Let's see.
Let's look at the first 10 natural numbers raised to the 4th power.
1^4 = 1 * 1 * 1 * 1 = 1
2^4 = 2 * 2 * 2 * 2 = 16
3^4 = 3 * 3 * 3 * 3 = 81
4^4 = 4 * 4 * 4 * 4 = 256
5^4 = 5 * 5 * 5 * 5 = 625
6^4 = 6 * 6 * 6 * 6 = 1296
7^4 = 7 * 7 * 7 * 7 = 2401
8^4 = 8 * 8 * 8 * 8 = 4096
9^4 = 9 * 9 * 9 * 9 = 6561
10^4 = 10 * 10 * 10 * 10 = 10000
Notice that of the first 10 natural numbers raised to the 4th power, only 5^4 and 10^4 do not have a 1 or a 6 as its units digit. All other 8 numbers have a 1 or a 6 as their units digit.
Now think of 11. If you raise 11 to the 4th power, it will end in 1 just 1^4 does. 12^4 will end in 6 just like 2^4 does. This holds true for the 4th powers of all of the natural numbers. Every natural number that ends in 1 has a 4th power that ends in 1. Every natural number that ends in 2 has a 4th power that ends in 6, etc. Since 8 out of 10 4th powers have a 1 or a 6 in the units digit, then out of 1000, you get 8/10 * 1000 = 800.
The center is the midpoint of the diameter.
The coordinates of the midpoint:
(x₁,y₁) - the coordinates of one endpoint
(x₂,y₂) - the coordinates of the other endpoint
The coordinates of the center are (-1.5,4.5) - the answer is A.
But where....is the histogram?
J/6 = 9/10 is the proportion that we are trying to solve. Let's use cross products, or multiplying the numerator of one fraction by the denominator of the other fraction, and setting these two numbers equal to one another in an equation.
9 (6) = 10 (j)
When we combine like terms (multiply), we get
54=10j
We need to divide both sides by 10, to get the variable alone.
j = 5.4