Charles has spent over 20 years in K-12 education in private and public schools, in the physical classroom and in virtual learning. His hobbies include sports, road trips to historic places, and binge watching TV.
(I) A rolling ball moves from $x_1 =$ 8.4 cm to $x_2 = -$4.2 cm during the time from $t_1 =$ 3.0 s to $t_2 =$ 6.1 s. What is its average velocity over this time interval?
11-12 Sketch the graph of the function and use it to determine the values of a for which $\lim _{x \rightarrow a} f(x)$ exists.$$f(x)=\left\{\begin{array}{ll}{1+x} & {\text { if } x<-1} \\ {x^{2}} & {\text { if }-1 \leq x<1} \\ {2-x} & {\text { if } x \geqslant 1}\end{array}\right.$$
Quiz grades Joey’s first 14 quiz grades in a marking period were$\begin{array}{lllllll}{86} & {84} & {91} & {75} & {78} & {80} & {74} \\ {87} & {76} & {96} & {82} & {90} & {98} & {93} \\ \hline\end{array}$Calculate the mean. Show your work. Interpret your result in context.
Teams chosen from 30 forest rangers and 16 trainees will be planting trees. An experienced team consisting of 2 rangers can plant 400 trees per week. A training team consisting of 1 ranger and 2 trainees can plant 300 trees per week.
Experienced Teams (x) | Training Teams (y) | TOTALRangers: 2 | 1 | 30Trainees: 0 | 2 | 16
Maximize equation: z = 400x + 300y
10. Graph and shade the system of constraints to find the feasible region.2x + y ≤ 302y ≤ 16x ≥ 0, y ≥ 0
11. Find the corner points of the feasible region.
12. How many of each type of team should be formed to maximize the number of trees planted?The maximum the number of trees planted would be ________ when x = ________ of the experienced teams and y = ________ of the training teams are utilized.
In the game of roulette, a player can place a $6 bet on the number 6 and have a 1/38 probability of winning. If the metal ball lands on 6, the player gets to keep the $6 paid to play the game and the player is awarded an additional $210. Otherwise, the player is awarded nothing and the casino takes the player's $6. Find the expected value E(x) to the player for one play of the game. If x is the gain to a player in a game of chance, then E(x) is usually negative. This value gives the average amount per game the player can expect to lose.The expected value is $.(Round to the nearest cent as needed.)
Use the following to answer the next two questions
The rate of radioactive decay is often described using the concept of half life – the time it takes for the amount of radioactivity to decay to half its initial amount.Radioactive cobalt-60 is often used in radio thearapy in hospitals. The half life of cobalt -60 is 5.2 years. The decay of cobalt-60 can be represents by the formula A(t) = A_0(1/2)^(t/5.2)
If the initial amount of cobalt – 60 is 150 grams, then the number of years, to the nearest tenth, it would take to reduce the cobalt – 60 to 30 grams is __________
To the nearest tenth of a gram, the number of grams remaining from a 250 gram sample of cobalt – 60 after 24 years is __________
The value of the expression 2log_9 3 – log_5 10 + log_5 2, to the nearest whole number, is
For the diagram shown above, determine the magnitude of the resultant force (sum of the forces) and its direction measured counterclockwise from the positive x-axis. The direction is the angle the resultant vector does with positive x-axis.
In 2000, park rangers decided to introduce catfish in Lake Reelywhet. The population of catfish (in thousands) in Lake Reelywhet is related to the number of years since 2000 by the following function: w(a) = 1.125 - 0.675 * 1.1^-a.
What is the significance of the point (0, 0.45) to the function w defined above?It does not lie on the graph of the function and therefore has no significance.It is a vertical asymptote for the function.It is the point where the graph intercepts the vertical axis.It is the point where the graph intercepts the horizontal axis.It is a horizontal asymptote for the function.
Publishing The following table shows the results of a survey of 400 authors by a publishing company.New Authors Established Authors TotalSuccessful 40 100 140Unsuccessful 68 192 260Total 108 292 400Compute the relative frequency of the given event if an author as specified is chosen at random.An author is successful.
