Answer:
Part A: Kimberly
Part B:
Becca = 22.5 miles, Kimberly = 25 miles
Step-by-step explanation:
Part A:
Given that Becca runs at a constant speed of 4.5 miles per hour, use the table to find the constant speed that Kimberly runs, and compare who runs faster.
Let x = time
y = distance
k = speed = y/x
Equation for each person can be written as: y = kx
Therefore:
✔️Equation for Becca if k = 4.5
y = 4.5x
✔️Find k (speed) of Kimberly using (2, 10):
Speed (k) = y/x
k = 10/2
k = 5 miles per hour
Equation for Kimberly would be:
y = 5x
Comparing their speed, Kimberly runs faster because she covers more miles per hour than Becca does.
Part B:
For Becca, substitute x = 5 into Becca's equation, y = 4.5x
Thus:
y = 4.5*5 = 22.5 miles
For Kimberly, substitute x = 5 into Kimberly's equation, y = 5x
Thus:
y = 5*5 = 25 miles
Answer:
Tap A will take 2 hours and tap B will take 6 hours to fill the tank when turned on alone.
Step-by-step explanation:
Let tap B fills the pool alone in the time = x hours
So in one hour part of pool will be filled = 
Another tap A when turned on, it takes time to fill the pool = x-5 hours
So in one hour part of the same pool filled = 
Now both the taps A and B are turned on then time taken to fill the pool = 3 hours.
Part of the pool filled in one hour by both the taps = 
Now we form an equation
Part of pool filled in one hour by tap A + Part of pool filled in one hour by tap B = Part of pool filled in one hour by both the taps when turned on



3(x - 4) = x(x - 5)
x² -5x = 3x - 12
x² - 8x + 12 = 0
x² - 6x - 2x + 12 = 0
x(x - 6) - 2(x - 6) = 0
(x -2)(x - 6) = 0
x = 2, 6 hours
We will take higher value of x as x = 6 hours for tap B.
Time taken by tap A = 6 - 4 = 2 hours.
Therefore, Tap A will take 2 hours and tap B will take 6 hours to fill the tank when turned on alone.
Answer:
(D)109
Step-by-step explanation:
Mean = 450 seconds
Standard deviation = 50
First, we determine the probability that the expected response time is between 400 seconds and 500 seconds, P(400<x<500)
Using the Z-Score,

From the Z-Score table
P(-1<x<1) = 0.68269
The probability that the expected response time is between 400 seconds and 500 seconds is 0.68269.
Since there are 160 Emergencies
Number whose expected time is between 400 seconds and 500 seconds
