1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ella [17]
3 years ago
7

A truck is being filled with cube-shaped packages that have side lengths of 1/4 foot. The part of the truck that is being filled

is in the shape of a rectangular prism with dimensions of 8 ft x 6 1/4 ft x 7 1/2 ft. What is the greatest number of packages that can fit in the truck?
Mathematics
1 answer:
n200080 [17]3 years ago
7 0

Answer:

24000 pieces.      

Step-by-step explanation:

Given:

Side lengths of cube = \frac{1}{4} \ foot

The part of the truck that is being filled is in the shape of a rectangular prism with dimensions of 8 ft x 6 1/4 ft x 7 1/2 ft.

Question asked:

What is the greatest number of packages that can fit in the truck?

Solution:

First of all we will find volume of cube, then volume of rectangular prism and then simply divide the volume of prism by volume of cube to find the greatest number of packages that can fit in the truck.

Volume\ of\ cube =a^{3}

                          =\frac{1}{4} \times\frac{1}{4}\times \frac{1}{4} =\frac{1}{64} \ cubic \ foot

                                   

Length = 8 foot, Breadth = 6\frac{1}{4} =\frac{25}{4} \ foot, Height =7\frac{1}{2} =\frac{15}{2} \ foot

Volume\ of\ rectangular\ prism =length\times breadth\times height

                                                =8\times\frac{25}{4} \times\frac{15}{2} \\=\frac{3000}{8} =375\ cubic\ foot

The greatest number of packages that can fit in the truck = Volume of prism divided by volume of cube

The greatest number of packages that can fit in the truck = \frac{375}{\frac{1}{64} } =375\times64=24000\ pieces\ of\ cube

Thus, the greatest number of packages that can fit in the truck is 24000 pieces.                                

You might be interested in
29) Adam’s sister wants to watch her intake of fat per day. Here is a guideline of the recommended daily allowances. Typical val
ziro4ka [17]
Basically all the information in this problem is useless. They included all those numbers to confuse you. If you read throughly you can see that all you need to know is that Adam's sister can only have 70 grams of fat each day and that her dinner will have 48 grams of fat.

To figure this out I use this formula all the time to figure out percentages.
is/of=x/100
Your trying to figure out what is 48 percent of 70 because that's how much Adam's sister is going to eat at dinner. So your is would be 48 and your of is 70. When you substitute those numbers your formula becomes 48/70=x/100. Now you cross multiply and get 70x=4800.All that's left is to divide 70 on both sides. Which gives you 68.57.The final answer is 69 percent.
8 0
3 years ago
In order to estimate the difference between the average hourly wages of employees of two branches of a department store, the fol
Julli [10]

Answer:

0.071,1.928

Step-by-step explanation:

                                                Downtown Store   North Mall Store

Sample size   n                             25                        20

Sample mean \bar{x}                         $9                        $8

Sample standard deviation  s       $2                        $1

n_1=25\\n_2=20

\bar{x_1}=9\\ \bar{x_2}=8

s_1=2\\s_2=1

x_1-x_2=9-8=1

Standard error of difference of means = \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}

Standard error of difference of means = \sqrt{\frac{2^2}{25}+\frac{1^2}{20}}

Standard error of difference of means = 0.458

Degree of freedom = \frac{\sqrt{(\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}})^2}{\frac{(\frac{s_1^2}{n_1})^2}{n_1-1}+\frac{(\frac{s_2^2}{n_2})^2}{n_2-1}}

Degree of freedom = \frac{\sqrt{(\frac{2^2}{25}+\frac{1^2}{20}})^2}{\frac{(\frac{2^2}{25})^2}{25-1}+\frac{(\frac{1^2}{20})^2}{20-1}}

Degree of freedom =36

So, z value at 95% confidence interval and 36 degree of freedom = 2.0280

Confidence interval = (x_1-x_2)-z \times SE(x_1-x_2),(x_1-x_2)+z \times SE(x_1-x_2)

Confidence interval = 1-(2.0280)\times 0.458,1+(2.0280)\times 0.458

Confidence interval = 0.071,1.928

Hence Option A is true

Confidence interval is  0.071,1.928

4 0
3 years ago
Arithmetic, geometric, or neither 16,21,26,31...
SVETLANKA909090 [29]

Answer:

Arithmetic

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Triangle ABC is similar to Triangle QRS. What is the degree measure of angle B?
GalinKa [24]

Answer:

you doing k12 geometry too?

Step-by-step explanation:

4 0
3 years ago
At noon, the high temperature was 54 degrees. During the course of the day, the temperature increased 8 degrees, decreased 3 deg
pychu [463]

Answer:

61

Step-by-step explanation:

Let's write out what we know:

Noon temp: 54

Over the day, the temperature:

increased 8, decreased 3, increased 14, decreased 2, and decreased 10.

54+8-3+14-2-10 = 61

7 0
2 years ago
Other questions:
  • The lengths of two sides of a right triangle are 12 inches and 15 inches. What is the difference between the two possible length
    6·1 answer
  • If ———— = 20, then x =<br> x
    15·1 answer
  • A teacher covered the exterior of a rectangular prism-shaped box that measured 8 inches by 9 inches by 10 inches using one sheet
    6·1 answer
  • 75,000 = _____ tens<br>please answer
    14·1 answer
  • HELPPPP HURRY pleaseeee
    9·1 answer
  • Subtract −b+3 ​​from −11b−4 ​
    8·2 answers
  • Ima need this in right now
    15·1 answer
  • Which number is not equal to one of the following expressions?
    11·1 answer
  • What are rational numbers​
    8·1 answer
  • john is cutting wood planks. He has a 3 foot plank. he needs to cut them in 3/8 length pieces. How many pieces will he have?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!