There are
total ways to draw any 6 numbers from the range 1 to 51, regardless of order.
Given 6 selected numbers that match those drawn by the lottery, there are
ways of rearranging them. So the probability of winning 1st prize is
Next, given 6 selected numbers of which 5 match those drawn by the lottery, there are
ways of rearranging those 5 matching numbers. There are 46 remaining numbers that didn't get drawn, so the probability of winning 2nd prize is
Answer:
The diameter of the circle is 40 units
Step-by-step explanation:
The equation of a circle is (x-h)^2 + (y-k)^2 = r^2. Where "x" and "y" are variables, "h" and "k" are the coordinates of the center of the circle, and "r" is the length of the radius. It is given that the center of the circle is (-27, 120). So, h= -27 and k= 120. If the circle passes through the origin, we can assume that the origin is on the circle. Since a circle's radius is constant no matter where it is drawn/is, we can find the radius of the circle by finding the distance between the circle's center (-27, 120) and the origin, (0, 0). The distance formula is: d= √((x[2]-x[1])^2-(y[2]-y[1])^2). If the coordinates of the center of the circle are (x[2}, y[2]), then x[2]= -27 and y[2]= 120. Then, the origin is the (x[1], y[1]). So, x[1] = 0 and y[1] = 0. Plugging the numbers in we get: √((-27-0)^2-(120-0)^2). This gives us √(729+14400) = 123. So since the distance between the center of the circle and a point on the circle is 123 (units), then the radius has a value of 123.
Plugging all the numbers into the equation of a circle, we get: (x-(-27))^2+(y-120)^2=123^2.
Compatible numbers are easy to divide mentally.
hope this helped
Answer:
sin X = 8/17
cos y = 8/17
relationship is that they are equal.