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zvonat [6]
3 years ago
8

Suppose that after 10 years of service, 40% of computers have problems with motherboards (MB), 30% have problems with hard drive

s (HD), and 15% have problems with both MB and HD. What is the probability that a 10-year old computer still has fully functioning MB and HD?
Mathematics
1 answer:
sergij07 [2.7K]3 years ago
5 0

Answer:

The probability that a 10-year old computer still has fully functioning MB and HD is 45%

Step-by-step explanation:

The probability of the union of two events, is equal to the sum of the individual probabilities of the two events, minus the probability of the intersection event.

That means that the probability of have a fully functional computer (PFC) is equal to the sum of probability of have a computer with a functional motherboards (PFMB) plus the probability of have a computer with a functional hard drives (PFHD), minus the probability of have a computer with both motherboards and hard drives functional (PBMH).

PFC = PFMB+PFHD-PBMH

  • Probability of functional motherboards (PFMB)

PFMB = 1 - probability of having problems with motherboards = 1 - 40 %

PFMB  = 1 - \frac{40}{100} = 1 - \frac{4}{10} = \frac{6}{10}

  • Probability of functional hard drive (PFHD)

PFHD = 1 - probability of having problems with hard drive = 1 - 30 %

PFHD = 1 - \frac{30}{100} = 1 - \frac{3}{10} = \frac{7}{10}

  • Probability of functional both (PFMH)

PFMH = 1 - probability of having problems with both = 1 - 15 %

PFMH = 1 - \frac{15}{100} = 1 - \frac{3}{20} = \frac{17}{20}

PFC = \frac{6}{10} + \frac{7}{10} - \frac{17}{20}

PFC = \frac{9}{20}

PFC = 0.45

<em>Multiply by 100 to get in in %</em>

The probability that a 10-year old computer still has fully functioning MB and HD is 45%

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2 years ago
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Misha Larkins [42]

Answer:

\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}

Step-by-step explanation:

We are given the trigonometric equation of:

\displaystyle{\sin 4x = \dfrac{\sqrt{3}}{2}}

Let u = 4x then:

\displaystyle{\sin u = \dfrac{\sqrt{3}}{2}}\\\\\displaystyle{\arcsin (\sin u) = \arcsin \left(\dfrac{\sqrt{3}}{2}\right)}\\\\\displaystyle{u= \arcsin \left(\dfrac{\sqrt{3}}{2}\right)}

Find a measurement that makes sin(u) = √3/2 true within [0, π) which are u = 60° (π/3) and u = 120° (2π/3).

\displaystyle{u = \dfrac{\pi}{3}, \dfrac{2\pi}{3}}

Convert u-term back to 4x:

\displaystyle{4x = \dfrac{\pi}{3}, \dfrac{2\pi}{3}}

Divide both sides by 4:

\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}

The interval is given to be 0 ≤ 4x < π therefore the new interval is 0 ≤ x < π/4 and these solutions are valid since they are still in the interval.

Therefore:

\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}

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1 year ago
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Step-by-step explanation:

6 0
3 years ago
If v = 6i + 3j, what is ||-10v||
tia_tia [17]

The values of ||-10v|| is 51.96 units

  • Complex numbers are square roots of negative numbers. They are expressions that consist of both the real and imaginary axis.

  • The general form of a complex number is expressed as z = x + iy

Given the complex number v = 6i + 3j,

10v is expressed as 10(6i + 3j)

10(6i + 3j) = 60i + 30j

Take the modulus of the complex number:

|10v|=\sqrt{60^2+30^2}\\|10v|= \sqrt{1800+900}\\|10v|= \sqrt{2700} \\|10v|=51.96units

Hence the values of ||-10v|| is 51.96 units

Learn more on the complex numbers here: brainly.com/question/10662770

6 0
2 years ago
I have three times as much money as does my brother. Our combined total is $42. How much does each of us have?
nika2105 [10]
For an instance, i stands for the money that you have, and b stands for the money that brother has.
An equation system based on the problem would be
i + b = 42 (equation 1)
i = 3b (equation 2)

Use substitution method to solve the problem
substitute 3b into i in the equation 1
i + b = 42
3b + b = 42
4b = 42
b = 42/4
b = 10.5

substitute the value of b into the equation 1
i = 3b
i = 3(10.5)
i = 31.5

You have $31.5 and your brother has $10.5
4 0
2 years ago
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