Answer:
7
Step-by-step explanation:
28 divided by 4 is 7
It looks like the vector field is
<em>F</em><em>(x, y)</em> = 3<em>x</em> ^(2/3) <em>i</em> + <em>e</em> ^(<em>y</em>/5) <em>j</em>
<em></em>
Find a scalar function <em>f</em> such that grad <em>f</em> = <em>F</em> :
∂<em>f</em>/∂<em>x</em> = 3<em>x</em> ^(2/3) => <em>f(x, y)</em> = 9/5 <em>x</em> ^(5/3) + <em>g(y)</em>
=> ∂<em>f</em>/∂<em>y</em> = <em>e</em> ^(<em>y</em>/5) = d<em>g</em>/d<em>y</em> => <em>g(y)</em> = 5<em>e</em> ^(<em>y</em>/5) + <em>K</em>
=> <em>f(x, y)</em> = 9/5 <em>x</em> ^(5/3) + 5<em>e</em> ^(<em>y</em>/5) + <em>K</em>
(where <em>K</em> is an arbitrary constant)
By the fundamental theorem, the integral of <em>F</em> over the given path is
∫<em>c</em> <em>F</em> • d<em>r</em> = <em>f</em> (0, 1) - <em>f</em> (1, 0) = 5<em>e</em> ^(1/5) - 34/5
Answer:
23/15
Step-by-step explanation:
Answer:
we will fail to reject the null hypothesis and conclude that there's insufficient evidence to support the claim that the percentage is actually more than the reported percentage
Step-by-step explanation:
We are given;
Population proportion; p = 30% = 0.3
Sample proportion; p^ = 37% = 0.37
Sample size; n = 100
Let's define the hypotheses;
Null hypothesis; H0: p ≤ 0.3
Alternative hypothesis; Ha: p > 0.3
Formula for the test statistic is;
z = (p^ - p)/√(p(1 - p)/n)
Thus;
z = (0.37 - 0.3)/√(0.3(1 - 0.3)/100)
z = 0.07/0.04582575695
z = 1.53
From z-distribution table, at z=1.53 we have;
p-value = 1 - 0.9370 = 0.063
This p-value is greater than the significance level of 0.02 and thus we will fail to reject the null hypothesis and conclude that there's insufficient evidence to support the claim that the percentage is actually more than the reported percentage
