The decisions of the supreme court in mcculloch
v. maryland (1819) and gibbons v. ogden (1824)
are important because they
(1) clarified constitutional limits on the right to
bear arms
(2) denied slaves the right to sue in federal courts
(3) increased the power of the federal government
over the states
(4) upheld funding for the erie canal
base your answer to question 12 on the passage
below and on your knowledge of social studies.
…i have no motive, my friends, to deceive you.
i am sincerely desirous to promote your welfare.
listen to me, therefore, while i tell you that
you cannot remain where you now are.
circumstances that cannot be controlled, and
which are beyond the reach of human laws,
render it impossible that you can flourish in the
midst of a civilized community. you have but one
remedy within your reach. and that is, to remove
to the west and join your countrymen, who are
already established there. and the sooner you do
this the sooner you will commence your career of
improvement and prosperity….
— president andrew jackson, 1835

part 1: the half-life of the element is 22 years.

part 2: it will take 132.02 year for the sample to decay from 308.0 g to 4.8125 g.

explanation:

part 1: there are two ways to determine the half life time.

first way: the half life time can be determined directly from its definition as it is the time required for the sample to decay to its half concentration.

from the data the initial concentration was 45.0 g and decayed to its half value (22.5 g) in 22.0 years.

second way: the radio active decay is considered first order reaction so we can use the laws of first order reactions.

k = (1/t) ln (a/a-x), where k is the rate constant of the reaction,

t is the time of the reaction

a is the initial concentration of the reactant

a-x is the remaining concentration at time (t)

a = 45.0 g the initial concentration at t = 0 year.

at t = 22 year, a-x = 22.5 g

then k = (1/22 year) ln (45.0 g/ 22.5 g) = 0.0315 year-1.

the half-life time (t1/2) = ln 2/ k = 0.693/ k =0.693/ 0.0315 = 22 years.

part 2:

using the same law k = (1/t) ln (a/a-x),

using the given data; a = 308.0 g and a-x = 4.8125 g and the calculated k from the part 1 (k = 0.0315 year-1)

t = (1/k) ln (a/a-x) = (1/0.0315) ln (308.0/ 4.8125) = 132.02 years

organisms are more likely to be more preserved in mud than sand because mud is moist and wet, while sand is very dry.

- lead + phosphoric acid = hydrogen + lead(ii) phosphate