Suppose that a person's birthday is a uniformly random choice from the 365 days of a year (leap years are ignored), and one pers

Answer:

0 < k < 2

Step-by-step explanation:

In the first quadrant, both x and y are positive, thus

• x > 0 and y > 0

• x = 2k, where k > 0

Substituting x with 2k into the second equation gives:

• 3x + 2y = 12
• 3*2k + 2y = 12
• 2y = 12 - 6k
• y = 6 - 3k

Given that y > 0:

• 6 - 3k > 0
• 2 - k > 0
• k < 2

By combining k > 0 and k < 2, we obtain:

• 0 < k < 2

The equations to determine the price in dollars for each large candle, x, and small candle, y are and .

Detailed explanation:

In this scenario, a customer bought 3 large candles and 4 small candles for a total of $64. Another customer paid $4 more for 1 large candle and 8 small candles at the same store. The prices of large and small candles remain constant. To identify the equations for determining the price in dollars of each large candle (x) and small candle (y), we can see the following:

Let the price of each large candle be x and each small candle be y. Thus,

A customer at a shop paid $64 for 3 large candles and 4 small candles

This results in the equation:

⇒ .....(1)

The second customer at the store paid $4 more than the previous customer for 1 large candle and 8 small candles.

This gives us the equation:

⇒ .......(2)

3(2)-(1) i.e.

⇒

⇒

⇒

Therefore, the equations to calculate the price in dollars for each large candle, x, and small candle, y are and .