Explanation:
First we will convert the given mass from lb to kg as follows.
157 lb = 
= 71.215 kg
Now, mass of caffeine required for a person of that mass at the LD50 is as follows.

= 12818.7 mg
Convert the % of (w/w) into % (w/v) as follows.
0.65% (w/w) = 
= 
= 
Therefore, calculate the volume which contains the amount of caffeine as follows.
12818.7 mg = 12.8187 g = 
= 1972 ml
Thus, we can conclude that 1972 ml of the drink would be required to reach an LD50 of 180 mg/kg body mass if the person weighed 157 lb.
Radius of nuclei is given by formula

now we can say volume of the nuclei is given as

now the density is given as
density = mass / volume
mass of nuclei = mass of neutron + mass of protons



Now density is given as

here we know that
= 1.2 fm


So from above we can say that density of all nuclei is almost same.
Cheese attributes its sour taste because of its lactic acid content. However, this should not be an indication to whether the cheese is spoiling already. We can tell its expiry date through the manufacturing details of the product. The product should be good to consume before the manufacturing expiry date. Every package must include expiry date in order to inform the consumer about the range of its consumability attributes. In the case where molds are present on the cheese already, cheese on some parts may not be edible already. Molds are due to the oxidation of glucose through the action of specific bacteria.
We are given the mass of an <span>aluminum sculpture which is 145 kg and a horizontal force equal to 668 Newtons. The coefficient of friction can be determined by dividing the horizontal force by the weight of the object. In this case, 668 N / 145 * 9.8 equal to coeff of friction of 0.47</span>