MATHEMATICS MIDDLE SCHOOL

You work part-time at the “Pack-it and Mail-it” that sells containers used for shipping items. Your photography teacher asks you to recommend the best package to ship 35 mm film containers. The film containers are 1 inch in diameter and 2 inches in height, and they are to be shipped in groups of twelve.A) Find the volume of twelve film containers. Round your result to two decimal places and show all calculations below.

B) Which container should be used to fit a dozen film containers with the least amount of wasted space? Explain your reasoning.

At work you get a list of package sizes. Your store has four box sizes that look like they might work. The sizes are given in the form l x w x h. They are 3 in. x 2 in. x 5 in., 4 in. x 3in. x 2 in., 5 in. x 6 in. x 5 in., and 3 in. x 2 in. x 3 in.

Answers

Answer 1
Answer:

Answer:

(a)18.85 Cubic Inches

(b)The box with dimensions of 4 in. x 3in. x 2 in.

Step-by-step explanation:

Part A

Volume of the 12 Containers

Height =2 Inches

Diameter=1 Inch

Radius=Diameter/2=1/2=0.5 Inch

Volume of a cylinder=\pi r^2 h

Volume of the 12 Containers

=12 X \pi r^2 h\n=12 X\pi X0.5^2X2\n=6\pi $ cubic inches\n=18.85 \text{cubic inches (to two decimal places)}

Part B

To determine the container which should be used, we first determine the volume of the available boxes.

Volume of the boxes

Volume of box with dimension 3 in. x 2 in. x 5 in.=3X2X5=30 Cubic Inches

Volume of box with dimension 4 in. x 3in. x 2 in.=4X3X2=24 Cubic Inches

Volume of box with dimension 5 in. x 6 in. x 5 in.=5X6X5=150 Cubic Inches

Volume of box with dimension 3 in. x 2 in. x 3 in. =3X2X3=18 Cubic Inches

The box that should be used with the least amount of wasted space is he box with volume 24 Cubic inches. i.e. box with dimensions 4 in. x 3in. x 2 in.

This is because the volume of the box(18 cubic inches) with dimension 3 in. x 2 in. x 3 in. is less than what is required.

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Four more than twice a number is 8

Answers

Lets say the number equals x

Four more than twice a number is 8

4 more than twice a number is 8    

4 more than twice x is 8        (twice means 2 times)

4 more than 2x is 8               (more than means to add)

2x + 4 is 8

2x + 4 = 8

2x = 8 - 4

2x = 4

x = 4/2

x = 2
Four more than twice a number…..the root of this problem is 2. Twice 2 is 2x2 = 4 and then four more that number is 4 + 4 = 8.

Hope this helps. :)

Some of the children at a school arrive by car.30% of the children at the school are boys
60% of the boys at the school arrive by car
80% of the girls at the school arrive by car
what is the probability that a child chosen at random from the school arrives by car? give your answer as a decimal

Answers

Answer:

  • 74%

Explanation:

You can build a two-way relative frequency table to represent the data:

These are the columns and rows:

               Car         No car      Total

Boys

Girl

Total

Fill the table

  • 30% of the children at the school are boys

             Car         No car      Total

Boys                                       30%

Girl

Total

  • 60% of the boys at the school arrive by car

That is 60% of 30% = 0.6 × 30% = 18%

             Car         No car      Total

Boys      18%                         30%

Girls

Total

By difference you can fill the cell of Boy and No car: 30% - 18% = 12%

             Car         No car      Total

Boy       18%           12%         30%

Girl

Total

Also, you know that the grand total is 100%

             Car         No car      Total

Boy       18%           12%         30%

Girl

Total                                     100%

By difference you fill the total of Girls: 100% - 30% = 70%

             Car         No car      Total

Boy       18%           12%         30%

Girl                                         70%

Total                                     100%

  • 80% of the girls at the school arrive by car

That is 80% of  70% = 0.8 × 70% = 56%

             Car         No car      Total

Boy       18%           12%         30%

Girl       56%                         70%

Total                                     100%

Now you can finish filling in the whole table calculating the differences:

             Car         No car      Total

Boy       18%           12%         30%

Girl        56%         14%         70%

Total     74%          26%      100%

Having the table completed you can find any relevant probability.

The probability that a child chosen at random from the school arrives by car is the total of the column Car: 74%.

That is because that column represents the percent of boys and girls that that  arrive by car: 18% of the boys, 56% of the girls, and 74% of all the the children.

Answer: 0.74

Step-by-step explanation:

If a couple files a return as married filing jointly how many returns will the irs get

Answers

In 2018, married filing separately taxpayers only receive a standard deduction of $12,000 compared to the $24,000 offered to those who filed jointly. If you file a separate return from your spouse, you are automatically disqualified from several of the tax deductions and credits mentioned earlier.

Jerry started playing video gamrs at 3:20. If he took a break at 7:15 how long had he been playing

Answers

4(60)-5 = 235 minutes or 3 hours 55 minutes

Multiply. √3 ⋅ 2√2 ⋅ 5√8 ⋅ √18 Enter your answer, in simplest radical form, in the box.

Answers

\sqrt3\n2\sqrt2\n5\sqrt8=5√(4\cdot2)=5\sqrt4\cdot\sqrt2=5(2)\sqrt2=10\sqrt2\n√(18)=√(9\cdot2)=\sqrt9\cdot\sqrt2=3\sqrt2\n\n\sqrt3\cdot2\sqrt2\cdot5\sqrt8\cdot√(18)=\sqrt3\cdot2\sqrt2\cdot10\sqrt2\cdot3\sqrt2\n\n=(2\cdot10\cdot3)(\sqrt3\cdot\sqrt2\cdot\sqrt2\cdot\sqrt2)=60√(3\cdot2)\cdot√(2\cdot2)\n\n=60\sqrt6\cdot\sqrt4=60\sqrt6\cdot2=(60\cdot2)(\sqrt6)\n\n=\boxed{120\sqrt6}

Answer:

120√6

Step-by-step explanation:

Simplify the 5√8 to 2√2

simplify the √18 to 3√2

so it would be √3 * 2√2 * 5 * 2√2 * 3√2

when a square root of an expression is multiplied by itself:

√3 * 2 * 2* 5 * 2 * 3√2

so as we calculate it, 2 * 2* 5 * 2 * 3 = 120 and √2 * √3 = 6

What is the median of, 18, 16, 13, 10, 9.5, 8.5, 7.5, and six????

Answers

you have to fist pot them in order 6,  7.5,  8.5,  9.5,  10,  13,  16,  18

so the middle numbers are 9.5 and 10 

add them together 9.5+10=19.5 then divide by 2 so 19.5/2=9.75  that is you answer
18 |16 | 13 | 10 | 9.5 | 8.5 | 7.5 | 6
                      
9.75 is the FINAL answer
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