The following table shows the hot dogs bought from a street vendor over the course of eight days​ ("Demand"). Also shown is the temperature for each day in degrees Celsius.  Temperature (°C)  21 13 22 19 5 13 16 23   Demand 45 30 34 42 16 21 40 35     y=10.99+1.33x   The predicted demand for hot dogs on a day with a temperature of 15°C is ​(Round to the nearest integer as​ needed.)

A researcher wants to determine if the exam scores of the students are dependent on the length of time spent in studying the subject. Ten students in a certain class were taken and the results are shown in the table below where X is the time spent in studying the subject in hours and Y is the examination scores. X (time) Y (score) 1.5 80 3.0 83 1.25 83 0.5 70 3.5 85 2.5 75 1.0 70 3.0 90 2.5 86 4.0 91 Determine the simple linear regression equation Y = a + bX. (round off values up to 1 decimal place)

The following table indicates the unit prices (in Rands) and quantities of three goods purchased every month by a small restaurant for the years 2023 and 2024.  GOOD 2023 2024 Unit Price (p0) Quantity (q0)) Unit Price (p1) Quantity (q1) Milk R12.60 2555 R12.85 2705 Eggs R11.00 114 R14.00 107 Flour R65.00 350 R68.50 400  Q.3.1 Using 2023 as the base year, compute the price relative in 2024 for milk and eggs. Interpret your answers.  Q.3.2 Using 2023 as the base year, compute the Laspeyres price index for all of the goods for 2024. Interpret your answer.  Q.3.3 Using 2023 as the base year, compute the Paasche price index for all of the goods for 2024. Interpret your answer.

The numbers of polio cases in the world are shown in the table for various years. Year Number of Polio Cases (thousands) 1988 1992 1996 2000 2005 2007 350 138 33 3 3.2 1.3 Let f(t) be the number of polio cases (in thousands) t years after 1980. Copy the data to Desmos to draw a scatterplot of the data. Make sure to adjust the years so they represent years after 1980. a) Is it better to model the data with a linear or with an exponential model? [Select an answer b) Use regression in Desmos to find an appropriate model for f. Make sure to check Log mode in the parameter window in Desmos if you are fitting an exponential model. f(t) Round the coefficients to 4 decimal places. Hint: Use the variablet from the drop down menu when entering the equation. Do not just type in t. c) Predict the number of polio cases in 2013. d) Find the approximate half-life of the number of polio cases. Round the answer to one decimal place. years