Normally, when 
the function
takes on a value of
so the graph of 
passes through the point (3, 3). This is the only place at which the cubic takes on a value of 3, since is one-to-one.
In the definition of 
, however, we remove this point from the curve and replace with the point (3, -2).
While is a standard cubic function, so that its range is all real numbers, the replacement made for removes 3 from the range set, so that the range of would be all real numbers *except* 3.
Answer:
5 ; 2.07 ; 1.85
Step-by-step explanation:
Given the data:
2, 3, 5, 6, 7
The range : ( highest - lowest)
The range = (7 - 2) = 5
Sample standard deviation :
sqrt[Σ(x - m)²/ (n - 1)]
The mean (m) = Σx / n
n = sample size = 5
Σx / n ;
(2+3+5+6+7) / 5
= 23 / 5
= 4.6
[(2-4.6)^2 + (3-4.6)^2 +(5-4.6)^2 + (6-4.6)^2+ (7-4.6)^2] / (5 - 1)
= 17.2 / 4
= 4.3
Sqrt(4.3) = 2.07
Population standard deviation :
sqrt[Σ(x - m)²/ n]
The mean = m = 4.6
n = sample size = 5
[(2-4.6)^2 + (3-4.6)^2 +(5-4.6)^2 + (6-4.6)^2+ (7-4.6)^2] / 5
= sqrt(17.2 / 5)
= sqrt(3.44)
= 1.8547 = 1.85
Answer:
22 ft/s
Step-by-step explanation:
15 mph is 1/4 of 60 mph. At 1/4 the speed, the car will travel 1/4 as far in a second.
1/4×(88 ft/s) = 22 ft/s
The equation that can be used to find the coldest temperature recorded in Siberia is y + 10 = -80
Let the coldest temperature in Alaska be x
The coldest temperature recorded in Alaska was –80°F
x = –80°F
Let the coldest temperature in Siberia be y
The coldest temperature recorded in Alaska was 10°F warmer than the coldest temperature recorded in Siberia
This can be interpreted as:
Coldest temperature in Alaska = Coldest temperature in Siberia + 10
x = y + 10................(*)
Since x = -80
Substitute x = -80 into equation (*)
-80 = y + 10
This can be re-written as:
y + 10 = -80
The equation that can be used to find the coldest temperature recorded in Siberia is y + 10 = -80
Learn more here: brainly.com/question/2159099
Answer:
x² - 16xy + 64y²
Step-by-step explanation:
The difference of x and 8y is x - 8y
The square of the difference is (x - 8y)² = (x - 8y)(x - 8y)
Expand by multiplying each term in the second factor by each term in the first factor, that is
x(x - 8y) - 8y(x - 8y) ← distribute both parenthesis
= x² - 8xy - 8xy + 64y² ← collect like terms
= x² - 16xy + 64y²
