Which of the following equations has a maximum at (9,7)
2 answers:
Answer:
Step-by-step explanation:
Answer:
option C ⇒ C) y = -x² + 18x - 74
Step-by-step explanation:
The given options are:
A) y = -x² + 14x - 40
B) y = -x² - 18x - 88
C) y = -x² + 18x - 74
D) y = -x² - 14x - 58
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The general equation of the parabola has the form:
y = f(x) = ax² + bx + c
The vertex of the parabola has the coordinates (h , k)
where h =
and k = f(h) = f()
Check option A: a = -1 , b = 14 ⇒ (h,k) = (7, f(7) ) = (7 , 9)
Check option B: a = -1 , b = -18 ⇒ (h,k) = (-9, f(-9) ) = (-9,-7)
Check option C: a = -1 , b = 18 ⇒ (h,k) = (9, f(9) ) = (9,7)
Check option D: a = -1 , b = -14 ⇒ (h,k) = (-7, f(7) ) = (-7,-9)
So the equation which has a maximum at (9,7) ⇒ y = -x² + 18x - 74
<u>So, the correct answer is option C</u>
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Answer:
Null hypothesis be H₀ : μ = 100
Alternative hypothesis Hₐ : μ < 100
There is sufficient statistical evidence to suggest that the average location of Wade Tract is 100
Step-by-step explanation:
Here we have;
Let our null hypothesis be H₀ : μ = 100 Average location of trees in the Wade Tract is 100
Our alternative hypothesis becomes Hₐ : μ < 100 at 95% confidence level
Proposed average location in Wade Tract, μ = 100
Sample mean, = 99.74
Standard deviation, s = 58
Sample size, n = 584
The t test formula is therefore;
Therefore, with df = 584 -1 = 583, and α = (1 - 0.95)/2 = 0.025
We have = -1.65
Plugging in the values into the t test formula, we have t = -0.108338, from which the p-value is given as p = 0.4569 which is much more than the value of α, therefore, we accept the null hypothesis as follows;
There is sufficient statistical evidence to suggest that the average location of Wade Tract = 100.
Answer:
Q1 a) 0.9545
b) 0.02275
c) 0.97725
Q2 z is approximately equal to -1.466
Step-by-step explanation:
Q1 The given information are;
The mean time to commute to work = 24.4 minutes
The standard deviation = 6.5 minutes
a) The z-score for 11.4 is given as follows;
Where;
x = Observed value 11.4
μ = The mean = 24.4 minutes
σ = The standard deviation = 6.5 minutes
The z-score for 37.4 is given as follows;
-2 < z < 2, which gives, from the z-score table;
The probability of commute time to be between 11.4 minutes and 37.4 minutes = 0.97725 - 0.02275 = 0.9545
b) From the z-score table, the probability that the commute time to be less than 11.4 minutes = The probability at z = -2 = 0.02275
c) From the z-score table, the probability that the commute time to be greater than 37.4 minutes = The probability at z = 2 = 0.97725
Q2 The the z-score that corresponds to a commute time of 15 minutes is given as follows;
Answer:
The whole numbers are 0 and 79.
Step-by-step explanation:
The numbers provided are as follows:
Whole numbers are a set of natural positive numbers and 0. This set basically consists of counting discrete numbers.
Such as: 0, 1, 2, 3, 4, 5....
From the provided set of numbers the whole numbers are:
S = {79 and 0}
Thus, the whole numbers are 0 and 79.