answer:Since Maria owes frac{13}{3} dollars for each of the frac{11}{4} lawns, the total amount owed is calculated as follows: [ frac{13}{3} cdot frac{11}{4} = frac{13 cdot 11}{3 cdot 4} = frac{143}{12} ] Thus, Maria owes Louise boxed{frac{143}{12}} dollars.

answer:# Problem: What is the minimum force needed to push a cube of volume 10 , text{cm}^3 and a material density of 400 , text{kg/m}^3 so that it is completely submerged in water? The density of water is 1000 , text{kg/m}^3. Provide the answer in SI units. Assume that the acceleration due to gravity is 10 , text{m/s}^2. 1. **Convert the volume from text{cm}^3 to text{m}^3:** [ 1 , text{cm}^3 = 1 times 10^{-6} , text{m}^3 ] Thus: [ 10 , text{cm}^3 = 10 times 10^{-6} , text{m}^3 = 10^{-5} , text{m}^3 ] 2. **Calculate the mass of the cube:** Using the formula ( rho = frac{m}{V} ): [ m = rho cdot V ] The density of the cube is 400 , text{kg/m}^3 and the volume is 10^{-5} , text{m}^3, so: [ m = 400 , text{kg/m}^3 times 10^{-5} , text{m}^3 = 4 times 10^{-3} , text{kg} ] 3. **Calculate the weight of the cube:** Using the formula ( F_g = m cdot g ): [ F_g = 4 times 10^{-3} , text{kg} times 10 , text{m/s}^2 = 4 times 10^{-2} , text{N} ] 4. **Calculate the buoyant force acting on the cube:** The buoyant force is given by Archimedes' principle ( F_b = rho_{text{fluid}} cdot V cdot g ): [ F_b = 1000 , text{kg/m}^3 times 10^{-5} , text{m}^3 times 10 , text{m/s}^2 = 10^{-1} , text{N} ] 5. **Determine the net force needed to submerge the cube:** To completely submerge the cube, the applied force ( F_{text{applied}} ) must counteract the buoyant force minus the weight of the cube: [ F_{text{applied}} = F_b - F_g ] Plug in the values obtained: [ F_{text{applied}} = 10^{-1} , text{N} - 4 times 10^{-2} , text{N} ] Simplify: [ F_{text{applied}} = 6 times 10^{-2} , text{N} = 0.06 , text{N} ] # Conclusion: The minimum force required to completely submerge the cube in water is ( boxed{0.06 , text{N}} ).

answer:Let ( n, d, ) and ( q ) represent the number of nickels, dimes, and quarters, respectively. We have the following conditions: 1. The total number of coins is 150. 2. The total value of the coins is 20.00, which is equivalent to 2000 cents. We can set up the following equations: [ begin{align*} n + d + q &= 150 quad text{(Equation 1)} 5n + 10d + 25q &= 2000 quad text{(Equation 2)} end{align*} ] To eliminate ( n ), multiply Equation 1 by 5: [ 5n + 5d + 5q = 750 quad text{(Equation 3)} ] Now, subtract Equation 3 from Equation 2: [ (5n + 10d + 25q) - (5n + 5d + 5q) = 2000 - 750 ] [ 5d + 20q = 1250 ] [ d + 4q = 250 quad text{(Equation 4)} ] Analyzing Equation 4 for non-negative integer solutions for ( d ) and ( q ): - If ( q = 0 ) (no quarters), then ( d = 250 ). - If ( d = 0 ) (no dimes), then ( 4q = 250 ), giving ( q = 62.5 ). We round down since ( q ) must be an integer, so ( q = 62 ) and ( d = 250 - 4 times 62 = 2 ). The smallest number of quarters ( q ) can be is 62 (when ( d = 2 )), and the largest number of quarters ( q ) can be is 0 (when ( d = 250 )). The difference between the largest and smallest number of quarters is: [ 62 - 0 = 62 ] Thus, the difference between the largest and smallest number of quarters that could be in the jar is 62. The final answer is boxed{B}.

answer:To find the least number that must be subtracted from 427398 to make it divisible by 13, we need to find the remainder when 427398 is divided by 13. The number that must be subtracted will be equal to this remainder. Let's perform the division: 427398 ÷ 13 = 32876 with a remainder of 2. Since the remainder is 2, we need to subtract 2 from 427398 to make it divisible by 13. Therefore, the least number that must be subtracted from 427398 is boxed{2} .