Step-by-step explanation: Since the number P(t) increases proportionally to the number of individuals unaware of the product, we establish that initially, nobody is aware of the product at the campaign's start and that 50% are aware after 50 days of advertisements. Thus, we determine: P(0) = 0 and P(50) = 1,500,000, leading to a first-order ordinary differential equation. The integrating factor must be calculated and both sides of the equation manipulated accordingly. Hence, upon integrating and solving, we arrive at the equation modeling the number of people (in millions) aware of the product over time.
The risk of down syndrome, in terms of the percentage of births per year, is changing at a rate given by the equation r(x) = 0.004641x² - 0.3012x + 4.9 for the range 20 ≤ x ≤ 45, where x signifies the maternal age at delivery. To derive the risk function as a percentage of births relative to maternal age x, we integrate r(x), leading to the function f(x) = 0.001547x³ - 0.1506x² + 4.9x + c. When x is 30, f evaluates to 0.14%. This means that 0.001547(30³) - 0.1506(30²) + 4.9(30) + c equals 0.14. Solving gives 41.769 - 135.54 + 147 + c = 0.14, which simplifies to c = -53.089. As a result, we establish that f(x) = 0.001547x³ - 0.1506x² + 4.9x - 53.089 for 20 ≤ x ≤ 45. The graph corresponding to this function is illustrated below.
Answer:
Yes
Step-by-step explanation:
This is because 46 multiplied by 1.06 equals 48.76, which is under $50.
At a wage of 8.75 per hour, total earnings for 40 hours would be 350. Calculate overtime at 8.75 times 1.5 which equals 13.13. Then, multiply 13.13 by 12 to get $158. So the total is 350 + 158 = 508, likely around 480 after taxes for the US.
