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Lana71 [14]
3 years ago
9

Hello! How do I find the surface area of this prism? Thanks!

Mathematics
1 answer:
Studentka2010 [4]3 years ago
8 0
Answer: Choice C) 124 square cm

------------------------------------------------------------------

Explanation:

Let's calculate the area of the trapezoid shown
b1 and b2 are the parallel bases; h is the height of the 2D trapezoid
b1 = 2
b2 = 5
h = 1.5

A = h*(b1+b2)/2
A = 1.5*(2+5)/2
A = 1.5*7/2
A = 10.5/2
A = 5.25
The area of one 2D trapezoid is 5.25 sq cm
There are two of these trapezoids that form the base faces of the trapezoidal prism. So the total base area is 2*5.25 = 10.5 sq cm
Keep this value (10.5) in mind. We'll use it later.

------------

Now onto the lateral surface area (LSA)
It turns out that the formula for the LSA is
LSA = p*d
where 
p = perimeter of the trapezoid shown
d = depth or height of the 3D trapezoid (I'm not using h as it was used earlier)
This formula works for any polygonal base. It doesn't have to be a trapezoid.

In this case the perimeter is,
p = 1.7+2+2.65+5
p = 11.35

So
LSA = p*d
LSA = 11.35*10
LSA = 113.5

Add this LSA to the base area found earlier
10.5+113.5 = 124

The total surface area is 124 square cm
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A computer manufacturing company has sent a mail survey to 2,800 of its randomly selected customers that have purchased a new la
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The 96% confidence interval for the population proportion of customers satisfied with their new computer is (0.77, 0.83).

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We have to calculate a 96% confidence interval for the proportion.

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The margin of error (MOE) can be calculated as:

MOE=z\cdot \sigma_p=2.054 \cdot 0.014=0.03

Then, the lower and upper bounds of the confidence interval are:

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The 96% confidence interval for the population proportion is (0.77, 0.83).

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Need an answer as soon as possible.
Elza [17]
Part A

Answer: The common ratio is -2

-----------------------------------

Explanation: 

To get the common ratio r, we divide any term by the previous one

One example:
r = common ratio
r = (second term)/(first term)
r = (-2)/(1)
r = -2

Another example:
r = common ratio
r = (third term)/(second term)
r = (4)/(-2)
r = -2
and we get the same common ratio every time

Side Note: each term is multiplied by -2 to get the next term

============================================================
Part B

Answer:
The rule for the sequence is 
a(n) = (-2)^(n-1)
where n starts at n = 1

-----------------------------------

Explanation:

Recall that any geometric sequence has the nth term
a(n) = a*(r)^(n-1)
where the 'a' on the right side is the first term and r is the common ratio

The first term given to use is a = 1 and the common ratio found in part A above was r = -2
So,
a(n) = a*(r)^(n-1)
a(n) = 1*(-2)^(n-1)
a(n) = (-2)^(n-1)

============================================================
Part C

Answer: The next three terms are 16, -32, 64

-----------------------------------

Explanation:

We can simply multiply each previous term by -2 to get the next term. Do this three times to generate the next three terms

-8*(-2) = 16
16*(-2) = -32
-32*(-2) = 64

showing that the next three terms are 16, -32, and 64

An alternative is to use the formula found in part B

Plug in n = 5 to find the fifth term
a(n) = (-2)^(n-1)
a(5) = (-2)^(5-1)
a(5) = (-2)^(4)
a(5) = 16 .... which matches with what we got earlier

Then plug in n = 6
a(n) = (-2)^(n-1)
a(6) = (-2)^(6-1)
a(6) = (-2)^(5)
a(6) = -32 .... which matches with what we got earlier

Then plug in n = 7
a(n) = (-2)^(n-1)
a(7) = (-2)^(7-1)
a(7) = (-2)^(6)
a(7) = 64 .... which matches with what we got earlier

while the second method takes a bit more work, its handy for when you want to find terms beyond the given sequence (eg: the 28th term)
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3 years ago
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