The location of the vertex tells you the horizontal and vertical shift. (The parent function f(x) = x² has its vertex at the origin, (0, 0). The vertical distance of the point 1 unit left or right of the vertex in relation to the vertex tells you the vertical scale factor (stretch).
g(x) = f(x +3) -3
horizontal shift left 3
vertical shift down 3
h(x) = -3f(x)
reflection across the x-axis
vertical stretch of 3
d(x) = f(x -3) -3
horizontal shift right 3
vertical shift down 3
Answer:
0
Step-by-step explanation:
We can find the slope by using
m = (y2-y1)/(x2-x1)
= (10-10)/(1-4)
= 0/-3
=0
Answer:
a) Null and alternative hypothesis:

b) A Type I error is made when a true null hypothesis is rejected. In this case, it would mean a conclusion that the proportion is significantly bigger than 10%, when in fact it is not.
c) The consequences would be that they would be more optimistic than they should about the result of the investment, expecting a proportion of students that is bigger than the true population proportion.
d) A Type II error is made when a false null hypothesis is failed to be rejected. This would mean that, although the proportion is significantly bigger than 10%, there is no enough evidence and it is concluded erroneously that the proportion is not significantly bigger than 10%
e) The consequences would be that the investment may not be made, even when the results would have been more positive than expected from the conclusion of the hypothesis test.
Step-by-step explanation:
a) The hypothesis should be carried to test if the proportion of students that would eat there at least once a week is significantly higher than 10%.
Then, the alternative or spectulative hypothesis will state this claim: that the population proportion is significantly bigger than 10%.
On the contrary, the null hypothesis will state that this proportion is not significantly higher than 10%.
This can be written as:

Use the distributive property.
9/10 (x + 8) = 18
9/10x + 7.2 = 18
9/10x + 7.2 - 7.2 = 18 - 7.2
9/10x = 10.8
9/10x / 9/10 = 10.8 / 9/10
x = 12