Find a counterexample to show that each conjecture is false.

Prove or disprove the following statement, (c):

Each of the following sets of hypotheses contains an error. Identify the error. a H p+0.75 H, p= 0.75 versus b) H, X= 56 H,:x< 56 versus

A box has 4 yellow, 8 gray, and 3 black marbles. Three marbles are drawn at the same time (i.e. without replacement) from the box. Let X be the number of gray marbles drawn. Find the following. (Round your answers to three decimal places.)a) P(X = 2) = b) P(X ≤ 2) =

For each of the following conjectures, determine what method of proofwould be the most efficient method for proving the statement. You neednot write a formal proof (though you can) but you must give an expla-nation for why the method you chose would be most efficient. (a) Given an integer x greater than 2 such that x3−x2+ 1 is even, provethat the x-th power of the x-th prime is always odd.(b) Prove that if x is a positive integer such that x4/log(x) > 3pln(x),then x3+ x > x2−x.

: Use he comparism test to prove hat n-2 Converyes

Given that P(A)=0.3 and P(B)=0.7, answer the following:(please round all numerical answers to four decimal placesa) Assuming that A and B are independent, what is P(A and B)? b) Assuming that A and B are independent, what is P(A or B)? c) Assuming that A and B are independent, what is P(A|B)? d) If we are given that P(A and B) = 0.1, what is P(A|B)?

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2) A diner has to be cleaned before it opens for breakfast at 7 am. Cindy can clean the diner by herself in 2 hours Fn 3 Ctri Paon Enter Insert Delete Math Nation https://web.algebranation.com/ to clean before breakfast service? If Yes. Approximately, they have 9 minutes to spare before the diner opens. B Yes. Approximately, they have 10 minutes to spare before the diner opens. No. Approximately, they still need at least 9 minutes to complete cleaning the diner. No. Approximately, they still need at least 10 minutes to complete cleaning the diner. S) Bud takes 60 minutes by himnself to empty a truck of boxes, Paul can do it by himself in 90 minutes. Which equations will determine the amount of time, r, in minutes it will take them together to empty the ddcki 글 + 를 3D 1 + = ! + 1s = 80 + 20 = = 00 * Flying against the jetstream, a plane travels 3,132 miles in 9 hours. The same plane flying with the jetstream daveis 1.5 times the distance it traveled going against the jetstream. If the…