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question:A company has 200 employees. 60% of the employees drive to work. Of the employees who don't drive to work, half take public transportation. How many more employees drive to work than take public transportation?
answer:First, let's find out how many employees drive to work. Since 60% of the employees drive to work, we can calculate this number as follows: 60% of 200 employees = 0.60 * 200 = 120 employees Now, let's find out how many employees do not drive to work. Since 120 employees drive to work, the remaining employees who do not drive to work are: 200 employees - 120 employees = 80 employees Half of these employees take public transportation, so we can calculate this number as follows: 1/2 of 80 employees = 0.5 * 80 = 40 employees Now, to find out how many more employees drive to work than take public transportation, we subtract the number of employees who take public transportation from the number of employees who drive to work: 120 employees (drive) - 40 employees (public transportation) = 80 employees So, boxed{80} more employees drive to work than take public transportation.
question:Which of the following statements is correct? ( ) ① Inductive reasoning is reasoning from the specific to the general; ② Inductive reasoning is reasoning from the general to the general; ③ Deductive reasoning is reasoning from the general to the specific; ④ Analogical reasoning is reasoning from the specific to the general; ⑤ Analogical reasoning is reasoning from the specific to the specific. A: ①②③； B: ②③④； C: ②④⑤； D: ①③⑤.
answer:The correct answer is boxed{D}. Brief explanation is omitted.
question:A family of some monkeys collected 10 piles of bananas. 6 piles had 9 hands, with each hand having 14 bananas, while the remaining piles had 12 hands, with each hand having 9 bananas. If they divide the bananas equally amongst themselves, each monkey would get 99 bananas. How many monkeys are in the family?
answer:First, let's calculate the total number of bananas in the 6 piles that have 9 hands with 14 bananas each. 6 piles * 9 hands/pile * 14 bananas/hand = 54 hands * 14 bananas/hand = 756 bananas Next, let's calculate the total number of bananas in the remaining 4 piles that have 12 hands with 9 bananas each. 4 piles * 12 hands/pile * 9 bananas/hand = 48 hands * 9 bananas/hand = 432 bananas Now, let's add the total number of bananas from both types of piles to get the grand total. 756 bananas + 432 bananas = 1188 bananas If each monkey gets 99 bananas, we can divide the total number of bananas by the number of bananas per monkey to find out how many monkeys there are. 1188 bananas / 99 bananas/monkey = 12 monkeys So, there are boxed{12} monkeys in the family.
question:Evaluate the expression: 3000 cdot (3000^{3001})^2. textbf{(A)} 3000^{9003} qquad textbf{(B)} 3000^{6003} qquad textbf{(C)} 6000^{3003} qquad textbf{(D)} 9000^{3001} qquad textbf{(E)} 3000^{301}
answer:1. **Identify the expression and apply the exponent rule**: We start with the expression 3000 cdot (3000^{3001})^2. Through properties of exponents, particularly (a^m)^n = a^{mn}: [ (3000^{3001})^2 = 3000^{3001 cdot 2} = 3000^{6002} ] 2. **Combine expressions using exponent rules**: Now, multiply the original base by the new exponentiated value: [ 3000 cdot 3000^{6002} = 3000^1 cdot 3000^{6002} ] Apply the property that a^m cdot a^n = a^{m+n}: [ 3000^1 cdot 3000^{6002} = 3000^{1+6002} = 3000^{6003} ] 3. **Conclusion with boxed answer**: Thus, the result simplifies to 3000^{6003}. The final answer is The final answer, given the choices, is boxed{textbf{(B)} 3000^{6003}}.