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There are 200 shirts and 100 pairs of trousers from last season that a retailer wants to get rid of. They've come up with two options, A and B, and are putting them together. Offer A is a $30 set that includes a shirt and a pair of trousers. Offer B is a $50 set that includes three shirts and two pairs of trousers. A total of 20 of Offer A and 10 of Offer B packages must be sold in order for the business to make a profit. Is there a maximum number of packets they need to sell in order to maximize profit?


  • An explorer walks 22km due North and then 45 degrees south of east for 47km.what’s the resultant displacement from the origin?

Suppose three coins are tosted.Let Y be the random variable representing the number of tails that occur.Find the values of the random variable Y.Make a table to show the values of the random variable

There are 7 defective light bulbs in a bin containing 80 light bulbs. In how many ways can you select at

least 6 defective light bulbs when you choose 8 light bulbs at random?


Problem: A sample with size n = 4 is drawn from the set 5, 6, 9, 12a 13. Construct the sampling distribution of the means. Find the mean and the standard deviation. Include your solution and box your final answer in mu overline x and 2 sigma overline x

A manufacturer of light bulbs produces bulbs that last a mean of 950 hours with a standard deviation of 120 hours. What is the probability that the mean lifetime of a random sample of 10 of these bulbs is less than 900 hours? what is the sampling distribution of the sample means


Determine whether ( 𝑝∨𝑞)∧(𝑝→𝑟)∧( 𝑞→𝑠)→𝑟∨𝑠 is a Tautology or a contradiction using a truth table

Give full truth table


Prove for all integers and b, if mod 8 = 5 and mod 8 = 3 then ab mod 8 = 7.



Prove for every integer nn4 has the form 8or 8+ 1 for some integer m. Hint: Use 2 cases.



In a large population 63% of the people have been vaccinated if 5 people are randomly selected what is the probability that at least one of them has been vaccinated


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