Reyna runs a textile company that manufactures T-shirts The profit, p, made by the company is modeled by the function p=s^2+9s-142 where s is the number of T-shirts sold.How many T-shirts should be sold to earn a profit of more than 2,000 slt 42 sgt 42 sgt 51 slt 51

To find the number of T-shirts that should be sold to earn a profit of more than $2,000, we need to solve the inequality:<br /><br />$p = s^2 + 9s - 142 > 2000$<br /><br />Subtract 2000 from both sides:<br /><br />$s^2 + 9s - 2142 > 0$<br /><br />Now, we need to solve this quadratic inequality. We can factor the quadratic expression:<br /><br />$(s - 42)(s + 51) > 0$<br /><br />The critical points are $s = 42$ and $s = -51$. Since the number of T-shirts sold cannot be negative, we only consider the positive critical point.<br /><br />The solution to the inequality is:<br /><br />$s < 42$ or $s > 51$<br /><br />Therefore, the correct answer is:<br /><br />$s < 42$ or $s > 51$