The right answer is C
Let me to explain. From the graph we know that the vertex of this parabola is
. This is a<em> maximum y-value.</em> We also know that the parabola <em>opens downward, </em>so the leading coefficient is negative. Given that the function is even and the leading coefficient is negative, it follows that the graph falls to the left and right. In a mathematical language this is:
<em> </em>
We first calculate the z-score corresponding to x = 1075 kWh. Given the mean of 1050 kWh, SD of 218 kWh, and sample size of n = 50, the formula for z is:
z = (x - mean) / (SD/sqrt(n)) = (1075 - 1050) / (218/sqrt(50)) = 0.81
From a z-table, the probability that z > 0.81 is 0.2090. Therefore, the probability that the mean of the 50 households is > 1075 kWh is 0.2090.
Fifty-two billion, six hundred and thirty-four million, two hundred and seventy-five thousand, three hundred and nine.
First, we need to solve the differential equation.

This a separable ODE. We can rewrite it like this:

Now we integrate both sides.

We get:

When we solve for y we get our solution:

To find out if we have any horizontal asymptotes we must find the limits as x goes to infinity and minus infinity.
It is easy to see that when x goes to minus infinity our function goes to zero.
When x goes to plus infinity we have the following:

When you are calculating limits like this you always look at the fastest growing function in denominator and numerator and then act like they are constants.
So our asymptote is at y=8.
To determine whether the corresponding terms of 2 arithmetic sequence's added will give new arithmetic sequence or not, Let' take 2 Arithmetic sequences.
In one first term is a1 and common difference is d1, in the other first term is a2 and common difference is d2.
Now nth term for first sequence = a1+(n-1) d1
nth term for second sequence = a2+(n-1) d2
Now add the 2 terms: a1+(n-1)d1 +a2 +(n-1)d2
= a1+a2 + (n-1)(d1+d2)
This is again new arithmetic sequence with first term a1+a2 and common difference d1+d2.
Hence if we add corresponding terms of 2 arithmetic sequence, we will again get an arithmetic sequence.