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2 years ago

Simplify hariy fractions

Mathematics

1 answer:

borishaifa [10]2 years ago

3 0

Um sounds nice i guess its kind of funny simplify hairy fractions

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Answer:

a.) f(x) = $\frac{1}{30}$ where 90 < x < 120

b.) $\frac{2}{3}$

c.) $\frac{2}{3}$

d.) $\frac{1}{2}$

Step-by-step explanation:

Let

X be a uniform random variable that denotes the actual charging time of battery.

Given that, the actual recharging time required is uniformly distributed between 90 and 120 minutes.

⇒X ≈ ∪ ( 90, 120 )

a.)

Probability density function , f (x) = $\frac{1}{120 - 90} = \frac{1}{30}$ where 90 < x < 120

b.)

P(x < 110) = $\int\limits^{110}_{90} {\frac{1}{30} } \, dx$

= $\frac{1}{30}[x]\limits^{110}_{90} = \frac{1}{30} [ 110 - 90 ] = \frac{1}{30} [ 20] = \frac{2}{3}$

c.)

P(x > 100 ) = $\int\limits^{120}_{100} {\frac{1}{30} } \, dx$

= $\frac{1}{30}[x]\limits^{120}_{100} = \frac{1}{30} [ 120 - 100 ] = \frac{1}{30} [ 20] = \frac{2}{3}$

d.)

P(95 < x< 110) = $\int\limits^{110}_{95} {\frac{1}{30} } \, dx$

= $\frac{1}{30}[x]\limits^{110}_{95} = \frac{1}{30} [ 110 - 95 ] = \frac{1}{30} [ 15] = \frac{1}{2}$

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3 years ago

-1/3x+2x=3 3/4 what does the variable represent?

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Start off by combining like terms on the LHS (the terms with x in them).

So we get $\frac{-1}{3}x+2x= \frac{-1}{3}x+ \frac{6}{3}x= \frac{-5}{3}x$

Replacing this result with what we had before on the LHS, we get $\frac{-5}{3}x=3 \frac{3}{4}= \frac{9}{4}$

⇒Solve for x (divide both sides $\frac{-5}{3}$ )
⇒Don't forget about reciprocity rules when dividing. This is the same as multiplying both sides by $\frac{3}{-5}$

⇒ $x= \frac{9}{4}( \frac{3}{-5})
$
⇒ $x= -\frac{27}{20}=-1\frac{7}{20}$ ***This is a proper fraction

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