In a circle, the distance from the center of the circle to any point on the circumference is the radius of the circle. The radius of the circle is a constant number and does not change from one point to another.
This means that:
OC = OD = radius of circle
6x + 2 = 10x - 16
2+16 = 10x-6x
18 = 4x
x = 4.5
Therefore radius of circle can be calculated by getting length of either OC or OD as follows:
radius of circle = 6(4.5) + 2 = 28 units
Answer:
C. ASA Similarity
Step-by-step explanation:
Using the Angle-Side-Angle Similarity Theorem is the only thing we can do because looking above we see that we know two angles and one side. Hence, this can be the only theorem that is fit for these two triangles.
If the first card (not replaced) is a 7, you're left with 51 cards, and the four aces are all there: you have probability 4/51 of picking an ace.
If the first card (not replaced) is an ace, you're left again with 51 cards, but these time only 3 aces are remaining in the pile: you have probability 3/51 of picking an ace.
Were the cards replaced, the information about the first card drawn would be completely meaningless, since the second pick would be a pick from a standard deck, and we'd have probability 4/52=1/13 of picking an ace.
In other words, if cards are replaced, it is like every pick is the first one, because whatever happened with the first pick has no consequences on the second.
On the other hand, if we do not replace cards, the outcome of the first pick is important, because we know that the card we picked will not be in the deck anymore.
Answer: Nevertheless, the theorem came to be credited to Pythagoras. It is also proposition number 47 from Book I of Euclid's Elements. According to the Syrian historian Iamblichus (c. 250–330 ce), Pythagoras was introduced to mathematics by Thales of Miletus and his pupil Anaximander.
Step-by-step explanation: