Determine whether the following argument is valid or invalid. argument: if a number is 4, then it is divisible by 2. if the number is divisible by 2, then it is even. therefore, if the number is 4, then it is even. question 2 options: the argument is valid by the law of syllogism. the argument is valid by the law of detachment. the argument is not valid. the argument is valid but does not follow the law of syllogism nor the law of detachment.

Aswimming pool has an input pump for filling the pool and an output pump for emptying the pool. the input pump can fill the pool in 3 hours, and the output pump can drain the pool in 5 hours. as you go to bed, the pool is full, but a neighbor’s kid turns on the output pump. at midnight, you awake to find the pool half empty. immediately, you turn on the input pump, but you are sleepy and forget to turn off the output pump. at what time will the pool become full?

(c) the diagram shows the first three shapes of a matchsticks arrangement.first shape = 3second shape = 5third shape = 7given m represents the number of matchstick used to arrange the n'th shape.(i) write a formula to represent the relation between m and n. express m as the subjectof the formula.(ii) 19 matchsticks are used to make the p'th shape. find the value of p.

Use a standard normal table to determine the probability. give your answer as a decimal to four decimal places. −1.5< < 1.5)