As is the case for any polynomial, the domain of this one is (-infinity, +infinity).
To find the range, we need to determine the minimum value that f(x) can have. The coefficients here are a=2, b=6 and c = 2,
The x-coordinate of the vertex is x = -b/(2a), which here is x = -6/4 = -3/2.
Evaluate the function at x = 3/2 to find the y-coordinate of the vertex, which is also the smallest value the function can take on. That happens to be y = -5/2, so the range is [-5/2, infinity).
1) Proportion a.
7 : 28 = 2 : 8
That means that the ratio 7 / 28 is equal to the ratio 2 : 8.
You can verify the equality by simplifying to the simplest form:
7 : 28 = 1 / 4 simplest form
2 : 8 = 1 / 4 simplest form, then the proportion is right.
In words that is 7 is to 28 as 1 is to 4 ← answer
2) Proportion b.<span>. 3⁄1 = 18⁄6
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</span><span>In words: 3 is to q as 18 is to 6 ← answer
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</span><span>You can verify the proportion by simplifiying the second fraction:
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</span><span> 18 / 6 = [18 / 6] / [ 6 / 6] = 3 / 1
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</span><span>3) Proportion c. 9 : 72 = 2 : 16
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</span><span>In words: 9 is to 72 as 2 is to 16 ← answer
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</span><span>Proove the proportion:
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</span><span> 9 / 72 = 1 / 8
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</span><span> 2 / 16 = 1 / 8
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</span><span>4) Proportion d. 81⁄9 = 45⁄5</span>
In words: 81 is to 9 as 45 is to 5 ← answer
Proove it:
81 / 9 = 9
45 / 9 = 9
Considering the Central Limit Theorem, we have that:
a) The probability cannot be calculated, as the underlying distribution is not normal and the sample size is less than 30.
b) The probability can be calculated, as the sample size is greater than 30.
<h3>What does the Central Limit Theorem state?</h3>
It states that the sampling distribution of sample means of size n is approximately normal has standard deviation 
, as long as the underlying distribution is normal or the sample size is greater than 30.
In this problem, the underlying distribution is skewed right, that is, not normal, hence:
- For item a, the probability cannot be calculated, as the underlying distribution is not normal and the sample size is less than 30.
- For item b, the probability can be calculated, as the sample size is greater than 30.
More can be learned about the Central Limit Theorem at brainly.com/question/16695444
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Answer:
Step-by-step explanation:
hello :
Part A : x+6y =6 means : 6y = - x+6
so : y = (-1/6)x+1 an equation for the line (D)
y = (1/3)x -2 is the line (D')
PartB : solution of the system : y = (-1/6)x+1 ....(1) color red
y = (1/3)x -2 ....(2) color bleu
is the intersection point : (6 ; 0)
PartC : Algebraically by (1) and (2) : (-1/6)x+1 = (1/3)x -2
(-1/6)x - (1/3)x = -2-1
(-x-2x)/6= -3
-3x = -18
so : x = 6 put this value in (1) or (2) : y = (-1/6)(6)+1 =0 the solution is : (6 ;0)
<u>Answer</u>
12 units
<u>Explanation</u>
This can be solved using the properties of a circle.
DG and EG are secants f the circle.
DG×HG =EG×FG
(x+3+5)×5 = (x+6)×6
(x+8)5 = 6x + 36
5x +40 = 6x + 36
x = 4
DG = (x+3+5)
= 4 + 3 + 5
= 12 units
