(x - 12)(x + 4) = 9
x² + 4x - 12x - 48 = 9
x² - 8x - 48 = 9 |add 48 to both sides
x² - 8x = 57
x² - 2x · 4 = 57 |add 4² to both sides
x² - 2x · 4 + 4² = 57 + 4² |use (a - b)² = a² - 2ab + b²
(x - 4)² = 57 + 16
(x - 4)² = 73 ⇔ x - 4 = √73 or x - 4 = -√73 |add 4 to both sides
x = 4 + √73 or x = 4 - √73
Step-by-step explanation:
circumference of a circle
U = 2 x pi x r
what you know:
U = 13
rearrange and solve for r
U/(2 x pi) = r
Answer:
A liter is 1000 mL so half of 1000 = 500
500 mL is the answer!Step-by-step explanation:
The answer is: g= 6y+8-9/y
Answer:
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
Where and
Since the distribution for X is normal then the we know that the distribution for the sample mean is given by:
And the standard error is given by:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
Where and
Since the distribution for X is normal then the we know that the distribution for the sample mean is given by:
And the standard error is given by: