Step-by-step explanation: The entertainment company’s net value after t months can be expressed by the equation; v(t) = 4t² - 24t - 28.
To factor this expression, we need to simplify the equation:
v(t) = 4t² - 24t - 28,
dividing everything by 4 yields:
v(t) = t² - 6t - 7,
v(t) = t² - 7t + t - 7,
v(t) = t(t-7) + 1(t-7),
v(t) = (t+1)(t-7).
Thus, the function in factored form is v(t) = (t+1)(t-7).
To find when the company hits its lowest value, substitute v(t) = 0 into the factored expression:
v(t) = (t+1)(t-7).
Setting equal to zero provides:
(t+1)(t-7) = 0, leading to t + 1 = 0 and t - 7 = 0; thus, t = -1 and t = 7.
Since time cannot be negative, therefore, t equals 7 months.
This indicates that after 7 months, the company will reach its minimal net value.
The calculated 95% confidence interval for the percentage of coffee drinkers expressing addiction ranges from 21% to 31%. By defining the sample proportion and acknowledging a sample size of 675, while also factoring in a maximum margin of sampling error set at ±5%, the final confidence interval for addiction rates among all surveyed coffee drinkers is established.
Response:
= 270 ⇒ Previous solution
Detailed breakdown:
* Given f(x) = 7 + 4x
* Given g(x) = 
* We aim to determine
- Initially, let’s calculate 
∵ f(x) = 7 + 4x
∵ g(x) =
∴ 
- Let’s perform division of the numerator by the denominator
∵ The numerator is 7 + 4x
∵ The denominator is
∴ (7 + 4x) ÷
- Now we will change the division sign to a multiplication sign and take the reciprocal of
the fraction following the division sign
∴ (7 + 4x) × 
∴ = 2x(7 + 4x)
∴ = 14x + 8x²
- Next, substitute x with 5
∴ = 14(5) + 8(5)² = 70 + 200 = 270
∴ = 270
The result is 3.6y. By multiplying 0.3 by 12, we arrive at 3.6, and we include the variable y.
To determine the lateral area of the pentagonal prism illustrated in the figure, we begin the calculation.
According to the definition:
Where:
: Represents the lateral area
: Refers to the perimeter of the base
h: Denotes the height
By substituting the known values:
Result:
