A carpenter's tool box is made up of nails, screws,

Mathematics

2 answers:

solniwko [45]3 years ago

8 0

Answer:

Step-by-step explanation:

One way to do this follows: Find the ratio, r, which when multiplied by each of the four numbers in the ratio produces the actual number of parts present:

4r + 11r + 9r + 6r = 60

Summing these up results in 30r = 60, so r is 2.

There are 4(2), or 8, nails,

11(2), or 22, screws,

9(2), or 18, washers, and

6(2), or 12, brackets.

Note that 8 + 22 + 18 + 12 = 60 (total number of parts)

If 5 carpenters have identical boxes, there will be 5(18), or 90, total washers.

DanielleElmas [232]3 years ago

7 0

Answer:

45 total washers

Step-by-step explanation:

Looking at the ratio of 4:11:9:6, we know that there are,

4 nails in each tool box

11 screws in each tool box

9 washers in each tool box

6 brackets in each tool.

Given that there are 5 carpenters with identical tool boxes, we can find the total amount of washers by multiplying the amount of washers in each box with how many carpenters there are.

9 * 5 = 45

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1. A movie theater designs two bags to hold 96 cubic inches of popcorn. a. Find the height of each bag b. Which bag should the t

MrRissso [65]

I have attached a screenshot with the images of the two popcorn bags used by the theater.

Part (a):
Bag A:
Volume of bag = area of base * height
Volume of bag = length * width * height
We have:
volume = 96 in³
length = 3 in
width = 4 in
Therefore:
96 = 3 * 4 * height
96 = 12 * height
height of bag A = 8 in
Bag B:
Volume of bag = area of base * height
Volume of bag = length * width * height
We have:
volume = 96 in³
length = 4 in
width = 4 in
Therefore:
96 = 4 * 4 * height
96 = 16 * height
height of bag B = 6 in

Part (b):
To determine the amount of paper needed, we will need to calculate the surface of each bag. Excluding the top base, each bag will have 5 faces. Four side faces (each two opposite are equal) and the base.
Bag A:
Surface area = area of base + 2*area of front face + 2*area of side face
Surface area = (3*4) + 2(8*4) + 2(8*3)
Surface area = 12 + 64 + 48
Surface area of bag A = 124 in²
Bag B:
Surface area = area of base + 2*area of front face + 2*area of side face
Surface area = (4*4) + 2(6*4) + 2(6*4)
Surface area = 16 + 48 + 48
Surface area of bag B = 112 in²
From the above calculations, we can deduce that the theater should choose bag B in order to reduce the amount of paper needed.

Hope this helps :)