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Furkat [3]
3 years ago
8

A shipping container holds 20 soft drink boxes. The dimensions of a soda box are 15 inches by 4 inches by 5 inches. What is the

minimum size the shipping container could be?
Mathematics
1 answer:
patriot [66]3 years ago
7 0

Answer:

6000 in³

Step-by-step explanation:

To solve this problem, we simply have to find the volume of the shipping container that will be just enough to contain the 20 soda boxes.

To do this, we find the volume of each soda box and multiply it by the total number of soda boxes held by the shipping container.

Volume of the box = L * B * H

L = length = 15 in

B = breadth = 4 in

H = height = 5 in

V = 15 * 4 * 5 = 300 in³

This is the volume of each soda box.

The volume of 20 soda boxes will then be:

V = 20 * 300 = 6000 in³

This is the volume of 20 soda boxes and hence, the minimum size the shipping container can be.

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Geometry
VMariaS [17]

A point P on the line segment GK may be parametrically represented as

P = (1-t)G + tK

t is a real parameter which controls where on the segment P is.  t=0 means P=G, t=1 means P=K.  We're interested in the t that gives a 3:2 ratio for PG:PK.  That's closer to K so t>1/2.   t=3/(3+2) = 3/5.

P=(1-3/5)(1,2) + (3/5)(8,12) = (2/5,4/5)+(24/5,36/5)=(26/5,40/5)=(26/5,8)

Answer: (26/5, 8)


3 0
3 years ago
Read 2 more answers
6. Tasha walked 6,618 feet. What is the distance she walked in yards?
juin [17]

The answer is 2206.

Step-by-step explanation:

3 feet = 1 yard

so you divide 6618 by 3 to get 2206

6 0
2 years ago
4- A manufacturing process produces items whose weights are normally distributed. It is known that 22.57% of all the items produ
galben [10]

Answer:

\\ \mu = 118\;grams\;and\;\sigma=30\;grams

Step-by-step explanation:

We need to use z-scores and a standard normal table to find the values that corresponds to the probabilities given, and then to solve a system of equations to find \\ \mu\;and\;\sigma.

<h3>First Case: items from 100 grams to the mean</h3>

For finding probabilities that corresponds to z-scores, we are going to use here a <u>Standard Normal Table </u><u><em>for cumulative probabilities from the mean </em></u><em>(Standard normal table. Cumulative from the mean (0 to Z), 2020, in Wikipedia) </em>that is, the "probability that a statistic is between 0 (the mean) and Z".

A value of a z-score for the probability P(100<x<mean) = 22.57% = 0.2257 corresponds to a value of z-score = 0.6, that is, the value is 0.6 standard deviations from the mean. Since this value is <em>below the mean</em> ("the items produced weigh between 100 grams up to the mean"), then the z-score is negative.

Then

\\ z = -0.6\;and\;z = \frac{x-\mu}{\sigma}

\\ -0.6 = \frac{100-\mu}{\sigma} (1)

<h3>Second Case: items from the mean up to 190 grams</h3>

We can apply the same procedure as before. A value of a z-score for the probability P(mean<x<190) = 49.18% = 0.4918 corresponds to a value of z-score = 2.4, which is positive since it is after the mean.

Then

\\ z =2.4\;and\; z = \frac{x-\mu}{\sigma}

\\ 2.4 = \frac{190-\mu}{\sigma} (2)

<h3>Solving a system of equations for values of the mean and standard deviation</h3>

Having equations (1) and (2), we can form a system of two equations and two unknowns values:

\\ -0.6 = \frac{100-\mu}{\sigma} (1)

\\ 2.4 = \frac{190-\mu}{\sigma} (2)

Rearranging these two equations:

\\ -0.6*\sigma = 100-\mu (1)

\\ 2.4*\sigma = 190-\mu (2)

To solve this system of equations, we can multiply (1) by -1, and them sum the two resulting equation:

\\ 0.6*\sigma = -100+\mu (1)

\\ 2.4*\sigma = 190-\mu (2)

Summing both equations, we obtain the following equation:

\\ 3.0*\sigma = 90

Then

\\ \sigma = \frac{90}{3.0} = 30

To find the value of the mean, we need to substitute the value obtained for the standard deviation in equation (2):

\\ 2.4*30 = 190-\mu (2)

\\ 2.4*30 - 190 = -\mu

\\ -2.4*30 + 190 = \mu

\\ \mu = 118

7 0
2 years ago
Find the length of the arc.
Bezzdna [24]

Answer:

18.84 ft

Step-by-step explanation:

¼×2×3.14×12 = 18.84 ft

5 0
2 years ago
Read 2 more answers
Find mPMA + mCMT. Please help..
juin [17]

PMA = 37

CMT =  101 - 54 =47

Total = 37 + 47 = 84

Answer: A. 84

8 0
2 years ago
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