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3 years ago

10

The volume of a triangular prism is 264 cubic feet. The area of a base of the prism is 48 square feet. Find the height of the pr

ism.

1 answer:

Elan Coil [88]3 years ago

4 0

The height is 1968 Hope i helped

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Rewrite using exponential notation \root(6)((4\pi )^(3))

Nezavi [6.7K]

$~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ \sqrt[6]{(4\pi )^3}\implies (4\pi )^{\frac{3}{6}}\implies (4\pi )^{\frac{1}{2}}$

5 0

2 years ago

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

morpeh [17]

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

Step-by-step explanation:

Since we have given that

P(n) = $\dfrac{15}{120}=0.125$

As we know the poisson process, we get that

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

So, for exactly one car would be

P(n=1) is given by

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

Hence, our required probability is 0.2599.

a. Approximate the number of these intervals in which exactly one car arrives

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%.

7 0

4 years ago

Solve for x. Write the smaller solution first, and the larger solution second.

Shkiper50 [21]

Answer:

Step-by-step explanation:

x^2 + 3x - 10 = 0

(x - 2)(x + 5) = 0

x - 2 = 0 x + 5 = 0

x = 2 x = -5

smaller x = -5

larger x = 2

5 0

3 years ago

Can someone please answer if itś right I will give the brainlist thing

deff fn [24]

Answer:

the answer would be 116.

This is because if half of the kernels popped you just multiply 58 by 2 to get 100 percent of the kernels.

I hope this helps! Please mark me Brainliest!

Step-by-step explanation:

4 0

3 years ago

Find the triangle sum theorem

GenaCL600 [577]

Answer:

x=37

Step-by-step explanation:

a triangle is equal to 180°. so if you already have 50+56 then you have 74° left for 2x. and 74/2=37

6 0

3 years ago

Read 2 more answers