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Dovator
5 days ago
13

Twenty percent of adults in a particular community have at least a​ bachelor's degree. Suppose x is a binomial random variable

that counts the number of adults with at least a​ bachelor's degree in a random sample of 100 adults from the community. If you are using a calculator with the binompdf and binomcdf​ commands, which of the following is the most efficient way to calculate the probability that more than 60 adults have a​ bachelor's degree, ​P(x?>60)?
a. P(x < 60)=binompdf(100,0 20,59)
b. P(x<60)=binompdf(100.0.20.60)
c. P(x<60)= binomcdf(100,0,20,59)
d. P(x<60)=binomcdf (100.0.20.60)
Mathematics
1 answer:
tester [8.8K]5 days ago
5 0
This scenario relates to binomial probability, where the results can either be a success or a failure. A success indicates that a selected adult possesses a bachelor's degree. Consequently, the success probability, denoted as p, is 20/100 = 0.2. The number of adults in the sample, represented as n, equals 100, and x, the count of successes, is 60. The probability of having more than 60 adults with a bachelor's degree, represented as P(x >60), can be noted internally as P(x < 60) = binomcdf (100, 0.20, 60). The function binompdf would indicate P(x = 60).
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When jumping, a flea rapidly extends its legs, reaching a takeoff speed of 1.0 m/s over a distance of 0.50 mm . part a what is t
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The flea experiences an acceleration of 1,000 m/s².

Detailed explanation

This scenario involves motion with constant acceleration.

The relevant variables include the following.

\boxed{u \ or \ v_i = initial \ velocity}

\boxed{u \ or \ v_t \ or \ v_i = terminal \ or \ final \ velocity}

\boxed{a = acceleration \ (constant)}

\boxed{d = distance \ travelled}

We know the flea attains a takeoff velocity of 1.0 m/s over a distance of 0.50 mm.

The flea starts from rest, so the initial velocity is zero. The question asks for the flea's acceleration during leg extension.

The equation we apply is:

\boxed{ \ v^2 = u^2 + 2ad \ }

  • a = acceleration (m/s²)
  • u = initial speed = 0 m/s
  • v = takeoff velocity = 1.0 m/s
  • d = displacement = 0.50 mm

First, convert 0.50 mm to meters: \boxed{0.50 \ mm = 0.50 \times 10^{-3} \ m = 5.0 \times 10^{-4} \ m}

Solution steps:

Rearrange the formula to isolate acceleration (a).

\boxed{ \ v^2 = u^2 + 2ad \ }

\boxed{ \ v^2 - u^2 = 2ad \ }

\boxed{ \ 2ad = v^2 - u^2 \ }

\boxed{ \ a = \frac{v^2 - u^2}{2d} \ }

Insert the given values into the rearranged equation.

\boxed{ \ a = \frac{(1.0)^2 - (0)^2}{2(5.0 \times 10^{-4})} \ }

\boxed{ \ a = \frac{1}{10 \times 10^{-4}} \ }

\boxed{ \ a = \frac{1}{1 \times 10^{-3}} \ }

\boxed{ \ a = 1 \times 10^{3}\ = 1,000 \ m/s^2 \ }

This yields the flea's acceleration as 1,000 m/s².

Additional resources

  1. Scientific notation: brainly.com/question/7263463
  2. Determining substance mass: brainly.com/question/4053884
  3. Conversion into cubic units: brainly.com/question/1446243

Keywords: flea, jumping, leg extension, takeoff velocity, initial speed, displacement, acceleration, constant acceleration, unit conversion

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