Suppose that you draw two cards from a deck. After drawing the first card, you do not put the first card back in the deck. What
1 answer:
Answer:
The correct answer is 0.05882.
Step-by-step explanation:
A deck of cards have 52 cards, 13 cards of each suit.
We are drawing two cards without replacement.
We need to find the probability of getting a diamond as the first card.
Favorable outcomes are 13 and total number of outcomes are 52.
Thus this probability is .
Now for the next draw we again want to pick a diamond card.
Favorable outcomes are 12 and total number of leftover cards are 51.
Thus this probability is .
Now the probability that both cards are diamonds is ×
=
= 0.0588235 ≈ 0.05882
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Given:
The shaded sector above covers of the circle.
Radius of the circle = 3 cm
To find:
The area of the sector in terms of π.
Solution:
The area of a circle is
Substituting , we get
It is given that the shaded sector above covers of the circle.
The area of shaded sector
Therefore, the area of shaded sector is 3π sq. cm.
Answer:
given you are asked to simplify
Step-by-step explanation:
You have to multiply the numerator and denominator by the denominator's conjugate.
The conjugate of a+bi is a-bi.
When you multiply conjugates, you just have to multiply first and last.
(a+bi)(a-bi)
a^2-abi+abi-b^2i^2
a^2+0 -b^2(-1)
a^2+-b^2(-1)
a^2+b^2
See no need to use the whole foil method; the middle terms cancel.
So we are multiplying top and bottom of your fraction by (-3+4i):
So you will have to use the complete foil method for the numerator. Let's do that:
(-3+5i)(-3+4i)
First: (-3)(-3)=9
Outer:: (-3)(4i)=-12i
Inner: (5i)(-3)=-15i
Last: (5i)(4i)=20i^2=20(-1)=-20
--------------------------------------------Combine like terms:
9-20-12i-15i
Simplify:
-11-27i
Now the bottom (-3-4i)(-3+4i):
F(OI)L (we are skipping OI)
First:-3(-3)=9
Last: -4i(4i)=-16i^2=-16(-1)=16
---------------------------------------------Combine like terms:
9+16=25
So our answer is