Answer:
the probability that the sample mean will be larger than 1224 is 0.0082
Step-by-step explanation:
Given that:
The SAT scores have an average of 1200
with a standard deviation of 60
also; a sample of 36 scores is selected
The objective is to determine the probability that the sample mean will be larger than 1224
Assuming X to be the random variable that represents the SAT score of each student.
This implies that ;
the probability that the sample mean will be larger than 1224 will now be:
From Excel Table ; Using the formula (=NORMDIST(2.4))
P(\overline X > 1224) = 1 - 0.9918
P(\overline X > 1224) = 0.0082
Hence; the probability that the sample mean will be larger than 1224 is 0.0082
The markup is 8%, meaning it costs 8% more.
The starting price is 100%.
Therefore, the markup is 108% of $12.
If we multiply 12 by 108% (1.08), we will get our answer of $12.96
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
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* 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.
x + 1/2 = 3/4
set denominators equal:
x + 2/4 = 3/4
-2/4 for both sides:
x = 1/4
there you go! hope this helps!
