4.

solve the given system, using the substitution method.

y = 4x – 6

8x – 2y = 14

a.

(14, 12)

b.

(12, 14)

c.

there are an infinite number of solutions.

d.

there is no solution.

3.

solve the given system, using the substitution method.

y = 3x – 7

6x – 2y = 12

a.

there is no solution.

b.

(12, 14)

c.

(14, 12)

d.

there are an infinite number of solutions.

5.

solve, using the substitution method.

y + 2x = 7

14 – 4x = 2y

a.

the solution is (1, 5)

b.

the solution is (21, 0)

c.

there are an infinite number of solutions.

d.

there is no solution.

Will mark brainliest with 20 points! the table shows how far object 1 traveled as a function of time. *time (seconds) - 2 4 6 8 *distance traveled (feet) - 18 36 54 72 the equation shows how far object 2 traveled in feet as a function of time in minutes. *f(x) = 10x which object traveled at a faster speed? justify your response.

Every weekday, mr. jones bikes from his home to his job. sometimes he rides along two roads, the long route that is shown by the solid lines. other times, he takes the shortcut shown by the dashed line. how many fewer kilometers does mr. jones bike when he takes the shortcut instead of the long route?

In january 2010, you began a one-year study of tuberculosis (tb) in a subsidized housing community in the lower east side of new york city. you enrolled 500 residents in your study and checked on their tb status on a monthly basis. at the start of your study on january 1st, you screened all 500 residents. upon screening, you found that 30 of the healthy residents had been vaccinated for tb and therefore were not at risk. another 20 residents already had existing cases of tb on january 1st. on february 1st, 5 residents developed tb. on april 1st, 10 more residents developed tb. on june 1st, 10 healthy residents moved away from new york city and were lost to follow-up. on july 1st, 10 of the residents who had existing tb on january 1st died from their disease. the study ended on december 31, 2010. assume that once a person gets tb, they have it for the duration of the study, and assume that all remaining residents stayed healthy and were not lost to follow-up. is the subsidized housing community in the lower east side of new york city a dynamic or fixed population? briefly explain the rationale for your answer. dynamic population it can changeable people can move out and move in into the population of a subsidized housing what was the prevalence of tb in the screened community on january 1st? prevalence = 30/500 0.06= 6% what was the prevalence of tb on june 30th? prevalence= 40/450=0.08= 8.88% what was the cumulative incidence of tb over the year? cumulative incidence = number of new cases/number in candidate population)over specified time period 10/450 = 2.2% suppose that you wanted to calculate the incidence rate of tb in the study population. calculate the amount of person-time that would go in the denominator of this incidence rate. be sure to show your work.