Ok, so we see in
y=a(x-h)^2+k
vertex is (h,k)
vertex is highest or lowest point
on one side, it goes up and other side it goes down
if a is positive, then it goes down then up
if a is negative, it goes up then down
we see
f(x)=2(x+3)^2+2
2 is positive
goes down then up
vertex is (-3,2)
so decreases from -infinity to -3 or ininterval
(-infinity,-3)
answer is first option
Answer: 25 percent
Step-by-step explanation:
Part A:
f(x)=30(1.2)^x
f(x)=45+3x
Part B: Neighborhood A is 74.6496, so that rounds to 75 homes, and Neighborhood C is exactly 60 homes
Part C:
i would graph them in a graphing calculator, and use the functions to see where the 2 lines intersect.
The x value for when they intersect (# of years) is 3.3207883, so approx. 3.3 years for them to be equal
Answer:
(a) Shown below
(b) There is a positive relation between the number of assemblers and production.
(c) The correlation coefficient is 0.9272.
Step-by-step explanation:
Let <em>X</em> = number of assemblers and <em>Y</em> = number of units produced in an hour.
(a)
Consider the scatter plot below.
(b)
Based on the scatter plot it can be concluded that there is a positive relationship between the variables <em>X</em> and <em>Y</em>, i.e. as the value of <em>X</em> increases <em>Y</em> also increases.
(c)
The formula to compute the correlation coefficient is:
![r=\frac{n\sum XY-\sum X\sum Y}{\sqrt{[n\sum X^{2}-(\sum X)^{2}][n\sum Y^{2}-(\sum Y)^{2}]}} }](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Bn%5Csum%20XY-%5Csum%20X%5Csum%20Y%7D%7B%5Csqrt%7B%5Bn%5Csum%20X%5E%7B2%7D-%28%5Csum%20X%29%5E%7B2%7D%5D%5Bn%5Csum%20Y%5E%7B2%7D-%28%5Csum%20Y%29%5E%7B2%7D%5D%7D%7D%20%7D)
Compute the correlation coefficient between <em>X</em> and <em>Y</em> as follows:
![r=\frac{n\sum XY-\sum X\sum Y}{\sqrt{[n\sum X^{2}-(\sum X)^{2}][n\sum Y^{2}-(\sum Y)^{2}]}} }=\frac{(5\times430)-(15\times120)}{\sqrt{[(5\times55)-15^{2}][(5\times3450)-120^{2}]}} =0.9272](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Bn%5Csum%20XY-%5Csum%20X%5Csum%20Y%7D%7B%5Csqrt%7B%5Bn%5Csum%20X%5E%7B2%7D-%28%5Csum%20X%29%5E%7B2%7D%5D%5Bn%5Csum%20Y%5E%7B2%7D-%28%5Csum%20Y%29%5E%7B2%7D%5D%7D%7D%20%7D%3D%5Cfrac%7B%285%5Ctimes430%29-%2815%5Ctimes120%29%7D%7B%5Csqrt%7B%5B%285%5Ctimes55%29-15%5E%7B2%7D%5D%5B%285%5Ctimes3450%29-120%5E%7B2%7D%5D%7D%7D%20%3D0.9272)
Thus, the correlation coefficient is 0.9272.
Answer:
if two sides and the included angle of one triangle are congruent to two sides and the angle of another triangle, then these two triangles are congruent.
If two triangles share two pairs of corresponding congruent sides are congruent and their included angle is also congruent, then these two triangles are congruent.
If any two sides and angles included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, then the two triangles are said to be congruent by the SAS rule.
