Question 3(Multiple Choice Worth 4 points) Simplify 32 ⋅ 35.
2 answers:
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<u>We are given:</u>
car and train leave at the same time
average velocity of car = 50 miles/hour
average velocity of train = 70 miles/hour
train arrives 2 hours early
<u>Assuming variables and making equations!</u>
let the time taken by the train = t hours
since the car arrived late, it took more time as compared to the train
time taken by the car = t + 2 hours
since the distance from Pasadena to Sacramento doesn't change, both the vehicles covered the same distance, d
<u>Distance travelled by the car:</u>
d = 50 * (t+2) hours [distance = velocity * time]
d = 50(t+2) miles
rewriting in terms of t
<u>Distance travelled by the train:</u>
d = 70 * t hours
d = 70t miles
rewriting in terms of t
now we have two expressions for t, both of which are equal because t is just the time taken by the train
<u>Finding the distance:</u>
<u></u><u></u>
<u></u><u></u>
because t is the same:
7(d - 100) = 5(d)
7d - 700 = 5d
(7d - 5d) - 700 = 0 [subtracting 5d from both sides]
2d = 700 [adding 700 on both sides]
d = 350 miles [dividing both sides by 2]
The distance between Pasadena and Sacramento is 350 miles!
We are given that a coin is toseed with two possible outcomes (head or tails) and a ball from a ball with balls of three different colors is picked.
We have that the possible outcomes are all possible combinations of the faces of the coin and the color of one of the balls.
Therfore, if:
The possible combinations are:
Therefore, the right answer is C.