answer:When m=0, the equation becomes 2x+1=0, which has one negative root. For mneq 0, mx^2+2x+1=0 is a quadratic equation in one variable. To ensure that the equation mx^2+2x+1=0 has at least one negative root, let the roots be x_1 and x_2. When Delta=4-4m=0, that is, m=1, the equation becomes x^2+2x+1=0, which has the solution x=-1, satisfying the condition. When Delta=4-4m>0, that is, m<1 and mneq 0, - If there is one negative root, then x_1x_2=frac{1}{m}<0, which leads to m<0. - If there are two negative roots, then begin{cases} x_{1}+x_{2}=-frac{2}{m}<0 x_{1}x_{2}=frac{1}{m}>0 end{cases}, which leads to 0<m<1. In summary, the range of the real number m is (-infty, 1]. Therefore, the answer is boxed{(-infty, 1]}. This problem involves discussing the distribution of the roots of a quadratic equation relative to its coefficients and requires a discussion of different cases: one negative root and two negative roots. It tests the understanding of the relationship between the roots of a quadratic equation and its coefficients, the mathematical thinking in discussing different cases, and the computational skills of students. It is considered a medium-level problem.

answer:Let's calculate the number of pairs of socks Lisa ended up with step by step: 1. Lisa bought 12 pairs of socks. 2. Sandra brought 20 pairs of socks. 3. Lisa's cousin brought one-fifth the number of pairs that Sandra bought, which is 20/5 = 4 pairs of socks. 4. Lisa’s mom brought 8 more than three times the number of pairs Lisa started with, which is 8 + (3 * 12) = 8 + 36 = 44 pairs of socks. Now, let's add all the pairs of socks together: Lisa's initial pairs + Sandra's pairs + Cousin's pairs + Lisa's mom's pairs = 12 + 20 + 4 + 44 = 80 pairs of socks So, Lisa ended up with boxed{80} pairs of socks to donate to the homeless shelter.

answer:To find the multiple of Bob's age that is related to Carol's age, we can use the information given: Carol's age = 50 years Bob's age = 16 years According to the problem, Carol's age is 2 more than a certain multiple of Bob's age. Let's call the multiple "m". So we can write the equation: Carol's age = m * Bob's age + 2 Now we can plug in the values for Carol's and Bob's ages: 50 = m * 16 + 2 Now we need to solve for "m": 50 - 2 = m * 16 48 = m * 16 Now divide both sides by 16 to find "m": m = 48 / 16 m = 3 So the multiple of Bob's age that is related to Carol's age is boxed{3} .

answer:1. **Define the cost and revenue variables**: Let the cost of each sheep be c dollars. Therefore, the total cost for 800 sheep is 800c dollars. 2. **Calculate the revenue from selling 600 sheep**: The farmer sold 600 sheep for the price of 700 sheep, which is 700c dollars. Thus, the price per sheep for these 600 sheep is: [ text{Price per sheep for first 600} = frac{700c}{600} = frac{7}{6}c text{ dollars} ] 3. **Calculate the revenue from selling the remaining 200 sheep**: The remaining 200 sheep were sold at 10% higher price per head than the first 600, thus: [ text{Price per sheep for remaining 200} = left(1.10right)left(frac{7}{6}cright) = frac{77}{60}c text{ dollars} ] The revenue from selling these 200 sheep is: [ 200 times frac{77}{60}c = frac{154}{3}c text{ dollars} ] 4. **Calculate the total revenue**: The total revenue from selling all 800 sheep is: [ 700c + frac{154}{3}c = left(frac{2100 + 154}{3}right)c = frac{2254}{3}c text{ dollars} ] 5. **Calculate the profit or loss**: The profit or loss is the total revenue minus the total cost: [ text{Profit or Loss} = frac{2254}{3}c - 800c = left(frac{2254 - 2400}{3}right)c = -frac{146}{3}c text{ dollars} ] 6. **Calculate the percentage loss**: The percentage loss is the absolute value of the loss divided by the total cost, multiplied by 100: [ text{Percentage Loss} = left(frac{left|-frac{146}{3}cright|}{800c}right) times 100 = left(frac{146}{2400}right) times 100 approx 6.08% ] 7. **Conclusion**: The percent loss on the entire transaction is approximately 6.08%. Therefore, the correct answer is: [ 6.08% ] The final answer is boxed{textbf{(B)} 6.08%}