What other points are on the line of direct variation through (5, 12)? Check all that apply. (0, 0) (2.5, 6) (3, 10) (7.5, 18) (
12.5, 24) (15, 36)
2 answers:
It is established that
A correlation between two variables, x and y, demonstrates a direct variation if it can be written in the format or
For this question, we have
the point lies on the direct variation line
therefore
Determine the constant of proportionality k
-------> substitute ------>
The equation is
Keep in mind that
If a point is located on the direct variation line
then
the point has to fulfill the direct variation equation
we will now validate each point
case A) point
Insert the values of x and y into the direct variation equation
-------> is valid
thus
the point lies on the direct variation line
case B) point
Insert the values of x and y into the direct variation equation
-------> is valid
thus
the point lies on the direct variation line
case C) point
Insert the values of x and y into the direct variation equation
-------> is not valid
thus
the point does not lie on the direct variation line
case D) point
Insert the values of x and y into the direct variation equation
-------> is valid
thus
the point lies on the direct variation line
case E) point
Insert the values of x and y into the direct variation equation
-------> is not valid
thus
the point does not lie on the direct variation line
case F) point
Insert the values of x and y into the direct variation equation
-------> is valid
thus
the point lies on the direct variation line
ultimately
the solution is
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Answer:
The likelihood of a battery being produced by Factory A and being defective is 0.012, which corresponds to 1.2%.
Step-by-step explanation:
We have two manufacturers of batteries for mobile phones: Factory A and Factory B. Factory A is responsible for 60% of the total battery production, while Factory B accounts for the remaining 40%.
Out of the batteries made by Factory A, 2% are found to be defective, whereas 4% of those from Factory B are defective.
Let P(A) denote the probability that a battery comes from Factory A, therefore P(A) = 0.60.
The probability that a battery originates from Factory B can be denoted as P(B) = 0.40.
Furthermore, define D as the event indicating that a battery is defective.
Thus, the probability of a defect given that a battery is from Factory A is P(D/A) = 0.02.
For Factory B, the probability of a defect given it is from there is P(D/B) = 0.04.
The probability for a battery being made at Factory A and also being defective can be calculated as follows:
Probability that Factory A produces batteries Probability that a battery from Factory A is defective
= P(A) P(D/A)
= 0.60 0.02 = 0.012 or 1.2%
Conclusively, the probability that a battery is both from Factory A and defective is 1.2%.
Finding a solution to an equation entails determining the value of x that renders the equation valid.
We must reverse the operations applied to x to isolate it.
Final Note:
The resulting equation is false, indicating that there is NO solution. Graphically, both equations will be represented as parallel lines that do not intersect.