CoolStuffYT

https://web2.0calc.com/questions/sorry-for-re-posting-but-i-really-need-an-answer

Let's think about it ...

If Daniel ate 3/10 and there was 2/10 remaining, that means 3/10+2/10=5/10 of the pizza was left.

Answer: 20 nickels, 26 dimes, 12 quarters

Explanation:

Let n = # of nickels, d = dimes, and q = quarters

d = 2q+2

n = q+8

5n+10d+25q = 660

Simple system of equations, after a couple minutes of solving, you'll get n=20, d = 26, and q = 12. So 20 nickels, 26 dimes, and 12 quarters.

You are very welcome!

:P

Answer: 2 km/h

Explanation:

Let s be the speed of the current.

Let x be the time it has traveled against the current and let y be the time it traveled with the current.

Obviously, d=rt.

The rate at going against is 20-s km/hr and with is 20+s km/hr.

d=rt, or, solving for t, t = d/r.

We set t to equal x, so x = d/r.

The distance is 36, as stated, so x = 36/r

And the rate is 20-s, so x = 36/20-s.

Similarly, for y, y=22/20+s

Add those two equations to get x+y=(36/20-s)+(22/20+s).

We know that x+y=3 since the total time traveled was 3 hours.

System of equations: \(x+y=\frac{36}{20-s}+\frac{22}{20+s}, x+y=3\).

We can now solve for s. I believe that you can solve this yourself, so I won't go over the hassle.

You should eventually get s = -20/3 or 2. Obviously, only the positive number works.

Therefore, the answer is 2 km/h.

(Can somebody check this? I'm not 100% sure about it. Thanks!)

You are very welcome!

:P

Answer: 67,600,000 license plates

Explanation:

There are ten digits and 26 letters.

This is simply \(10 \times 10 \times 26 \times 26 \times 10 \times 10 \times 10\), or \(10^5 \times 26^2\).

This equals 67,600,000.

You are very welcome!

:P

Answer: 50.8 degrees

Explanation:

Obviously, by Pythagorean Theorem, the longer leg is 6.

Longer leg is opposite larger angle.

We can use law of cosines to get \(6^2=(2\sqrt{15})^2+(2\sqrt{6})^2-2 \times (2\sqrt{15})\times (2\sqrt6) \times \cos{\theta}\)

Simplifying, \(-48=-24\sqrt{10} \times \cos{\theta}\), so \(\frac{\sqrt{10}}{5}=\cos{\theta}\).

Assuming you can use a calculator, use inverse cosine function to get \(\theta \approx 50.7685 \circ\), and rounding to the nearest tenth, the angle is 50.8 degrees.

You are very welcome!

:P

There are 6 choose 3 or 20 total arrangements of questions.

The chance that a student gets one right is 1/5 and wrong is 4/5.

Since we want to find 3 questions correct, it is \((\frac{1}{5})^3\times (\frac{4}{5})^3\), or 64/15625

But we have to multiply by 20 to get 1280/15625, simplified to 256/3125.

You are very welcome!

:P

To be honest, I would just plug in values.

Let a = 2, b = 2, and c = -1.

Then simply solve.

The question is how many do YOU have, not how many are left.
So two, since you took two.

Two, since you take two.

Lol