A candy company is designing the packaging for its new candy bar. The bars will be packed in cartons which are 1 foot wide, 1 foot high, and 1 foot long. How many of these cartons can they pack into the shipping crate which is 5 ft long, 12 ft wide, and 4 ft high?show your work.

Answers

Answer 1

Answer:

Answer:

240 cartons

Step-by-step explanation:

If the bars will be packed in cartons which are 1 foot wide, 1 foot high, and 1 foot long, the volume of the carton will be expressed as shown;

Volume of carton = Length * Breadth * Height

Volume of carton = 1ft*1ft*1ft

= 1ft³

Given the dimension of shipping crate to be 5 ft long, 12 ft wide, and 4 ft high, the volume of the tank will be 5*12*4 = 240ft³

Number of cartons they pack into the shipping crate = Volume of the shipping crate/volume of one carton

Number of cartons they pack into the shipping crate = 240ft³/1ft³

= 240 cartons

Answer 2

Answer:

Answer:

number of cartons that can be packed in the shipping crate = 240 cartons

Step-by-step explanation:

The cartons are cube since the face all have the same dimension . The length = 1 ft, width = 1 ft and height = 1 ft.

The shipping crate is a rectangular prism or cuboid . The dimension is given as follows.

length = 5 ft

width = 12 ft

height = 4 ft

The number of the cartons that can be packed in the shipping crate can be calculated as follows.

volume of the cubed carton = L³

where

L = length

volume of the cubed carton = 1³ = 1 ft³

Volume of the shipping crate = LWH

where

L = length

W = width

H = height

Volume of the shipping crate = 5 × 12 × 4

Volume of the shipping crate = 240 ft³

number of cartons that can be packed in the shipping crate = 240/1 = 240 cartons

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The use of social networks has grown dramatically all over the world. In a recent sample of 24 American social network users and each was asked for the amount of time spent (in hours) social networking each day. The mean time spent was 3.19 hours with a standard deviation of 0.2903 hours. Find a 99% confidence interval for the true mean amount of time Americans spend social networking each day

Answers

Answer:

The 99% confidence interval for the true mean amount of time Americans spend social networking each day is (3.02 hours, 3.36 hours).

Step-by-step explanation:

The (1 - α)% confidence interval for population mean when the population standard deviation is not known is:

$CI=\bar x\pm t_(\alpha/2, (n-1))* (s)/(√(n))$

The information provided is:

$n=24\n\bar x=3.19\ \text{hours}\ns=0.2903\ \text{hours}$

Confidence level = 99%.

Compute the critical value of t for 99% confidence interval and (n - 1) degrees of freedom as follows:

$t_(\alpha/2, (n-1))=t_(0.01/2, (24-1))=t_(0.005, 23)=2.807$

*Use a t-table.

Compute the 99% confidence interval for the true mean amount of time Americans spend social networking each day as follows:

$CI=\bar x\pm t_(\alpha/2, (n-1))* (s)/(√(n))$

$=3.19\pm 2.807* (0.2903)/(√(24))\n\n=3.19\pm 0.1663\n\n=(3.0237, 3.3563)\n\n\approx (3.02, 3.36)$

Thus, the 99% confidence interval for the true mean amount of time Americans spend social networking each day is (3.02 hours, 3.36 hours).

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