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.
Answer:
Noah’s average: 87
Noah’s median: 85.5
Noah’s mode: 85
Gabriel’s average: 87.17
Gabriel’s median: 86
Gabriel’s mode: 86
Step-by-step explanation:
The mean is calculated as (total/number of items), or the average.
The median refers to the central value in a dataset.
The mode represents the number that appears most frequently.
I will designate the hourly rate for weekdays as x and for weekends as y. The equations are arranged as follows:
13x + 14y = $250.90
15x + 8y = $204.70
This gives us a system of equations which can be solved by multiplying the first equation by 4 and the second by -7. This leads to:
52x + 56y = $1003.60
-105x - 56y = -$1432.90
By summing these two equations, we arrive at:
-53x = -$429.30 --> 53x = $429.30 --> (dividing both sides by 53) x = 8.10. This represents her hourly wage on weekdays.
Substituting our value for x allows us to determine y. I will utilize the first equation, but either could work.
$105.30 + 14y = $250.90. To isolate y, subtract $105.30 from both sides --> 14y = $145.60 divide by 14 --> y = $10.40
Thus, we find that her earnings are $8.10 per hour on weekdays and $10.40 per hour on weekends. The difference shows she earns $2.30 more on weekends than on weekdays.
