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3 years ago

7

Consider the function f(x) = 4x2 + 5. Find the value of f(x) when x = 2 and select the correct answer below. A. 13 B. 21 C. 69 D

. 89

2 answers:

Advocard [28]3 years ago

8 0

The answer is B. 21

f(x) = 4(2)^2 + 5
f(x) = 4(4) + 5
f(x) = 16 + 5

f(x) = 21

egoroff_w [7]3 years ago

3 0

Substitute 2 for x

$f(2)=4(2)^2+5$
$f(2)=4(4)+5$
$f(2)=16+5$
$f(2)=21$

answer is B
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At a specific point on a highway, vehicles arrive according to a Poisson process. Vehicles are counted in 12 second intervals, a

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Answer: a) 4.6798, and b) 19.8%.

Step-by-step explanation:

Since we have given that

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$P(n)=\dfrac{(\lambda t)^n\times e^{-\lambda t}}{n!}\\\\P(n=0)=0.125=\dfrac{(\lambda \times 14)^0\times e^{-14\lambda}}{0!}\\\\0.125=e^{-14\lambda}\\\\\ln 0.125=-14\lambda\\\\-2.079=-14\lambda\\\\\lambda=\dfrac{2.079}{14}\\\\0.1485=\lambda$

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$=\dfrac{(0.1485\times 14)^1\times e^{-0.1485\times 14}}{1!}\\\\=0.2599$

Hence, our required probability is 0.2599.

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Number of these intervals in which exactly one car arrives is given by

$0.2599\times 18=4.6798$

We will find the traffic flow q such that

$P(0)=e^{\frac{-qt}{3600}}\\\\0.125=e^{\frac{-18q}{3600}}\\\\0.125=e^{-0.005q}\\\\\ln 0.125=-0.005q\\\\-2.079=-0.005q\\\\q=\dfrac{-2.079}{-0.005}=415.88\ veh/hr$

b. Estimate the percentage of time headways that will be 14 seconds or greater.

so, it becomes,

$P(h\geq 14)=e^{\frac{-qt}{3600}}\\\\P(h\geq 14)=e^{\frac{-415.88\times 14}{3600}}\\\\P(h\geq 14)=0.198\\\\P(h\geq 14)=19.8\%$

Hence, a) 4.6798, and b) 19.8%.

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