\( 5 \mid x \) means There exists an integer \( t \) such that \( x=5 t \). There exists an integer \( t \) such that \( t=5 x \). \( \frac{5}{x} \) is an integer.

A test consists of 10 truefalse questions, To pass the tost a student must answer at least 6 questions correctly, If a student guesses on each question, what is the probability that the student will pass the test? Round to three decimal places. A. 0.377 B. 0.172 C. 0.828 D. 0.205

3.) How much of a \( 30 \% \) acid solution must be mixed with 70 gallons of a \( 12 \% \) acid solution to obtain a solution that is \( 20 \% \) acid? \( \begin{array}{llll}\text { (A) } 5.6 \mathrm{gal} & \text { (B) } 49 \mathrm{gal} & \text { [C] } 56 \mathrm{gal} & \text { (D) none of these }\end{array} \)

Suppose an investment earns \( 3.4 \% \) interest compounded continuously. How long will it take an investment of \( \$ 3000 \) to be worth \( \$ 4000 \) ? Round your answer to the nearest hundredth.

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 55 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 3000 aspirin tablets actually has a \( 3 \% \) rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected? The probability that this whole shipment will be accepted is (Round to four decimal places as needed.)

Simplify: \( \sqrt{2 a}\left(2 \sqrt{8 a}+\sqrt{2 a^{3}}\right) \)