answer:To determine the number of laps each athlete runs in a 5000 , mathrm{m} race on a standard running track, we will follow these steps: 1. **Identify the length of one lap:** One lap of the standard running track is ( 400 , mathrm{m} ). 2. **Set up the division problem:** To find the number of laps in a 5000 , mathrm{m} race, divide the total distance by the length of one lap: [ text{Number of laps} = frac{5000 , mathrm{m}}{400 , mathrm{m}} ] 3. **Simplify the fraction:** Simplify the division to make the calculation easier: [ frac{5000}{400} = frac{5000 div 100}{400 div 100} = frac{50}{4} ] 4. **Perform the division:** Carry out the division to find the number of laps: [ frac{50}{4} = 12 frac{2}{4} = 12 frac{1}{2} ] 5. **Verify the result:** Convert the mixed number back into its decimal form to verify: [ 12 frac{1}{2} = 12.5 ] Hence, the number of laps each athlete runs in a 5000 , mathrm{m} race is ( 12 frac{1}{2} ). # Conclusion: [ boxed{E} ]

answer:Let's denote the smaller interior angle as x degrees. Since the larger interior angle is 90° more than the smaller one, we can express the larger interior angle as x + 90°. In a parallelogram, the sum of the interior angles on one side is 180° because opposite angles are equal and consecutive angles are supplementary. Therefore, we can set up the following equation: x (smaller angle) + (x + 90°) (larger angle) = 180° Now, let's solve for x: 2x + 90° = 180° 2x = 180° - 90° 2x = 90° x = 90° / 2 x = 45° So, the measure of the smaller interior angle of the parallelogram is boxed{45°} .

answer:A positive integer is a factor of n if and only if its prime factorization is of the form 2^a cdot 3^b cdot 5^c cdot 7^d where 0 leq a leq 4, 0 leq b leq 2, 0 leq c leq 1, and 0 leq d leq 1. Since the integer must be even, the exponent of 2 (a) must be at least 1. Thus, we have: - a: 4 choices for a (from 1 to 4 instead of 0 to 4) - b: 3 choices for b (from 0 to 2) - c: 2 choices for c (from 0 to 1) - d: 2 choices for d (from 0 to 1) The total number of even positive factors is calculated by multiplying these choices: [ text{Total even factors} = 4 times 3 times 2 times 2 = boxed{48} ]

answer:To find the average and variance of the new set of data, we start with the given information about the original set of data x_{1}, x_{2}, ldots, x_{n}, which has an average of 3 and a variance of 3. **Step 1: Calculating the Average of the New Data** The transformation applied to each data point is 3x - 2, where x is an original data point. To find the average of the new data, we apply this transformation to the average of the original data: - The original average is 3. - Applying the transformation: 3 times 3 - 2. This simplifies to: [3 times 3 - 2 = 9 - 2 = 7.] So, the average of the new data is boxed{7}. **Step 2: Calculating the Variance of the New Data** The variance transformation rule for a data set where each data point x is transformed to ax + b (with a and b being constants) is a^2 times the original variance. In this case, a = 3 and the original variance is 3. - The original variance is 3. - Applying the transformation rule: 3^2 times 3. This simplifies to: [3^2 times 3 = 9 times 3 = 27.] So, the variance of the new data is boxed{27}. Therefore, the average and variance of the new set of data are 7 and 27, respectively.