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Law Incorporation [45]
2 years ago
9

A new medical test has been designed to detect the presence of the mysterious Brainlesserian disease. Among those who have the d

isease, the probability that the disease will be detected by the new test is 0.7. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.04. It is estimated that 19 % of the population who take this test have the disease.
If the test administered to an individual is positive, what is the probability that the person actually has the disease?

30. Factories A, B and C produce computers. Factory A produces 2 times as many computers as factory C, and factory B produces 7 times as many computers as factory C. The probability that a computer produced by factory A is defective is 0.032, the probability that a computer produced by factory B is defective is 0.034, and the probability that a computer produced by factory C is defective is 0.056.
A computer is selected at random and it is found to be defective. What is the probability it came from factory C?

32. What is the probability that a 7-digit phone number contains at least one 7? (Repetition of numbers and lead zero are allowed).
Mathematics
1 answer:
astra-53 [7]2 years ago
3 0

Answer:

Step-by-step explanation:

The persons who have diseases = 19%

The persons who do not have diseases = 81%

Probability for the test showing positive = Prob of actual disease and shows positive + Prob of no disease but test shows wrong

= 0.7*0.19+0.04*0.81\\=0.133+0.0324\\=0.1654

Prob that the person actually has the disease given that the test administered to an individual is positive= \frac{0.133}{0.1654} \\=0.0804

30) A    B   C   total

    2x  7x   x      10x

P(A) = 0.2, P(B) = 0.7, P(C) = 0.1

Let D be the event that the product is defective

P(D/A) = 0.032, P(D/B) = 0.034 and P(D/C) = 0.056

Required probability =P(C/D)

= \frac{P(D/C) P(C)}{P(D/A) P(a)+P(D/B) P(B)+P(D/C) P(C)}

by using Bayes theorem for conditional probability

= \frac{0.1*0.056}{0.2*0.032+0.7*0.034+0.1*0.056} \\=\frac{0.0056}{0.0064+0.0238+0.0056} \\\\=0.156425

32) 7 digit phone numbers with repitition including 0 will be

= 10^7

Numbers which have atleast one 7 = total number - numbers which do not have a single 7

= 10^7 -9^7

the probability that a 7-digit phone number contains at least one 7

=\frac{10^7-9^7}{10^7}

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If a translation of (x, y) → (x + 6, y – 10) is applied to figure ABCD, what are the coordinates of D'?
Mice21 [21]

Answer:

<em> (x , y) is translated to Horizontal translation right '6' units and </em>

<em>Vertical translation down '10' units      </em>

<em>(x ,y ) →  ( x +6 , y - 10)</em>

Step-by-step explanation:

<u><em>Explanation</em></u>:-

<em>Type of Transformation                              Change to co-ordinate point</em>

<em></em>

<em>Vertical translation up 'd' units                         (x, y) → (x , y+d)</em>

<em>Vertical translation down 'd' units                    (x, y) → (x , y-d)</em>

<em>Horizontal translation left 'c' units                  (x ,y ) → (x - c , y)</em>

<em>Horizontal translation right 'c' units              (x ,y ) → (x + c , y)</em>

<em></em>

<em>Given (x , y) is translated to Horizontal translation right '6' units and </em>

<em>Vertical translation down '10' units      </em>

<em>There fore </em>

<em>(x ,y ) →  ( x +6 , y - 10)</em>

7 0
3 years ago
Read 2 more answers
What is an equation of the line that passes through the points (-3, 7) and (3, 3)?
Margarita [4]

Answer:

y = -\frac{2}{3}x + 5

Step-by-step explanation:

First you have to find the slope

m = \frac{7 - 3}{-3 - 3} = \frac{4}{-6} = -\frac{2}{3}

Now use the point-slope form by using one of the points and the slope.  Let's use the point (3, 3)

y - 3 = -\frac{2}{3} (x - 3)

Multiply thru the equation by 3 to remove the fraction

3y - 9 = -2(x - 3) =

3y - 9 = -2x +6

3y = -2x + 15

y = -\frac{2}{3}x + 5 is the equation in slope-intercept form

3 0
2 years ago
Find the slope of each line.<br> 1)<br> (-1, 1), (-1, 4)
Andrews [41]

Answer:

The line presented has an undefined slope.

Step-by-step explanation:

We are given two points of a line: (-1, 1) and (-1, 4).

Coordinate pairs in mathematics are labeled as (x₁, y₁) and (x₂, y₂).

  • The x-coordinate is the point at which if a straight, vertical line were drawn from the x-axis, it would meet that line.
  • The y-coordinate is the point at which if a straight, horizontal line were drawn from the y-axis, it would meet that line.

Therefore, we know that the first coordinate pair can be labeled as (x₁, y₁), so, we can assign these variables these "names" as shown below:

  • x₁ = -1
  • y₁ = 1

We also can use the same naming system to assign these values to the second coordinate pair, (-1, 4):

  • x₂ = -1
  • y₂ = 4

We also need to note the rules about slope. There are different instances in which a slope can either be defined or it cannot be defined.

<u>Circumstance 1</u>: As long as the slope is not equal to zero, there can be a

  • positive slope, \frac{1}{3}
  • negative slope, -\frac{5}{6}

<u>Circumstance 2</u>: If the slope is completely vertical (there is not a "run" associated with the line), there is an undefined slope. This is the slope of a vertical line. An example would be a vertical line (the slope is still zero).

<u>Circumstance 3</u>: If the line is a horizontal line (the line does not "rise" at all), then the slope of the line is zero.

Therefore, a slope can be positive, negative, zero, or undefined.

Now, we need to solve for the line we are given.

The slope of a line is determined from the slope-intercept form of an equation, which is represented as \text{y = mx + b}.

The slope is equivalent to the variable <em>m</em>. In this equation, y and x are constant variables (they are always represented as y and x) and <em>b</em> is the y-intercept of the line.

We can do this by using the coordinates of the point and the slope formula given two coordinate points of a line: m=\frac{y_2-y_1}{x_2-x_1}.

Therefore, because we defined our values earlier, we can substitute these into the equation and solve for <em>m</em>.

Our values were:

  • x₁ = -1
  • y₁ = 1
  • x₂ = -1
  • y₂ = 4

Therefore, we can substitute these values above and solve the equation.

\displaystyle{m = \frac{4 - 1}{-1 - -1}}\\\\m = \frac{3}{0}\\\\m = 0

Therefore, we get a slope of zero, so we need to determine if this is a vertical line or a horizontal line. Therefore, we need to check to see if the x-coordinates are the same or if the y-coordinates are the same. We can easily check this.

x₁ = -1

x₂ = -1

y₁ = 1

y₂ = 4

If our y-coordinates are the same, the line is horizontal.

If our x-coordinates are the same, the line is vertical.

We see that our x-coordinates are the same, so we can determine that our line is a vertical line.

Therefore, finding that our slope is vertical, using our rules above, we can determine that our slope is undefined.

4 0
2 years ago
Read 2 more answers
Other answers are<br> C) 75<br> D) 105
Sever21 [200]
The answer to your problem is C) 75
8 0
2 years ago
trang can test message about 38 words per minute. if she types at this rate for 20 minutes about how many words will she type?
sineoko [7]

Answer:

760 words for 20 minutes.

Step-by-step explanation:

38 words = 1 minute

1 x 20 = 20

38 x 20 = 760 words

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