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Elena L [17]
2 years ago
9

The orthodontist estimated how long brian would have to wear braces when she put them on his teeth. brian was pleasantly surpris

ed when, after 16 months, the orthodontist said it was time to take the braces off. her original estimate had been 12.5% longer than that. how long was the original estimate?
Mathematics
1 answer:
USPshnik [31]2 years ago
7 0

Using the given information, the original estimate was 18 months

<h3>Percentages </h3>

From the question, we are to determine how long the original estimate was

Let the original estimate the x

Then, from the given information, we ca write that

x = 16 + (12.5% × 16)

x = 16 + (0.125 × 16)

NOTE: 12.5%  = 12.5/100 = 0.125

∴ x = 16 + 2

x = 18

Hence, the original estimate was 18 months

Learn more on Percentages here: brainly.com/question/7459025

#SPJ1

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Find the surface area of composite figure. use 3.14 for π. round to the nearest tenth
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Answer:

  334 in²

Step-by-step explanation:

The total surface area of the composite figure is the sum of the total area of the bottom cuboid and the lateral area of the top cuboid.

<h3>Total cuboid area</h3>

The area of a cuboid is given by the formula ...

  A = 2(LW +H(L+W))

For the bottom cuboid, the area is ...

  A = 2((9 in)(7 in) +(5 in)(9 in +7 in)) = 2(63 in² +5(16) in²) = 286 in²

<h3>Lateral area</h3>

The lateral area of a cuboid is the product of its perimeter and height. The perimeter is the sum of side lengths, or twice the sum of length and width.

  LA = Ph = (2(l +w))h

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<h3>Total composite area</h3>

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  SA = (48 in²) +(286 in²) = 334 in²

The surface area of the composite figure is 334 square inches.

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<em>Additional comment</em>

The exposed area of the bottom cuboid is its total area less the area of the very top face.

The exposed area of the top cuboid is its lateral area plus the area of the very top face.

When we add these two exposed areas together, we find the area of the very top face is both subtracted and added from the sum of the total bottom area and the lateral top area. We skipped that step of adding and subtracting, because its net effect is zero.

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2 years ago
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Answer:

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third term = -9 + 6(2) = 3

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and 81 = -9 + (6*15).

So the answer is  Sigma (-9 + 6n)  from n= 0 to n = 15.

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