A coin is flipped 8 times in a row (assume all outcomes are equally likely). For each of the following questions, you should write your answer as an expression. Do not give the final numeric value. For example, you should write C(4,2)/24 instead of 0.375. Q1.1 What is the probability that it lands on heads exactly four times?
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- Correct answer will be upvoted else downvoted. Computer science. You are given a positive integer x. Check whether the number x is representable as the amount of the solid shapes of two positive integers. Officially, you really want to check in case there are two integers an and b (1≤a,b) to such an extent that a3+b3=x. For instance, in the event that x=35, the numbers a=2 and b=3 are reasonable (23+33=8+27=35). In the event that x=4, no pair of numbers an and b is reasonable. Input The primary line contains one integer t (1≤t≤100) — the number of experiments. Then, at that point, t experiments follow. Each experiment contains one integer x (1≤x≤1012). Kindly note, that the input for some experiments will not squeeze into 32-cycle integer type, so you should use something like 64-bit integer type in your programming language. Output For each experiment, output on a different line: "Indeed" in case x is representable as the amount of the 3D shapes of two…Question 4 Rewrite the following statement without using variables. Then, give an exam- ple that shows the statement is true. There exist two real numbers a and b such that ab > a + b. Question 5 Rewrite the following statement without using variables. Then, give an exam- ple that shows the statement is false. For any positive integer n, n³ > n².Correct answer will be upvoted else Multiple Downvoted. Computer science. You are given a positive number x. Observe the littlest positive integer number that has the amount of digits equivalent to x and all digits are unmistakable (extraordinary). Input The principal line contains a solitary positive integer t (1≤t≤50) — the number of experiments in the test. Then, at that point, t experiments follow. Each experiment comprises of a solitary integer number x (1≤x≤50). Output Output t replies to the experiments: on the off chance that a positive integer number with the amount of digits equivalent to x and all digits are diverse exists, print the littlest such number; in any case print - 1.
- Correct answer will be upvoted else downvoted. Computer science. You have w white dominoes (2×1 tiles, the two cells are hued in white) and b dark dominoes (2×1 tiles, the two cells are shaded in dark). You can put a white domino on the board in case both board's cells are white and not involved by some other domino. Similarly, you can put a dark domino if the two cells are dark and not involved by some other domino. Would you be able to put all w+b dominoes on the board if you can put dominoes both on a level plane and in an upward direction? Input The main line contains a solitary integer t (1≤t≤3000) — the number of experiments. The primary line of each experiment contains three integers n, k1 and k2 (1≤n≤1000; 0≤k1,k2≤n). The second line of each experiment contains two integers w and b (0≤w,b≤n). Output For each experiment, print YES in case it's feasible to put all w+b dominoes on the board and negative, in any case. You might print each letter…EXERCISE - You go to a market to pick out some gourds to decorate your house for Halloween. The market has a special October deal where you get 3 randomly chosen gourdss for $10. Each gourd can either be an orange pumpkin, a green pumpkin or a squash. The probabilities for picking each one of them are: P(orange pumpkin) = 0.6, P(green pumpkin) = 0.3, and P(squash) = 0.1. A: What is the probability that the first gourd is an orange pumpkin, the second is a green pumpkin, and the third is a squash? B: What is the probability that you get all 3 as orange pumpkins? C: What is the probability that you get no squashes? D: What is the probability that you get at least one orange pumpkin? (ANSWERE USING PYTHON)The cost of renting a room at a hotel is, say $100.00 per night. For special occasions, such as a wedding or conference, the hotel offers a special discount as follows: If the number of rooms booked is at least 10, the discount is 10%; at least 20, the discount is 20%; and at least 30, the discount is 30%. Also if rooms are booked for at least three days, then there is an additional 5% discount. Write a program that prompts the user to enter the cost of renting one room, the number of rooms booked, the number of days the rooms are booked, and the sales tax (as a percent). The program outputs the cost of renting one room, the discount on each room as a percent, the number of rooms booked, the number of days the rooms are booked, the total cost of the rooms, the sales tax, and the total billing amount. Your program must use appropriate named constants to store special values such as various discounts.
- When you use a mortgage to purchase a home, the lending institution effectively owns the home. You buy back part ownership in the home with each monthly payment. The part you have bought back is your equity in the home. If the mortgage amount is P dollars, the monthly interest rate is r as a decimal, and the term of the mortgage is t months, then your equity after k payments is E(k) = P((1 + r)k − 1) (1 + r)t − 1 dollars. In this exercise, assume that the mortgage amount is $200,000, the APR is 6% so r = .06/12 and the term of the loan is 30 years (360 months). (a) Find a formula for the equity. (b) Make a graph of the equity over 360 months, the term of the loan. (c) Does the graph show that you have half-ownership in the home halfway through the term of the mortgage? Halfway through the term of the mortgage corresponds to k1 = _______ payments. From the graph, we see that E(k1) is ________ half of the mortgage amount, so we _______ have half-ownership in the home…Q1. Let’s play a dice game with a pair of dice following these rules:1. At the beginning, you throw a pair of dice. If the two numbers add up to 5, 6, 7, 8, or 9, thegame immediately stops.2. If your first throw does not meet those 5 totals, you would continue until you get either 11 or12.Get 1000 simulations of this paired dice game. What is the average number of dice throw per game?You can use the sample() function to simulate the dice.Interest on a credit card’s unpaid balance is calculated using the average daily balance. Suppose that netBalance is the balance shown in the bill, payment is the payment made, d1 is the number of days in the billing cycle, and d2 is the number of days payment is made before billing cycle. Then, the average daily balance is: averageDailyBalance =netBalance x d1-payment x d2d1 If the interest rate per month is, say, 0.0152, then the interest on the unpaid balance is: Interest= averageDailyBalance * 0.0152 Write a program using c++ compiler that accepts as inputnetBalance, payment, d1,d2, and interest rate per month. The program outputs the interest. Format your output to two decimal places.
- he Dice game of “Pig” can be played with the following rules. Roll two six-sided dice. Add the face values together. Choose whether to roll the dice again or pass the dice to your opponent. If you pass, then you get to bank any points earned on your turn. Those points become permanent. If you roll again, then add your result to your previous score, but you run the risk of losing all points earned since your opponent had rolled. Continue to roll as much as you want. However, once a “1” comes up on either die, your score is reduced to 0, leaving you only with points that you have previously "banked." Furthermore, you must pass the dice to your opponent. The first person to 100 points is the winner. When a player rolls two dice, the possible outcomes are as follows: Die #2 Roll Roll a 1 Roll a 2 Roll a 3 Roll a 4 Roll a 5 Roll a 6 Die #1 Roll Roll a 1 0 0 0 0 0 0 Roll a 2 0 4 5 6 7 8 Roll a 3 0 5 6 7 8 9 Roll a 4 0 6 7 8 9 10 Roll a 5 0 7 8 9 10 11 Roll a 6 0 8 9 10…Dynamic Programming: Two coins X and YFlip coin X: gain 1 point for the head, and lose 1 point for the tailFlip coin Y: gain 3 points for the head, lose 3 points for the tail. After n round, if the final score is positive, you win. Otherwise, you lose. The score does not matter. Pr(s) be the probability of winning; r is the round; s is the score.P0(s) = 1 for s >= 1; P0(s) = 0 if s <= 0. a. Explain why P1(s) = 0 when s <= -3; P1(s) = 0.5 when -2 <= s <= 1; P1(s) = 1 for s >= 2. b. Explain why you must select X if s is 2 or 3, and you must select Y if s is −2 or −1. b. Determine P2(s) for each possible value of s and explain. (each probability will be one of 0, ¼, 1/2, ¾, 1) c. Fine a recurrence relation for Pr(s) with form Pr(s) = max[(?+?)/2, (?+?)/2]. Explain. d. Use Dynamic Programming to compute probability P100(0) (win the game if it has 100 rounds).Suppose a person can buy a chocolate bar from the vending machine for $1 each. Inside every chocolate bar is a coupon. A person can redeem 3 coupons for one chocolate bar from the machine. This means that once a person has started buying chocolate bars from the machine, he/she always has some coupons. A person would like to know how many chocolate bars can be bought, if a person starts with N dollars and always redeem coupons, if he/she has enough for an additional chocolate bar. For example: With 3 dollars a person could buy 4 chocolate bars after purchasing 3 bars giving him/her 3 coupons and then redeeming the 3 coupons for one bar. This would leave him/her with one extra coupon. Thus, will have 4 chocolate bars and still have one coupon leftover. For 11 dollars, a person can have 16 chocolate bars and still have one coupon leftover. For 12 dollars, a person can have 17 chocolate bars and have two coupons leftover. Write a complete Python program that prompts a buyer to input…