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question:the manufacture of a certain product, there are three stages in the production process. In the first stage, 6 percent of the units produced are defective. In the second stage, an additional 3 percent of the remaining nondefective units from the first stage become defective due to a manufacturing error. In the third stage, 2 percent of the nondefective units after the second stage are found to be defective due to a packaging issue. After the production process, the units go through three stages of shipping and handling. In the first stage, 4 percent of the total defective units from the production process are shipped for sale. In the second stage, 3 percent of the defective units that were not shipped in the first stage are accidentally shipped for sale due to a labeling error. In the third stage, 2 percent of the remaining defective units that were not shipped in the previous stages are mistakenly shipped for sale. What percent of the units produced are defective units that are shipped for sale, considering all stages of production, shipping, and handling?

answer:Let's assume that we start with 100 units for simplicity. **Stage 1: Production** - 6% of the units are defective, so 6 units are defective, leaving 94 non-defective units. **Stage 2: Production** - 3% of the remaining 94 non-defective units become defective, which is 0.03 * 94 = 2.82 units. We'll round this to 3 units for simplicity, so now we have 6 + 3 = 9 defective units and 94 - 3 = 91 non-defective units. **Stage 3: Production** - 2% of the remaining 91 non-defective units become defective, which is 0.02 * 91 = 1.82 units. We'll round this to 2 units for simplicity, so now we have 9 + 2 = 11 defective units and 91 - 2 = 89 non-defective units. **Stage 1: Shipping** - 4% of the 11 defective units are shipped for sale, which is 0.04 * 11 = 0.44 units. We'll round this to 0 units for simplicity, as we can't ship a fraction of a unit. So, 0 units are shipped and 11 units remain defective. **Stage 2: Shipping** - 3% of the remaining 11 defective units are shipped for sale, which is 0.03 * 11 = 0.33 units. We'll round this to 0 units for simplicity. So, 0 units are shipped and 11 units remain defective. **Stage 3: Shipping** - 2% of the remaining 11 defective units are shipped for sale, which is 0.02 * 11 = 0.22 units. We'll round this to 0 units for simplicity. So, 0 units are shipped and 11 units remain defective. Since we rounded down at each stage of shipping, we have underestimated the number of defective units shipped. However, even if we had not rounded down, the total percentage of defective units shipped would still be less than 1% of the original 100 units. Therefore, the percent of the units produced that are defective units shipped for sale, considering all stages of production, shipping, and handling, is less than boxed{1%} .

question:Given the quadratic function y=(m2)x^24x+m^2+2m8 passes through the origin, the value of m is ( ) A: 2 B: 4 C: 2 or 4 D: Cannot be determined

answer:Since the equation of the quadratic function is y=(m-2)x^2-4x+m^2+2m-8, it follows that (m-2) neq 0, thus m neq 2. Since the graph of the quadratic function y=(m-2)x^2-4x+m^2+2m-8 passes through the origin, we have m^2+2m-8=0, which gives m=-4 or m=2. Since m neq 2, we conclude m=-4. Therefore, the correct choice is boxed{text{B}}.

question:Given that a, b in mathbb{R} and i is the imaginary unit, if the complex number frac{2+bi}{1i} = ai, then a+b= ______.

answer:To solve the equation frac{2+bi}{1-i} = ai, we will firstly rationalize the denominator by multiplying both numerator and denominator by the conjugate of the denominator, which is 1+i. Thus, we have begin{align*} frac{2+bi}{1-i} &= ai implies frac{(2+bi)(1+i)}{(1-i)(1+i)} &= ai implies frac{2+2i+b(i^2)+bi}{1-i^2} &= ai implies frac{2+2i-b+b i}{2} &= ai quad text{(since i^2=-1)} implies frac{2(1+i)+b(i-1)}{2} &= ai implies 1+i+frac{b}{2}(i-1) &= ai implies 1 + left(1+frac{b}{2}right)i &= ai. end{align*} For the above equality to hold, the real and the imaginary parts on both sides must be equal. Hence, we set up the following system of equations: begin{align*} 1 &= 0a && text{(equating real parts)} 1+frac{b}{2} &= a && text{(equating imaginary parts)} end{align*} From the first equation, we get that a = 0 times 1 = 0. However, this does not align with the second equation. Thus, there must be a mistake in our calculation. Let's revisit the step where we compare the real and imaginary parts: begin{align*} 1 &= a && text{(equating real parts, corrected)} 1+frac{b}{2} &= a && text{(equating imaginary parts)} end{align*} Now that we have the correct system, solving for a and b gives us: begin{align*} a &= 1 b &= 2(a - 1) b &= 2(1 - 1) b &= 0. end{align*} Therefore, the sum of a and b is: a + b = 1 + 0 = boxed{1}.

question:A certain type of cell divides once every 20 minutes, and each division results in one cell splitting into two. Therefore, the number of cells that can be obtained from one such cell after 3 hours and 20 minutes is ( ) A: 512 B: 511 C: 1024 D: 1023

answer:**Analysis** This question examines the application of exponential functions in real-world problems and is considered a medium-level question. **Solution** Given that a certain type of cell divides once every 20 minutes, with one cell splitting into two, Then, after 3 hours and 20 minutes, therefore there are a total of 10 divisions, therefore the number of cells that can be obtained is 2^{10} = 1024, Hence, the correct answer is boxed{C}.

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