So all you do is you divide 2 1/2 by .25 and you get 10 then you know one fourth or 25% of that package is 10 berries so the rest or 30% left over is 30 berries.
D) is correct
Length is 12, width is t less than length, so width is 12-t. Based on right triangle, 12^2 + (12-t)^2 = 32^2. So D is correct.
You have Lagrangian
with partial derivatives (set equal to 0)
Solving the first four equations for
, respectively, we can substitute these solutions in terms of
into the fifth equation to find
, which in turn will lead to
. Denoting by
, we have
and substituting into the fifth equation yields
From either choice of
we arrive at
, i.e. exactly two critical points at
, for which we get a maximum value of 14 and minimum value of -14, respectively.
Let be the random variable representing the winnings you get for playing the game. Then
First thing to do is determine the probability of each of the above events. You roll two dice, which offers 6 * 6 = 36 possible outcomes. You find the probability of the above events by dividing the number of ways those events can occur by 36.
- The sum is odd if one die is even and the other is odd. This can happen 2 * 3 * 3 = 18 ways. (3 ways to roll even with the first die, 3 ways to roll odd for the die, then multiply by 2 to count odd/even rolls)
- The sum is 4 if you roll (1, 3), (2, 2), or (3, 1), and the sum is 8 if you roll (2, 6), (3, 5), (4, 4), (5, 3), or (6, 2). 8 ways.
- The sum is 2 if you roll (1, 1), and the sum is 12 if you roll (6, 6). 2 ways.
- There are 36 total possible rolls, from which you subtract the 18 that yield a sum that is odd and the other 10 listed above, leaving 8 ways to win nothing.
So the probability mass function for this game is
The expected value of playing the game is then
or about $7.89.
Answer:
$7826.78
Step-by-step explanation:
Total income = 7950
With a service fee charge of 1.55%, the service fee charge =
Net income = 7950 - 123.225 = 7826.775 = $7826.78
An alternative solution:
Service charge = 1.55%
Net income = (100 - 1.55)% × 7950
= 98.45% × 7950 =