Y = 2x^2-12x+25 write in vertex form plz show work
1 answer:
The vertex form of y = 2x² - 12x + 25 is y = 2(x - 3)² + 7
Step-by-step explanation:
The vertex form of the quadratic equation y = ax² + bx + c is
y = a(x - h)² + k, where
- (h , k) are the coordinates of the vertex point
- a, b, c are constant where a is the leading coefficient of the function (coefficient of x²) , b is the coefficient of x and c is the y-intercept
- k is the value of y when x = h
∵ y = 2x² - 12x + 25
∵ y = ax² + bx + c
∴ a = 2 , b = -12 , c = 25
∵
∴
∴
∴ h = 3
To find k substitute y by k and x by 3 in the equation above
∵ k is the value of y when x = h
∵ h = 3
∴ k = 2(3)² - 12(3) + 25 = 7
∵ The vertex form of the quadratic equation is y = a(x - h)² + k
∵ a = 2 , h = 3 , k = 7
∴ y = (2)(x - 3)² + 7
∴ y = 2(x - 3)² + 7
The vertex form of y = 2x² - 12x + 25 is y = 2(x - 3)² + 7
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Percent of red lights last between 2.5 and 3.5 minutes is 95.44% .
<u>Step-by-step explanation:</u>
Step 1: Sketch the curve.
The probability that 2.5<X<3.5 is equal to the blue area under the curve.
Step 2:
Since μ=3 and σ=0.25 we have:
P ( 2.5 < X < 3.5 ) =P ( 2.5−3 < X−μ < 3.5−3 )
⇒ P ( (2.5−3)/0.25 < (X−μ)/σ < (3.5−3)/0.25)
Since, Z = (x−μ)/σ , (2.5−3)/0.25 = −2 and (3.5−3)/0.25 = 2 we have:
P ( 2.5<X<3.5 )=P ( −2<Z<2 )
Step 3: Use the standard normal table to conclude that:
P ( −2<Z<2 )=0.9544
Percent of red lights last between 2.5 and 3.5 minutes is % .
Answer:
(a) <em> </em><em>n</em> : 20 50 100 500
P (-200 < <em>X</em> - <em>μ </em>< 200) : 0.2886 0.4444 0.5954 0.9376
(b) The correct option is (b).
Step-by-step explanation:
Let the random variable <em>X</em> represent the amount of deductions for taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return.
The mean amount of deductions is, <em>μ</em> = $16,642 and standard deviation is, <em>σ</em> = $2,400.
Assuming that the random variable <em>X </em>follows a normal distribution.
(a)
Compute the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $200 of the population mean as follows:
- For a sample size of <em>n</em> = 20
- For a sample size of <em>n</em> = 50
- For a sample size of <em>n</em> = 100
- For a sample size of <em>n</em> = 500
<em> n</em> : 20 50 100 500
P (-200 < <em>X</em> - <em>μ </em>< 200) : 0.2886 0.4444 0.5954 0.9376
(b)
The law of large numbers, in probability concept, states that as we increase the sample size, the mean of the sample () approaches the whole population mean (
).
Consider the probabilities computed in part (a).
As the sample size increases from 20 to 500 the probability that the sample mean is within $200 of the population mean gets closer to 1.
So, a larger sample increases the probability that the sample mean will be within a specified distance of the population mean.
Thus, the correct option is (b).