Find the first 4 term and the 10th term of 2n-1
1 answer:
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Answer:
The mean value of the chemical to be added to every bottle of syrup so that the bottle wont be rejected would be = 1.41750 ml
Step-by-step explanation:
Standard deviation ( σ )= 0.250 ml
assume the required amount of chemical to be deposited in each syrup bottle to be X
Hence the distribution of X in each bottle can be represented as :
X Г N ( u , 0.250 )
for a bottle not to be rejected : P ( X ≤ 2 )
To determine the setting so that no more than 1% of the bottles of cough syrup prepared by this machine will be rejected we have to standardize the variable X
at X = 2 ml
z = = z ----------- ( 1 )
probability for a bottle to be rejected : P( x >2 ) = 1 - P ( x ≤ 2 )
= 0.01
attached below is a normal distribution curve showing probability values
from the curve
p( 0 < Z < z ) = 0.5 - 0.01 = 0.49
Area = 0.49 hence from the Normal table where area = 0.49 the value of z = 2.33
Referring back to equation 1 above: z = = 2.33 --------- (2)
<em>u</em> = mean value that should be added so that the bottle will not be rejected
make <em>u</em> subject of the equation : u = 2 - ( 2.33 * 0.250 )
u = 1.41750
The mean value of the chemical to be added to every bottle of syrup so that the bottle wont be rejected would be = 1.41750 ml
- Put brackets around the first two terms on the right. y = (-4x^2 - 16x) - 14
- Pull out the common factor in the first two terms. y = -4(x^2 + 4x) - 14
- Divide the middle term by 2. Add that inside the brackets. square y = -4(x^2 +4x +(4/2)^2 - 14
- y = -4(x^2 + 4x + 4) - 14 + 16 This is the step where most people stumble. The point is why is 16 added? It is because what you have done inside the brackets is multiplied 4 by - 4 (on the left). That means you have changed the equation by -16. To counter that, you must add 16 after the - 14. The result is y= -4(x^2 + 4x+4) + 2
- Express the terms inside the brackets as a square. y = - 4(x + 2)^2 + 2
B and D are both wrong. B has +4 outside the brackets. It is - 4
D is wrong because there is no 4 of any kind outside the brackets.
A is incorrectly represented inside the brackets as 16. That's not right
That only leaves C. <<<< Answer
Graphs
Notice that the red parabola and the green one are the same thing.
Red: y = -4x^2 - 16x - 14
Green: y = -4(x + 2)^2 + 2
