Revenue = 7.5x - 100
Operation Costs = 5.8x + 79.86
To break even, operation cost = Revenue
⇒ 7.5x - 100 = 5.8x + 79.86
7.5x = 5.8x + 179.86 (Add 100 to both sides)
7.5x - 5.8x = 179.86
1.7x = 179.86
x = 105.8
This implies that the company will need to sell at least 106 items to make a profit.
The inequality that will determine the number of items at need to be sold to make a profit is x ≥ 106
The solution to the inequality is as follows
Revenue = 7.5x - 100
if x =106
Revenue = 7.5(106) - 100
Revenue = 695
Operational Cost = 5.8x + 79.86
if x = 106
Operational Cost = 5.8(106) + 79.86
Operational Cost = 694.66
Profit ≥ (695 - 694.66)
Profit ≥ 0.34
The company must sell at least 106 items to make a profit.
Answer: The expression is in the explanation.
Step-by-step explanation:
Please find the attached file for the solution.
If you're adding positive numbers together, then the order in which you write or group the addends doesn't matter.
If you're "adding" a negative number to a positive number, it's a little easier to visualize this problem if you write the positive number first, followed by the negative number.
But if you're "adding" -15 to 8, it'd make sense to write the -15 first (because its magnitude is greater) and then the 8: -15 + 8 = -7
Answer:
|0.254 ≤ p ≤ 0.286|
Step-by-step explanation:
Given that:
In a made up poll :
Proportion of people who like dark chocolate than milk chocolate (p) = 27%
Margin of Error = 1.6%
Hence,
p ± margin of error
27% ± 1.6%
(27 - 1.6)% ; (27 + 1.6)%
25.4% ; 28.6%
0.254 ; 0.286
Therefore ;
Lower bound = 0.254
Upper bound = 0.286
Expressing p as an absolute value Inequality ;
|0.254 ≤ p ≤ 0.286|
Answer:
D. The mathematical expectation of Option A is 1. The mathematical expectation of Option B is 1.5. Option B offers a greater likelihood of advancing to the finish line.
Step-by-step explanation:
The result of a product is odd only when the two numbers are odds.
There are 6*6 = 36 possible outcomes when two dice are rolled. Only 9 of them are a combination of two odd numbers: {1, 1} {1, 3} {1, 5} {3, 1} {3, 3} {3, 5} {5, 1} {5, 3} {5, 5}. Then 36 - 9 = 27 outcomes are even.
P(even) = 27/36 = 0.75
Option A) Mathematical expectation: 0.75*4 + 0.25*(-8) = 1
Option B) Mathematical expectation: 0.75*5 + 0.25*(-9) = 1.5
