answer:1. **Define Variables:** Let m represent the total amount of money Brianna has. Let p represent the total cost of all the books she wants to buy. 2. **Establish Relationships:** Given that Brianna uses one fourth of her money to buy one half of the books, we can establish the equation: [ frac{1}{4}m = frac{1}{2}p ] 3. **Solve for Total Cost of Books:** Rearrange the equation to find the total cost of all the books: [ p = 2 left(frac{1}{4}mright) = frac{1}{2}m ] This equation tells us the total cost of all the books is frac{1}{2}m. 4. **Calculate Remaining Money:** The amount of money Brianna will have left after purchasing all the books is: [ m - frac{1}{2}m = frac{1}{2}m ] 5. **Conclusion:** The fraction of her money that Brianna will have left after buying all the books is frac{1}{2}. Hence, the correct answer is frac{1{2}}. The final answer is boxed{textbf{(C) } frac{1}{2}}

answer:First, let's find out how many seagulls are scared away by the kids throwing stones. Since 1/4 of the seagulls are scared away: 36 seagulls * 1/4 = 9 seagulls are scared away. Now, let's subtract the number of seagulls that were scared away from the total number to find out how many are left: 36 seagulls - 9 seagulls = 27 seagulls remain on the roof. Next, 1/3 of the remaining seagulls decide to fly to McDonald's parking lot: 27 seagulls * 1/3 = 9 seagulls fly away to McDonald's. Finally, let's subtract the number of seagulls that flew away to McDonald's from the remaining seagulls on the roof: 27 seagulls - 9 seagulls = boxed{18} seagulls are left on the roof of the Taco Bell.

answer:Each shelter services 30 people, and Mark decides to buy 10 cans of soup per person. So for each shelter, he donates 30 * 10 = 300 cans of soup. Since there are 6 homeless shelters, Mark donates a total of 6 * 300 = boxed{1800} cans of soup.

answer:1. **Rewrite the expression using negative exponents:** [ frac{3b^{-1} + frac{b^{-2}}{3}}{b + b^2} ] Use that b^{-1} = frac{1}{b} and b^{-2} = frac{1}{b^2}. Then, the expression becomes: [ frac{3left(frac{1}{b}right) + frac{frac{1}{b^2}}{3}}{b + b^2} ] Simplify the fraction inside the numerator: [ 3frac{1}{b} + frac{1}{3b^2} = frac{9}{3b} + frac{1}{3b^2} = frac{3b + 1}{3b^2} ] Hence, the entire fraction becomes: [ frac{frac{3b + 1}{3b^2}}{b + b^2} ] 2. **Simplify further by combining the terms properly:** [ frac{3b + 1}{3b^2} div (b + b^2) ] Simplify the division: [ left(frac{3b + 1}{3b^2}right) cdot frac{1}{b(1+b)} = frac{3b + 1}{3b^3(1+b)} ] 3. **Substitute b = 3 into the simplified expression:** [ frac{3(3) + 1}{3(3)^3(1+3)} = frac{9 + 1}{3cdot27cdot4} = frac{10}{324} = frac{5}{162} ] Conclusion: The value of the expression when b = 3 is frac{5{162}}. The final answer is boxed{textbf{(C)} frac{5}{162}}