Donna Meagle notices that on 12 out of 14 days, her clumsy coworker Jerry Gergich spills his lunch on himself. She concludes that the probability that Jerry will spill his lunch on himself tomorrow is about 86%. Is this an example of a theoretical or empirical probability?

Select one:
a. Empirical
b. Theoretical

It is an example of an empirical probability.

Step-by-step explanation:

The empirical probability, also called experimental probability of an event is the ratio of the number of outcomes in which a specified event occurs to the total number of trials, not in a theoretical sample space but in an actual experiment.

Theoretical probability is probability that is determined on the basis of reasoning.

It is evident that the probability in the question was arrived at after the outcome of 14 days of whether Jerry Gergich spilled his lunch on himself or not.

It's an actual result of an experiment, hence the 12/14 = 0.86 = 86% that he spills his lunch on himself tomorrow.

Hope this Helps!!!

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).