Answer:
2
Step-by-step explanation:
Answer:
c. 0.1151
Step-by-step explanation:
d) the probability that, on average, fish are larger than 86 centimeters in length.The area under part of a normal probability curve is directly proportional to probability and the value is calculated as
z = (x₁−x) /σ
where z = propability of normal curve
x₁ = variate mean = 86cm
x = mean of 80cm
σ = standard deviation = 5cm
applying the formula,
z= (86-80)/5
z = 6/5 =1.2
Using a table of partial areas beneath the standardized normal curve (see Table of normal curve, a z-value of 1.2 corresponds to an area of 0.3849 between the mean value. but, because the standard curve has 0.5, then will minus 0.3849 from 0.5= 0.5 - 0.3849 = 0.1151
Thus the probability of a fish are larger than 86 centimeters in length is 0.1151
Answer:
The average rate of change of the function from x=1 to x=2 will be: 10.5
Step-by-step explanation:
Given the function

at x₁ = 1,
f(x₁) = f(1) = -14/(1)² = -14/1 = -14
at x₂ = 2,
f(x₂) = f(2) = -14/(2)² = -14/(4) = -3.5
Using the formula to determine the average rate of change at which the total cost increases will be:
Average rate of change = [f(x₂) - f(x₁)] / [ x₂ - x₁]
= [-3.5 - (-14)] / [2 - 1]
= [-3.5 + 14] / [1]
= 10.5 / 1
= 10.5
Therefore, the average rate of change of the function from x=1 to x=2 will be: 10.5
ANSWER
D.

EXPLANATION
The given function is

Comparing to the general form of a trigonometric sine function,


The amplitude is absolute value of A


The period is given by



is a shift to the right of 4 units.
and

is an upward shift of 9 units
Therefore the phase shift is (4,9).
The correct answer is D