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2 years ago

The reaction time (in seconds) to a certain stimulus is a continuous random variable with pdf f(x) 5 5 3 2 ? 1 x2 1

Mathematics

1 answer:

muminat2 years ago

7 0

The probability that the reaction time for this density function is at most 2.5 seconds is equal to 0.9.

<h3>What is a density function?</h3>

A density function can be defined as a type of function which is used to represent the density of a continuous random variable that lies within a specific range.

<h3>How to calculate the probability that reaction time is at most 2.5 seconds?</h3>

P(X ≤ 2.5) = Fx(2.5)

Fx(2.5) = 3/2 - 3/2(2.5)

Fx(2.5) = 3/2 - 3/5

Fx(2.5) = 0.9.

Read more on density function here: brainly.com/question/14448717

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Complete Question:

The reaction time (in seconds) to a certain stimulus is a continuous random variable with pdf:

f(x) = $\left \{ {{\frac{3}{2x^2} \;1 \leq x\leq 3} \atop {0}\;otherwise} \right$

What is the probability that reaction time is at most 2.5 seconds?

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At 2 PM, a thermometer reading 80°F is taken outside where the air temperature is 20°F. At 2:03 PM, the temperature reading yiel

Alexeev081 [22]

Use Law of Cooling:
$T(t) = (T_0 - T_A)e^{-kt} +T_A$
T0 = initial temperature, TA = ambient or final temperature

First solve for k using given info, T(3) = 42
$42 = (80-20)e^{-3k} +20 \\ \\ e^{-3k} = \frac{22}{60}=\frac{11}{30} \\ \\ k = -\frac{1}{3} ln (\frac{11}{30})$

Substituting k back into cooling equation gives:
$T(t) = 60(\frac{11}{30})^{t/3} + 20$

At some time "t", it is brought back inside at temperature "x".
We know that temperature goes back up to 71 at 2:10 so the time it is inside is 10-t, where t is time that it had been outside.
The new cooling equation for when its back inside is:
$T(t) = (x-80)(\frac{11}{30})^{t/3} + 80 \\ \\ 71 = (x-80)(\frac{11}{30})^{\frac{10-t}{3}} + 80$
Solve for x:
$x = -9(\frac{11}{30})^{\frac{t-10}{3}} + 80$
Sub back into original cooling equation, x = T(t)
$-9(\frac{11}{30})^{\frac{t-10}{3}} + 80 = 60 (\frac{11}{30})^{t/3} +20$
Solve for t:
$60 (\frac{11}{30})^{t/3} +9(\frac{11}{30})^{\frac{-10}{3}}(\frac{11}{30})^{t/3} = 60 \\ \\ (\frac{11}{30})^{t/3} = \frac{60}{60+9(\frac{11}{30})^{\frac{-10}{3}}} \\ \\ \\ t = 3(\frac{ln(\frac{60}{60+9(\frac{11}{30})^{\frac{-10}{3}}})}{ln (\frac{11}{30})}) \\ \\ \\ t = 4.959$

This means the exact time it was brought indoors was about 2.5 seconds before 2:05 PM

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3 years ago

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Molodets [167]

It is 46 if you divide 34 by 16 you get 2.125 then divide 100 by 2.125 and you get 47.05 the 0 means go down if you are rounding which brings it to 46

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3 years ago

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The rectangle below is enlarged using a scale factor of 1.5. What will be the new length and width of the rectangle?

Likurg_2 [28]

Answer: length = 4.5 m, width = 3 m

Step-by-step explanation:

When a shape is enlarged using a scale factor, you simply multiply each of the sides by the scale factor.

length = 3 * 1.5 = 4.5 m

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3 years ago

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mojhsa [17]

Answer:

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Step-by-step explanation:

Given the function:

t(c)=-3970.9(ln c)

c = % of carbon remaining ; t = time

1.) c = 47% = 47/100 = 0.47

t(0.47) = - 3970.9(In 0.47)

t = - 3970.9 * −0.755022

t = 2998.119

t = 2998

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7000 = - 3970.9(In c)

7000 / - 3970.9 = In c

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c = exp(−1.762824)

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c = 0.1715596 * 100%

c = 17.156% ; c = 17%

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Step-by-step explanation:

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