<span>Find the range of the function. f(x) = x^2 + 3
</span>A: (3,infinity)
Answer:
Step-by-step explanation:
A and B are the side lengths. C is the hypotenuse (the longest side).
For triangle A)
a^2+b^2=c^2
(it won't let me add exponents but you get the point)
4^2+2^2=c^2
8+4=c^2
12=c^2
c=square root of 12
For B)
a^2+b^2=c^2
2^2+5^2=c^2
4+10=c^2
After solving, it doesnt
add up to 45
Answer:
Step-by-step explanation: The answer is the surface area of the above triangular prism is 156 square inches.
Okay, lets write down what we do know...
4 out of the 12 cups are decaf, so the odds of selecting a decaf cup by random is 4/12 or 1/3
Alternatively 8 of the 12 cups are caffeinated, so the odds of selecting a caffeinated cup by random is 8/12 or 2/3
P(decaf)=1/3
P(caf)=2/3
But those odds are only for the first cup picked. The second cup has 4 probabilities...
1. Picking a decaf cup for the second time
2. Picking a decaf cup for the first time
3. Picking a caf cup for the second time
4. Picking a caf cup for the first time
So lets find the probability of each event...
1. Picking a decaf cup for the second time. If a decaf cup has already been picked, then the odds of drawing another one is 3/11
2. Picking a decaf cup for the first time. If a decaf cup hasn't already been picked, then the odds of drawing one is 4/11
3. Picking a caf cup for the second time. If a caf cup has already been picked, then the odds of drawing one is 7/11
4. Picking a caf cup for the first time. If a car cup hasn't already been picked, then the odds of drawing one is 8/11.
Okay, so now we can solve for the various possibilities.
1. Picking a decaf cup for the second time
1/3*3/11=3/33
2. Picking a decaf cup for the first time
2/3*4/11=8/33
3. Picking a caf cup for the second time
2/3*7/11=14/33
4. Picking a caf cup for the first time
2/3*8/11=16/33
Both cups were caffeinated, so neither were decaf.
Answer= Neither cup is decaf.