Answer: 
, 
, 
and 
Step-by-step explanation:
Here, x represents the number of hours Zoe spent running on her wheel and y represents the number of hours spent scratching her cage.
Julie was awoke for at least an hour running on her exercise wheel and scratching the of her cage.
⇒
She ran on her wheel at least twice as long as she scratched at the corners of her cage.
⇒
Also, She spent more than 1/4 hour running on her wheel.
⇒
And, we know that number of hours can not be negative.
⇒
Therefore, the complete system of inequality which shows the given situation is,
, and ,
Note: the feasible region ( covered by the given system) is shown in the below graph.
Answer:
Step-by-step explanation:
Given that X is a normal random variable with parameters µ = 10 and σ 2 = 36,
X is N(10, 6)
Or z = 
is N(0,1)
a) P(X > 5),
=
(b) P(4 < X < 16),
=
(c) P(X < 8),
=
(d) P(X < 20),
=
(e) P(X > 16).
=P(Z>-0.6667)
= 0.2524
Start with how much profit they are making off each race entry. People pay $55 to race, but $15 of that is expenses so they are only profiting $40 for each entry. Now write one side of the equality. They start with $10,000 in donations, and then have a $40 profit for each race entry. So 10,000+40x. X will represent the unknown number of race entries. What do we want that expression to be equal to? We want 10000+40x>55000. It can also be greater than or equal to, not just greater than.
Solve for x. Subtract 10000 from each side resulting in 40x>45000. Divide each side by 40 to solve for x. X>1125. X needs to bbe greater than or equal to 1125. If there are 1125 race entries, the charity will profit exactly $55000, so the lowest number of race entries is 1125
Draw per week = $1,300
Draw for four weeks = 1300 x 4 = $5,200
Four week sales amount = $186,900
6% commission on sales = 0.06 x 186,900 = $11,214
<span>Thus the amount equal to mike’s commission minus the
draw = 11,214 – 5,200 = $6,014</span>
