Answer: 0.0228
Step-by-step explanation:
Given : The mean and the standard deviation of finish times (in minutes) for this event are respectively as :-
If the distribution of finish times is approximately bell-shaped and symmetric, then it must be normally distributed.
Let X be the random variable that represents the finish times for this event.
z score : 
Now, the probability of runners who finish in under 19 minutes by using standard normal distribution table :-
Hence, the approximate proportion of runners who finish in under 19 minutes = 0.0228
Answer:
x = -2.5
Step-by-step explanation:
Step 1: Write equation
-6.2 - 12.6x = 5.8 - 7.8x
Step 2: Solve for <em>x</em>
<u>Add 12.6x on both sides:</u> -6.2 = 5.8 + 4.8x
<u>Subtract 5.8 on both sides:</u> -12 = 4.8x
<u>Divide both sides by 4.8:</u> x = -2.5
Step 3: Check
<em>Plug in x to verify if it's a solution.</em>
-6.2 - 12.6(-2.5) = 5.8 - 7.8(-2.5)
-6.2 + 31.5 = 5.8 + 19.5
25.3 = 25.3
They would make a profit of $187.50
(if that is what you were trying to ask)
Answer:
-2-2√3, -2+2√3
Step-by-step explanation:
Let x represent one of the numbers. Then the other number is -4-x. We want the product to be -8:
x(-4-x) = -8
-4x -x^2 = -8 . . . . . eliminate parentheses
x^2 +4x = 8 . . . . . . multiply by -1
x^2 +4x +4 = 12 . . . add 4 to complete the square
(x +2)^2 = 12
x +2 = ±√12 = ±2√3
x = -2±2√3
The two numbers are -2-2√3 ≈ -5.4641, and -2+2√3 ≈ 1.4641.
