Problem of the Week Problem C
CADET
We can take any word and rearrange all the letters to get another "word". These
new "words" may be nonsensical. For example, you can rearrange the letters in
MATH to get MTHA. Geordie wants to rearrange all the letters in the word
CADET. However, he uses the following rules:
• the letters A and D must be beside each other, and
• the letters E and T must be beside each other.
How many different arrangements of the word CADET can Geordie make if he
follows these rules?

One expression below in undefined, and the other expression has a well defined value. which expression is undefined and explain why it has no value. which expression is defined? what is the value of that expression and how do you know? what is a different expression using a trig inverse function that is also undefined?

Afactory makes propeller drive shafts for ships. a quality assurance engineer at the factory needs to estimate the true mean length of the shafts. she randomly selects four drive shafts made at the factory, measures their lengths, and finds their sample mean to be 1000 mm. the lengths are known to follow a normal distribution whose standard deviation is 2 mm. calculate a 95% confidence interval for the true mean length of the shafts. input your answers for the margin of error, lower bound, and upper bound.

Asix-sided die of unknown bias is rolled 20 times, and the number 3 comes up 6 times. in the next three rounds (the die is rolled 20 times in each round), the number 3 comes up 6 times, 5 times, and 7 times. the experimental probability of rolling a 3 is 10 %, which is approximately % more than its theoretical probability. (round off your answers to the nearest integer.)