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dimulka [17.4K]
3 years ago
11

A five question multiple choice test has 4 choices for each question and only 1 correct answer each. What is the probability of

guessing at least 3 out of the 5 questions correctly?
Mathematics
1 answer:
crimeas [40]3 years ago
4 0

Answer:

Prob = 13/1024 = 0.0127

Step-by-step explanation:

Prob {A correct answer} = Correct option / Total options = 1/4

Prob {A wrong answer} = Wrong options / Total options = 3/4

Prob [3 answers correct] = P (3 correct ,& 2 wrong) or P (4 correct ,& 1 wrong) or P (5 correct, & no wrong)

= [ (1/4) x (1/4) x (1/4) x (3/4) x (3/4) ]  +  [ (1/4) x (1/4) x (1/4) x (1/4) x (3/4) ] + [ (1/4) x (1/4) x (1/4) x (1/4) x (1/4) ]

( 9/1024 ) + ( 3/1024 ) + ( 1/1024 )

13/1024 = 0.0127

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Find the equation of the line which passes through the point (7,2) and is perpendicular to y=5x-2
MariettaO [177]

Answer:

\displaystyle y=-\frac{1}{5}x+\frac{17}{5}

Step-by-step explanation:

<u>Equation of a line</u>

A line can be represented by an equation of the form

y=mx+b

Where x is the independent variable, m is the slope of the line, b is the y-intercept and y is the dependent variable.

We need to find the equation of the line passing through the point (7,2) and is perpendicular to the line y=5x-2.

Two lines with slopes m1 and m2 are perpendicular if:

m_1.m_2=-1

The given line has a slope m1=5, thus the slope of our required line is:

\displaystyle m_2=-\frac{1}{m_1}=-\frac{1}{5}

The equation of the line now can be expressed as:

\displaystyle y=-\frac{1}{5}x+b

We need to find the value of b, which can be done by using the point (7,2):

\displaystyle 2=-\frac{1}{5}*7+b

Operating:

\displaystyle 2=-\frac{7}{5}+b

Multiplying by 5:

10=-7+5b

Operating:

10+7=5b

Solving for b:

\displaystyle b=\frac{17}{5}

The equation of the line is:

\boxed{\displaystyle y=-\frac{1}{5}x+\frac{17}{5}}

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