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3 years ago

Help and explain

Mathematics

1 answer:

krok68 [10]3 years ago

5 0

Answer:

The surface area of the composite figure is 1108 square inches.

Step-by-step explanation:

The surface area of the composite figure ( $A_{T}$ ) is equal to the sum of external faces of the rectangular and triangular prisms, all measured in square inches:

$A_{T} = 20\,in \times 12\,in + 2\times 5\,in \times 12\,in + 2\times 20\,in \times 5\,in + 2\times 20\,in \times 11\,in + 2\times \frac{1}{2}\times 12\,in \times 9\,in$

$A_{T} = 1108\,in^{2}$

The surface area of the composite figure is 1108 square inches.

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A company makes paper labels for paint cans. As shown below, each can is in the shape of a cylinder

sineoko [7]

The company needs 41 labels on average, each minute.

<h3>What is the circumference of a circle?</h3>

The perimeter of a circle (circumference): 2 π radius

Replacing with the values given:

C = 2 (3.14) 2 = 12.56 cm

So, the area of one label is:

Area of a rectangle: length x width = 12.56 x 7 = 87.92 cm sq.

Now, the number of label be n

87.92 x n = 3612.64 cm2

n = 3612.64 / 87.92

n = 41.09

Hence, The company needs 41 labels on average, each minute.

Learn more about circumference;

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6 0

2 years ago

A survey was conducted that asked 1003 people how many books they had read in the past year. Results indicated that x overbar eq

Sergio [31]

Answer:

The 99% confidence interval would be given (11.448;14.152).

Step-by-step explanation:

1) Important concepts and notation

A confidence interval for a mean "gives us a range of plausible values for the population mean. If a confidence interval does not include a particular value, we can say that it is not likely that the particular value is the true population mean"

$s=16.6$ represent the sample deviation

$\bar X=12.8$ represent the sample mean

n =1003 is the sample size selected

Confidence =99% or 0.99

$\alpha=1-0.99=0.01$ represent the significance level.

2) Solution to the problem

The confidence interval for the mean would be given by this formula

$\bar X \pm z_{\alpha/2} \frac{s}{\sqrt{n}}$

We can use a z quantile instead of t since the sample size is large enough.

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.