Answer:
A.) gf(x) = 3x^2 + 12x + 9
B.) g'(x) = 2
Step-by-step explanation:
A.) The two given functions are:
f(x) = (x + 2)^2 and g(x) = 3(x - 1)
Open the bracket of the two functions
f(x) = (x + 2)^2
f(x) = x^2 + 2x + 2x + 4
f(x) = x^2 + 4x + 4
and
g(x) = 3(x - 1)
g(x) = 3x - 3
To find gf(x), substitute f(x) for x in g(x)
gf(x) = 3( x^2 + 4x + 4 ) - 3
gf(x) = 3x^2 + 12x + 12 - 3
gf(x) = 3x^2 + 12x + 9
Where
a = 3, b = 12, c = 9
B.) To find g '(12), you must first find the inverse function of g(x) that is g'(x)
To find g'(x), let g(x) be equal to y. Then, interchange y and x for each other and make y the subject of formula
Y = 3x + 3
X = 3y + 3
Make y the subject of formula
3y = x - 3
Y = x/3 - 3/3
Y = x/3 - 1
Therefore, g'(x) = x/3 - 1
For g'(12), substitute 12 for x in g' (x)
g'(x) = 12/4 - 1
g'(x) = 3 - 1
g'(x) = 2.
8 + 7 = 15, so 6 + 9 = 15
Angle B equals angle D
angle A equals angle C
so △ABE =△CDE
i think thats the answer
Answer:
6.25 mins (6 minutes 15 seconds)
Step-by-step explanation:
96 tests = 2mins
300 tests = x mins
X = 2/96 x 300
X = 6.25 mins
Answer:
a) 96% CI: 
b) If we estimate that the fraction of voters is 0.57, we can claim with 96% confidence that the error is equal or less than 0.06 from the estimated proportion.
Step-by-step explanation:
The proportion of the sample is
The standard deviation of the sample proportion is
For a 96% CI, the z-value is z=1.751.
Then, the 96% CI can be written as:
b) If we estimate that the fraction of voters is 0.57, we can claim with 96% confidence that the error is equal or less than 0.06 from the estimated proportion.
