A motor is providing  2 HP to the helical pinion at 1000 rpm. Gear has twice as many teeth as pinion. They both have full-depth teeth. The helix angle Ψ  is 30 degrees. The normal pressure angle ϕn is 25.  Hence, the transverse pressure angle ϕt is atan( tanϕn/cosΨ ) =  28.3001 deg.   The normal diametral pitch Pn is 12 teeth/inch. Hence, the transverse diametral pitch Pt is 12*cos(30) = 10.3923 teeth/inch.  Answer the questions below: 

Describe three reasons why achieving effective governance and meaningful representation can be difficult even when people agree on these principles.  

Explain why the Articles of Confederation were not strong enough to provide effective governance.

If the pinion has 10 teeth, what will the maximum number of teeth on the gear to avoid interference?

List 2 leading health indicators for Healthy People 2030 initiative that our government has published to promote health and prevent illness:

Suppose you have a jar of marbles that contains 10 blue, 13 red, 9 yellow, and 2 gold.  If you select a marble at random, determine the probability of each event. Selecting a marble that is gold or yellow. Selecting a marble that is not blue.

Find the particular solution of

Suppose you draw one card from a standard deck of 52 cards.  Find the probability of each event . An ace or a King is drawn. A red face card is drawn.

Which of the following is a critical point of the system

You are considering buying a new laptop, and have decided on an Asus Zenbook Gaming laptop with an OLED 4K 120Hz touch display which has the following options to choose from. GPU: RTX 3070 or RTX 4070. Memory: 32GB, or 64GB. List the sample space for possible laptop choices. (Write your final answer here, and you do not need to show work in your File Upload for this question.)