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Sample Practice Test Questions
The total water usage for a city is 50,000 gallons each day. Of that total, 32% is for personal use and 59% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
59% of the water consumption is industrial use and 32% is personal use so (59% - 32%) = 27% more water is used for industrial purposes. 50,000 gallons are consumed daily so industry consumes \( \frac{27}{100} \) x 50,000 gallons = 13,500 gallons.
Which of the following is the name for a transmission that incorporates the differential in one package?
transaxle
A differential is designed to drive a pair of wheels while allowing them to rotate at different speeds. A transaxle is a transmission that incorporates the differential in one package. Most front-wheel drive cars use a transaxle while rear-wheel drive cars use a transmission and separate differential connected via a drive shaft. The differential is incorporated into the drive axle which splits engine power delivered by the drive shaft between the two drive wheels. All-wheel drive cars typically use a transaxle that includes an output shaft to the rear differential.
The valence shell of n insulator is how full of electrons?
more than half full
Insulators have valence shells that are more than half full of electrons and, as such, are tightly bound to the nucleus and difficult to move from one atom to another.
Find the value of a:
5a + y = -1
-2a - 3y = -3
You need to find the value of a so solve the first equation in terms of y:
5a + y = -1
y = -1 - 5a
then substitute the result (-1 - 5a) into the second equation:
-2a - 3(-1 - 5a) = -3
-2a + (-3 x -1) + (-3 x -5a) = -3
-2a + 3 + 15a = -3
-2a + 15a = -3 - 3
13a = -6
a = \( \frac{-6}{13} \)
a = -\(\frac{6}{13}\)
If 15 lbs. of force is applied 8 ft. from the fulcrum at the blue arrow and the green box is 7 ft. from the fulcrum, how much would the green box have to weigh to balance the lever?
To balance this lever the torques at the green box and the blue arrow must be equal. Torque is weight x distance from the fulcrum so the equation for equilibrium is:
Rada = Rbdb
where a represents the green box and b the blue arrow, R is resistance (weight/force) and d is the distance from the fulcrum.Solving for Ra, our missing value, and plugging in our variables yields:
Ra = \( \frac{R_bd_b}{d_a} \) = \( \frac{15 lbs. \times 8 ft.}{7 ft.} \) = \( \frac{120 ft⋅lb}{7 ft.} \) = 17.14 lbs.
If A = 9 ft. and the green box weighs 30 lbs. what is the torque acting on the A side of this lever?