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jenyasd209 [6]
3 years ago
15

On a six-question multiple-choice test there are five possible answers for each question, of which one is correct (C) and four a

re incorrect (I). If a student guesses randomly and independently, find the probability of (a) Being correct only on questions 1 and 4 (i.e., scoring C, I, I, C, I, I). (b) Being correct on two questions.
Mathematics
1 answer:
Anon25 [30]3 years ago
5 0

Answer:

(a) 1.64%

(b) 24.58%

Step-by-step explanation:

As for each question there are one correct answer in five possible answers, the probability of guessing the correct answer is 1/5 = 0.2, so the probability of guessing the wrong answer is (1 - 0.2) = 0.8.

(a) The probability of being correct only on questions 1 and 4 is calculated multiplying all the following probabilities:

question 1 correct: 0.2

question 2 wrong: 0.8

question 3 wrong: 0.8

question 4 correct: 0.2

question 5 wrong: 0.8

question 6 wrong: 0.8

P = (0.2)^2 * (0.8)^4 = 0.0164 = 1.64%

(b) The probability of being correct in two questions is calculated similarly to the question in (a), but now we also have a combination problem: The 2 correct questions can be any group of 2 questions inside the 6 total questions, so we also multiply the probability of each question being correct or wrong by the combination of 6 choose 2:

C(6,2) = 6!/(4!*2!) = 6*5/2 = 15

P = 15 * (0.2)^2 * (0.8)^4 = 0.2458 = 24.58%

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A helicopter is flying above a town. the local high school is directly to the east of the helicopter at a 20° angle of depressio
guapka [62]
Answer: 4.5 miles

Explanation:

When you draw the situation you find two triangles.

1) Triangle to the east of the helicopter

a) elevation angle from the high school to the helicopter = depression angle from the helicopter to the high school = 20°

b) hypotensue = distance between the high school and the helicopter

c) opposite-leg to angle 20° = heigth of the helicopter

d) adyacent leg to the angle 20° = horizontal distance between the high school and the helicopter = x

2) triangle to the west of the helicopter

a) elevation angle from elementary school to the helicopter = depression angle from helicopter to the elementary school = 62°

b)  distance between the helicopter and the elementary school = hypotenuse

c) opposite-leg to angle 62° = height of the helicopter

d) adyacent-leg to angle 62° = horizontal distance between the elementary school and the helicopter = 5 - x

3) tangent ratios

a) triangle with the helicpoter and the high school

tan 20° = Height / x ⇒ height = x tan 20°

b) triangle with the helicopter and the elementary school

tan 62° = Height / (5 - x) ⇒ height = (5 - x) tan 62°

c) equal the height from both triangles:

x tan 20° = (5 - x) tan 62°

x tan 20° = 5 tan 62° - x tan 62°

x tan 20° + x tan 62° = 5 tan 62°

x  (tan 20° + tan 62°) = 5 tan 62°

⇒ x = 5 tant 62° / ( tan 20° + tan 62°)

⇒ x = 4,19 miles

=> height = x tan 20° = 4,19 tan 20° = 1,525 miles

4) Calculate the hypotenuse of this triangle:

hipotenuese ² = x² + height ² = (4.19)² + (1.525)² = 19.88 miles²

hipotenuse = 4.46 miles

Rounded to the nearest tenth = 4.5 miles

That is the distance between the helicopter and the high school.
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3 years ago
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An arithmetic sequence is defined by the recursive formula t1 = 9, tn = tn - 1 - 4, where n ∈N and n > 1. The sequence is
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T2 = t1 - 4 = 9 - 4 = 5
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3 years ago
I need help with this
Arturiano [62]

Answer:

Bc,AB,Ac

Step-by-step explanation:

Bc because

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Ab is 150

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4 0
3 years ago
Factor the quadratic equation <br> 3x^2+3x-6=0
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The answer would be...

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Find the surface area of the cylinder. Round your answer to the nearest tenth.
kirill [66]

Given:

Height of cylinder = 12 cm

Diameter of cylinder = 6 cm

To find:

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8 0
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