A student has a container with a volume of 2.5 estimates the volume to be 2.6 By what percent is the student's estimate off
2 answers:
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The two temperatures could be removed so that the average of the remaining numbers is the same as the average of the original set of numbers are -1 and -9
Step-by-step explanation:
The formula of the average of a set of data is , where
- S is the sum of the data in the set
- N is the number of the data in the set
∵ The low temperatures in Anchorage, Alaska, for a week were
− 6, − 3, − 1, 1, − 3, − 9, and − 14 degrees Celsius
∴ The set of the data is { -6 , -3 , -1 , 1 , -3 , -9 , -14}
- Add the data in the set
∵ S = -6 + -3 + -1 + 1 + -3 + -9 + -14
∴ S = -35
∵ The set has 7 data
∴ N = 7
- Use the formula of the average above to find it
∴
∴ A = -5
∴ The average of the original set of numbers is -5
To keep the average the same after removing two numbers multiply the average by the new number of data to find the new sum
∵ The number of data after removing two numbers is 5
∴ N = 5
∵ A = -5
- By using the rule of average
∴
- Multiply both sides by 5
∴ -25 = S
∴ The new sum is -25
- Lets find which two numbers of have a sum of -10 because
the difference between -35 and -25 is -10
∵ -1 + -9 = -10
∵ -6 + -3 + 1 + -3 + -14 = -25
∴ We could removed -1 and -9
The two temperatures could be removed so that the average of the remaining numbers is the same as the average of the original set of numbers are -1 and -9
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Answer:
31
Step-by-step explanation:
Given
x² + 5x - 3 = 0
with a = 1, b = 5, c= - 3 , then
sum of roots x₁ + x₂ = - = -
= - 5
product of roots = =
= - 3
Now
(x₁ + x₂)² = x₁² + 2x₁x₂ + x₂² , that is
(- 5)² = x₁² + 2(- 3) + x₂²
25 = x₁² - 6 + x₂² ( add 6 to both sides ), then
x₁² + x₂² = 31