Amovie theater manager wants to determine whether popcorn sales have increased since the theater switched from using “butter-flavored topping” to real butter. historically the average popcorn revenue per weekend day was approximately $3,500. after the theater started using real butter, the manager randomly sampled 12 weekend days and calculated the sample’s summary statistics. the average revenue per weekend day in the sample was approximately $4,200 with a standard deviation of $140. select the function that would correctly calculate the 90% range of likely sample means.
a. 3,500±confidence. t(0.10,140,12)
b. 4,200±confidence. t(0.10,140,12)
c. 3,500±confidence. norm(0.10,140,12)
d. 4,200±confidence. norm(0.10,140,12)

Name and describe the three most important measures of central tendency. choose the correct answer below. a. the mean, sample size, and mode are the most important measures of central tendency. the mean of a data set is the sum of the observations divided by the middle value in its ordered list. the sample size of a data set is the number of observations. the mode of a data set is its highest value in its ordered list. b. the sample size, median, and mode are the most important measures of central tendency. the sample size of a data set is the difference between the highest value and lowest value in its ordered list. the median of a data set is its most frequently occurring value. the mode of a data set is sum of the observations divided by the number of observations. c. the mean, median, and mode are the most important measures of central tendency. the mean of a data set is the product of the observations divided by the number of observations. the median of a data set is the lowest value in its ordered list. the mode of a data set is its least frequently occurring value. d. the mean, median, and mode are the most important measures of central tendency. the mean of a data set is its arithmetic average. the median of a data set is the middle value in its ordered list. the mode of a data set is its most frequently occurring value.

Two trains leave a station on different tracks. the tracks make an angle of 130°, with the station as a vertex. the first train travels 100 km and makes its first stop at point a, while the second train travels 200 km and makes it first stop at point b. how far apart are the trains when both are at their first stop? round the answer to the nearest integer. a) 65 km b) 139 km c) 224 km d) 275 km

Problem ann increased the quantities of all the ingredients in a recipe by 60\%60%. she used 8080 grams (\text{g})(g) of cheese. how much cheese did the recipe require?