Explanation:
Let's denote the fourth number as x. Since the average of the first three numbers is double the fourth number, the sum of the first three numbers is 2x. Since the average of all four numbers is 14, the sum of all four numbers is 14×4=56. Thus, we have the equation 2x+x=56, which simplifies to 3x=56. Solving for x=56/3. The nearest whole number to 56/3 is 18.667, which rounds to 6 when rounded to the nearest whole number. Therefore, the fourth number is 8.
Explanation:
When we multiply an odd integer (odd) by an even integer (even), the result is always an even integer.
Explanation:
The mean of a set of numbers is found by adding all the numbers together and then dividing by the total count of numbers. The first 17 natural numbers are 1, 2, 3, ..., 17.
To find their mean, we add them together: 1+2+3+…+17=153.
Then, we divide the total sum by the count of numbers, which is 17.
So, 153÷17=9.
Explanation:
To find the temperature difference, we subtract the initial temperature from the final temperature.
Temperature difference = Final temperature - Initial temperature = 17°C - 27°C = -10°C
However, since the temperature dropped, we consider the difference as positive, so the temperature difference is 10°C.
Explanation:
Tap A fills the tank in 4 hours, so in 1 hour it fills 1/4 of the tank. Tap B empties the tank in 5 hours, so in 1 hour it empties 1/5 of the tank. When both taps are open together, they work simultaneously, so the net filling rate is (1/4)−(1/5)=1/20 of the tank per hour. Therefore, it takes 20 hours to fill the tank.
Explanation:
Let's denote the fourth number as x. Since the average of the first three numbers is double the fourth number, the sum of the first three numbers is 2x. Since the average of all four numbers is 28, the sum of all four numbers is 28×4=112. Thus, we have the equation 2x+x=112, which simplifies to 3x=112. Solving for x=112/3=37.33. Rounding to the nearest whole number, the fourth number is 37.33. Therefore, the fourth number is 16.
Explanation:
To find the average temperature, we add up all the measurements and then divide by the total number of measurements.
Sum of measurements: (−3+2+1−1−3)=−4
Total number of measurements: 5
Average temperature: (−4)/5=−0.8
Explanation:
To find the average temperature, we add up all the measurements and then divide by the total number of measurements.
Sum of measurements: −2+1+2+0−4+2+2=1
Total number of measurements: 7
Average temperature: 1/7=0.14
So, the final answer to her experiment is 0.14.
Explanation: The first 8 prime numbers are 2, 3, 5, 7, 11, 13, 17, and 19. To find their product, we simply multiply them together: 2×3×5×7×11×13×17×19=9,699,690. Therefore, the correct answer is 9,700.
Explanation:
Archana answered 47 questions correctly, earning 47×3=141 marks. She attempted all 60 questions, so the number of incorrect answers is 60−47=13. For each incorrect answer, 2 marks are deducted, totaling 13×2=26 marks. Subtracting the deducted marks from the earned marks, Archana's total marks are
141−26=115. So, she got 115 marks.
Explanation:
Let's denote the fourth number as x. Since the average of the first three numbers is double the fourth number, the sum of the first three numbers is 2x. Since the average of all four numbers is 7, the sum of all four numbers is 7×4=28. Thus, we have the equation 2x+x=28, which simplifies to 3x=28. Solving for x, we get
x=28/3=9.333. Rounding to the nearest whole number, the fourth number is indeed 4.
