A market research firm used a sample of individuals to rate the purchase potential of a particular product before and after the individuals saw a new television commercial about the product. The purchase potential ratings were based on a 0 to 10 scale, with higher values indicating a higher purchase potential. The null hypothesis stated that the mean rating "after" would be less than or equal to the mean rating "before." Rejection of this hypothesis would show that the commercial improved the mean purchase potential rating. Use α = 0.05 and the following data to test the hypothesis and comment on the value of the commercial.

Individual Purchase After Rating Before Individual After Purchase After Rating Before
1 6 5 5 3 5
2 6 4 6 9 8
3 7 7 7 7 5
4 4 3 8 6 6

Cumulative examcumulative exam active13time remaining02: 44: 18the graph represents the data cost for monthly internetservice for a cell phone.which function, c(x), represents the monthly cost in dollarsin terms of x, the number of gigabytes used in a month? cell phone internet service(15,5x + 10150,0sx522 < x < 664x115, osx< 25x + 20, 2< x< 650, 65815%,monthly cost (s)20x + 5| 50x,0 < x < 22 < x < 664x( 15x, osx< 2c(x) = 5x + 10, 2< x< 6150x, 65 x5+1234 5 6 7 8 9 10 11 12gigabytes used

How many solutions does the nonlinear system of equations graphed below have?

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are fewer free variables than equations. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 12 c. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 8 d. no, overdetermined systems cannot be consistent because there are no free variables. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 24