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 MAT H to get MT HA. 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?
Note: ADCET and ADT EC are acceptable words, while ADT CE is not.

Design a number line containing five (5) points2.benin, one of the smallest countries in africa, has a total area of 43,475 square miles. the population of the country was recently estimated at 10,160,555. about 3,657,790 people live in rural areas. the country has only about 870 miles of surfaced roads. a. round off the total population to the nearest hundred thousand people. b. round off benin’s area in square miles to the nearest thousand. c. round off the number of miles of surfaced roads to the nearest ten. d. round off the number of people who live in rural areas to the nearest million.

The coverage of a base station of a telecommunication company forms a disk with a radius of (kilometers). let be the distance of a cellphone from a base station. assume that the location of cellphones in use are randomly uniformly distributed within the disk. calculate the mean and variance for the random variable.

The perimeter of △cde is 55 cm. a rhombus dmfn is inscribed in this triangle so that vertices m, f, and n lie on the sides cd , ce , and de respectively. find cd and de if cf=8 cm and ef=12 cm. the answer is not cd=20 and de=15. i have tried that one, it does not work.