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Anika [276]
3 years ago
11

A study by a reputable research organization found that when presented with prints from the same​ individual, a fingerprint expe

rt will correctly identify the match 94​% of the time. In​ contrast, a novice will correctly identify the match 74​% of the time. Consider a sample of six different pairs of​ fingerprints, where each pair is a match. Complete parts a and b below.
a. What is the probability that an expert will correctly identify the match in all seven pairs of​ fingerprints?
b. What is the probability that an novice will correctly identify the match in all seven pairs of​ fingerprints?
Mathematics
1 answer:
Llana [10]3 years ago
7 0

Answer:

a. 0.6899

b. 0.1642

Step-by-step explanation:

a. Given the probability of success is 0.94 for an expert and that the number of pairs, n=6:

-Each attempt is independent and therefore the probability of  the events is calculated as:

P(A \ and \B )=P(A)\times P(B)\\\\P(6)=0.94\times0.94\times0.94\times0.94\times0.94\times0.94\\\\=0.6899

Hence, the probability of correctly identifying the 6 matches is 0.6899

b.Given the probability of success is 0.74 for a novice and that the number of pairs, n=6:

-Each attempt is independent and therefore the probability of  the events is calculated as:

P(A \ and \B )=P(A)\times P(B)\\\\P(6)=0.74\times0.74\times0.74\times0.74\times0.74\times0.74\\\\=0.1642

#Hence, the probability of correctly identifying the 6 matches is 0.1642

*I have used the sample size of 6(due to conflicting info/question size).

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If P is the orthocenter of △ABC, AB = 13, BF = 9,and FC = 5.6, find each measure & the perimeter of triangle ABC.
harina [27]

Answer:

Perimeter = 38.6

Step-by-step explanation:

Given

A\ B = 13

B\ F = 9

F\ C = 5.6

Required

Calculate the perimeter of A B C

To calculate the perimeter of A B C, we sum up the sides of the triangle

i.e.

Perimeter = A B + B\ C + A\ C

AB is given in the question already.

So, we need to calculate B F and F C

To solve for BF, we consider triangle B F C

Using Pythagoras Theorem, we have:

B\ C^2 = B\ F^2 + F\ C^2

Substitute values for BF and FC;

B\ C^2 = 9^2 + 5.6^2

B\ C^2 = 81 + 31.36

B\ C^2 = 112.36

B\ C^2= \sqrt{112.36

B\ C = 10.6

Next, we calculate A C.

To calculate A C, we need to calculate A F, considering triangle B F A

Using Pythagoras Theorem, we have:

A\ B^2 = B\ F^2 + A\ F^2

Substitute values for B F and A B;

13^2 = 9^2 + A\ F^2

169= 81 + A\ F^2

A\ F^2 = 169 - 81

A\ F^2 = 88

A\ F = \sqrt{88

A\ F = 9.4

Since F lies on line A C:

A\ C = A\ F + F\ C

A\ C = 9.4 + 5.6

A\ C = 15.0

Recall that:

Perimeter = A\ B + B\ C + A\ C

Perimeter = 13 + 10.6 + 15.0

Perimeter = 38.6

<em>Hence, the perimeter is 38.6</em>

3 0
3 years ago
Suppose that a large mixing tank initially holds 400 gallons of water in which 70 pounds of salt have been dissolved. Pure water
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Answer:

Step-by-step explanation:

Given that a large mixing tank initially holds 400 gallons of water in which 70 pounds of salt have been dissolved. Pure water is pumped into the tank at a rate of 4 gal/min, and when the solution is well stirred, it is then pumped out at the same rate.

Let Q(t) be the quantity of salt at time t.

Q(0) = 70 pounds

Inflow of water = outflow = 4 gal/min

So resulting volume of tank at time t = 400 gallons

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= 0 - \frac{Q(t)}{400}

i.e. \frac{dQ}{dt} =\frac{-Q(t)}{400}

This is a variable separable equation

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So A(t) = Q(t) = 70 e^{-\frac{t}{400}} and

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Answer:

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A right rectangular prism is one in which each side makes an angle of 90^{0} with its base, which is a square. It is a three dimensional figure with six faces.

The point where the horizontal plane and the prism coincides would take the shape of the base of the prism. This is because the prism rests with its base on the horizontal plane. Thus, the shape required is in the form of a square since its base is a square. The length and width of its base are equal.

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