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weeeeeb [17]
3 years ago
7

Zoe is packaging a gift to send in the mail. A smaller gift box is placed inside a similar yet larger packaging box. The empty s

pace inside the packaging box is filled with tissue paper to keep the gift box from moving. The dimensions of the larger box are each 2.1 times longer than the corresponding dimensions of the smaller box. The volume of the smaller box is 24 cubic centimeters. What is the volume of the tissue paper in the packaging box?
81.84 cubic centimeters
105.84 cubic centimeters
198.264 cubic centimeters
222.264 cubic centimeters
Mathematics
2 answers:
8_murik_8 [283]3 years ago
7 0

Answer: 198.264\text{ cubic centimeters}

Step-by-step explanation:

Let l, w, h are be the dimensions of the smaller box such that the volume of the box is

\text{Volume}=lwh=24

Since, the dimensions of the larger box are each 2.1 times longer than the corresponding dimensions of the smaller box.

Now, the volume of the larger packing box will be

\text{Volume}\\\\=2.1l\times2.1w\times2.1w\\\\=9.261lwh\\\\9.261(24)\\\\=222.264\text{ cubic centimeters}

Hence, the volume of the tissue paper in the packaging box= 222.264-24=198.264\text{ cubic centimeters}

rjkz [21]3 years ago
6 0
The answer is letter C) 198.264 cubic centimeters
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3 years ago
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Zigmanuir [339]

Answer:

Ai. Arithmetic sequence

Aii. Tn = 5 + 7n

Bi. Geometric

Bii. Tn = 8 × 2ⁿ¯¹

Step-by-step explanation:

To successfully answer the questions given above, note the following:

1. If the sequence is Arithmetic, then:

2nd – 1st = 3rd – 2nd = common difference (d)

2. If the sequence is geometric, then,

2nd / 1st = 3rd / 2nd = common ratio (r)

3. A sequence can not be arithmetic geometric at the same time.

4. The nth term of arithmetic sequence is:

Tn = a + (n – 1)d

5. The nth term of geometric sequence is:

Tn = arⁿ¯¹

A. Sequence => 12, 19, 26

i. Determination of the type of sequence.

We'll begin by calculating the common difference

1st term = 12

2nd term = 19

3rd term = 26

Common difference (d) = 2nd – 1st

d = 19 – 12 = 7

OR

d = 3rd – 2nd

d = 26 – 19 = 7

Since a common difference exist in the sequence, the sequence is arithmetic sequence.

ii. Determination of the nth term.

Common difference (d) = 7

1st term (a) = 12

nth term (Tn) =?

Tn = a + (n – 1)d

Tn = 12 + (n – 1)7

Tn = 12 + 7n – 7

Tn = 5 + 7n

B. Sequence => 8, 16, 32

Bi. Determination of the type of sequence.

Let us begin by calculating the common ratio.

1st term = 8

2nd term = 16

3rd term = 32

Common ratio (r) = 2nd / 1st

r = 16 / 8

r = 2

OR

r = 3rd / 2nd

r = 32 / 16

r = 2

Since a common ratio exist in the sequence, the sequence is geometric.

Bii. Determination of the nth term.

Common ratio(r) = 2

1st term (a) = 8

nth term =?

Tn = arⁿ¯¹

Tn = 8 × 2ⁿ¯¹

8 0
2 years ago
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