answer:1. **Total Arrangements**: Determine the ways to arrange 4 red and 3 green chips: [ binom{7}{3} = frac{7 times 6 times 5}{3 times 2 times 1} = 35 ] 2. **Favorable Arrangements**: Count the scenarios where the last chip drawn is green (implying all red chips are drawn before all green chips): - We need all four reds and two greens in the first six positions, with green as the seventh chip. - The ways to organize six chips where four are red and two are green: [ binom{6}{2} = frac{6 times 5}{2 times 1} = 15 ] 3. **Probability Calculation**: The probability that all red chips are drawn before the green chips are: [ text{Probability} = frac{text{Favorable Arrangements}}{text{Total Arrangements}} = frac{15}{35} = frac{3}{7} ] The probability that all four red chips are drawn before all three green chips are drawn is frac{3{7}}. The correct answer is boxed{A) dfrac{3}{7}}.

answer:First, we calculate the total number of rods: Each row increases the number of rods by 3. Hence, for a ten-row triangle: [ 3 + 6 + 9 + cdots + 30 = 3(1 + 2 + 3 + cdots + 10) ] The sum of the first 10 natural numbers is: [ frac{10 times (10 + 1)}{2} = 55 ] Thus, the total number of rods is: [ 3 times 55 = 165 ] Next, we calculate the connectors: A ten-row triangle will have eleven rows of connectors, as it always has one more row of connectors than rods: [ 1 + 2 + 3 + cdots + 11 = frac{11 times (11 + 1)}{2} = 66 ] Therefore, the total number of pieces (rods + connectors) is: [ 165 + 66 = boxed{231} ]

answer:Since f(x) is an odd function, we have f(-x)=-f(x). This implies that lg dfrac {1-ax}{1+2x}=-lg dfrac {1+ax}{1-2x}. By simplifying, we get lg dfrac {1-ax}{1+2x}=lg dfrac {1-2x}{1+ax}, which further simplifies to dfrac {1-ax}{1+2x}= dfrac {1-2x}{1+ax}. Solving this equation, we get 1-a^{2}x^{2}=1-4x^{2}, which gives us a^{2}=4. Since a > 0, we have a=2. Substituting a=2 into g(x), we get g(x)=log _{ frac {1}{2}}(x^{2}-6x+5). This function is a composite function made up of t=x^{2}-6x+5 and y=log _{ frac {1}{2}}t. Since y=log _{ frac {1}{2}}t is a decreasing function for t > 0, the monotonically decreasing interval of g(x) is (5,+infty). Therefore, the final answer is boxed{(5,+infty)}.

answer:Let h represent the number of hardcovers and p the number of paperbacks Isabella bought. She bought twelve volumes in total, so we have: 1. h + p = 12 The total cost for the books is 300, and using the prices for each type, we get: 2. 30h + 20p = 300 We can simplify the second equation by dividing through by 10: 3. 3h + 2p = 30 Now, solve the system of equations. Multiply the first equation by 2: 4. 2h + 2p = 24 Subtract equation 4 from equation 3: 5. 3h + 2p - 2h - 2p = 30 - 24 6. h = 6 Thus, Isabella bought boxed{6} hardcover volumes.