Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Roscoe has punch cards for his favorite tea house and his favorite coffee shop. He currently has 7 punches on the tea punch card and 10 punches on the coffee punch card. Given his regular routine, he consistently earns 7 new punches per week on the tea punch card and 6 on the coffee punch card. Before too long, Roscoe will have the same number of punches on each card. How many punches will Roscoe have on each card? How long will that take?

Roscoe will havepunches on each card in weeks.

Is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis.

Simplify 1/3 12x - 6 a. -2x-1 b.-2x-8 c.-x+4 d.3x+10 e. 4x-2

Agroup of student volunteers participates in a study designed to assess several behavioral interventions for improving output in a repetitive task. prior to the beginning of the study, all volunteers unknowingly observed, and their output is measured. at the beginning of the study, prior to any intervention, the volunteers perform the same task under the observation of a study administrator, and their overall output increases. which of the following terms describes this phenomenon? a. simpson's paradox b. hawthorne effect are d. novelty effect d. pygmalion effect e. observer-expectancy effect