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topjm [15]
3 years ago
6

Plot a rectangle with vertices (–1, –4), (–1, 6), (3, 6), and (3, –4).

Mathematics
2 answers:
11111nata11111 [884]3 years ago
5 0

Answer: 4 units.

Step-by-step explanation:

Once each point is plotted, you get the rectangle attached.

You can observe in the figure that the base of the rectangle is its longer side.

 Since the length of the base of the rectangle goes from x=-1 to x=3, you can say that the lenght of the base is the difference between 3 and -1.

So, you need to subtract this two coordinates, getting that the lenght of the base of the rectangle attached is:

lenght_{(base)}=3-(-1)\\\\lenght_{(base)}=3+1\\\\lenght_{(base)}=4\ units

aliina [53]3 years ago
4 0

Answer: 4 units

Step-by-step explanation:

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The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first deter
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Answer:

He must survey 123 adults.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the z-score that has a p-value of 1 - \frac{\alpha}{2}.

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

Assume that a recent survey suggests that about 87​% of adults have heard of the brand.

This means that \pi = 0.87

90% confidence level

So \alpha = 0.1, z is the value of Z that has a p-value of 1 - \frac{0.1}{2} = 0.95, so Z = 1.645.

How many adults must he survey in order to be 90​% confident that his estimate is within five percentage points of the true population​ percentage?

This is n for which M = 0.05. So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.05 = 1.645\sqrt{\frac{0.87*0.13}{n}}

0.05\sqrt{n} = 1.645\sqrt{0.87*0.13}

\sqrt{n} = \frac{1.645\sqrt{0.87*0.13}}{0.05}

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Rounding up:

He must survey 123 adults.

6 0
3 years ago
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