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alexandr1967 [171]
3 years ago
8

Which transformation below preserves similarity between the preimage and image, but does not preserve congruence?

Mathematics
1 answer:
Dmitry [639]3 years ago
3 0
Im more then likely sure that it is dilation becuase you still have the same shape but with dilation you can make the shape smaller or bigger
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Customers experiencing technical difficulty with their Internet cable hookup may call an 800 number for technical support. Itake
Paladinen [302]

Answer:

(A) The percent of the problems takes more than 5 minutes to resolve is 60.87%.

(B) The problem solving time will be 50% as long as the difference between the two end points is 5.75.

(C) <em>a</em> = 0.50 minutes, <em>b</em> = 12 minutes.

(D) Mean = 6.25 minutes, Standard deviation = 3.32 minutes

Step-by-step explanation:

Let the random variable <em>X</em> represent the time it takes the technician to resolve the problem.

The random variable <em>X</em> follows an Uniform distribution with parameters <em>a</em> =  0.50 minutes and <em>b</em> = 12 minutes.

The probability density function of <em>X</em> is:

f_{X}(x)=\frac{1}{b-a};\ a

(A)

Compute the probability that the problems takes more than 5 minutes to resolve as follows:

P(X>5)=\int\limits^{12}_{5}{\frac{1}{12-0.50}}\, dx

               =\frac{1}{11.50}\cdot \int\limits^{12}_{5}{1}\, dx \\\\=\frac{1}{11.50}\cdot [x]\limits^{12}_{5}\\\\=\frac{1}{11.50}\cdot [12-5]\\\\=\frac{7}{11.50}\\\\=0.608696\\\\\approx 0.6087

Thus, the percent of the problems takes more than 5 minutes to resolve is 60.87%.

(B)

Let the middle 50% of the problem-solving times be between <em>u</em> and <em>v</em>.

Then,

P (<em>u</em> < X < <em>v</em>) = 0.50

\int\limits^{v}_{u}{\frac{1}{12-0.50}}\, dx=0.50\\\\\frac{1}{11.50}\cdot \int\limits^{v}_{u}{1}\, dx=0.50\\\\\frac{v-u}{11.50}=0.50\\\\(v-u)=5.75

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(C)

The interval in which the technician can solve the problem is 30 seconds to 12 minutes.

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<em>a</em> = 30 seconds = 0.50 minutes

<em>b</em> = 12 minutes.

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The mean time is:

\mu=\frac{a+b}{2}=\frac{0.50+12}{2}=6.25\ \text{minutes}

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\sigma=\sqrt{\frac{(b-a)^{2}}{12}}=\sqrt{\frac{(12-0.50)^{2}}{12}}=3.3197\approx 3.32\ \text{minutes}

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