Two cardboard boxes are stacked on top of each other. The top box is a cube with sides of 10 in. The bottom box is a rectangular prism with a length of 20 in, width of 15 in, and height of 8 in. Find the surface area of the composite shape. Select the correct answer.A. 1,605 in²
B. 1,506 in²
C. 1,560 in²
Answers
The surface area of the composite shape is 1560 square inches
Step-by-step explanation:
The surface area of the top cardboard is,
SA = 5 x area of each side
Because one side is attached with another cardboard box . So while finding the area only 5 sides are calculated.
SA = 5 ( 10 x 10)
= 500 square inches
The surface area of the rectangular prism cardboard,
Given that,
l = 20 in
w =15 in
h = 8 in
A = 2(lw + wh + hl) - 100
We are subtracting 100 because it is the area of one side of the square cardboard box on top of the rectangular prism box .
A = 2(300 + 120 + 160) - 100
= 2(580) - 100
= 1160-100
= 1060 square inches
Total surface area = SA + A
= 500 + 1060
= 1560 square inches
The surface area of composite shape is 1760 square inches, if two cardboard boxes are stacked on top of each other. The top box is a cube with sides of 10 in and the bottom box is a rectangular prism with a length of 20 in, width of 15 in, and height of 8 in.
Step-by-step explanation:
The given is,
The top box is a cube with sides of 10 in
The bottom box is a rectangular prism with a length of 20 in, width of 15 in, and height of 8 in.
Step:1
Surface area of composite figure = Surface area of cube +
Surface area of rectangular prism
Step:2
Formula for surface area of cube,
( Only 5 sides area considered )
Where, a - Side of cube
From given, a = 10 inches
From the surface area equation,
= (5)(100)
= 500
Surface area of cube = 500 square inches
Step:3
Formula surface area of rectangular prism,
Where, w - Width
l - Length
h - Height
From the given values.
w = 15 inches
l = 20 inches
h = 8 inches
Surface area equation becomes,
= 2 ( 300 + 160 + 120 )-100
= 2 (580)-100
Surface area of rectangular prism = 1060 square inches
From the step 1,
Surface area of composite shape = 500+1060
= 1560 square inches
Result:
The surface area of composite shape is 1560 square inches.
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Answers
Answer:
- 13
Step-by-step explanation:
f(1) = 7
f(n) = f(n − 1) – 4
f(₂) = f(1) – 4 = 7 - 4 = 3
f(₃) = f(₂) – 4 = 3 - 4 = -1
f(₄) = f(3) – 4 = (-1) - 4 = - 5
f(₅) = f(₄) – 4 = (- 5) - 4 = - 9
f(₆) = f(₅) – 4 = (- 9) - 4 = - 13
Final answer:
The value of f(6) is -13, calculated based on the provided recursive formula where each term is four less than the previous.
Explanation:
We are given that f(1) = 7, and the recursive equation for n is f(n) = f(n − 1) – 4. Since the equation shows that each next term is four less than the previous one, we can calculate the following iterations:
- f(2) = f(2-1) - 4 = f(1) - 4 = 7 - 4 = 3
- f(3) = f(3-1) - 4 = f(2) - 4 = 3 - 4 = -1
- f(4) = f(4-1) - 4 = f(3) - 4 = -1 - 4 = -5
- f(5) = f(5-1) - 4 = f(4) - 4 = -5 - 4 = -9
- f(6) = f(6-1) - 4 = f(5) - 4 = -9 - 4 = -13
So, the value of f(6) is -13.
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Answers
Mixed fraction is converted to improper 17/8.
What is Fraction?
A fraction represents a part of a whole.
Fractions are of three types.
Proper, Improper and mixed fractions.
In proper fraction the numerator is less than the denominator.
The improper fraction is a fraction whose numerator is larger than the denominator.
The given mixed fraction is converted to improper
2×8+1/8
16+1/8
17/8
Hence, mixed fraction is converted to improper 17/8.
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Answer:
amount invested in mutual fund B; $4,800
amount invested in mutual fund A; $8,200
Step-by-step explanation:
Let the amount invested in mutual fund B be x. Then the amount invested in fund A would be;
(13000-x)
The loss emanating from fund B would be;
3.5% of x
=(3.5/100)*x
=0.035x
The profit resulting from investment in fund A would be;
6% of (13000-x)
= (6/100)*(13000-x)
=0.06(13000-x)
=780-0.06x
The total profit earned from funds A and B in terms of x will be;
780 - 0.06x + (-0.035x)
=780 - 0.095x
The total profit earned was 324, thus;
780 - 0.095x = 324
solving for x;
780 - 324 = 0.095x
456 = 0.095x
x = 4800
Then the amount invested in fund A would be;
13000 - 4800 = 8200
Answers
A Mathematical sentence that compares expressions that are not equal is an inequality.
What is the inequality?
An inequality is a mathematical sentence that compares the value of two expressions using a inequality symbol.
An inequality is a relationship between two different quantities or expressions.
An inequality may be expressed by a mathematical sentence that uses the following symbols:
< is less than
> is greater than
≤ is less than or equal to
≥ is greater than or equal to
≠ is notequal to
Hence, a mathematical sentence that compares expressions that are not equal is an inequality.
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Answer:
This would be an inequality. They use greater than (>) and less than (<) signs.
Step-by-step explanation: