What are the discontinuity and zero of the function f(x) = quantity x squared plus 6 x plus 8 end quantity over quantity x plus
1 answer:
Answer:
Discontinuity at (-4,-2), zero at (-2,0).
Step-by-step explanation:
We are given that a function
We have to find the discontinuity and zero of the given function.
Discontinuity: It is that point where the function is not defined.
It makes the function infinite.
When x=-4 then
It is indeterminate form
Function is not defined
After cancel out x+4 in numerator and denominator then we get
Substitute x=-4
Therefore, the point of discontinuity is (-4,-2).
Zero: The zero of the function is that number when substitute it in the given function then the function becomes zero.
When substitute x=-2
Then ,
The function is zero at (-2,0).
Hence, option C is true.
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Answer:
Step-by-step explanation:
Hello!
The objective is to test if rising the process temperature reduces the thickness of the plastic film that coats a substrate material To do so, two samples of substrates are coated at different temperatures:
Sample 1
X₁: Thickness of the plastic film after the substrate is coated at 125F
n₁=11
X[bar]₁= 101.28
S₁= 5.08
Sample 2
X₂: Thickness of the plastic film after the substrate is coated at 150F
n₂= 13
X[bar]₂= 101.70
S₂= 20.15
Does the data support this claim? Use the P-value approach and assume that the two population standard deviations are not equal.
Now if the higher the heat, the thinner the thickness of the plastic coating, then the average thickness of the coating done at 150F should be less than the average thickness of the coating done at 125F, symbolically: μ₂ < μ₁
Then the hypotheses are:
H₀: μ₂ ≥ μ₁
H₁: μ₂ < μ₁
α:0.05 (there is no α level stated so I've chosen the most common one)
Assuming that both variables have a normal distribution since the population standard deviations are not equal, the statistic to use is the Welch's t-test:
This test is one-tailed to the left, meaning that you'll reject the null hypothesis at small values of t. The p-value is also one-tailed and has the same direction as the test. To calculate it you have to first calculate the degrees of freedom of the Welch's t:
The distribution is a Student's t with 13 degrees of freedom, then you can calculate the p-value as:
P(t₁₃≤0.072)= 0.4718
Using the p-value approach, the decision rule is:
If the p-value ≤ α, the decision is to reject the null hypothesis.
If the p-value > α, the decision is to not reject the null hypothesis.
The p-value is greater than the significance level, so the decision is to nor reject the null hypothesis.
Using a significance level of 5%, there is no significant evidence to support the claim that the average thickness pf the plastic coat processed at 150F is less than the average thickness pf the plastic coat processed at 125F.
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