Amajor issue facing many states is whether to legalize casino gambling. suppose the governor of one state believes that more than 55% of the state's registered voters would favor some form of legal casino gambling. however, before backing a proposal to allow such gambling, the governor has instructed his aides to conduct a statistical test on the issue. to do this, the aides have hired a consulting firm to survey a simple random sample of 300 voters in the state. of these 300 voters, 175 actually favored legalized gambling. state the appropriate null and alternative hypotheses.

Null hypothesis Uo = 165

Alternative Hypothesis U1 > 165

Step-by-step explanation:

Null hypothesis = 55% of registered voters

In this case we sampled on 300 voters

55/100 × 300= 165voters

Null hypothesis Uo= 165

That is 165 out of 300 voters will favour legalized gambling.

Alternative Hypothesis U1 > 165

That is more than 165 out of 300 voters will favour legalized gambling.

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1