Explain how an estimate helps you place the decimal point when multiplying 3.9 × 5.3
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Complete Question
Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and inexpensive to manufacture. However, their nondegradable nature has prompted development of environmentally friendly composites using natural materials. An article reported that for a sample of 10 specimens with 2% fiber content, the sample mean tensile strength (MPa) was 51.1 and the sample standard deviation was 1.2. Suppose the true average strength for 0% fibers (pure cellulose) is known to be 48 MPa. Does the data provide compelling evidence for concluding that true average strength for the WSF/cellulose composite exceeds this value? (Use α = 0.05.)
t=8.169
P-value= ?
Answer:
a)
b) Hence,We FAil to reject the alternative hypothesis and accept that the true average strength for the WSF/ cellulose composite exceeds 48 MPa.
Step-by-step explanation:
From the question we are told that:
Sample size
Mean
Standard deviation
Significance level is taken as
t test statistics
Therefore
Critical point
Therefore
P-value from T distribution table
Conclusion
We Reject the Null Hypothesis
Hence,We FAil to reject the alternative hypothesis and accept that the true average strength for the WSF/ cellulose composite exceeds 48 MPa.
The values of BMW after 2 years and 4 years according to the EXPONENTIAL FUNCTION are $33,462 and $20,358.28
Using the parameters given, we define an decreasing exponential function :
Where,
= initial amount ; r = Rate ; t = time ; A = final amount
Value after 2 years :
t = 2
A = 55000(1 - 0.22)²
A = 55000(0.78)²
A = $33,462
Value after 4 years :
t = 4
A = 55000(1 - 0.22)^4
A = 55000(0.78)^4
A = $20,358.28
Therefore, the value of BMW after 2 years and 4 years $33,462 and $20,358.28 respectively.
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