Alan

First set y = sinx and solve:   2y² + y - 1 = 0 for y.

Since the LHS factors nicely, we have (y+1)*(2y-1) = 0

so y = -1 and y = 1/2

sin(x) = -1 implies x = 3pi/2 + 2npi  where n is an integer

I'll leave you to work out what values of x make sin(x) = 1/2 .

The probability of getting an answer right is 1/5, so the expected number of right answers is (1/5)*20 = 4.

The probability of getting exactly 14 right is (1/5)¹⁴*(4/5)⁶*nCr(20,14)  (nCr(20,14) is the numb er of ways of choosing 14 out of 20).

The probability of getting exactly 15 right is  (1/5)¹⁵*(4/5)⁵*nCr(20,15) 

The probability of getting exactly 16 right is  (1/5)¹⁶*(4/5)⁴*nCr(20,16) 

... etc. to

The probability of getting exactly 20 right is  (1/5)²⁰*(4/5)⁰*nCr(20,16) 

Calculating all these and adding them up we find the probability of getting a C is approximately 2*10^-6, so the probability of getting less than a C is 1 - 2*10^-6.

Successive powers of 443 end in 443; 249; 307; 001.  These then repeat (see below).

The first of these occurs when mod(power,4) = 1, the second when mod(power,4) = 2, the third when mod(power,4) = 3 and the fourth when mod(power,4) = 0.

Since mod(443,4) = 3, the last three digits of 443⁴⁴³ are 307.

Multiply the weight of one cubic foot by the 3(1/5) cubic feet.  Probably easiest to write 1/5 as 0.2 here, so you have 62.2*3.2 (which is 199.04, as Anonymous noted). 

If this is the equation x = 2 + (1/x) then first multiply through by x to get:

x² = 2x + 1

Rearrange:

x² - 2x - 1 = 0

Solve using the quadratic formula:

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{1}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{1}}{\mathtt{\,-\,}}{\sqrt{{\mathtt{2}}}}\\
{\mathtt{x}} = {\sqrt{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{0.414\: \!213\: \!562\: \!373\: \!095}}\\
{\mathtt{x}} = {\mathtt{2.414\: \!213\: \!562\: \!373\: \!095}}\\
\end{array} \right\}$$

Not quite!

log₄(2x-1) + log₄(3) = log₄((2x-1)*3)

So we should have

(2x-1)*3 = 5x+12

6x - 3 = 5x + 12

x = 15

Check:

$${{log}}_{{\mathtt{4}}}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{15}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{\mathtt{\,\small\textbf+\,}}{{log}}_{{\mathtt{4}}}{\left({\mathtt{3}}\right)} = {\mathtt{3.221\: \!471\: \!747\: \!924\: \!364\: \!5}}$$

$${{log}}_{{\mathtt{4}}}{\left({\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{15}}{\mathtt{\,\small\textbf+\,}}{\mathtt{12}}\right)} = {\mathtt{3.221\: \!471\: \!747\: \!924\: \!364\: \!4}}$$

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{6}}}{{\mathtt{3.14}}}}{\mathtt{\,\times\,}}{\mathtt{29}}\right)} = {\mathtt{88.966\: \!153\: \!896\: \!812^{\circ}}}$$

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{6}}}{\left({\mathtt{3.14}}{\mathtt{\,\times\,}}{\mathtt{29}}\right)}}\right)} = {\mathtt{3.769\: \!805\: \!197\: \!875^{\circ}}}$$

Use tan(angle) = height(opposite)/distance(adjacent)

So height = distance*tan(angle)

height = 200*tan(35°) m

-9 + (-8) = -9 -8 = -17

Two minuses make a plus, but a plus and minus makes a minus!

First rearrange by adding y to both sides:

2x = 1 + y

Divide both sides by 2:

x = (1 + y)/2

Now substitute 7 for y:

x = (1 + 7)/2

or x = 4