Alan

Density is mass per unit volume, so volume = mass/density.  Volume of a sphere is (4/3)pi*r³, where r is the radius.  Put these together to get 

r = (3*mass/[4pi*density])^1/3.

$${\mathtt{r}} = {\left({\frac{{\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{60\,000}}}{\left({\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{\pi}}{\mathtt{\,\times\,}}{\mathtt{19.5}}\right)}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)} \Rightarrow {\mathtt{r}} = {\mathtt{9.022\: \!827\: \!957\: \!982\: \!585}}$$

r ≈ 9 cm

(Note that I've expressed the mass as 60000 grams because the density is given as grams/cm³)

I've not come across the term "covertices" before either Melody.  However, it is clear that they are the vertices of the hyperbola obtained by interchanging the signs of the x and y terms.  See graph below:

Rosala, the 4th of July is a special holiday in the USA, celebrated every year.  It is Independence Day; celebrating the Declaration of Independence (the day the US declared its independence from Great Britain). 

Are you sure it's not 4*3 - 6/2, which would be 9; or 4*3 + 6/2, which would be 15?

Density is mass per unit volume.

$${\mathtt{density}} = {\frac{{\mathtt{4}}}{{\mathtt{39}}}} \Rightarrow {\mathtt{density}} = {\mathtt{0.102\: \!564\: \!102\: \!564\: \!102\: \!6}}$$

density ≈ 0.103 g/cc

Assuming the distribution of larceny cases is normal (Gaussian), then the following information should help you to answer the question.

 ±1.282 standard deviations away from the mean define a 90% confidence interval.

 ±1.645 standard deviations away from the mean define a 95% confidence interval.

 ±2.326 standard deviations away from the mean define a 99% confidence interval.

The margin of error is half the confidence interval (so for the 90% case here, for example, the margin of error is 1.282*40.5; unless the 40.5 is meant to be the sample σ, in which case the population σ is 40.5/√28 ≈ 7.65 and should be used instead of 40.5)

The 1.2m refers to the height above the ground, and the time it takes to shatter is just the time taken to fall to the ground. Since the puck starts with zero vertical velocity this can be obtained from the following (if we ignore air resistance):

h = (1/2)gt², where h = 1.2m, g = 9.81m/s², and t is the time.

Rearranging, we have t = √(2h/g)

$${\mathtt{t}} = {\sqrt{{\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{1.2}}}{{\mathtt{9.81}}}}}} \Rightarrow {\mathtt{t}} = {\mathtt{0.494\: \!619\: \!366\: \!829\: \!497\: \!9}}$$

t ≈ 0.495 seconds.

The horizontal velocity is irrelevant in determining the time.  It becomes relevant if we want to know how far away from the table it got before it shattered!

jboy314 has answered a slightly different question from the one asked; forgetting that all even numbers were specified!

With all even numbers we have n + (n+2) + (n+4) = 108 or 3n + 6 = 108, so 3n = 102 and n = 34.

The largest number is therefore 34 + 4 = 38.

The link just takes you to a place where you can buy the book.