Answer:
<u>The Eastbound train speed is 76.5 miles per hour and the Westbound train speed is 79.5 miles per hour.</u>
Step-by-step explanation:
1. Let's review all the information provided for solving this question:
Eastbound train speed = x
Westbound train speed = x + 3 miles per hour (The speed of the westbound train is 3mph greater than the speed of the eastbound train)
Duration of trip = 3 hours
Distance between trains after 3 hours = 468 miles
2. Let's find the speed of each train, using the following equation:
3x + 3(x + 3) = 468
3x + 3x + 9 = 468
6x + 9 = 468
6x = 468 - 9 (Subtracting 9 at both sides)
6x = 459
x = 459/6 (Dividing by 6 at both sides)
x = 76.5 miles per hour
<u>The Eastbound train speed is 76.5 miles per hour and the Westbound train speed is 79.5 miles per hour.</u>
3. Proof that x = 76.5 is correct
3x + 3(x + 3) = 468
3 (76.5) + 3 (76.5 + 3) = 468
229.5 + 238.5 = 468
<u>468 = 468</u>
<u>The value of x = 76. 5 is correct. And now we know that the Eastbound train has traveled 229.5 miles since the departure from Cleveland and the Westbound train 238.5 miles.</u>
The red graph is the result of a vertical translation, 4 units down, of the black graph.
This means that, whenever the black graph associates

The red graph must associate 4 less to the same input:

So, the equation for the red graph is

or, equivalently,

Answer:
The probability of picking a yellow marble is 2/13
Step-by-step explanation:
First of all, we need to know the total number of marbles that are in the bag. To do this, we will have to add up all the marble colors together.
This will give us 6 + 2 +4+ 1 = 13 marbles in total.
The next step is to find the number of yellow marbles in the bag.
We can get this from the question. There are 2 yellow marbles in the bag.
The probability of selecting a yellow marble can be obtained by dividing the number of yellow marbles by the total number of marbles in the bag
This will give us 2/13.
Therefore, the probability of picking a yellow marble is 2/13
Answer:
scale factor P to Q: 4/5 scale factor Q to P: 5/4
Step-by-step explanation:
Divide original length over new length and you'll get the scale factor.