This is quite challenging; I’m not entirely certain, but I recognize it originates from Savas Realize Reader.
Wanda encounters Hector after 4.5 hours. Wanda will not be able to reach Hector before the end of the race because at his current pace (16m/h), he would finish when both reach mile 72, while the race is only 42 miles.
To catch up with Hector at the finish line, Wanda must raise her speed to 21m/h. I have included the answers.
Answer:
F(t) = 10 + 5(t)
Step-by-step explanation:
The complete question is as follows;
Anumeha is mowing lawns for a summer job. For each lawn she mows, she charges a $10 starting fee plus an hourly rate. For example, her fee for a 5-hour job is $35. Let f(t) denote Anumeha's fee for a job f (in dollars) based on how many hours (t) were needed to finish it. Write the formula for this function.
Solution
We aim to establish the formula F(t) representing the fee Anumeha charges per job.
Key to formulating this function is understanding the constant charge she applies per job.
We know she earns $35 for mowing for 5 hours.
Therefore, the constant fee can be deduced as follows;
Since it’s a $10 starting fee along with an hourly rate;
35 = 10 + 5(x)
where x refers to the hourly rate
35 = 10 + 5x
5x = 35-10
5x = 25
x = 25/5
x = $5
This indicates that she charges a constant fee of $5 per hour
Thus, we can now write the equation.
F(t) = 10 + 5(t)
where t represents the number of hours spent on each job
In detail: Based on the central limit theorem, the distribution appears normal due to the large sample size. The confidence interval is presented in the format: (Sample mean - margin of error, sample mean + margin of error). The sample mean, denoted as x, serves as the point estimate for the population mean. The confidence interval is computed as: mean ± z × σ/√n, where σ represents the population standard deviation. The formula transforms into confidence interval = x ± z × σ/√n, with specific values: x = $75, σ = $24. To find the z score, we subtract the confidence level from 100% which gives α as 1 - 0.96 = 0.04; halving this results in α/2 = 0.02, signifying the tail areas. To ensure we account for the center area, we have 1 - 0.02 = 0.98, corresponding to a z score of 2.05 for the 96% confidence level. The confidence interval becomes 75 ± 2.05 × 24/√64 = 75 ± 2.05 × 3 = 75 ± 6.15. The lower limit is 75 - 6.15 = 68.85, while the upper limit stands at 75 + 6.15 = 81.15. For n = 400, with x = $75 and σ = $24, the z score remains 2.05, resulting in the confidence interval calculated as 75 ± 2.05 × 24/√400 = 75 ± 2.05 × 1.2 = 75 ± 2.46. Subsequently, the lower bound becomes 75 - 2.46 = 72.54, and the upper limit adds up to 75 + 2.46 = 77.46. Lastly, when n = 400, x = $200, and σ = $80, the z score tied to a 94% confidence level is 1.88. Thus, the confidence interval is expressed as 200 ± 1.88 × 80/√400 = 200 ± 1.88 × 4 = 200 ± 7.52, giving us a margin of error of 7.52.
Answer:
C. 4x^3 - 14x^2y + 14xy^2 - 4y^3
Step-by-step explanation:
Given:
Multiplication of 2x^2 – 3xy + y^2 and 2x – 4y
Multiplication refers to the product
(2x^2 – 3xy + y^2) (2x – 4y)
Expand the brackets
= 4x^3 - 8x^2y - 6x^2y + 12xy^2 + 2xy^2 - 4y^3
Combine like terms
= 4x^3 - 14x^2y + 14xy^2 - 4y^3
The result is
C. 4x^3 - 14x^2y + 14xy^2 - 4y^3
