Activity 2. Incomplete Directions: Read and analyze the given situations. Write your answers on a separate sheet. A. Carmen kept a tally of the number of calls she received each day for a week. Plot the missing point by using the data in the table and connect the points to complete the line graph below. Calls Carmen received Day | Calls Monday | 3 Tuesday | 0 Wednesday | 6 Thursday | 7 Friday | 10 B. A junior high school student counted the number of bricks in each fence in his neighborhood. Draw the missing bar by using the data in the table to complete the histogram below. Bricks per fence Number of bricks | Number of fences 0-19 | 3 20-39 | 2 40-59 | 4 60-79 | 1 80-99 | 3 C. The owner of an orchard measures the height of every tree in centimeters (cm). Plot the missing point by using the data in the table and connect the points to complete the ogive below. Height of the tree (cm) | Frequency | Cumulative Frequency | Cumulative Percentage 1-50 | 5 | 5 | 5% 51-100 | 30 | 35 | 32% 101-150 | 25 | 60 | 55% 151-200 | 50 | 110 | 100%
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The purpose of this article is to examine how technology has impacted computer graphics and data presentation. It is important to note that not all data can be represented accurately with a straight line. In some cases, a scatter plot may be more appropriate. Additionally, different colors and shapes can be used to represent different data sets. It is also important to consider the slope and intercept of the trend line when analyzing the relationship between variables. Overall, graphs should be clear and concise, and should accurately represent the data being presented.
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Math 103: College Algebra 3.3 applications HW Directions: Complete all problems on separate paper. For each problem, you must find a function to maximize or minimize. For full credit, the function must be correct. Upload pictures or a scan of your solutions no later than Monday, October 19, 11:59 p.m. CST. 1. You have a 1200-foot roll of fencing and a large field. You want to make two paddocks by splitting a rectangular enclosure in half. What are the dimensions of the largest such enclosure? 2. Your factory produces lemon-scented air fresheners. You know each unit is cheaper, the more your produce. But you also know that costs will eventually go up if you make too many, due to storage of the overstock. The guy in accounting says that your cost for producing x thousand units a day can be approximated by the formula C(x)=0.04x^2-8.504x+25302. Find the daily production level that will minimize your costs. 3. Find a pair of numbers whose product is a maximum if twice the first number plus the second number is 48. 4. The sum of the length and width of a rectangle is 25 cm. Find the maximum area. 5. A piece of wire 20 feet long is cut into two pieces and each piece is bent to form a square. Determine the length of the two pieces so that the sum of the areas of the two squares is a minimum. 6. You run a canoe-rental business on a small river. You currently charge $12 per canoe and average 36 rentals a day. An industry journal says that, for every fifty-cent increase in rental price, the average business can expect to lose two rentals a day. Use this information to attempt to maximize your income. What should you charge? 7. The table lists the number of Americans (in thousands) who are expected to be over 100 years old for selected years. Year 1994 1996 1998 2000 2002 2004 Number (in thousands) 50 56 65 75 94 110 a. Find a quadratic function to fit the data set. Write it in proper form. b. How many Americans will be over 100 years old in the year 2008? c. In what year will the number of Americans over 100 years old exceed 200,000? 8. There is a sweet "shoot a pumpkin out of a cannon" contest held in the middle of nowhere. To be fair, pumpkins of nearly equal size are launched each time. The table shows the horizontal distance (in feet) said pumpkins travel when launched at different angles. Angle (in degrees) 20 30 40 50 60 70 Distance (in feet) 372 462 509 501 437 323 a. Explain why it's practical to use a quadratic function to model this data set (and the reason can't just be because the scatter plot looks like a parabola-think about why this scatter plot should look like it does!). b. Find a quadratic function to fit the data set. Write it in proper form. c. Use your model to determine at which angle the pumpkin should be launched in order for it to travel the farthest.
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Solve each problem. Several years ago, mathematical ecologists created a model to analyze population dynamics of the endangered northern spotted owl in the Pacific Northwest. The ecologists divided the female owl population into three categories: juvenile (up to $1 \text { yr old }),$ subadult $(1$ to 2 yr old ) and adult (over 2 yr old). They concluded that the change in the makeup of the northern spotted owl population in successive years could be described by the following matrix equation. $$ \left[\begin{array}{c} j_{n+1} \\ s_{n+1} \\ a_{n+1} \end{array}\right]=\left[\begin{array}{rrr} 0 & 0 & 0.33 \\ 0.18 & 0 & 0 \\ 0 & 0.71 & 0.94 \end{array}\right]\left[\begin{array}{c} j_{n} \\ s_{n} \\ a_{n} \end{array}\right] $$ The numbers in the column matrices give the numbers of females in the three age groups after $n$ years and $n+1$ years. Multiplying the matrices yields the following. $j_{n+1}=0.33 a_{n}$ Each year 33 juvenile females are born for each 100 adult females. $s_{n+1}=0.18 j_{n}$ Each year 18\% of the juvenile females survive to become subadults. $a_{n+1}=0.71 s_{n}+0.94 a_{n} \quad$ Each year $71 \%$ of the subadults survive to become adults, and $94 \%$ of the adults survive. (a) Suppose there are currently 3000 female northern spotted owls made up of 690 juveniles, 210 subadults, and 2100 adults. Use the matrix equation on the preceding page to determine the total number of female owls for each of the next 5 yr. (b) Using advanced techniques from linear algebra, we can show that in the long run, $$ \left[\begin{array}{c} j_{n+1} \\ s_{n+1} \\ a_{n+1} \end{array}\right] \approx 0.98359\left[\begin{array}{c} j_{n} \\ s_{n} \\ a_{n} \end{array}\right] $$ What can we conclude about the long-term fate of the northern spotted owl? (c) In the model, the main impediment to the survival of the northern spotted owl is the number 0.18 in the second row of the 3 $\times 3$ matrix. This number is low for two reasons. The first year of life is precarious for most animals living in the wild. In addition, juvenile owls must eventually leave the nest and establish their own territory. If much of the forest near their original home has been cleared, then they are vulnerable to predators while searching for a new home. Suppose that, thanks to better forest management, the number 0.18 can be increased to $0.3 .$ Rework part (a) under this new assumption.
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