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MrMuchimi
3 years ago
8

Consider the rectangular prism with length 3 cm, width 4 cm, and height of 6 cm. Will doubling one of the dimensions of the rect

angular prism double the surface area of the prism? Justify your answer.
Mathematics
1 answer:
yawa3891 [41]3 years ago
6 0

Answer:

NO

Step-by-step explanation:

Surface area = 2lw+ 2 lh + 2 hw  Where h = height, w= width and l = length

We will double w

SA becomes 2l(2w) + 2lh + 2h(2w)

 SA = 4lw + 2lh + 4lw

Doubling the SA

2SA = 2(2lw+ 2 lh + 2 hw)

        = 4lw + 4lh +4 hw

2SA =? SA for 2w

4lw + 4lh +4 hw =   4lw + 2lh + 4lw

This is not the same

Doubling one dimension does not double the surface area

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Find the slope of the line passing through each of the following pairs of points and draw the graph of the line. (5, 2), (3, 3)
Strike441 [17]

Answer:

-0.5

Step-by-step explanation:

  • slope=rise/run or y/x in other words(y2-y1/x2-x1)
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8 0
2 years ago
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Although cities encourage carpooling to reduce traffic congestion, most vehicles carry only one person. For example, 64% of vehi
ira [324]

Answer:

a) 0.7291 is the probability that more than half out of 10 vehicles carry just 1 person.

b) 0.996 is the probability that more than half of the vehicles  carry just one person.    

Step-by-step explanation:

We are given the following information:

A) Binomial distribution

We treat vehicle on road with one passenger as a success.

P(success) = 64% = 0.64

Then the number of vehicles follows a binomial distribution, where

P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 10

We have to evaluate:

P(x \geq 6) = P(x =6) +...+ P(x = 10) \\= \binom{10}{6}(0.64)^6(1-0.64)^4 +...+ \binom{10}{10}(0.64)^{10}(1-0.79)^0\\=0.7291

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B) By normal approximation

Sample size, n = 92

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\mu = np = 92(0.64) = 58.88

\sigma = \sqrt{np(1-p)} = \sqrt{92(0.64)(1-0.64)} = 4.60

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P(x \geq 47)

After continuity correction, we will evaluate

P( x \geq 46.5) = P( z > \displaystyle\frac{46.5 - 58.88}{4.60}) = P(z > -2.6913)

= 1 - P(z \leq -2.6913)

Calculation the value from standard normal z table, we have,  

P(x > 46.5) = 1 - 0.004 = 0.996 = 99.6\%

0.996 is the probability that more than half out of 92 vehicles carry just one person.

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2 years ago
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Ivenika [448]
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A 1:12 is the answer for this question
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3 years ago
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