PLEASE HELP!! a bag contains six black cubes numbered one to six. the bag also contains four purple cubes numbered one to four. you randomly pick acube. are the events "purple cube" and "a number greater than 5" mutually exclusive? explain your reasoning​

It is saturday morning and jeremy has discovered he has a leak coming from the water heater in his attic. since plumbers charge extra to come out on the weekends, jeremy is planning to use buckets to catch the dripping water. he places a bucket under the drip and steps outside to walk the dog. in half an hour the bucket is 1/5 of the way full. what is the rate at which the water is leaking per hour?

Find the maximum value of p= 4x + 5y subject to the following constraints :

What is the area of the original rectangle? 8 cm² 20 cm² 25 cm² 40 cm²