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Leni [432]
3 years ago
6

Kevin had to measure the diameter of a hair strand and the diameter of a grain of sand for his science experiment. He found the

diameter of the hair strand to be 0.00006 inches and the diameter of a grain of sand to be 1.3 × 10-3 inches.
Mathematics
1 answer:
scZoUnD [109]3 years ago
5 0
This is the concept of linear scale factors. 
Diameter of hair strand is 0.00006=6×10^-5 inches
Diameter of sand grain is 1.3x10^-3 inches
Thus the the number of times the hair sand grain is bigger than hair strand will be:
linear scale factor=(diameter of sand grain)/(diameter of hair strand)
=(1.3×10^-3)/(6×10^-5)
=21 2/3 times


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Step-by-step explanation:

You need to find the total number of votes first. Just add 13 and 39 which would equal 52.

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Seventy percent of all vehicles examined at a certain emissions inspection station pass the inspection. Assuming that successive
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Answer:

(a) 0.343

(b) 0.657

(c) 0.189

(d) 0.216

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Step-by-step explanation:

Let P(a vehicle passing the test) = p

                        p = \frac{70}{100} = 0.7  

Let P(a vehicle not passing the test) = q

                         q = 1 - p

                         q = 1 - 0.7 = 0.3

(a) P(all of the next three vehicles inspected pass) = P(ppp)

                           = 0.7 × 0.7 × 0.7

                           = 0.343

(b) P(at least one of the next three inspected fails) = P(qpp or qqp or pqp or pqq or ppq or qpq or qqq)

      = (0.3 × 0.7 × 0.7) + (0.3 × 0.3 × 0.7) + (0.7 × 0.3 × 0.7) + (0.7 × 0.3 × 0.3) + (0.7 × 0.7 × 0.3) + (0.3 × 0.7 × 0.3) + (0.3 × 0.3 × 0.3)

      = 0.147 + 0.063 + 0.147 + 0.063 + 0.147 + 0.063 + 0.027

      = 0.657

(c) P(exactly one of the next three inspected passes) = P(pqq or qpq or qqp)

                 =  (0.7 × 0.3 × 0.3) + (0.3 × 0.7 × 0.3) + (0.3 × 0.3 × 0.7)

                 = 0.063 + 0.063 + 0.063

                 = 0.189

(d) P(at most one of the next three vehicles inspected passes) = P(pqq or qpq or qqp or qqq)

                 =  (0.7 × 0.3 × 0.3) + (0.3 × 0.7 × 0.3) + (0.3 × 0.3 × 0.7) + (0.3 × 0.3 × 0.3)

                 = 0.063 + 0.063 + 0.063 + 0.027

                 = 0.216

(e) Given that at least one of the next 3 vehicles passes inspection, what is the probability that all 3 pass (a conditional probability)?

P(at least one of the next three vehicles inspected passes) = P(ppp or ppq or pqp or qpp or pqq or qpq or qqp)

=  (0.7 × 0.7 × 0.7) + (0.7 × 0.7 × 0.3) + (0.7 × 0.3 × 0.7) + (0.3 × 0.7 × 0.7) + (0.7 × 0.3 × 0.3) + (0.3 × 0.7 × 0.3) + (0.3 × 0.3 × 0.7)

= 0.343 + 0.147 + 0.147 + 0.147 + 0.063 + 0.063 + 0.063

                  = 0.973  

With the condition that at least one of the next 3 vehicles passes inspection, the probability that all 3 pass is,

                         = \frac{P(all\ of\ the\ next\ three\ vehicles\ inspected\ pass)}{P(at\ least\ one\ of\ the\ next\ three\ vehicles\ inspected\ passes)}

                         = \frac{0.343}{0.973}

                         = 0.353

3 0
4 years ago
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Usimov [2.4K]

Answer:

see explanation

Step-by-step explanation:

let ∠BCE = x then ∠ECD = 5x - 6 and

∠BCE + ∠ECD = ∠BCD, substitute values

x + 5x - 6 = 162, that is

6x - 6 = 162 ( add 6 to both sides )

6x = 168 ( divide both sides by 6 )

x = 28

Hence

∠BCE = x = 28°

∠ECD = 5x - 6 = (5 × 28) - 6 = 140 - 6 = 134°

5 0
3 years ago
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