Π=7x−2y can someone please help to find y

To respond effectively, one would need a table showing the number of males and females who prefer pink or yellow lemonade at the state fair. Male preferences are captured as Pink Lemonade: 156, Yellow Lemonade: 104, totaling 260. Female preferences recorded as Pink Lemonade: 72, Yellow Lemonade: 48, totaling 120. Overall, totaling: Pink Lemonade: 228, Yellow Lemonade: 152, 380 in sum. P(pink lemonade | female) is computed as 72/(72+48) = 72/120 = 0.6. P(pink lemonade) is calculated as (156+72)/(260+120) = 228/380 = 0.6. Consequently, the events of preferring pink lemonade and being female are independent given P(pink lemonade | female) equals P(pink lemonade) which both equal 0.6.

1. 1/3. 2. 7.

A) To establish a sampling plan, follow these 5 steps:
    1) Identify the sample population: which customers will you reach out to?
       Those who purchased a new car during a specific year.
    2) Determine the population size: how many customers will you contact?
       From the 30,000 car buyers, select 1,000 customers to contact.
    3) Select contact method: what is your means of contacting customers?
       Since you have a list with names and addresses, mailing questionnaires is feasible.
    4) Define the sampling frame: what is the timeline or deadline for contacting customers?
       Send out questionnaires and allow two months for responses.
    5) Decide on the analysis approach: is your research qualitative or quantitative?
     You aim for quantitative research, so you will use probabilistic sampling.

B) The 32.5% probability relates only to those customers who experienced mechanical issues, specifically power door lock problems, and does not account for those without any problems or those reporting issues after the first 5,000 miles.

C) To estimate the probability of power door lock problems among all customers within the first 5,000 miles, consider the entire sample:
P = 13 / 1000 = 0.013

Therefore,
N = 0.013 × 30,000 = 390

Thus, the estimated number of new cars that had power door lock issues within 5,000 miles is 390.
         

Answer:

a) S={(head,1),(head,2),(head,3),(head,4),(head,5),(head,6),(tails,1),(tails,2),(tails,3),(tails,4),(tails,5),(tails,6)}

b) S={top,bottom,side}

c) S={(Ace of diamonds),(Two of diamonds),(Three of diamonds),(Four of diamonds),(Five of diamonds),(Six of diamonds),(Seven of diamonds), (Eight of diamonds),(Nine of diamonds),(Ten of diamonds), (Jack of diamonds), (Queen of diamonds),(King of diamonds),(Ace of hearts),(Two of hearts),(Three of hearts),(Four of hearts),(Five of hearts),(Six of hearts),(Seven of hearts), (Eight of hearts), (Nine of hearts),(Ten of hearts), (Jack of hearts), (Queen of hearts),(King of hearts),(Ace of clubs),(Two of clubs),(Three of clubs),(Four of clubs),(Five of clubs),(Six of clubs),(Seven of clubs), (Eight of clubs), (Nine of clubs),(Ten of clubs), (Jack of clubs),(Queen of clubs),(King of clubs),(Ace of spades),(Two of spades),(Three of spades),(Four of spades),(Five of spades),(Six of spades),(Seven of spades),(Eight of spades), (Nine of spades),(Ten of spades),(Jack of spades),(Queen of spades),(King of spades)}

Step-by-step explanation:

The sample space consists of all potential outcomes for each experiment:

a) The sample encompasses the outcomes resulting from tossing a coin (heads or tails) and throwing a die (a number between 1 and 6):

S={(head,1),(head,2),(head,3),(head,4),(head,5),(head,6),(tails,1),(tails,2),(tails,3),(tails,4),(tails,5),(tails,6)}

b) A paper cup can settle in one of three different positions: on its top, bottom, or side:

S={top,bottom,side}

c) The entire set of cards within a standard deck constitutes the sample space:

S={(Ace of diamonds),(Two of diamonds),(Three of diamonds),(Four of diamonds),(Five of diamonds),(Six of diamonds),(Seven of diamonds), (Eight of diamonds),(Nine of diamonds),(Ten of diamonds), (Jack of diamonds), (Queen of diamonds),(King of diamonds),(Ace of hearts),(Two of hearts),(Three of hearts),(Four of hearts),(Five of hearts),(Six of hearts),(Seven of hearts), (Eight of hearts), (Nine of hearts),(Ten of hearts), (Jack of hearts), (Queen of hearts),(King of hearts),(Ace of clubs),(Two of clubs),(Three of clubs),(Four of clubs),(Five of clubs),(Six of clubs),(Seven of clubs), (Eight of clubs), (Nine of clubs),(Ten of clubs), (Jack of clubs),(Queen of clubs),(King of clubs),(Ace of spades),(Two of spades),(Three of spades),(Four of spades),(Five of spades),(Six of spades),(Seven of spades),(Eight of spades), (Nine of spades),(Ten of spades),(Jack of spades),(Queen of spades),(King of spades)}

90kg of sand was divided into 3 bags, constituting a total of 2+3+7=12 sections.
90kg/12=7.5kg
The smaller bag comprises 2 sections, hence it weighs 7.5kg*2=15kg
The medium-sized bag consists of 3 sections, leading to a total weight of 7.5kg*3=22.5kg
The larger bag encompasses 7 sections, resulting in a weight of 7.5kg*7=52.5kg
Thus, the ratio 2:3:7 translates to 15kg:22.5kg:52.5kg
Verifying, 15kg+22.5kg+52.5kg equals 90kg