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melisa1 [442]
3 years ago
5

A banner is hung for a party. The

Mathematics
1 answer:
rewona [7]3 years ago
3 0

Answer:

  • 8.5 feet

Explanation:

The function that can determine the distance from a point on the bottom edge of the banner to the floor is:

f(x)=0.25x^2-x+9.5

That function is a quadratic function which means that it is a parabola. Given that the coefficient of the quadratic term (0.25) is positive, the parabola open upwards, and the vertex is the lowest point of the parabola and it represents how high above the floor is the lowest point on the bottom edge of the banner.

So, you need to find the vertex of the parabola.

I will complete squares to find the form A(x -h)² + k, where h and k are the coordinates of the vertex (h, k).

f(x)=0.25x^2-x+9.5\\ \\ 4(f(x))=4(0.25x^2-x+9.5)\\ \\ 4f(x)=x^2-4x+38\\ \\ 4f(x)-38=x^2-4x\\ \\ 4f(x)-38+4=x^2-4x+4\\ \\ 4f(x)-34=(x-2)^2\\ \\ 4f(x)=(x-2)^2+34\\ \\ f(x)=(1/4)(x-2)^2+8.5

Hence, the vertex (h,k) is (2, 8.5), meaning that the lowest point on the bottom edge of the banner is at 2 feet from the left edge of the banner and 8.5 feet above the floor.

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1455

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0.03% x 1500 = 45

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Before changes to its management staff, an automobile assembly line operation had a scheduled mean completion time of minutes. T
Sergio [31]

No, we don't have evidence to support that the mean completion time under new management has decreased but we can conclude that it remains at 15.5 minutes.

Given mean of 15.5 minutes , standard deviation of 1.7 minutes, sample size of 90 and sample mean of 15.4 minutes.

We can do the following study for conclusion:

Firstly the null hypothesis is

H_{0}: x=15.5

The alternate hypothesis is

H_{1}: x < 15.5

since the value is less than this is a one tailed test.

Z=x bar-x/d/\sqrt{n}

where x is sample mean and d is standard deviation.

Z=15.4-15.5/1.7/\sqrt{90}

=-0.1/1.7/9.4868

=-0.560

Critical value of Z at 0.1 level of significance

Z=-1.28

We fails to reject the null hypothesis since -0.560>-1,28

Hence we don't have evidence to support that the mean completion time under new management has decreased but we can conclude that it remains at 15.5 minutes.

Learn more about hypothesis at brainly.com/question/11555274

#SPJ4

Question is incomplete. It should include:

mean of 15.5 minutes ,

standard deviation of 1.7 minutes,

sample size of 90

and sample mean of 15.4 minutes.

5 0
1 year ago
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