Answer:
Null hypothesis is 
Alternative hypothesis is 
Test Statistics z = 2.65
CONCLUSION:
Since test statistics is greater than critical value; we reject the null hypothesis. Thus, there is sufficient evidence to support the claim that the modified components have a longer mean time between failures.
P- value = 0.004025
Step-by-step explanation:
Given that:
Mean 
= 960 hours
Sample size n = 36
Mean population 
937
Standard deviation 
= 52
Given that the mean time between failures is 937 hours. The objective is to determine if the mean time between failures is greater than 937 hours
Null hypothesis is
Alternative hypothesis is
Degree of freedom = n-1
Degree of freedom = 36-1
Degree of freedom = 35
The level of significance ∝ = 0.01
SInce the degree of freedom is 35 and the level of significance ∝ = 0.01;
from t-table t(0.99,35), the critical value = 2.438
The test statistics is :
Z = 2.65
The decision rule is to reject null hypothesis if test statistics is greater than critical value.
CONCLUSION:
Since test statistics is greater than critical value; we reject the null hypothesis. Thus, there is sufficient evidence to support the claim that the modified components have a longer mean time between failures.
The P-value can be calculated as follows:
find P(z < - 2.65) from normal distribution tables
= 1 - P (z ≤ 2.65)
= 1 - 0.995975 (using the Excel Function: =NORMDIST(z))
= 0.004025
A consistent system of equations has at least one solution.
A consistent system is considered to be an independent system if it has a single solution, such as the example we just explored. The two lines have different slopes and intersect at one point in the plane.
A consistent system is considered to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide so the equations represent the same line. Every point on the line represents a coordinate pair that satisfies the system. Thus, there are an infinite number of solutions.
Another type of system of linear equations is an inconsistent system, which is one in which the equations represent two parallel lines. The lines have the same slope and different y-intercepts. There are no points common to both lines; hence, there is no solution to the system.
For more information on slopes click on the link below:
brainly.com/question/3493733
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For this case we have the following number written in scientific notation:
We know that this number is greater than zero because it is a positive number.
Therefore, the following statements are true:
p ∈ (-∞, ∞)
n must be between 1 and 10
n ∈ [1, 10]
Answer:
The following statements are correct about the number written in scientific notation:
p ∈ (-∞, ∞)
n ∈ [1, 10]
X^4 because it has 4 zeroes ( the graph crosses the x axis 4 times
