Answer: the function that has the smaller minimum is g(x), and the cordinates are (0,3)
Step-by-step explanation:
We have a function for f(x) and a table for g(x)
first, quadratic functions are symmetrical.
This means that if the minimum/maximum is located at x = x0, we will have that:
f(x0 + A) = f(x0 - A)
For any real value of A.
Then when we look at the table, we can see that:
g(-1) = 7
g(0) = 3
g(1) = 7
then the minimum of g(x) must be at x = 0, and we can see that the minimum value of g(x) is 3.
Now let's analyze f(x).
When we have a quadratic equation of the shape.
y = a*x^2 + b*x + c
the minimum/maximum will be located at:
x = -b/2a
In our function we have:
a = 3
b = 6
then the minimum is at:
X = -6/2*3 = -1
f(-1) = 3*(-1)^2 + 6*-1 + 7 = 3 - 6 + 7 = 3 + 1 = 4
Then the function that has the smaller minimum is g(x), and the cordinates are (0,3)
Answer:
Step-by-step explanation:
The answer is fifteen
Explanation: 6-3/0.4-0.2=3 over 0.2 which is equivalent to 15
There is 100 N pushing the box to the right and 10 N pushing the box to the left
since there is force being applied in opposite directions, the net force is found by subtracting the 2
100 - 10 = 90 N ( Net Force)
and because the higher force is pushing the box to the right, the direction will accelerate to the right.
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Answer:
d. The interval contains only negative numbers. We cannot say at the required confidence level that one region is more interesting than the other.
Step-by-step explanation:
Hello!
You have the data of the chemical measurements in two independent regions. The chemical concentration in both regions has a Gaussian distribution.
Be X₁: Chemical measurement in region 1 (ppm)
Sample 1
n= 12
981 726 686 496 657 627 815 504 950 605 570 520
μ₁= 678
σ₁= 164
Sample mean X[bar]₁= 678.08
X₂: Chemical measurement in region 2 (ppm)
Sample 2
n₂= 16
1024 830 526 502 539 373 888 685 868 1093 1132 792 1081 722 1092 844
μ₂= 812
σ₂= 239
Sample mean X[bar]₂= 811.94
Using the information of both samples you have to determina a 90% CI for μ₁ - μ₂.
Since both populations are normal and the population variances are known, you can use a pooled standard normal to estimate the difference between the two population means.
[(X[bar]₁-X[bar]₂)±
*
]

[(678.08-811.94)±1.648*
]
[-259.49;-8.23]ppm
Both bonds of the interval are negative, this means that with a 90% confidence level the difference between the population means of the chemical measurements of region 1 and region 2 may be included in the calculated interval.
You cannot be sure without doing a hypothesis test but it may seem that the chemical measurements in region 1 are lower than the chemical measurements in region 2.
I hope it helps!