67. the goldbach conjecture. recall that a prime number is a
natural number whose only factors are itself and 1 (examples
of primes are 2, 3, 5, 7, and 11). the goldbach conjecture,
posed in 1742, claims that every even number greater than
2 can be expressed as the sum of two primes. for example,
4 = 2 + 2,6 = 3 + 3, and 8 = 5 + 3. a deductive proof
of this conjecture has never been found. test the conjecture
for at least 10 even numbers, and present an inductive argu-
ment for its truth. do you think the conjecture is true? why
or why not?

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.

In dire need~! describe how to use area models to find the quotient 2/3 divided by 1/5. check your work by also finding the quotient 2/3 divided by 1/5 using numerical operations only.

Which description is represented by a discrete graph? kiley bought a platter for $19 and several matching bowls that were $8 each. what is the total cost before tax? the temperature at 9 a.m. was 83° f and is heating up at an average rate of 6°f per hour. what is the temperature x hours later? juan ate an egg with 78 calories and some cereal with 110 calories per serving for breakfast. what is the total amount of calories he consumed? a bottle contained 2,000 ml of liquid and is being poured out at an average rate of 300 ml per second. how much liquid is left in the bottle after x seconds?