Alan

m = 21 kg

α = 10°

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Yes!

$${\mathtt{FV}} = {\frac{{\mathtt{200}}{\mathtt{\,\times\,}}\left[{\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{0.07}}}{{\mathtt{12}}}}\right)}^{\left({\mathtt{13}}{\mathtt{\,\times\,}}{\mathtt{12}}\right)}{\mathtt{\,-\,}}{\mathtt{1}}\right]}{\left({\frac{{\mathtt{0.07}}}{{\mathtt{12}}}}\right)}} \Rightarrow {\mathtt{FV}} = {\mathtt{50\,666.157\: \!719\: \!730\: \!719\: \!797\: \!1}}$$

You can just copy and paste the right-hand side of your expression into the calculator on the home page here.

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1.  11011₂ = 1*2⁴ + 1*2³ + 0*2² + 1*2¹ + 1*2⁰ = 16 + 8 + 0 + 2 + 1 = 27

2.  999₁₆ = 9*16² + 9*16¹ + 9*16⁰ =2304 + 144 + 9 = 2457

3.  537₁₀ :  

16³ > 537

16² = 256, 2*256 = 512

537 - 512 = 25

25 = 16¹ + 9 or 16¹ + 9*16⁰

So 537₁₀ = 2*16² + 1*16¹ + 9*16⁰ = 219_h     (h for hexadecimal)

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$$log_2{(x+1)}=-3\rightarrow x+1=2^{-3}\rightarrow x=\frac{1}{8}-1\rightarrow x=-\frac{7}{8}$$

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There isn't a unique answer to this!

First, find how many times 6 (almost) goes into 80:  floor(80/6) = 13, and 13*6 = 78, so one solution is 13 goals and 2 behinds (13*6 + 2*1 = 80).

However, 12 goals gives 72 points so 12 goals and 8 behinds also gives 80 points.

11 goals gives 66 points so there would be more than 11 behinds needed to make 80 points in total, so this doesn't comply with more goals than behinds.

So the possible solutions are 13 goals and 2 behinds or 12 goals and 8 behinds.

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You can simplify it as follows:

1. Collect the terms with b in the denominator together:

$$\frac{a}{3b}-\frac{a}{12b}\rightarrow \frac{4a}{12b}-\frac{a}{12b}\rightarrow \frac{3a}{12b}\rightarrow \frac{a}{4b}$$

2. Collect the tems with a in the denominator together:

$$\frac{-b}{2a}-\frac{3a-2b}{4a}\rightarrow \frac{-2b}{4a}-\frac{3a-2b}{4a}\rightarrow -\frac{3}{4}$$

3. Put it all together:

$$\frac{a}{4b}-\frac{3}{4}+2\rightarrow \frac{a}{4b}+1\frac{1}{4}\rightarrow \frac{a+5b}{4b}$$

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If you are referring to the Desmos calculator, just type your function into the box near the top left.

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20% off means you pay 80% of the price so you multiply by 0.8, and 7% tax means you multiply by 1.07

Resulting cost = 18.99*0.8*1.07 = 16.26

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