What is 61/4 as a decimal
1 answer:
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Answer:
There is enough evidence to support the claim that the true proportion of monitors with dead pixels is greater than 5%.
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 300
p = 5% = 0.05
Alpha, α = 0.05
Number of dead pixels , x = 24
First, we design the null and the alternate hypothesis
This is a one-tailed(right) test.
Formula:
Putting the values, we get,
Now, we calculate the p-value from excel.
P-value = 0.00856
Since the p-value is smaller than the significance level, we fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.
Conclusion:
Thus, there is enough evidence to support the claim that the true proportion of monitors with dead pixels is greater than 5%.
Now, bearing in mind that, for a graph, to be "differentiable", means a "smooth transition", not an abrupt edge or a "cusp", the first subfunction of the piece-wise is just a quadratic, the second subfunction is a linear, well, so the linear needs to hit the quadratic "smoothly", not make an abrupt edge, for that, the linear must continue the quadratic from 2 onwards, since 2 is the range edge.
now, what is the piece-wise when x = 2? well, f(2) = x² or (2)² or 4
that means, the linear needs to hit it at that point, to make it so, let's make it the slope of the linear, the same as the quadratic's.
what's the quadratic's slope? well, simple enough
so we have y = 4x + b
now, recall, for the quadratic, when x =2, y = 4, so for the linear, when x = 2, y = 4 as well, this means
check the picture below.
now, what is the piece-wise when x = 2? well, f(2) = x² or (2)² or 4
that means, the linear needs to hit it at that point, to make it so, let's make it the slope of the linear, the same as the quadratic's.
what's the quadratic's slope? well, simple enough
so we have y = 4x + b
now, recall, for the quadratic, when x =2, y = 4, so for the linear, when x = 2, y = 4 as well, this means
check the picture below.