1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
svetoff [14.1K]
3 years ago
6

A student takes a multiple choice test. Each question has N answers. If the student knows the answer to a question, the student

gives the right answer, and otherwise guesses uniformly and at random. The student knows the answer to 70% of the questions. Write K for the event a student knows the answer to a question and R for the event the student answers the question correctly. (a) What is P(K)? (b) What is P(RIK)? (c) What is P(KR), as a function of N? (d) What values of N will ensure that P(K|R) >99%?
Mathematics
1 answer:
alexgriva [62]3 years ago
8 0

Answer:

Step-by-step explanation:

a) P(K) = 0.7

b) P(R|K) = 1

c) P(K|R) = P(KnR) /P(R)

= P(K) x P(R|K) / ( P(K) x P(R|K) + P(K') P(R|K')

= 0.7 x 1 / ( 0.7 x 1 + (1-0.7) x 1/N)

= 0.7/(0.7 + 0.3/N)

d) P(K|R) > 0.99

0.7/(0.7 + 0.3/N) > 0.99

N > 42.86

N = 43 will be the value of N that will ensure that P(K|R) >99%

You might be interested in
Will give BRAINLIEST to the correct answer!!!
iren2701 [21]
Here is a key that showed up online

8 0
3 years ago
Read 2 more answers
Use multiplication or division of power series to find the first three nonzero terms in the Maclaurin series for each function.
Lunna [17]

Answer:

The first three nonzero terms in the Maclaurin series is

\mathbf{ 5e^{-x^2} cos (4x)  }= \mathbf{ 5 ( 1 -9x^2 + \dfrac{115}{6}x^4+ ...) }

Step-by-step explanation:

GIven that:

f(x) = 5e^{-x^2} cos (4x)

The Maclaurin series of cos x can be expressed as :

\mathtt{cos \ x = \sum \limits ^{\infty}_{n =0} (-1)^n \dfrac{x^{2n}}{2!} = 1 - \dfrac{x^2}{2!}+\dfrac{x^4}{4!}-\dfrac{x^6}{6!}+...  \ \ \ (1)}

\mathtt{e^{-2^x} = \sum \limits^{\infty}_{n=0}  \ \dfrac{(-x^2)^n}{n!} = \sum \limits ^{\infty}_{n=0} (-1)^n \ \dfrac{x^{2n} }{x!} = 1 -x^2+ \dfrac{x^4}{2!}  -\dfrac{x^6}{3!}+... \ \ \  (2)}

From equation(1), substituting x with (4x), Then:

\mathtt{cos (4x) = 1 - \dfrac{(4x)^2}{2!}+ \dfrac{(4x)^4}{4!}- \dfrac{(4x)^6}{6!}+...}

The first three terms of cos (4x) is:

\mathtt{cos (4x) = 1 - \dfrac{(4x)^2}{2!}+ \dfrac{(4x)^4}{4!}-...}

\mathtt{cos (4x) = 1 - \dfrac{16x^2}{2}+ \dfrac{256x^4}{24}-...}

\mathtt{cos (4x) = 1 - 8x^2+ \dfrac{32x^4}{3}-... \ \ \ (3)}

Multiplying equation (2) with (3); we have :

\mathtt{ e^{-x^2} cos (4x) = ( 1- x^2 + \dfrac{x^4}{2!} ) \times ( 1 - 8x^2 + \dfrac{32 \ x^4}{3} ) }

\mathtt{ e^{-x^2} cos (4x) = ( 1+ (-8-1)x^2 + (\dfrac{32}{3} + \dfrac{1}{2}+8)x^4 + ...) }

\mathtt{ e^{-x^2} cos (4x) = ( 1 -9x^2 + (\dfrac{64+3+48}{6})x^4+ ...) }

\mathtt{ e^{-x^2} cos (4x) = ( 1 -9x^2 + \dfrac{115}{6}x^4+ ...) }

Finally , multiplying 5 with \mathtt{ e^{-x^2} cos (4x) } ; we have:

The first three nonzero terms in the Maclaurin series is

\mathbf{ 5e^{-x^2} cos (4x)  }= \mathbf{ 5 ( 1 -9x^2 + \dfrac{115}{6}x^4+ ...) }

7 0
3 years ago
What the sheet says
dmitriy555 [2]
Jenny spent 25 minutes reading
5 0
3 years ago
PLEASE ANSWER ASAP FOR BRAINLEST, REALLY EASY QUESTION!!!!!!!!!!!!!!!!!!!!!!!
Tresset [83]

Answer:

i think its 200

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Given the function h of x equals three times the square root x plus 1 end root minus 2, which statement is true about h(x)? The
andreev551 [17]

A function assigns the values. The correct option is D.

<h3>What is a Function?</h3>

A function assigns the value of each element of one set to the other specific element of another set.

Given the function h(x)=3√(x+1) - 2, therefore, if we plot the function on the graph, then the statement that is true about the function is that the function is increasing on the interval (–1, ∞).

Hence, the correct option is A.

Learn more about Function:

brainly.com/question/5245372

#SPJ1

5 0
2 years ago
Other questions:
  • Which of the following is the correct sl unit to use in measuring amount of material contained in a solid sphere
    5·1 answer
  • A car travels 450 miles in the same time that a motorcycle travels 390 miles. if the car’s speed is 10 miles per hour more than
    6·1 answer
  • Can y’all help me with 5 thank you
    10·1 answer
  • What is the volume of the box?
    9·2 answers
  • How to write 999,858,411
    14·1 answer
  • a bakery made 230 muffins in the morning it made 160 more muffins in the afternoon by the end of the day the bakery had sold 260
    12·1 answer
  • Need help will mark Brainliest
    6·1 answer
  • (Daily math question for points!!) A circle has a circumference of 50.26cm
    5·2 answers
  • Tom started texting friends. In hour 1 he texted 3 friends. In hour 2 he texted 9 friends. In hour 3 he texted 27 friends. The p
    8·1 answer
  • Mister mayor has asked that you pass a geometry quiz before you begin building. He wants you to make sure you are qualified befo
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!