1 - Derivative of arcsin x.
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The derivative of f(x) = arcsin x is given by
</span><span> f '(x) = 1 / sqrt(1 - x 2) </span><span>
</span>2 - Derivative of arccos x.
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The derivative of f(x) = arccos x is given by
</span><span> f '(x) = - 1 / sqrt(1 - x 2) </span><span>
</span>3 - Derivative of arctan x.
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The derivative of f(x) = arctan x is given by
</span><span> f '(x) = 1 / (1 + x 2) </span><span>
</span>4 - Derivative of arccot x.
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The derivative of f(x) = arccot x is given by
</span><span> f '(x) = - 1 / (1 + x 2) </span><span>
</span>5 - Derivative of arcsec x.
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The derivative of f(x) = arcsec x tan x is given by
</span><span> f '(x) = 1 / (x sqrt(x 2 - 1))</span><span>
</span>6 - Derivative of arccsc x.
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The derivative of f(x) = arccsc x is given by
</span><span> f '(x) = - 1 / (x sqrt(x 2 - 1)) </span><span>
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The first thing you have to do is:
subtract: 11-5
Then subtract: -4-(-2)
then you put it as a fraction: 6/-2 or -3
That -3 would be considered the slope.
So now you have: y=-3x+ b
So what you have to do is plug in one of the points into the equation to find out what b is.
For example: 11 = -3(-4) + b
11=12 + b
-12 -12
b = -1
So the answer is: y = -3x -1
So it is basically extended by 75%. 25% of 3.5 is 0.875. 0.875 times 3 is 2.625. That is 3/4 of the segment. Now you have to add it to the 3.5. Your final answer would be 6.125.
Answer:
Option B) Do not reject null hypothesis, there is not enough evidence to support the claim that the proportion of homes in Oregon heated by natural gas is different from the 48% that the US Department of Energy reported.
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 333
p = 48% = 0.48
Alpha, α = 0.01
Number of women belonging to union , x = 149
First, we design the null and the alternate hypothesis
This is a two-tailed test.
Formula:
Putting the values, we get,
Now, we calculate the p-value from the table.
P-value = 0.273079
Since the p-value is greater than the significance level, we fail to reject the null hypothesis and accept the null hypothesis.
Thus, there is not enough evidence to support the claim that proportion of homes in Oregon that were heated by natural gas is different from what was reported.
B. Do not reject null hypothesis, there is not enough evidence to support the claim that the proportion of homes in Oregon heated by natural gas is different from the 48% that the US Department of Energy reported.
