Round 3,989.23655 to the nearest tenth.
1 answer:
You might be interested in
Answer:
Center: (1,3)
Radius: 6
Step-by-step explanation:
Hi there!
Typically, the equation of a circle would be in the form where
is the center and
is the radius.
To get the given equation into this form, we must complete the square for both x and y.
<u>1) Complete the square for x</u>
Let's take a look at this part of the equation:
To complete the square, we must add to the expression the square of half of 2. That would be 1² = 1:
Great! Now, let's add this to our original equation:
We cannot randomly add a 1 to just one side, so we must do the same to the right side of the equation:
Complete the square:
<u>2) Complete the square for y</u>
Let's take a look at this part of the equation :
To complete the square, we must add to the expression the square of half of 6. That would be 3² = 9:
Great! Now, back to our original equation:
Remember to add 9 on the other side as well:
Complete the square:
<u>3) Determine the center and the radius</u>
Now, we can see that (1,3) is in the place of (h,k). 36 is also in the place of r², making 6 the radius.
I hope this helps!
Answer:
(a) The sample space is {00, 0, 1, 2, . . . , 30}.
(b) If the wheel is spun 1,000 times, it is expected about 31 of those times to result in the ball landing in slot 3.
(c) If the wheel is spun 100 times, it is expected about 47 of those times to result in the ball landing in an odd number.
Step-by-step explanation:
We are given that in the game of roulette, a wheel consists of 32 slots numbered 00, 0, 1, 2, . . . , 30.
To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots.
(a) The sample space is {00, 0, 1, 2, . . . , 30} which means the metal ball can land on any of these numbers.
(b) As we know that there is an equal probability of the metal ball landing on any of the slots marked in the sample space.
Total number of slots = 32
Number of slots marked with 3 = 1
So, the probability that the metal ball falls into the slot marked 3 is given by = = 0.031 or 3.1%
This means that if the wheel is spun 100 times, it is expected about 3.1 of those times to result in the ball landing in slot 3.
So, if the wheel is spun 1,000 times, it is expected about 31 of those times to result in the ball landing in slot 3 because (0.031 1000) = 31.
(c) As we know that the odd slot in the given sample space is {1, 3, 5,......, 29}.
Total number of slots = 32
Number of odd slots = 15
So, the probability that the metal ball lands in an odd slot is given by = = 0.47 or 47%.
This means that if the wheel is spun 100 times, it is expected about 47 of those times to result in the ball landing in an odd number.