cynara has a bag of red, blue, and black pens. She randomly selects a pen, records the color, and puts it back in the bag, She d

Response:

15.9

Detailed explanation:

Answer:

Step-by-step explanation:

To establish independence between two events, we must understand the concept of independence:

Events are deemed independent if , which means that the occurrence of one does not influence the probability of the other event.

In this situation, the only selection that aligns with the independence criterion is . Other options do not comply with the independent events definition.

Answer:

Possible values for X include;

15, 30, 45, 60, and so on

Step-by-step explanation:

The parameters provided are

Number of chocolates Tanmay possessed = X

Number of chocolates given to Akash = 1/3 × X

Number of chocolates given to Sharad = 1/5 × X

Consequently, since both 3 and 5 divide X,

3 × 5 = 15 is the smallest single factor of X.

Thus, the values of X based on this minimum factor are as follows;

15 × 1 = 15

15 × 2 = 30

15 × 3 = 45

15 × 4 = 60

Therefore, potential values for X form an arithmetic series: a + (n - 1) × d

Where:

a = 15

n = 1, 2, 3, 4,...

d = 15

This results in;

15, 30, 45, 60

Solution

To find the angle m∠p.

Method of proof

In triangle ΔDAB, which is a right triangle

Applying the Pythagorean theorem gives us

Hypotenuse² = Perpendicular² + Base²

DB² = AB² + AD²

Where AB = 5 units

AD = 6 units

Substituting in the formula outcomes in

DB² = 5² + 6²

      = 25 + 36

     = 61

           = approximately 7.8 units

The triangle ΔDCB is also right-angled.

Using the trigonometric identity here.

Given that DC = 4 units and DB ≈ 7.8 units,

Substituting these values into the trigonometric identity gives us.

Thus, we find that ∠p ≈ 59.15 °