Elephant200

To prove this, we can simply provide a counterexample. Let's input x=0. We see that for f(x)=(0+5)/(0-7), we have -5/7. For h(x), we have (0+5)(0-7)= -35.

Because -5/7 is not equal to -35, they are different functions.

https://web2.0calc.com/questions/counting_95164

This has already been asked and answered

Day 1: It had 45

Day 2: After selling 1/3 of them it has 2/3 * 45 = 30 magazines.

Day 3: After selling 1/5 of them it has 4/5 * 30 = 24 magazines.

It has 24 magazines

This question is incomplete, please enter a value for the number of yellow tiles there are. 

The key here is to find the volume of a cone with height 6 inches and radius 1 inch. Using \(V=\dfrac{\pi r^2h}{3}\), we have \(V=\dfrac{6\pi}{3}=2\pi\approx6.28\). For the purposes of this problem, approximating it to \(6.28\) is close enough.

Dividing, we get \({370\over6.28}=58.9\). Unfortunately, the 0.9 does not count; it asks for full cups. 0.9 is not full. Therefore, the answer is \(58.\)

(c)

The sum of n natural numbers is \(n(n+1)\over 2\), so we have \(\dfrac{99(100)}{2}=4950\)

(b)

He didn't write down a 0. Using \(\text{Probability}=\dfrac{\text{number of successful outcomes}}{\text{total possible outcomes}}\), the probability is 0.

(a)

Let's look at a simplified version: 1, 2, 3, 4. How many numbers are in that?

Obviously 4. That's the last number in the sequence. 

Therefore, using the same logic, Sam wrote down 99 digits.

Using the factor theorem (This states that if \(r\) is a solution to \(f(x)=0\), then \((x-r)\) is a factor of \(f(x)\)), we have \(f(x)=(x+1)(x-2)(x-3)=x^3-4x^2+x+6\).