6.4 Q2.) Use the trapezoidal rule to approximate and use the fundamental theorem of calculus to find the exact value of the defi
nite integral.
1 answer:
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Answer: See explanation
Step-by-step explanation:
1. Use the five steps of hypothesis testing.
Step 1: The aim of the research is to conduct the five steps of hypothesis testing.
Step 2:
Null hypothesis: H0 u= 4
Population mean: H1 u = 4
Alternate hypothesis: u ≠ 4
Population mean: u ≠ 4
Step 3 and step 4 are attached.
Step 5: Based on the calculation, the calculated value of t is less than the t critical value, therefore, the null hypothesis will be failed to be rejected.
2. Sketch the distributions involved
This has been attached.
3. Explain the logic of what you did to a person who is familiar with hypothesis testing, but knows nothing about t tests of any kind.
The distribution is "t".
The means is tested by using T-test.
Chi-square is used to test the single variance.
Answer:
The system of inequalities " x + 2 y ≤ 5 and 3 x + y ≤ 4 " is represented by the graph ⇒ D
Step-by-step explanation:
To find the answer let us find the equation of each line
Blue line:
∵ The line passes through points (5 , 0) and (0 , 2.5)
- Find the slope of the line
∵ m = Δy/Δx
∴
∴ m = -0.5
- The form of the equation is y = m x + b, where b is the
y-intercept (value y at x = 0)
∵ y = 2.5 at x = 0
∴ b = 2.5
- Write the equation of the line
∴ y = - 0.5 x + 2.5
- Multiply both sides by 2
∴ The equation of the blue line is 2 y = - x + 5
- The shading is under the line and the line is solid, that means
2 y is less than or equal - x + 5
∴ The inequality of the blue line is 2 y ≤ - x + 5
Red line:
∵ The line passes through points (3 , -5) and (0 , 4)
- Find the slope of the line
∴
∴ m = -3
∵ y = 4 at x = 0
∴ b = 4
- Write the equation of the line
∴ y = -3 x + 4
∴ The equation of the red line is y = -3 x + 4
- The shading is below the line and the line is solid, that means
y is less than or equal -3 x + 4
∴ The inequality of the red line is y ≤ -3 x + 4
Let us find which answer is the same with this system of inequalities
∵ 2 y ≤ - x + 5
- Add x to both sides
∴ x + 2 y ≤ 5 ⇒ same as the first inequality of answer D
∵ y ≤ -3 x + 4
- Add 3 x to both sides
∴ 3 x + y ≤ 4 ⇒ same as the second inequality of answer D
The system of inequalities " x + 2 y ≤ 5 and 3 x + y ≤ 4" is represented by the graph