppose that each time a customer deposits money, the machine dispenses one soft drink A with probability p1, or one soft drink B with probability p2. We have p1 + p2 = 1, p1 > 0, p2 > 0. Let X(t) be the number of type A soft drinks dispensed up to time t; and Y (t) be the number of type B soft drinks dispensed up to time t.

y aces or twos, you lose the game immediately. You also lose if you draw picture cards(J,Q,K) more than twice. In this question, you’ll study the probability of winning this game.(a) What is the probability of drawing no aces or twos after thirteen draws?(b) Given you have drawn thirteen times, none of which is aces or twos, what is the probability that you draw at most two picture cards?(c) What is the probability to win this game? 12. Suppose you are tossing an unbiased coin for100times.(a) What is the probability of getting50heads and50tails?(b) LetXbe the random variable counting the number of heads you observe in this exper-iment. What is the expected value ofX? What is the variance ofX? What is thestandard deviation ofX? 13. The following are probability distributions for two random variablesX,Y. kPr(X=k) 0,0.4 1,0.3 2,0.3 kPr(Y=k) 0,0.5 1,0.3 2,0.2 (a) Construct the probability distribution table for the random variableXY.(b) Find E[X],E[Y] and E[XY]. Is is true that E[XY] =E[X]E[Y]?(c) Find the variances σ2X,σ2Y,σ2XY of X,Y and XY. Is it true that σ2XY=σ2Xσ2Y? 14. The aliens who are fond of gambling came back to play another game with you. In this game, you first toss a coin5times. If you observe3or fewer tails, you roll a die3times. If youobserve4or more tails, you roll a die20times. What is the probability that you end up with at most two6’s in your dice rolls? 15. (Challenge question, worth2points) You have two bags, each of which contains10marbles.Each time you remove a marble from a random bag. What is the probability that after one of the bags is emptied, there are still exactly3marbles in the other bag?

rt once a week, and 50% of the time he doesn't attend a concert at all in a given week. What is the expected value for the number of times Danny attends a concert during a week?

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.

units. Chemical Equation: Write a generic chemical equation for the dehydration of cobalt (II) chloride ∙ x hydrate (include the state symbols of the reactant and two products). [T2] Mass of Reactants and Products: a) Calculate the initial mass of the hydrated cobalt (II) chloride. [T1] b) Calculate the final mass of the anhydrous cobalt (II) chloride remaining in the cruiio8icible. [T1] c) Calculate the mass of water given off by the sample of hydrated cobalt (II) chloride. [T1] Moles of Products: a) Calculate the moles of anhydrous cobalt (II) chloride remaining in the crucible. [T1] b) Calculate the moles of water released from the hydrate. {T1] 4. Mole Ratio a) Create an experimental mole ratio between the b) and a). [T1] 5. Formula of Hydrate: State the chemical formula you have determined for this hydrate. Round the formula to the closest whole number value for x. [T1] Discussion/Conclusion Questions: [T6] Based on the chemical formula of the hydrate, calculate the percentage composition (percent by mass) of the hydrated cobalt (II) chloride. Remember to determine the percentage of each element (Co, Cl, H, and O). [T2] A possible source of systematic error in this experiment is insufficient heating. Suppose that the hydrate was not completely converted to the anhydrous form. Describe how this would affect: the calculated percent by mass of water and the experimental molecular formula (i.e. would x be higher, lower or the same). Suppose a student spilled some of the hydrated cobalt (II) chloride. Describe how this would affect the calculated percent by mass of water (would it be higher, lower or the same) and the experimental chemical formula of the hydrate. [T2]

of CoCl2 . H2O. The hydrate became anhydrous through this. Suppose a student spilled some of the hydrated cobalt (II) chloride. Describe how this would affect the calculated percent by mass of water (would it be higher, lower or the same) and the experimental chemical formula of the hydrate. [T2] A possible source of systematic error in this experiment is insufficient heating. Suppose that the hydrate was not completely converted to the anhydrous form. Describe how this would affect: the calculated percent by mass of water and the experimental molecular formula (i.e. would x be higher, lower or the same).

y its diagonals, assuming no three diagonals have a common point. Define a0=0. Show that an=an−1+(nC3)+n (n≥1)

by the equation LaTeX: Q\left(t\right)=2000e^{-0.05t}Q ( t ) = 2000 e − 0.05 t. How many grams remain after 25 seconds? Round to the nearest gram.

l-time freshmen from 270 four-year colleges and universities in the U.S. 71.2% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly pick eight first-time, full-time freshmen from the survey. You are interested in the number that believes that same-sex couples should have the right to legal marital status. Construct the probability distribution function (PDF). (Round your probabilities to five decimal places.)

chases frozen turkeys at a constant wholesale price of $1/turkey, which is its full marginal cost for supplying turkeys. During July, only a small number of wealthy people are interested in buying turkeys in Pilgrim. Their demand curve is P = 10 – .02 Q, where P is Wegboys’ retail price for turkeys during the month and Q is the quantity of turkeys purchased. The demand curve for these wealthy people is constant – it is the same curve in both November and July. During November, a large number of less wealthy people enter the market to purchase turkeys for Thanksgiving. Their demand curve for Wegboys’ turkeys is P = 4 – .0005Q. In other months of the year, they do not purchase turkeys at any price. a. (5 points) What price should Wegboys charge in July to maximize its profits? Calculate its profits from turkey sales. b. (5 points) Demonstrate that Wegboys can earn a higher profit if it lowers its retail price for turkeys during November (you can do this without finding the optimal price). Explain the basic economic intuition.

that a and b are two integers with GCD 1. Prove that if p is any odd prime which divides a^2 + b^2 then p ≡ 1 (mod 4).

is Imagine that in the voting for a certain​ award, 7 points are awarded for first​ place, 4 points for​ second, 3 points for​ third, 2 points for​ fourth, and 1 point for fifth. Suppose there were five candidates​ (A, B,​ C, D, and​ E) and 47 voters. When the points were​ tallied, A had 155 ​points, B had 173 ​points, C had 170 ​points, and D had 154 points. Find how many points E had and give the ranking of the candidates.​ (Hint: Each of the 47 ballots hands out a fixed number of points. Figure out how​ many, and take it from​ there.)

is a multiple of three or greater than eight. A certain game consist of rolling a single fair die and pays off as follows nine dollars for a six, six dollars for a five, one dollar for four and no payoffs otherwise.Find the expected winnings for this game. A fair die is rolled four times. A 6 is considered success While all other outcomes are failures find the probability of three successes. A pet store has nine puppies including 4 poodles 3 terriers and 2 retrievers. If Rebecca an errand in that order each select one puppy at random without replacement find the probability that Aaron select a retriever given that from last Rebecca selects a poodle. Experience shows that a ski lodge will be for (166 guests) if there is a heavy snowfall in December, well only partially full (52 guests) With a light snowfall. What is the expected number of guests if the probability for a heavy snowfall is 0.40? I assume that heavy snowfall and light snowfall are the only two possibilities. A pet store has six puppies Including two poodles two Terriers and to retrievers. If Rebecca and Aaron in that order each select one puppy random with replacement (They both may select the same one) Find the probability That Rebecca selects a terrier and Aaron selects a retriever. Three married couples arrange themselves randomly in six consecutive seats in a row. Determine (A) the number of ways the following event can occur, And (B) the probability of the event. (The denominator of the probability fraction will be 6!=720, The total number of ways to arrange six items ). Each man was that immediately to the right of his wife. A coin is tossed five times. Find the probability that all our heads. Find the probability that at least three are heads. A certain prescription drug is known to produce undesirable facts and 35% of all patients due to drug. Among a random sample of a patient using a drug find the probability of the stated event. Exactly 5 have undesired effects. 10,000 raffle tickets are sold. One first prize of 1600, for second prizes of 800 each, And 9/3 prizes of 300 each or to be awarded with all winners selected randomly. If you purchase one ticket what are your expected winnings. Suppose a charitable organization decides to Raise money by raffling A trip worth 500. If 3000 tickets are sold at one dollar each find the expected net winnings for a person who buys one ticket. Round to the nearest cent Three men and seven women are waiting to be interviewed for jobs. If they are selected in random order find the probability that all men will be interviewed first A fair diet is rolled. What is the probability of rolling on our number or a number less than three. The pet store has 15 puppies, including five poodles, five Terriers, and five retrievers. If Rebecca and Aaron, in that order, select one puppy at random without replacement, find the probability that both select a poodle Beth is taking a nine question multiple-choice test for which each question Has three answer choices, only one of which is correct. Beth decides on answering By rolling a fair die And making the first answer choice if the die shows one or two, The second If the die shows three or four, and the third if the die shows five or six. Find the probability of the stated event. Exactly 6 correct answers For the experiment of drawing a single card from a standard 52 card deck find (a) the probability and (b) the odds are in favor that they do not drive six