How are the functions f(x) = 16* and 19(x) = 161/2 related?
1 answer:
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Answer:
I) f + g = 10/3
II) 4f + 2g = 20/3
III) f = 2 and g = 4/3
Step-by-step explanation:
From the chart,
P = 25
q = 40
The total number of one centimeter lines in the first n diagrams is given by the expression
2/3n^3 + fn^2 + gn.
When n = 1, the total number of line = 4. So,
2/3(1)^3 + f(1)^2 + g(1) = 4
2/3 + f + g = 4
Make f+g the subject of formula
f + g = 4 - 2/3
f + g = (12 - 2)/3
f + g = 10/3 ......(1)
When n = 2
Total number of line = 12
2/3(2)^3 + f(2)^2 + g(2) = 12
2/3×8 + 4f + 2g = 12
16/3 + 4f + 2g = 12
4f + 2g = 12 - 16/3
4f + 2g = (36 - 16)/3
4f + 2g = 20/3 ......(2)
(iii) To find the values of f and g, solve equation 1 and 2 simultaneously
f + g = 10/3 × 2
4f + 2g = 32/3
2f + 2g = 20/3
4f + 2g = 32/3
- 2f = - 12/3
f = 12/6
f = 2
Substitutes f in equation 1
f + g = 10/3
2 + g = 10/3
g = 10/3 - 2
g = (10 - 6)/3
g = 4/3
Answer:
z≈3.16
p≈0.001
we reject the null hypothesis and conclude that the student knows more than half of the answers and is not just guessing in 0.05 significance level.
Step-by-step explanation:
As a result of step 2, we can assume normal distribution for the null hypothesis
<em>step 3:</em>
z statistic is computed as follows:
z= where
- X is the proportion of correct answers in the test (
)
- M is the expected proportion of correct answers according to the null hypothesis (0.5)
- p is the probability of correct answer (0.5)
- N is the total number of questions in the test (40)
z= ≈ 3.16
And corresponding p value for the z-statistic is p≈0.001.
Since p<0.05, we reject the null hypothesis and conclude that the student knows more than half of the answers and is not just guessing in 0.05 significance level.