One circle labeled likes 13 overlaps another circle labeled male 16. The overlap is labeled 6. A 4-column table with 3 rows. The first column has no label with entries female, male, total. The second column is labeled likes with entries a, c, 19. The third column is labeled dislikes with entries 15, 16, e. The fourth column is labeled total with entries b, d, 50. A group of 50 people were asked their gender and if they liked cats. The data from the survey are shown in the Venn diagram.

Determine the value for each variable in the two-way table.

a =

b =

c =

d =

e =
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The table shows the relationship between the number of cups of cereal and the number of cups of raisins in a cereal bar recipe: number of cups of cereal number of cups of raisins 8 2 12 3 16 4 molly plotted an equivalent ratio as shown on the grid below: a graph is shown. the title of the graph is cereal bars. the horizontal axis label is cereal in cups. the x-axis values are 0, 20, 40, 60, 80,100. the vertical axis label is raisins in cups. the y-axis values are 0, 10, 20, 30, 40, 50. a point is plotted on the ordered pair 40,20. which of these explains why the point molly plotted is incorrect? (a) if the number of cups of cereal is 40, then the number of cups of raisins will be10. (b)if the number of cups of raisins is 40, then the number of cups of cereal will be10. (c) if the number of cups of cereal is 40, then the number of cups of raisins will be 80. (d) if the number of cups of raisins is 40, then the number of cups of cereal will be 80.

The graph of y x3 is translated so that the point (1. 1) is moved to (1, 4). what is the equation of the new graph?

Find the volume of the solid obtained by rotating the region enclosed by the curves y=1x and y=7^-x about the x-axis. (use symbolic notation and fractions where needed.) volume =