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VMariaS [17]
3 years ago
11

A student takes an exam containing 1818 true or false questions. If the student guesses, what is the probability that he will ge

t exactly 66 questions right? Round your answer to four decimal places.
Mathematics
2 answers:
creativ13 [48]3 years ago
8 0

Probability

p=66×100/1818=3.6303630363%

After rounding to 4 decimals:

p=3.6304%

Juli2301 [7.4K]3 years ago
7 0

Answer:

0.0708 = 7.08% probability that he will get exactly 6 questions right.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the student guesses the correct answer, or he guesses the wrong answer. The probability of guessing the correct answer in a question is independent from other questions. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

18 questions

This means that n = 18

True or false, guessed.

Each question has two possible answers, so p = \frac{1}{2} = 0.5

If the student guesses, what is the probability that he will get exactly 6 questions right?

This is P(X = 6)

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

P(X = 6) = C_{18,6}.(0.5)^{6}.(0.5)^{12} = 0.0708

0.0708 = 7.08% probability that he will get exactly 6 questions right.

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A crew consists of 1​ apprentice, 1​ journeyman, and 1 master carpenter. The crew receives a check for ​$4800 for a job they jus
tamaranim1 [39]

Answer:

Apprentice=$800

Journeyman=$1600

Master=$2400

Step-by-step explanation:

We have that all the crew won a total of $4800 then it is the salary of the apprentice, the journeyman and the master carpenter. It say that the journeyman makes 200% of the apprentice, then it means that the journeyman won the double of the apprentice. The master won 150% of what a journeyman, it means that the master won 1.5 of the salary of the journeyman.

With this information we can write the next set of equations.

A+J+M=\$4800\\J=2A\\M=1.5J

Using the second equation in the third equation we can know how much won the master in terms of the salary of the apprentice, then:

M=1.5J\\M=1.5(2A)\\M=3A

With this we could rewrite the first equation as:

A+J+M=\$4800\\A+2A+3A=\$4800\\6A=\$4800\\A=\dfrac{\$4800}{6}\\A=\$800

Then the aprentice earn $800, the journeyman $1600 and the master $2400

6 0
3 years ago
What’s is the inverse function of a(m)=0.6735e^0.423m
natta225 [31]

Answer:

a^{-1}(m)=\frac{ln(\frac{m}{0.6735})}{0.423}

Step-by-step explanation:

The function is  a(m)=0.6735e^{0.423m}

Changing functional notation of a(m) to y:

y=0.6735e^{0.423m}

Now, interchanging m and y:

m=0.6735e^{0.423y}\\

Now, solving for y:

e^{0.423y}=\frac{m}{0.6735}\\ln[e^{0.423y}]=ln[\frac{m}{0.6735}]\\0.423y=ln(\frac{m}{0.6735})\\y=\frac{ln(\frac{m}{0.6735})}{0.423}

Thus, the inverse function is:

a^{-1}(m)=\frac{ln(\frac{m}{0.6735})}{0.423}

5 0
3 years ago
The length of a rectangle is twice the width. If the perimeter of the rectangle is 69 units, find the area of the garden.
8_murik_8 [283]

Answer:

area= 264.5 unit square

Step-by-step explanation:

let the width of the rectangle be x units then the length would be 2x units

perimeter = 2(l+b)= 2(2x+x)=2(3x)=6x

69=6x

x=69/6=11.5units

width is 11.5 units and length is 23 units

area= lxb= 11.5* 23= 264.5 units square

6 0
3 years ago
Given the relationship x2 + 3y2 =12, with y > 0 and dx, dt = 2 units/min., find the value of dy, dt at the instant y = 1 unit
matrenka [14]
\bf x^2+3y^2=12\implies \stackrel{chain~rule}{2x\cfrac{dx}{dt}}+3 \stackrel{chain~rule}{\left(2y\cfrac{dy}{dt}\right)}=0
\\\\\\
2x\cfrac{dx}{dt}+6y\cfrac{dy}{dt}=0
\implies 
6y\cfrac{dy}{dt}=-2x\cfrac{dx}{dt}\implies \cfrac{dy}{dt}=\cfrac{-2x\frac{dx}{dt}}{
6y\frac{dy}{dt}}
\\\\\\
\boxed{\cfrac{dy}{dt}=-\cfrac{x\frac{dx}{dt}}{3y}}\\\\
-------------------------------

\bf \textit{now, when y = 1, what is \underline{x}?}\qquad x^2+3y^2=12\implies x^2+3(1)^2=12
\\\\\\
x^2=9\implies x=\sqrt{9}\implies x=3\\\\
-------------------------------\\\\
\begin{cases}
y=1\\
x=3\\
\frac{dx}{dt}=2
\end{cases}\implies \cfrac{dy}{dt}=-\cfrac{3\cdot 2}{3\cdot 1}\implies \cfrac{dy}{dt}=-2
7 0
3 years ago
6. An urn contains 15 red balls and 8 blue balls. In each draw, one ball is extracted at random. It is then returned to the urn,
Leviafan [203]

Answer:

P(C4) = 0.0711

Step-by-step explanation:

consider the first draw = 15/23  since it cannot be a blue ball

The second draw = 21/29 since 6 more red balls will be added after the draw since a blue ball cannot be drawn

the third draw = 27/35 since 6 more red balls will be added after each draw since a blue ball cannot be drawn

therefore the total number of red balls will be = 15 + 6 + 6 + 6 = 33 red balls after the 4th draw. the total ball now in the urn= 33 red + 4 blue = 41

Hence the probability of drawing a blue ball at the fourth draw after drawing red balls at the previous attempts = 8/41

P(C4) = P ( fourth ball is blue ) * P( first ball red)*P(second ball red) *P(third ball red )

= (8/41) * (15/23) * (21/29)* (27/35) = 0.0711

8 0
3 years ago
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