What are the values of a and b in the relative frequency table for the survey results? Round answers to the nearest percent. a = 12%, b = 17% a = 12%, b = 18% a = 40%, b = 18% a = 41%, b = 63%

The data that we have is:

Carrots = 84

Turnips = 25

Both = 17

Neither = 15

Root vegetables = 84 + 25 - 17 + 15 = 107

"a" is the percentage of carrots that also are turnips.

we know that 17 carrots are also turnips. so the relative frequency is:

17/107 = 0.158, in percent form this can be rounded to 16%.

b is the number of NOT carrots, that also are turnips.

This will be equal to the 25 turnips minus the 17 turnips that also are carrots

25 - 17 = 8

So we have 8 turnips that are not carrots.

Then we have:

b = 8/107 = 0.075

rounded to the nearest percent we get b = 8%.

So the values do not coincide with the options, and neither some of the data, for example the carrots that are not turnips are:

84 total carots, 17 of them are turnips, so we have 84 - 17 carrots that are not turnips:

84 - 17 = 67

then the relative frequency is:

P = 67/107 = 0.626, rounded to the nearest percent we get 63%

So there may be a number wrong in the diagram.