Answer: C 4
Step-by-step explanation:
Use the formula: distance = rate x time
We can say that train 1 travels a distance of x, and train 2 travels a distance of 700 - x
The rate of train 1 is 75 mph, and the rate of train 2 is 100 mph
The time traveled for the two trains will be the same. We can represent that with the variable t.
We have the following equation for train 1:
x = 75t
For train 2, we have this equation:
700 - x = 100t
Use the Substitution Method by replacing x in the equation for train 2 with the value 75t.
700 - 75t = 100t
700 = 175t
700/175 = 4 hours.
It will take 4 hours for the two trains to meet.
Answer:
16
Step-by-step explanation:
Start by adding 9 to both sides, obtaining: √(x + 9) = 5.
Square both sides, obtaining: x + 9 = 25.
Subtract 9 from both sides: x = 16
Note that √(16+9) - 9 = -4, as required.
Answer:
x = 4, -6
Step-by-step explanation:
x = 4, -6
Answer:
1. 68%
2. 50%
3. 15/100
Step-by-step explanation:
Here, we want to use the empirical rule
1. % waiting between 15 and 25 minutes
From what we have in the question;
15 is 1 SD below the mean
25 is 1 SD above the mean
So practically, we want to calculate the percentage between;
1 SD below and above the mean
According to the empirical rule;
1 SD above the mean we have 34%
1 SD below, we have 34%
So between 1 SD below and above, we have
34 + 34 = 68%
2. Percentage above the mean
Mathematically, the percentage above the mean according to the empirical rule for the normal distribution is 50%
3. Probability that someone waits less than 5 minutes
Less than 5 minutes is 3 SD below the mean
That is 0.15% according to the empirical rule and the probability is 15/100
Answer:
in the ordered pair; ( x = 27/4 , y = 1/4 )
Step-by-step explanation:
Given that:
The system of the equation shown below is:
-2x - 14y = 10
2x + 2y = 14
We are to use the elimination method to determine the ordered pair.
From the above equation:
-2x - 14y = 10 --- (1)
2x + 2y = 14 --- (2)
Add both equation 1 and 2 together in order to eliminate x, then we can solve for y first.
-2x - 14y = 10
<u> 2x + 2y = 14 </u>
<u> 0 - 16y = -4 </u>
<u />
- 16 y = - 4
divide both sides by - 16, Then:
-16y /-16 = -4/-16
y = 1/4
Since y = 1/4, Then from equation (2), x will be :
2x + 2y = 14
2x + 2(1/4) = 14
2x + 1/2 = 14
2x = 14 - 1/2
2x = 13.5
x = 13.5/2
x = 27/4
Thus, in the ordered pair; ( x = 27/4 , y = 1/4 )
