Select the correct answer. This graph represents a quadratic function. What is the value of a in this function’s equation? A)-1
B)2 C)1 D)-2
2 answers:
Answer:
Step-by-step explanation:
We will use the work form of a quadratic to determine what a is...in fact we will write the equation for the whole thing in the process, because it's part of solving for a.
y = ±|a|(x - h)² + k
where x and y are from a coordinate point on the graph, h and k are the coordinates of the vertex, the absolute value of a indicates how steep or flat the graph is compared to the parent graph, and the ± is because a positive parabola opens up and a negative one opens upside down.
The vertex is (0, 9) and the coordinate point I chose to use is (3, 0). Filling those in and solving for a:
0 = ±|a|(3 - 0)² + 9 and
0 = ±|a|(3)² + 9 and
-9 = ±|a|9 and
-1 = ±|a| so a = 1. Because this is an upside down parabola the negative is out front, but a is independent of it. The correct choice is C. The quadratic function is
or in more detailed form:
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Answer:
We conclude that the plant should shut down.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 60
Sample mean, = 61.498
Sample size, n = 100
Alpha, α = 0.05
Population standard deviation, σ = 6
a) First, we design the null and the alternate hypothesis such that the power plant will be shut down when the null hypothesis is rejected.
We use One-tailed(right) z test to perform this hypothesis.
b) Formula:
Putting all the values, we have
Now,
Since,
We reject the null hypothesis and accept the alternate hypothesis. Thus, the temperature of waste water discharged is greater than 60°F. We conclude that the power plant will shut down.
Calculating the p-value from the z-table:
P-value = 0.0063
Since,
P-value < Significance level
We reject the null hypothesis and accept the alternate hypothesis. Thus, the temperature of waste water discharged is greater than 60°F. We conclude that the power plant will shut down.