You want to save for a brand-new car. You put the $5,000 your Grandma gave you when you graduated in an account that pays 6% int
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Answer:
{y | y ≥ -11 }
Step-by-step explanation:
To answer a question like this, it is often helpful to graph the function or to rewrite it to vertex form.
f(x) = 3x^2 +6x -8
f(x) = 3(x^2 +2x) -8 . . . . factor the leading coefficient from x terms
f(x) = 3(x^2 +2x +1) -8 -3(1) . . . . complete the square*
f(x) = 3(x +1)^2 -11
The form of this equation tells you that the graph is a parabola that opens upward. Its vertex is (-1, -11), so the minimum value is -11. The range is the vertical extent of the function values, so goes upward from -11:
y ≥ -11
_____
* Vertex form is ...
f(x) = a(x -h)^2 +k
where "a" is the vertical scale factor and (h, k) is the vertex. When "a" is positive, the parabola opens upward; when it is negative, the parabola opens downward.
The square is completed by adding the square of half the x-coefficient inside parentheses, and subtracting the equivalent amount outside parentheses. Here, we had 2x inside parentheses, so we added (2/2)^2 = 1 inside and -3(1) outside, because "a" was 3.
_____
Brainly provides tools for properly rendering math symbols. 2-11 is not the same as ≥-11.
Answer:
C.I = 0.7608 ≤ p ≤ 0.8392
Step-by-step explanation:
Given that:
Let consider a random sample n = 400 candidates where 320 residents indicated that they voted for Obama
probability
= 0.8
Level of significance ∝ = 100 -95%
= 5%
= 0.05
The objective is to develop a 95% confidence interval estimate for the proportion of all Boston residents who voted for Obama.
The confidence internal can be computed as:
where;
=
= 1.960
SO;
= 0.8 - 0.0392 OR 0.8 + 0.0392
= 0.7608 OR 0.8392
Thus; C.I = 0.7608 ≤ p ≤ 0.8392
Answer:
A. (–8, 2)
Step-by-step explanation:
(1) y = ½x + 6
(2) y = -¾x – 4 Set (1) = (2)
½x + 6 = -¾x – 4 Multiply each side by 4
2x + 24 = -3x – 16 Add 16 to each side
2x + 40 = -3x Subtract 2x from each side
40 = -5x Divide each side by -5
(3) x = -8 Substitute (2) into (1)
y = ½(-8) +6
= -4 + 6
= 2
The solution to the system of equations is (-8 ,2).
You can see the graphs of the two functions in the figure below. The two lines intersect at (-8, 2).
Check:
2 = ½(-8) + 6 2 = -¾(-8) - 4
2 = -4 +6 2 = 6 - 4
2 = 2 2 = 2
