At a local coffee shop, 10% of customers order decaf coffee and 30% are students. Given that 5% of students order decaf coffee, what is the probability that a randomly selected customer is a student AND orders decaf coffee? Round to 3 decimal places.

0.015

Step-by-step explanation:

We know that 30% of the customers are students, and 5% of these students order decaf coffee, so we can say that 5% of that 30% (=1.5%) is the percentage of customers that are students and order decaf coffee.

So, the probability of randomly selecting a customer that is a student and orders decaf coffee is 1.5% = 0.015

The percentage of customers that order decaf coffee (10%) is not applied in this solution, as we can have the percentage of students that order decaf coffee just using the percentage of customers that are students, and the percentage of students that order decaf coffee.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

substitute,

circle 1 = 5

circle 2 = 20

circle 3 = 44

in this case no matter how you add, you will always get a perfect square..

hence proved

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