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timurjin [86]
2 years ago
9

All island taxi charges an initial fee of $5 plus $2 per mile driven. Lyft charges a flat rate $25 for any distance. After how m

any miles will both companies charge the same amount
Mathematics
1 answer:
vladimir2022 [97]2 years ago
6 0

Answer:

10 miles.

Step-by-step explanation:

The island taxi charges $5 for initial fee and $2 per mile.

For the island taxi to be $25 it would have to drive for 10 miles. (25-5=20) due to the initial fee puts you at 20. 20÷2 is 10. Meaning 10 miles for the island taxi.

Since the lyft charges a flat rate of $25 for any distance the only distance that matters is the island taxi.

Your answer is 10 miles.

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2 years ago
Suppose the time a child spends waiting at for the bus as a school bus stop is exponentially distributed with mean 7 minutes. De
Gala2k [10]

Answer:

The probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.

Step-by-step explanation:

Let the random variable <em>X</em> represent the time a child spends waiting at for the bus as a school bus stop.

The random variable <em>X</em> is exponentially distributed with mean 7 minutes.

Then the parameter of the distribution is,\lambda=\frac{1}{\mu}=\frac{1}{7}.

The probability density function of <em>X</em> is:

f_{X}(x)=\lambda\cdot e^{-\lambda x};\ x>0,\ \lambda>0

Compute the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning as follows:

P(6\leq X\leq 9)=\int\limits^{9}_{6} {\lambda\cdot e^{-\lambda x}} \, dx

                      =\int\limits^{9}_{6} {\frac{1}{7}\cdot e^{-\frac{1}{7} \cdot x}} \, dx \\\\=\frac{1}{7}\cdot \int\limits^{9}_{6} {e^{-\frac{1}{7} \cdot x}} \, dx \\\\=[-e^{-\frac{1}{7} \cdot x}]^{9}_{6}\\\\=e^{-\frac{1}{7} \cdot 6}-e^{-\frac{1}{7} \cdot 9}\\\\=0.424373-0.276453\\\\=0.14792\\\\\approx 0.148

Thus, the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.

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Answer:

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Step-by-step explanation:

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