Find the truth set of each predicate. (If your answer is an interval, enter it using interval notation; otherwise enter it as a

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.
         

Solution:

In Mr. Skinner's class, the count of students bringing lunch from home is 12 out of 20.

Fraction of students who brought lunch from home in Mr. Skinner's class=

For Ms. Cho's class, the number who brought lunch from home is 14 out of 21.

Fraction of students who brought lunch from home in Ms. Cho's class=

Siloni is utilizing two spinners with 15 equal sections to randomly select students from the classes and predict whether they brought lunch or will purchase it from the cafeteria.

Number of Equal sections in each Spinner=15

To visualize the students from Mr. Skinner's class who brought lunch using a Spinner with 15 equal sections =

For Ms. Cho's class, using a Spinner with 15 equal sections =

Mr. Skinner's Class +1 = Ms. Cho's Class

This means that the spinner for Ms. Cho's class will include one additional section representing students who brought lunch.

Option A signifies that one additional section on Mr. Skinner's spinner represents students who brought lunch, reflecting Ms. Cho's class.

Answer : y>0

f(x) = 9*2^x

This function is exponential in form

Substituting positive numbers for x yields positive y values

Substituting negative numbers for x also results in positive y values

Therefore, y remains positive regardless of the value of x.

The range comprises all possible y outputs of the function

Since y is always positive, the range is y > 0

Let the number of years Brad has been on the soccer team be represented by x, and let y represent the number of years Scott has been on the same team.

From the information given, we formulate the equations:
5y - 2 = x -----(1)

x + y = 10 -----(2)

Now, substituting equation (1) into equation (2):
5y - 2 + y = 10
6y - 2 = 10
6y = 12
y = 2
Next, substituting this value back to find x:
x = 5×2 - 2
x = 8

So, Brad has spent a total of 8 years in the team.

1) 4.55

2) Short hit

Step-by-step explanation:

1)

The score and corresponding probabilities are shown in the following table:

Score 3 4 5 6 7

Probability 0.15 0.40 0.25 0.15 0.05

Let us define

X = Miguel's score on the Water Hole

The expected value of the variable X can be represented as:

where

represents the different possible outcomes of X

denotes the associated probabilities

Accordingly, the expected value of Miguel's score is calculated as follows:

2)

Here, we will again consider:

X = Miguel's score on the Water Hole

In this case:

- For a successful long hit, the expected value of X is

- Conversely, if the long hit isn't successful, the expected value of X becomes

We also know that the likelihood of succeeding with a long hit is

Consequently, the chance of failure in a long hit is

Thus, the expected value of X when opting for the long hit strategy is:

In the first part of this question, we calculated the expected value using the short hit strategy, yielding:

Given that the expected value for X is smaller (which is better) when utilizing the short hit option, we can conclude that this approach is superior.