Answer:
<2 = 75
<1 = 105
Step-by-step explanation:
<2 and 75 are alternate interior angles and since the lines are parallel, they are equal
<2 = 75
<2 + <1 = 180 since the angles form a line
75+ <1 = 180
Subtract 75 from each side
<1 = 180-75
<1 = 105
Answer:
e) The mean of the sampling distribution of sample mean is always the same as that of X, the distribution from which the sample is taken.
Step-by-step explanation:
The central limit theorem states that
"Given a population with a finite mean μ and a finite non-zero variance σ2, the sampling distribution of the mean approaches a normal distribution with a mean of μ and a variance of σ2/N as N, the sample size, increases."
This means that as the sample size increases, the sample mean of the sampling distribution of means approaches the population mean. This does not state that the sample mean will always be the same as the population mean.
Part A: Explain why the x-coordinates of the points where the graphs of
the equations y = 4-x and y = 2x + 3 intersect are the solutions of the
equation
4-x = 2x + 3.
Because the point where the graphs intersect is a point that meets both rules (functions) y = 4 - x and y = 2x + 3 meaning that y from y = 4 - x equals y from 2x + 3 and also both x have the same value.
Part B: Make tables to find the solution to 4-x = 2x + 3. Take the integer values of x between -3 and 3.
x values 4 -x 2x + 3
-3 4-(-3)=7 2(-3)+3 =-3
-2 4-(-2)=6 2(-2)+3 =-1
-1 4-(-1)=5 2(-1)+3 = 1
0 4-0=4 2(0)+3 = 3
1 4-1=3 2(1)+3=5
2 4-2=2 2(2)+3 = 7
3 4-3=1 2(3)+3 = 9
The the solution is between x = 0 and x =1
Part C: How can you solve the equation 4-x = 2x + 3 graphically?
Draw in a same graph both functions y= 4 - x and y = 2x +3.
Then read the x-coordinates of the intersection point. That is the solution.
