A direct variation function contains the points (–8, –6) and (12, 9). Which equation represents the function? y = –4/3x y = –3/4

Part A:

Considering the best possible outcome

The ideal case occurs if the two missing socks are from the same pair.
Consequently, there are 4 complete pairs remaining.

To choose 2 from the total of 10 socks (5 pairs), the number of combinations is given by 10C2 = 45.

Choosing 2 that are from the same pair means selecting one from 5 pairs, so the count is 5C1 = 5.

Thus, the probability for this best case is 5 / 45 = 1 / 9.

Part B:

Considering the worst-case outcome

This scenario occurs when the two missing socks are from different pairs.
As a result, we have 3 complete pairs left.

The total ways to select 2 socks from 10, again, is 10C2 = 45.

To select 2 that do not belong to the same pair, we calculate as follows: 10C2 - 5C1 = 45 - 5 = 40.

Therefore, the probability for the worst-case scenario is 40 / 45 = 8 / 9.

Answer: y = 2/5 --> y = 0.4

Step-by-step explanation:

The equation 5y = 2 represents a horizontal line at y = 2/5.

This means that the y-coordinate holds the value of 2/5 = 0.4 for any x-coordinate.

Answer:

a. Alice

b. Briana

c. 0.51 minutes

Step-by-step explanation:

a. Alice's formula is applicable for any t > 0 minutes, while Briana’s is only applicable when

2t - 1 > 0

2t > 1

t > 1/2 minutes

b. They complete the race when their total distance equals 5 kilometers. For Alice:

t/4 = 5

t = 20 minutes

For Briana:

√(2t - 1) = 5

2t - 1 = 25

2t = 26

t = 13 minutes

c. They reach the same point when they have traveled the same distance, expressed as:

t/4 = √(2t - 1)

(t/4)² = 2t - 1

t²/16 = 2t - 1

t² = 16(2t - 1)

t² = 32t - 16

t² - 32t + 16 = 0

Using the quadratic formula:

Only the second solution fits this scenario because the race concluded before they took 31.49 minutes.

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%.

Response:

Step-by-step explanation:

A line is defined as a one-dimensional entity that lacks thickness and stretches infinitely in both directions.

A line segment contains two endpoints, while a ray consists of a single endpoint.

The equation given is .

Objective: to identify a line completely within the set designated by this equation.

Solution:

Consider .

Verification:

.

Thus, fulfills the criteria of the given equation.