Write the following expression in simplest form pls i neeeeed help! Its a quiz!
2 answers:
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Answer:
a) 0.25
b) 0.25
c) 0.0625
Step-by-step explanation:
The complete question is:
Do you remember when breakfast cereal companies placed prizes in boxes of cereal? Possibly you recall that when a certain prize or toy was particularly special to children, it increased their interest in trying to get that toy. How many boxes of cereal would a customer have to buy to get that toy? Companies used this strategy to sell their cereal.
One of these companies put one of the following toys in its cereal boxes: a block (B), a toy watch (W), a toy ring (R), and a toy airplane (A). A machine that placed the toy in the box was programmed to select a toy by drawing a random number of 1 to 4. If a 1 was selected, the block (or B) was placed in the box; if a 2 was selected, a watch (or W) was placed in the box; if a 3 was selected, a ring (or R) was placed in the box; and if a 4 was selected, an airplane (or A) was placed in the box. When this promotion was launched, young children were especially interested in getting the toy airplane.
What is the probability of getting an airplane in the first cereal box?
Since the machine randomly selects toys, each toy has the same probability of being obtained in a cereal box.
Then, the total outcomes are 4 and the probability of getting an airplane in the first cereal box is 0.25 (25%).
What is the probability of getting an airplane in the second cereal box?
Two independent events do not change the probability of occurrence of one event or another.
The probability of getting an airplane in the second cereal box is 0.25 (25%).
What is the probability of getting airplanes in both cereal boxes?
P(1°∩2°)= P(1°) × P(2°) =
P(1°∩2°)= 0.0625 = 6.25%
Answer:
Step-by-step explanation:
<span>The rate of the express train is 15 mph faster than the freight train.
Let's grasp onto this piece of information.
The rate at which the freight train goes will be labeled "x" (keep in mind rate is just the speed)
If the freight train has a speed of "x" then the express train which is going 15mph faster than the freight train can be represented as "x + 15mph."
Our result is in HOURS, but our speed is in Miles per Hour (Miles/Hour). Meaning we need to multiply our speeds by some time (t).
Let's set up two equations:
Freight Train: 18 hours * x mph = distance
Express Train: 15 hours * (x mph + 15mph) = distance
They are both the same distance so we can set the two equations equal to each other like this:
18 hours * x mph = 15 hours * (x mph + 15mph)
That right side is a bit of a thorn in our side, so let's simplify it by multiplying all the terms in the parenthesis by 15 hours (keep in mind the hours in the units cancel out).
18 hours * x mph = 15x miles + 15 * 15 miles
18 hours * x mph = 15x miles + 225 miles
Let's simplify the left side (</span>
)
18x miles = 15x miles + 225 miles
Get all the "x" terms on one side by subtracting 15x on both sides.
18x - 15x = 225 miles
Simplify
3x = 225 miles
Divide by 3 on both sides to solve for x.
225/3
225 = 25*9
(25*9)/3 = 25*3 = 75mph
So "x" which we chose was the rate of the freight train is 75mph.
Adding 15mph to the freight train rate gives you the express trains rate which is 90mph.
Hope that helped.
Let's grasp onto this piece of information.
The rate at which the freight train goes will be labeled "x" (keep in mind rate is just the speed)
If the freight train has a speed of "x" then the express train which is going 15mph faster than the freight train can be represented as "x + 15mph."
Our result is in HOURS, but our speed is in Miles per Hour (Miles/Hour). Meaning we need to multiply our speeds by some time (t).
Let's set up two equations:
Freight Train: 18 hours * x mph = distance
Express Train: 15 hours * (x mph + 15mph) = distance
They are both the same distance so we can set the two equations equal to each other like this:
18 hours * x mph = 15 hours * (x mph + 15mph)
That right side is a bit of a thorn in our side, so let's simplify it by multiplying all the terms in the parenthesis by 15 hours (keep in mind the hours in the units cancel out).
18 hours * x mph = 15x miles + 15 * 15 miles
18 hours * x mph = 15x miles + 225 miles
Let's simplify the left side (</span>
18x miles = 15x miles + 225 miles
Get all the "x" terms on one side by subtracting 15x on both sides.
18x - 15x = 225 miles
Simplify
3x = 225 miles
Divide by 3 on both sides to solve for x.
225/3
225 = 25*9
(25*9)/3 = 25*3 = 75mph
So "x" which we chose was the rate of the freight train is 75mph.
Adding 15mph to the freight train rate gives you the express trains rate which is 90mph.
Hope that helped.