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4 years ago

What is the value of x?

Mathematics

1 answer:

daser333 [38]4 years ago

4 0

Answer:

x=22.5

Step-by-step explanation:

BM||DT

Using Intercept theorem/Intercept theorem

$\frac{6}{6+15} =\frac{9}{9+x}$

6(9+x)=9*21

54+6x=189

6x=135

x=22.5

At least I think so

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2. A spike train, commonly used to study neural activity, is a sequence of recorded times at which a neuron fires an action pote

nika2105 [10]

Answer:

a) X ~ exp ( 10 )

b) E(X) = 0.1 , Var (X) = 0.01

c) P ( X < 0.07 ) = 0.00698

Step-by-step explanation:

Solution:-

- The spike train, used to study neural activity, the given time in between consecutive spikes (ISI) where the firing rate = 10 neurons per seconds.

- Denote a random variable "X"represent a single interspike interval (ISI) having an exponential distribution.

- Where X follows exponential distribution defined by event rate parameter i.e λ.

X ~ Exp ( λ )

- The event rate (λ) is the number of times an event occurs per unit time. Since we are studying a single interspike interval (ISI) - which corresponds to the firing rate. So, event rate (λ) = firing rate = 10 neurons per second. Hence, the distribution is:

X ~ Exp ( 10 )

- The expected value E(X) denotes the amount of time in which a single an event occurs; hence, the time taken for a single neuron.

E(X) = 1 / λ

E(X) = 1 / 10

E(X) = 0.1 s per neuron.

- The variance is the variation in the time taken by a single neuron to be emitted. It is defined as:

Var (X) = 1 / λ^2

Var (X) = 1 / 10^2

Var (X) = 0.01 s^2

- The probability that ISI is less than t = 0.07 seconds: P ( X < t = 0.07 s):

- The cumulative distribution function for exponential variate "X" is:

P ( X < t ) = 1 - e^(-λ*t)

- Plug the values and the determine:

P ( X < 0.07 ) = 1 - e^(-0.1*0.07)

= 1 - 0.99302

= 0.00698

5 0

3 years ago

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Yanka [14]

Answer:

It will take 1 week for both classmates to catch up with each other
Each child has passed about 9 tests.

Step-by-step explanation:

We know that:

Q = 8 + 1(w)
S = 4 + 5(w)
Q = S

Work:

8 + w = 4 + 5w
=> 8 - 4 = -w + 5w
=> 4 = 4w
=> w = 1

Hence, it will take 1 week for both classmates to catch up with each other. Now, let's substitute the value of w into the first equation to find how many tests have each child passed.