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AVEN JOHNNNNNNNNN

Answer: 60

Explanation:

We know f(1) = 4. Then we can find f(1+1) = f(2), because of the formula they give. Plugging in x=y=1 we get f(1+1)=f(1)+f(1)+1*1 --> f(2) = 4+4+1 --

f(2) = 9.

We can continue on until we get f(8). Letting x=y=2 we get f(2+2)=f(2)+f(2)+2*2 --> f(4) = 22. Finally, letting x=y=4 we get f(4+4)=f(4)+f(4)+4*4 --> f(8) = 60.

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Answer: 182/243

Explanation:

The common ratio is 1/3, because 1/2 * 1/3 = 1/6.

So listing them out, we get 1/2, 1/6, 1/18, 1/54, 1/162, 1/486. Adding these up gets us 364/486 which simplifies to 182/243.

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Hint: use the quadratic formula

Answers: 6.084 for (a), 2.721 for (b)

Generally, \(\log_a x\cdot y = \log_a x + \log_a y\). So log_a (5 * 7) = log_a (5) + log_a (7) = 2.935 + 3.149 = 6.084

Next, log_a (5*5) = log_a (5) + log_a (5) = 2.935 + 2.935 = 5.87. Then \(log_a {\frac{x}{y}} = log_a x - log_a y\). So log_a (25/7) = log_a (25) - log_a (7) = 5.87 - 3.149 = 2.721. Log rules are very important :)

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Answer: 1

\(3Y 2\) means that a = 3 and b = 2.

Then, we can plug in and solve. 3^2 - 2 * 3 * 2 + 2^2 = 9-12+4 = 1.

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Answer: 8/17

There are 18 marbles in total. Say we get a red, then blue. The prob of red is 12/18, and then blue is 6/17, since the red marble takes away one from 18. So 12/18 * 6/17 = 4/17. Do the same for blue, then red. You should get 4/17. Adding the two gets the answer of 8/17.

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Part A: 20.9

First, note that there are 2+3+1+4+1=11 players. We add their ages. So 19+19+20+20+20+21+22+22+22+22+23 = 230.

Therefore, the mean age is 230/11 = 20.9090, rounded to 20.9.

Part B: 34

When we get one more member, the player count goes to 12. The mean goes to 22. So 22*12 is the sum of all the player's ages, which is 264. We already know 230 for the 11 original players, so the new player must be 264-230 = 34 years old.

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Can you please tell me what you have tried? Hint: make a system of equations; let x be the number of hot dogs and y be sodas.

I'm going to assume the question means "the ladder makes a ___ angle with the wall."

In this case, we can draw a diagram. What we get is a right triangle with one leg as 8 and the hypotenuse as 16. This is a 30-60-90 triangle (because the leg is half the hypotenuse)! They want the angle the ladder makes with the wall, so the angle between hypotenuse and leg, which is 60 degrees.

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