O.9c + 1.89r = 17.01 c=18.9 - 2.1r equation answer

For Chris, the calculation for his monthly telephone expense is as follows:

Where "x" denotes each minute used.

Given that Chris can afford a bill of $86, we have:

The total minutes of usage must not exceed 500 per month. Consequently, the viable choice is option C.

Answer:

Option C

Answer:

• a. Refer to the table below

• b. Refer to the table below

• c. 0.548

• d. 0.576

• e. 0.534

• f) i) 0.201, ii) 0.208

Explanation:

To begin with, organize the data provided:

Table: "Who excels at obtaining deals?"

                       Who Excels?

Respondent      I Am        My Spouse     We are Equal

Husband           278             127                 102

Wife                   290            111                   102

a. Create a joint probability table and utilize it to respond to the ensuing inquiries.

The joint probability table presents identical details expressed as proportions. The values from the table need to be divided by the total number of responses involved.

1. Total responses: 278 + 127 + 102 + 290 + 111 + 102 = 1,010.

2. Determine each proportion:

• 278/1,010 = 0.275
• 127/1,010 = 0.126
• 102/1,010 = 0.101
• 290/1,010 = 0.287
• 111/1,010 = 0.110
• 102/1,010 = 0.101

3. Construct the table containing these values:

Joint probability table:

Respondent      I Am        My Spouse     We Are Equal

Husband           0.275           0.126                 0.101

Wife                   0.287           0.110                  0.101

This table illustrates that the joint probability of identifying as a husband while choosing 'I am' equals 0.275. Each cell conveys the joint probability associated with each gender's response.

Consequently, this delineates the purpose of a joint probability table.

b. Generate marginal probabilities for Who Excels (I Am, My Spouse, We Are Equal). Provide commentary.

Marginal probabilities are computed for each row and column of the table, indicated in the margins, which is their namesake.

For the column titled "I am," it amounts to: 0.275 + 0.287 = 0.562

Similarly, perform calculations for the other two columns.

For the row designated 'Husband,' it would thus be 0.275 + 0.126 + 0.101 = 0.502. Apply the same for the row labeled 'Wife.'

Table Marginal probabilities:

Respondent      I Am        My Spouse     We Are Equal     Total

Husband           0.275           0.126                 0.101             0.502

Wife                   0.287           0.110              0.101             0.498

Total                 0.562           0.236            0.202             1.000

Notably, when summing the marginal probabilities for both rows and columns, the results will always equate to 1. This is a consistent truth for marginal probabilities.

c. Given the respondent is a husband, what is the likelihood that he believes he is better at securing deals than his wife?

This requires the utilization of conditional probability.

The goal here is to ascertain the probability of the response being "I am" when the respondent identifies as a "Husband."

Using conditional probability:

• P ( "I am" / "Husband") = P ("I am" ∩ "Husband) / P("Husband")

• P ("I am" ∩ "Husband) = 0.275 (obtained from the intersection of columns "I am" and rows "Husband")

• P("Husband") = 0.502 (derived from total of row "Husband")

• P ("I am" ∩ "Husband) / P("Husband") = 0.275 / 0.502 = 0.548

d. In the instance that the respondent is a wife, what probability exists that she believes she is superior to her husband in acquiring deals?

We seek to identify the probability wherein the response claims "I am" while the respondent is labeled a "Wife," applying the conditional probability formula again:

• P ("I am" / "Wife") = P ("I am" ∩ "Wife") / P ("Wife")

• P ("I am" / "Wife") = 0.287 / 0.498

• P ("I am" / "Wife") = 0.576

e. When responding that "My spouse" is better at scoring deals, what is the likelihood that the claim originated from a husband?

We aim to compute: P ("Husband" / "My spouse")

Applying the conditional probability formula:

• P("Husband" / "My spouse") = P("Husband" ∩ "My spouse")/P("My spouse")

• P("Husband" / "My spouse") = 0.126/0.236

• P("Husband" / "My spouse") = 0.534

f. When the response indicates "We are equal," what likelihood exists that this response is from a husband? What is the chance that it hails from a wife?

What is the likelihood that this response came from a husband?

• P("Husband" / "We are equal") = P("Husband" ∩ "We are equal") / P ("We are equal")

• P("Husband" / "We are equal") = 0.101 / 0.502 = 0.201

What is the chance the response originated from a wife:

• P("Wife") / "We are equal") = P("Wife" ∩ "We are equal") / P("We are equal")

• P("Wife") / "We are equal") = 0.101 / 0.498 = 0.208

Answer:

12 pencils per package.

Step-by-step explanation:

Details provided:

Ethan purchased 4 packages of pencils.

Number of Packages = 4

Number of pencils shared with friend = 8 pencils

Pencils remaining = 40 pencils

∴Total Number of Pencils = Pencils given to friend + Pencils remaining =

Total Pencils in each package =

Answer:

Error made by Andrew: He identified incorrect factors based on the roots.

Step-by-step explanation:

The roots of the polynomial consist of: 3, 2 + 2i, 2 - 2i. By the factor theorem, if a is a root of the polynomial P(x), then (x - a) must be a factor of P(x). According to this premise:

(x - 3), (x - (2 + 2i)), (x - (2 - 2i)) represent the factors of the polynomial.

(x - 3), (x - 2 - 2i), (x - 2 + 2i) as the respective factors.

This is where Andrew's mistake occurred. Factors should always be in the form (x - a), not (x + a). Andrew expressed the complex factors incorrectly, resulting in an erroneous conclusion.

Thus, the polynomial can be expressed as:

Answer:

7 years

Step-by-step explanation:

Suri is 17 years old.

Her cousin's age is c.

Suri's age is stated to be 4 less than 3 times her cousin’s age.

This means we take 3 times her cousin’s age and subtract 4.

17 = 3c - 4

We now need to solve for c, which represents her cousin's age.

Add 4 to each side:

17 + 4 = 3c - 4 + 4

17 + 4 = 3c

21 = 3c

Now divide both sides by 3:

21/3 = 3c/3

7 = c

Thus,

Her cousin is 7 years old.