In a recent month, 88% of automobile drivers filled their vehicles with regular gasoline, 2% purchased midgrade gas, and 10% bought premium gas. of those who bought regular gas, 28% paid with a credit card; of customers who bought midgrade and premium gas, 34% and 42%, respectively, paid with a credit card. suppose we select a customer at random. given that the customer paid with a credit card, find the probability that she bought premium gas. show your work.

The required probability is 0.1422.

Step-by-step explanation:

Since we have given that

Probability that drivers filled their vehicles with regular gasoline P(R) = 88%

Probability that drivers purchased midgrade gas P(M) = 2%

Probability that bought premium gas P(P) = 10%

Let A be the given event that it is paid with credit card.

Probability that who bought regular gas paid with credit card P(A|R) = 285

Probability that who bought midgrade gas with credit card P(A|M) = 34%

Probability that who bought premium gas with credit card P(A|P) = 42%

According to Bayes theorem, we get that

P(P|A) is given by

Hence, the required probability is 0.1422.

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation:

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is