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astra-53 [7]
3 years ago
5

Given triangle ABC with coordinates A(−2, 7), B(−2, 4), and C(−4, 3), and its image A′B′C′ with A′(2, 3), B′(−1, 3), and C′(−2,

1), find the line of reflection.
The line of reflection is at y =
Mathematics
1 answer:
Setler [38]3 years ago
6 0

Answer:

y = x + 5

Step-by-step explanation:

given an obtuse scalene triangle (∆ABC) with vertices A(-2,7), B(-2,4), and C(-4,3) (representing the preimage of the reflection). And congruent triangle (∆A'B'C') with vertices A'(2,3), B'(-1,3), and C'(-2,1) (representing the image of the reflection / triangle after the reflection).

The easiest way to look at this is by taking the inverse of each point on the preimage (swapping y and x coordinates) and the adding 5 to the y and subtracting 5 from the x to get the image.

You can test this, and you will see that this will match with vertices of the image.

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the number of employees for a certain company has been decreasing each year by 2% if the company currently has 870 employees and
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Step-by-step explanation:

Number of employees in 9 years

= 870 * (1 - 0.02)⁹

= 870 * (0.98)⁹

≈ 725 employees.

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How many minutes have passed between the time shown on the first clock and the time shown on the second clock
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Latoya is on her way home in her car. She has driven 15 miles so far, which is three-fourths of the way home. What is the total
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Answer:

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Step-by-step explanation:

6 0
3 years ago
According to a study done by a university​ student, the probability a randomly selected individual will not cover his or her mou
Sergio [31]

Using the binomial distribution, it is found that:

a) There is a 0.1618 = 16.18% probability that among 18 randomly observed individuals exactly 6 do not cover their mouth when​ sneezing.

b) There is a 0.104 = 10.4% probability that among 18 randomly observed individuals fewer than 3 do not cover their mouth when​ sneezing.

c) 9 is more than 2.5 standard deviations below the mean, hence it would not be surprising if fewer than half covered their mouth when​ sneezing.

<h3>What is the binomial distribution formula?</h3>

The formula is:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

C_{n,x} = \frac{n!}{x!(n-x)!}

The parameters are:

  • x is the number of successes.
  • n is the number of trials.
  • p is the probability of a success on a single trial.

The values of the parameters are given as follows:

n = 18, p = 0.267.

Item a:

The probability is P(X = 6), hence:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 6) = C_{18,6}.(0.267)^{6}.(0.733)^{12} = 0.1618

There is a 0.1618 = 16.18% probability that among 18 randomly observed individuals exactly 6 do not cover their mouth when​ sneezing.

Item b:

The probability is:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).

Then:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{18,0}.(0.267)^{0}.(0.733)^{18} = 0.0037

P(X = 1) = C_{18,1}.(0.267)^{1}.(0.733)^{17} = 0.0245

P(X = 2) = C_{18,2}.(0.267)^{2}.(0.733)^{16} = 0.0758

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0037 + 0.0245 + 0.0758 = 0.104.

There is a 0.104 = 10.4% probability that among 18 randomly observed individuals fewer than 3 do not cover their mouth when​ sneezing.

item c:

We have to look at the mean and the standard deviation, given, respectively, by:

  • E(X) = np = 18 x 0.267 = 4.81.
  • \sqrt{V(X)} = \sqrt{18(0.267)(0.733)} = 1.88

9 is more than 2.5 standard deviations below the mean, hence it would not be surprising if fewer than half covered their mouth when​ sneezing.

More can be learned about the binomial distribution at brainly.com/question/24863377

#SPJ1

6 0
2 years ago
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