Find the limit, if it exists: lim_{x rightarrow infty}(8+frac{1}{x})

Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station. The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task. ${\displaystyle (1,3),(2,6),(3,12),(4,24)}$
Part A: Is this data modeling an algebraic sequence or a geometric sequence? Explain your answer.
Part B: Use a recursive formula to determine the time she will complete station 5.
Part C: Use an explicit formula to find the time she will complete the 9th station.

A parks and recreation department is constructing a new bike path. The path will be parallel to the railroad tracks shown and pass through the parking area al the point ${\displaystyle (4,5).}$ Write an equation that represents the path.

The article “Modeling Sediment and Water Column Interactions for Hydrophobic Pollutants” (Water Research, 1984: 1169-1174) suggests the uniform distribution on the interval (7.5, 20) as a model for depth (cm) of the bioturbation layer in sediment in a certain region. a. What are the mean and variance of depth? b. What is the cdf of depth? c. What is the probability that observed depth is at most 10? Between 10 and 15? d. What is the probability that the observed depth is within 1 standard deviation of the mean value? Within 2 standard deviations?

A weather forecaster predicts that the temperature in Antarctica will decrease ${\displaystyle 8^{\circ }F}$ each hour for the next 6 hours. Write and solve an inequality to determine how many hours it will take for the temperature to drop at least ${\displaystyle {36}^{\circ }F}$

The following table represents the Frequency Distribution and Cumulative Distributions for this data set: 12, 13, 17, 18, 18, 24, 26, 27, 27, 30, 30, 35, 37, 41, 42, 43, 44, 46, 53, 58

$\begin{array}{|cccc|}\hline \text{Class}& \text{Frequency}& \text{Relative Frequency}& \text{Cumulative Frequency}\\ \text{10 but les than 20}& 5\\ \text{20 but les than 30}& 4\\ \text{30 but les than 40}& 4\\ \text{40 but les than 50}& 5\\ \text{50 but les than 60}& 2\\ \text{TOTAL}\\ \hline\end{array}$

What is the Relative Frequency for the class: 20 but less than 30? State you answer as a value with exactly two digits after the decimal. for example 0.30 or 0.35

Modeling ${\displaystyle C{O}_2}$ emissions
a) Use the data from 1960 and 1990 to find a linear function that models the ${\displaystyle C{O}_2}$
b) Use your linear function to predict the ${\displaystyle C{O}_2}$ emissions in 2005. Compare your prediction with the actual ${\displaystyle C{O}_2}$ emission in 2005

Suppose $10,000 is invested at an annual rate of ${\displaystyle 2.4\mathrm{\%}}$ for 10 years. Find the future value if interest is compounded as follows