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Tasya [4]
3 years ago
15

What is the vertex of the parabola

Mathematics
1 answer:
katovenus [111]3 years ago
6 0

Let's consider the equation of parabola, y = a·(x - α)·(x - β)

where α, β are the x-intercepts.

From the given graph, the y-intercept is (0, -3).

From the given graph, the x-intercept are (-1, 0) and (3, 0) i.e. α = -1, β = 3.

So the equation of parabola would be now, y = a·(x + 1)·(x - 3)

We can plug the y-intercept (0, -3) in the equation to find value of 'a'.

-3 = a·(0+1)·(0-3)

-3 = -3a

a = 1

So the equation of parabola would be now, y = (x + 1)·(x - 3) = x² - 2x - 3

Comparing it with y = ax² + bx + c

The x-coordinate of vertex would be, x = \frac{-b}{2a} = \frac{-(-2)}{2(1)} =\frac{2}{2} = 1

the y-coordinate of vertex would be, y = (1)² - 2(1) - 3 = -4.

Hence, vertex would be (1, -4).

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The life times of light bulbs produced by a particular manufacturer have a mean of 1,200 hours and a standard deviation of 400 h
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Answer:

a. 1200hours

b.  σ² = 400² =160000hour

c. standard error = 133.33

d. for 9 lightbulb it is likely that 9*0.146 = 1.31 bulbs will have lives of fewer than 1,050 hours?

Step-by-step explanation:

mean of 1,200 hours

σ, a standard deviation of 400 hours.

Sample size, N =  nine bulbs,

a) mean of the sample mean lifetime: is given as 1,200 hours

b) variance of the sample mean is the square of the  σ, a standard deviation of 400 hours.

σ² = 400² =160000hours

c) What is the standard error of the sample mean?

The standard deviation of a sampling distribution of mean values is called the standard error of the means,

standard error of the means,  σx = σ √N

The formula for the standard error of the means is true for all values infinite number of sample, N.

σx = σ √N

     =400  √9 = 400/3 =133.3333

d) the probability that, on average, those nine lightbulbs have lives of fewer than 1,050 hours

The area under part of a normal probability curve is  directly proportional to probability and the value is calculated as

z = ( x₁−x) /σ

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x₁ = variate mean = 1050hours

x = mean of 1200hours

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applying the formula,

z= (1050-1200)/400

z = 150/400 =0.375

Using a table of partial areas beneath the standardized normal curve (see Table of normal curve, a z-value of 0.375 corresponds to an area of 0.1460 between the mean value.

Thus the probability of a lightbulbs having lives of fewer than 1,050 hours is 0.1460.

for 9 lightbulb it is likely that 9*0.146 i.e. 1.31 bulbs will have lives of fewer than 1,050 hours?  

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Answer:

they are both 0 since they would not appear on a graph

Step-by-step explanation:

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