In many fast food restaurants, there is a strong correlation between a menu item's fat content (measured in grams) and its calorie content. We want to investigate this relationship. Using all of the food menue items at a well known fast food restuarant, the fat content and calorie contents were measured. We decide to fit the LSRL to the data, with fat content (x) as the explanatory variable and (y) as the response variable. One of the menu items is a hamburger with 107 grams of fat and 1410 calories. r = correlation between x and y = 0.979

x bar = mean of the values of x = 40.35 grams

y bar = mean of values of y = 662.88 calories

sx = standard deviation of the values of x = 27.99 grams

sy = standard devation of the values of y = 324.90 calories

The slope of the least-squares regressin line is

a. -11.36

b 11.36

c. 0.979

d. 16.08

The distance between two cities is 368 miles. if the scale on the map is 1/4 inch=23 miles, what is the distance between the cities on the map?

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are fewer free variables than equations. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 12 c. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 8 d. no, overdetermined systems cannot be consistent because there are no free variables. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 24

Geometry - finding area of regular polygons and sectors (check my math, i can’t find the error)