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Georgia [21]
4 years ago
12

Explain the steps you would use to solve the equation. Find the solution. 8^2x = 4096

Mathematics
1 answer:
Wewaii [24]4 years ago
7 0

Answer:

x =2

Step-by-step explanation:

To solve this we will follow the step below;

8^2x = 4096

Simply find 8 to the power of what number will give 4096 at the left-hand side of the equation

8⁴ = 4096

Substitute 8⁴ by  4096 at the right hand side of the equation

8²ˣ = 8⁴

The 8 at the right-hand side will cancel-out the 8 at the left-hand side

2x = 4

Divide both-side of the equation by 2

2x/2 = 4/2

x=2

The solution is x =2

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4 years ago
Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The m
marshall27 [118]

Answer:

1. 0.0000454

2. 0.01034

3. 0.0821

4. 0.918

Step-by-step explanation:

Let X be the random variable denoting the number of passengers arriving in a minute. Since the mean arrival rate is given to be 10,  

X \sim Poi(\lambda = 10)

1. Requires us to compute

P(X = 0) = e^{-10} \frac{10^0}{0!} = 0.0000454

2.  We need to compute P(X \leq 3) = P(X =0) + P(X =1) + P(X =2) + P(X =3)

P(X =1) = e^{-10} \frac{10^1}{1!} = 0.000454

P(X =2) = e^{-10} \frac{10^2}{2!} = 0.00227

P(X =3) = e^{-10} \frac{10^3}{3!} = 0.00757

P(X \leq 3) =0.0000454+ 0.000454 + 0.00227 + 0.00757 = 0.01034

3. The expected no. of arrivals in a 15 second period is = 10 \times \frac{1}{4} = 2.5. So if Y be the random variable denoting number of passengers arriving in 15 seconds,

Y \sim Poi(2.5)

P(Y=0) = e^{-2.5} \frac{2.5^0}{0!} = 0.0821

4. Here we use the fact that Y can take values 0,1, \dotsc. So, the event that "Y is either 0 or \geq 1" is a sure event ( i.e it has probability 1 ).

P(Y=0) + P(Y \geq 1) = 1 \implies P(Y \geq 1) = 1 -P(Y=0) = 1 - 0.0821 = 0.918

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3 years ago
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Answer:

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Step-by-step explanation:

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3 years ago
Tony bikes 8 miles in one hour. How far would he bike in 5 hours?
Yanka [14]

Answer:

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3 years ago
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makkiz [27]

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Step-by-step explanation:

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