His annual salary as a pharmacist is $51,200
There are a total of 52 weeks in an year.
(a) Weekly salary = annual salary/ number of weeks = 51,200/52 = $984.62 (rounded to the nearest cent)
Howard's weekly salary to the nearest cent = $984.62
(b) His salary in first three weeks = 984.62*3 = $2,953.85
Howard's earnings during the first three weeks to the nearest cent = $2,953.85
(c) He has to pay the agency 40% of his three week salary which is = 0.4*2953.85 =1,181.54
Howard must pay to the employment agency to the nearest dollar = $1,182
we have

we know that
<u>The Rational Root Theorem</u> states that when a root 'x' is written as a fraction in lowest terms

p is an integer factor of the constant term, and q is an integer factor of the coefficient of the first monomial.
So
in this problem
the constant term is equal to 
and the first monomial is equal to
-----> coefficient is 
So
possible values of p are 
possible values of q are 
therefore
<u>the answer is</u>
The all potential rational roots of f(x) are
(+/-)
,(+/-)
,(+/-)
,(+/-)
,(+/-)
,(+/-)
Answer:
The answer is below
Step-by-step explanation:
Let x represent the number of small hat purchased, y represent the number of medium hat purchased and z represent the number of large hat purchased.
Since a total of 47 hats where purchased, hence:
x + y + z = 47 (1)
Also, he spent a total of $302, hence:
5.5x + 6y + 7z = 302 (2)
He purchases three times as many medium hats as small hats, hence:
y = 3x
-x + 3y = 0 (3)
Represent equations 1, 2 and 3 in matrix form gives:
![\left[\begin{array}{ccc}1&1&1\\5.5&6&7\\-3&1&0\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}47\\302\\0\end{array}\right] \\\\\\\\ \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}1&1&1\\5.5&6&7\\-3&1&0\end{array}\right] ^{-1} \left[\begin{array}{c}47\\302\\0\end{array}\right] \\\\\\ \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}6\\18\\23\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%261%5C%5C5.5%266%267%5C%5C-3%261%260%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D47%5C%5C302%5C%5C0%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5C%5C%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%261%5C%5C5.5%266%267%5C%5C-3%261%260%5Cend%7Barray%7D%5Cright%5D%20%5E%7B-1%7D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D47%5C%5C302%5C%5C0%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D6%5C%5C18%5C%5C23%5Cend%7Barray%7D%5Cright%5D)
Therefore he purchases 6 small hats, 18 medium hats and 23 large hats
Tan socks = 4
Grey socks = 7
Total number of socks = 4+7 = 11 socks
Probability of picking a tan sock then grey sock:
P(T)*P(G) = (4/11)*(7/10) = 14/54
Probability of picking a Grey sock then Tan sock
P(G)*P(T) = (7/11)*(4/10) = 14/55
Probability of two different colored socks
P(T&G)+P(G&T) = (14/55)+(14/55) = 28/55