let's recall that the graph of a function passes the "vertical line test", however, that's not guarantee that its inverse will also be a function.
A function that has an inverse expression that is also a function, must be a one-to-one function, and thus it must not only pass the vertical line test, but also the horizontal line test.
Check the picture below, the left-side shows the function looping through up and down, it passes the vertical line test, in green, but it doesn't pass the horizontal line test.
now, check the picture on the right-side, if we just restrict its domain to be squeezed to only between [0 , π], it passes the horizontal line test, and thus with that constraint in place, it's a one-to-one function and thus its inverse is also a function, with that constraint in place, or namely with that constraint, cos(x) and cos⁻¹(x) are both functions.
Answer:
Triangles ABE and CDE are congruent by AAS.
Step-by-step explanation:
AB ≅ DC (Opposite sides of a parallelogram are congruent.
m < AEB = m < DEC (Vertical angles).
m < ABE = m < EDC ( Alternate Interior angles).
So triangles ABE and CDE are congruent by AAS.
Answer:
The standard error of the mean is 0.85.
Step-by-step explanation:
The given standard deviation of a population (σ) = 7.8
sample size (N) = 85
We have to find standard error of the mean.
The formula to find standard error of the mean
= (standard deviation of the distribution) / (square root of sample size)
= (σ) / (√N)
= 7.8 / (√85)
= 7.8 / 9.219544457
= 0.8460
= 0.85 (approximately taken to two decimal places)
We have got the required answer.
The standard error of the mean is 0.85.
28 times 1/7 would give you 4
The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept of this line is the value of y at the point where the line crosses the y axis.
