Rom

if you mean what per cent of 330 is 295.5

$${\frac{{\mathtt{295.5}}}{{\mathtt{330}}}}{\mathtt{\,\times\,}}{\mathtt{100}} = {\frac{{\mathtt{985}}}{{\mathtt{11}}}} = {\mathtt{89.545\: \!454\: \!545\: \!454\: \!545\: \!5}}$$

so 295 is 89.55% of 330

if you mean what percent of 295.5 is 330

$${\frac{{\mathtt{330}}}{{\mathtt{295.5}}}}{\mathtt{\,\times\,}}{\mathtt{100}} = {\mathtt{111.675\: \!126\: \!903\: \!553\: \!299\: \!5}}$$

so 330 is 111.68% of 295.5

$$\sqrt[3]{-27}=\sqrt[3]{27}\sqrt[3]{-1}=3\sqrt[3]{-1}$$

$$\sqrt[3]{-1}=\sqrt[3]{e^{\imath \pi}}=\sqrt[3]{e^{\imath (\pi +2k \pi)}}~~k\in \mathbb{Z}$$

and we pick values corresponding to k=0,1,2

$$\sqrt[3]{-1}=e^{\imath \pi/3}$$

$$\sqrt[3]{-1}=e^{\frac{\imath(\pi + 2\pi)}{3}}=e^{\imath\pi}=-1$$

$$\sqrt[3]{-1}=e^{\frac{\imath(\pi + 4\pi)}{3}}=e^{\imath 5\pi/3}=e^{-\imath \pi/3}$$

so

$$\sqrt[3]{-27}=-3, ~3e^{\imath \pi/3}, ~3e^{-\imath \pi/3}$$

Oh I see it wants the answers in rectangular form

To do this, convert the complex exponential into rectangular form as follows

$$e^{\imath x}=\cos(x)+\imath \sin(x)$$

$$-3 = -3 \\$$

$$3e^{\imath \pi/3} = 3(1/2 + \imath \sqrt{3}/2)=3/2+\imath 3\sqrt{3}/3$$

$$3e^{-\imath \pi/3} = 3(1/2 - \imath \sqrt{3}/2)=3/2-\imath 3\sqrt{3}/3$$

(x > -1)+(y>3)=x+y>2

so

2 < x+y < 8

and that's all you can simplify it

find all the common factors and bring them to the front of the expression.

In this case 10y is a common factor.

$$30y^3-50y=10y\left(3y^2-5\right)$$

it should be fine to stop there, but if you want to go nuts you can do this.

$$30y^3-50y=30y\left(y^2-\frac 5 3\right)=30y\left(y-\sqrt{\frac 5 3}\right)\left(y+\sqrt{\frac 5 3}\right)$$

Let the amount Ethan has saved be x.

175 = 25 + 3x

150 = 3x

50 = x

Ethan has saved $50.

$${\frac{{\mathtt{122}}}{{\mathtt{0.2}}}} = {\mathtt{610}}$$

$${\mathtt{108}}{\mathtt{\,\times\,}}{\mathtt{108}} = {\mathtt{11\,664}}$$

"Two glasses, C and D, have exactly the same size and shape. Glass C is empty, and glass D has some water in it. Half the water in D is then poured in to C. This process is repeated two more times. Each time, half the remaining water in D is poured into C. After three pourings, C is half full. What fraction of a glassfull is now left in D?"

Suppose glass D starts out with d amount of water in it.

after 1 pouring glass C has d/2, and glass D has d/2 water left in whatever units

after the 2nd pouring C has (d/2+d/4) and D has d/4

after the 3rd pouring C has (d/2+d/4+d/8) and D has d/8

We are told that glass C now is half full.  

So 7/8d=1/2 a glass

d = 4/7 of a glass

and there is d/8 left in glass D at this point so

glass D now has 1/8(4/7) = 4/56 = 1/14 of a glassful

$${\mathtt{22}}{\mathtt{\,\small\textbf+\,}}{\mathtt{19}} = {\mathtt{41}}$$

given the survey data the best guess you can make for how likely it it someone will get the right answer is

25/150 = 1/6

So applying this to 500 people you get 500 * 1/6 = 500/6

$${\frac{{\mathtt{500}}}{{\mathtt{6}}}} = {\frac{{\mathtt{250}}}{{\mathtt{3}}}} = {\mathtt{83.333\: \!333\: \!333\: \!333\: \!333\: \!3}}$$

So about 83 people will get the answer correct out of 500.