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JulsSmile [24]
3 years ago
12

helPpppPPppPPPppppPppppPPppppppPPPPPPPPpppppppPPPPpppppppPPPPppppppPPPPppppppPPPPPpppppPPPPPPPPPPPPPPPPPPppppPPPPPPPppppPPPppppp

PPpp THANK YOU

Mathematics
1 answer:
Snezhnost [94]3 years ago
7 0

Answer:

1) rectangle

2) rectangle

Step-by-step explanation:

Any cross section of a rectangular prism is a rectangle.

<em>Hope it helps <3</em>

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If a dart board was thrown randomly at the dartboard shown below, what is the probability that it will land in the bull’s-eye? T
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Answer:

Correct option: C -> 2%

Step-by-step explanation:

To find this probability we just need to divide the area of the bull's-eye circle by the total area of the outer circle.

The area of a circle is given by the equation:

area = \pi * radius^2

The outer radius is 14 cm, so:

outer\ area = \pi * 14^2 = 196\pi\ cm^2

The inner radius is 2 cm, so:

inner\ area = \pi * 2^2 = 4\pi\ cm^2

So the probability is:

inner\ area / outer\ area = 4\pi / 196\pi = 0.02 = 2\%

Correct option: C

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Steps to simplifying fractions

Therefore, 9/9 simplified to lowest terms is 1/1.

Reduce 9/8 to lowest terms

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3 years ago
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A laboratory scale is known to have a standard deviation (sigma) or 0.001 g in repeated weighings. Scale readings in repeated we
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Answer:

99% confidence interval for the given specimen is [3.4125 , 3.4155].

Step-by-step explanation:

We are given that a laboratory scale is known to have a standard deviation (sigma) or 0.001 g in repeated weighing. Scale readings in repeated weighing are Normally distributed with mean equal to the true weight of the specimen.

Three weighing of a specimen on this scale give 3.412, 3.416, and 3.414 g.

Firstly, the pivotal quantity for 99% confidence interval for the true mean specimen is given by;

        P.Q. = \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } } ~ N(0,1)

where, \bar X = sample mean weighing of specimen = \frac{3.412+3.416+3.414}{3} = 3.414 g

            \sigma = population standard deviation = 0.001 g

            n = sample of specimen = 3

            \mu = population mean

<em>Here for constructing 99% confidence interval we have used z statistics because we know about population standard deviation (sigma).</em>

So, 99% confidence interval for the population​ mean, \mu is ;

P(-2.5758 < N(0,1) < 2.5758) = 0.99  {As the critical value of z at 0.5% level

                                                            of significance are -2.5758 & 2.5758}

P(-2.5758 < \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } } < 2.5758) = 0.99

P( -2.5758 \times {\frac{\sigma}{\sqrt{n} } } < {\bar X - \mu} < 2.5758 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.99

P( \bar X-2.5758 \times {\frac{\sigma}{\sqrt{n} } } < \mu < \bar X+2.5758 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.99

<u>99% confidence interval for</u> \mu = [ \bar X-2.5758 \times {\frac{\sigma}{\sqrt{n} } } , \bar X+2.5758 \times {\frac{\sigma}{\sqrt{n} } } ]

                                             = [ 3.414-2.5758 \times {\frac{0.001}{\sqrt{3} } } , 3.414+2.5758 \times {\frac{0.001}{\sqrt{3} } } ]

                                             = [3.4125 , 3.4155]

Therefore, 99% confidence interval for this specimen is [3.4125 , 3.4155].

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