Because the vertex of the parabola is at (16,0), its equation is of the formy = a(x-10)² + 15
The graph goes through (0,0), thereforea(0 - 10)² + 15 = 0100a = -15a = -0.15
The equation is y = f(x) = -0.15(x - 10)² + 15
The graph is shown below.
Part A
Note that y = f(x).
The x-intercepts identify values where the function or y=0. The x-intercepts occur at x=0 and x=20, or at (0,0) and (20,0).
The maximum value of y occurs at the vertex (10, 15) because the curve is down due to the negative leading coefficient of -0.15.
The curve increases in the interval x = (-∞, 10) and it decreases in the interval x = (10, ∞).
Part B
When x=12, y = -0.15(12 - 10)² + 15 = 14.4When x=15, y = -0.15(15 - 10)² + 15 = 11.25
The average rate of change between x =12 to x = 15 is(11.25 - 14.4)/(15 - 12) = -1.05
This rate of change represents the slope of the secant line from A to B. It approximates the rate at which f(x) decreases in the interval x =[12, 15].
Answer: 5
Step-by-step explanation:
If;
5 gallons = $12.50 / 5 = $2.50/gallon
11 gallons = $26.40 / 11 = $2.40/gallon
In conclusion, 5 gallons cost more per gallon than 11.
Answer:The percentage of bottles expected to have a volume less than 32 or is 40.13%
Step-by-step explanation: The volumes of soda in quart soda bottles can be represented by a Nomal model with a= 32.3 oz
b=1.2 oz
Let S be the volume of randomly selected soda bottles
Y-score: S-a/b
For S=32 oz
Substitute the values of S,a and b into the equation
Y=32-32.3/1.2
Y=-0.25
Probability of bottles that have a volume less than 32 oz is
P(S<32)=P(Y<-025)= 0.40129
Percentage of bottles that have volume less than 32 oz will be
0.40127×100%=40.13%
(a)7x4=28
2x2=4
28-4=24
24-1=23 points
(b)20/4=7 correct answers
