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:
1/5
Step-by-step explanation:
What is the probability 1/5.
Answer:
14 days
Step-by-step explanation:
Amount earned by gardener for each day worked = $60
Amount paid by gardener for each day when absent = $15
Total number of days = 20
Let the total number of days when the gardener was working = x
Then he was absent for (20 - x) days.
Total amount earned during this period = $750
Then, ![\[60x - 15(20-x) = 750\] ](https://tex.z-dn.net/?f=%5C%5B60x%20-%2015%2820-x%29%20%3D%20750%5C%5D%0A)
=> ![\[60x + 15x - 300 = 750\]](https://tex.z-dn.net/?f=%5C%5B60x%20%2B%2015x%20-%20300%20%3D%20750%5C%5D)
=> \[75x = 1050\]
=> x = 14
So the gardener worked for 14 days out of 20.
The equation of circle with center (g,f) and radius r is given by,
(x-g)² + (y-f)² = r²
Now, compare equation (x-2)² + (y+4)² = 6 with the above equation.
g = 2 and f = -4
Therefore, center of the circle is (2,-4)
Answer:
The absolute value graph below does not flip.
Step-by-step explanation:
New graphs are made when transformed from their parents graphs. The parent graph for an absolute value graph is f(x) = |x|.
The equation used for a new graph transformed from the parent graph is in the form f(x) = a |k(x - d)| + c.
"a" shows vertical stretch (a>1) or vertical compression (0<a<1), and <u>flip across the x-axis if "a" is negative</u>.
"k" shows horizontal stretch (0<k<1) or horizontal compression (k>1), and <u>flip across the y-axis if "k" is negative</u>.
"d" shows horizontal shifts left (positive number) or right (negative number).
"c" shows vertical shifts up (positive) or down (negative).
The function f(x)=2|x-9|+3 has these transformations from the parent graph:
a = 2; Vertical stretch by a factor of 2
k = 1; No change
d = 9; Horizontal shift right 9 units
c = 3; Vertical shift up 3 units
Since neither "a" nor "k" was negative, there were no flips, <u>also known as reflections</u>.
