Answer:
x^3 + 1/x^3 = 488
Step-by-step explanation:
- x^2 + 1/x^2 = 62
- x^2 + 1/x^2 + 2 = 64
- ( adding 2 in both sides )
- (x + 1/x ) ^2 = 64
- x + 1/x = 8
now,
- ( x+ 1/x ) ^ 3 = 512
- x^3 + 1/x^3 + 3 × x × 1/x ( x + 1/x )
- x^3 + 1/x^3 + 3 ( 8 )
- ( since x + 1/x = 8 )
- x^3 + 1/x^3 + 24 = 512
- x^3 + 1/x^3 = 488
hence, we got x^3 + 1/x^3 = 488
Answer:
<h2>(0.3, -18.45).</h2>
Step-by-step explanation:
We need to recur to the extreme value theorem, which states: "If a function is continuous on a closed interval, then that function has a maximum and a minimum inside that interval".
Basically, as the theorem states, if a dunction is continuous, then it has maxium or minium.
In this case, we have a quadratic function, which is a parabola. An important characteristic of parabolas is that they have a maximum or a minium, but they don't have both. When the quadratic term of the fuction is positive, then it has a minium at its vertex. When the quadratic term of the function is negative, then it has a maximum at its vertex.
So, the given function is , where the quadratic term is positive, so the functions has a minimum at , where and , let's find that point
<h3>
</h3><h3>
</h3><h3 /><h3>Therefore, the minium of the function is at (0.3, -18.45).</h3>
Answer:
Based on the data, if we find moderate/strong evidence against the null hypothesis and conclude the mean arsenic level of the water is greater than 8.0 ppb, we have made ____________.
a correct decision.
Step-by-step explanation:
Since there is enough evidence to conclude that the mean level of arsenic is greater than 8.0 ppb, the correct decision has been made. There is no type I or type II error. The type I error (called a false positive) occurs if we reject the null hypothesis when it is true. Since we have simply rejected the null hypothesis when the alternate hypothesis is true, and the null hypothesis should be rejected, a correct decision has been made.