Question

1. (y < -x + a) (y>x + b) in the xy - plane, if ((0,0)) is a solution to the system of inequalities above, which of the following relationships between (a) and (b) must be true? a) (a>b) b) (b > a) c) (|a|>|b|) d) (a=-b) 19. a food truck sells salads for (6.50) each and drinks for (2.00) each. the food trucks revenue from selling a total of 209 salads and drinks in one day was (836.50). how many salads were sold that day? a) 77 b) 93 c) 99 d) 105 20. alma bought a laptop computer at a store that gave a 20 percent discount off its original price. the total amount she paid to the cashier was (p) dollars, including an 8 percent sales tax on the discounted price. which of the following represents the original price of the computer in terms of (p)? a) (0.88p) b) (\frac{p}{0.88}) c) ((0.8)(1.08)p) d) (\frac{p}{(0.8)(1.08)}) 21. dreams recalled during one week none 1 to 4 5 or more total group x 15 28 57 100 group y 21 11 68 100 total 36 39 125 200 the data in the table above were produced by a sleep researcher studying the number of dreams people recall when asked to record their dreams for one week. group x consisted of 100 people who observed early bedtimes, and group y consisted of 100 people who observed later bedtimes. if a person is chosen at random from those who recalled at least 1 dream, what is the probability that the person belonged to group y? a) (\frac{68}{100}) b) (\frac{79}{100}) c) (\frac{79}{164}) d) (\frac{164}{200})

Explanation:

18

Step1: Substitute (0,0) into inequalities

Substitute \(x = 0\) and \(y=0\) into \(y < -x + a\) and \(y>x + b\). We get \(0 < a\) and \(0>b\).

Step2: Analyze the relationship

Since \(a>0\) and \(b < 0\), then \(a>b\).

Step1: Express \(y\) in terms of \(x\) from first - equation

From \(x + y=209\), we have \(y = 209 - x\).

Step2: Substitute \(y\) into the second - equation

Substitute \(y = 209 - x\) into \(6.5x+2y = 836.5\). So \(6.5x+2(209 - x)=836.5\).

Step3: Expand and solve for \(x\)

Expand: \(6.5x + 418-2x=836.5\). Combine like - terms: \(4.5x=836.5 - 418\), \(4.5x = 418.5\), then \(x=\frac{418.5}{4.5}=93\).

Step1: Solve for \(x\)

First, expand the right - hand side: \(p = 1.08\times0.8x\). Then \(x=\frac{p}{(0.8)(1.08)}\).

Answer:

A. \(a > b\)

19

Let the number of salads be \(x\) and the number of drinks be \(y\). We know that \(x + y=209\) (total number of items sold) and \(6.5x + 2y=836.5\).