An insurance company has information that 93% of its auto policy holders carry collision coverage or unsecured motorist coverage on their policies. eighty percent of the policy holders carry collision coverage, and 60% have uninsured motorist coverage.
i. what percentage of these policy holders carry both collision and unsecured motorist coverage?
ii. what percentage of these policy holders carry collision but not unsecured motorist coverage?

i) The percentage of both collision and unsecured is 47%

ii) The percentage of carry collision but not unsecured is 33%

Step-by-step explanation:

* Lets study the meaning of "or" , "and" on probability

- The use of the word "or" means that you are calculating the

  percentage that either event A or event B happened

- The use the word "and" means that both event A and B have

  to happen

* The addition rules is:

# P(A or B) = P(A) + P(B) - P(A and B)

- The union is written as A∪B or “A or B”.  

- The Both is written as A∩B or “A and B”

* Lets solve the question

∵ P(collision) = 80%

∵ P(unsecured) = 60%

∵ P(collision or unsecured) = 93%

i)

- To find P(collision and unsecured) use the rule:

  P(A or B) = P(A) + P(B) - P(A and B)

∴ P(collision or unsecured) = P(collision) + P(unsecured) - P(collision

   and unsecured)

- Substitute the values of P(collision) , P(unsecured) ,

  P(collision or unsecured)  in the rule

∵ 93% = 80% + 60% - P(collision and unsecured)

- Add the like terms

∴ 93% = 140% - P(collision and unsecured)

- Subtract 140% from both sides

∴ 93% - 140% = - P(collision and unsecured)

∴ - 47% = - P(collision and unsecured)

- Multiply both sides by -1

∴ 47% = P(collision and unsecured)

∴ P(collision and unsecured) = 47%

∴ The percentage of both collision and unsecured is 47%

ii)

∵ The percentage of policy holders carry collision is 80%

∵ The percentage of both collision and unsecured is 47%

- The percentage of policy holders carry collision but not unsecured

 is the difference between the collision and the collision and

 unsecured

∴ The percentage of policy holders carry collision but not unsecured

   = 80% - 47% = 33%

∴ The percentage of carry collision but not unsecured is 33%

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

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.