Answer:
volume = 450 mm³
Step-by-step explanation:
Given:
- height = 18 mm
- area of base = 25 mm²
Volume of a rectangular prism = area of base x height
⇒ volume = 25 x 18 = 450 mm³
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 inBag 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 inPart (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 in²Bag 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 in²From 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 :)
Answer:
segment EF over segment LM equals segment FG over segment MN
Step-by-step explanation:
The triangles are similar, not congruent, so any answer choice with the word "congruent" can be ignored.
The sequence of letters in the triangle name tells you the corresponding segments:
- EF corresponds to LM
- EG corresponds to LN
- FG corresponds to MN
Corresponding segments have the same ratio, so ...
EF/LM = FG/MN . . . . . . matches the first answer choice
EF/LM = EG/LN . . . . does not match the 3rd answer choice
Answer:
-139
Step-by-step explanation:
Evaluate 1/4 (4 x^3 - 2 y - 2 z^3) y^2 - 16 x^2 where x = 2, y = -5 and z = 3:
(4 x^3 - 2 y - 2 z^3)/4 y^2 - 16 x^2 = (4×2^3 - -5×2 - 2×3^3)/4×(-5)^2 - 16×2^2
(4×2^3 - 2 (-5) - 2×3^3)/4×(-5)^2 = ((4×2^3 - 2 (-5) - 2×3^3) (-5)^2)/4:
((4×2^3 - 2 (-5) - 2×3^3) (-5)^2)/4 - 16×2^2
(-5)^2 = 25:
((4×2^3 - 2 (-5) - 2×3^3) 25)/4 - 16×2^2
2^3 = 2×2^2:
((4×2×2^2 - 2 (-5) - 2×3^3) 25)/4 - 16×2^2
2^2 = 4:
((4×2×4 - 2 (-5) - 2×3^3) 25)/4 - 16×2^2
2×4 = 8:
((4×8 - 2 (-5) - 2×3^3) 25)/4 - 16×2^2
3^3 = 3×3^2:
((4×8 - 2 (-5) - 23×3^2) 25)/4 - 16×2^2
3^2 = 9:
((4×8 - 2 (-5) - 2×3×9) 25)/4 - 16×2^2
3×9 = 27:
((4×8 - 2 (-5) - 227) 25)/4 - 16×2^2
4×8 = 32:
((32 - 2 (-5) - 2×27) 25)/4 - 16×2^2
-2 (-5) = 10:
((32 + 10 - 2×27) 25)/4 - 16×2^2
-2×27 = -54:
((32 + 10 + -54) 25)/4 - 16×2^2
| 3 | 2
+ | 1 | 0
| 4 | 2:
(42 - 54 25)/4 - 16×2^2
42 - 54 = -(54 - 42):
(-(54 - 42) 25)/4 - 16×2^2
| 5 | 4
- | 4 | 2
| 1 | 2:
(-12×25)/4 - 16×2^2
(-12)/4 = (4 (-3))/4 = -3:
-3×25 - 16×2^2
2^2 = 4:
-3×25 - 164
-3×25 = -75:
-75 - 16×4
-16×4 = -64:
-64 - 75
-75 - 64 = -(75 + 64):
-(75 + 64)
| 7 | 5
+ | 6 | 4
1 | 3 | 9:
Answer: -139
The numbering system we commonly use is called the decimal numbering system because it uses <u> 10 </u> symbols to represent all possible numbers.
A way of writing numbers is known as a number system.
There are the following number systems:
- Decimal number system: "Deci" meaning 10, implies that the number system consists of 10 digits or symbols, namely 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
- Binary number system: "Bi" meaning 2, implies that the number system consists of 2digits or symbols, namely 0, and 1.
- Octal number system: "Oct" meaning 8, implies that the number system consists of 8 digits or symbols, namely 0, 1, 2, 3, 4, 5, 6, 7, and 8.
- Hexa-Decimal number system: "Hexa-Deci" meaning 16, implies that the number system consists of 16 symbols, namely 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F.
Hence, we can say that the numbering system we commonly use is called the decimal numbering system because it uses <u> 10 </u> symbols to represent all possible numbers.
Learn more about number systems at
brainly.com/question/14567654
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