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3 years ago

9

A randomly generated password has four characters. Each character is either A, B, C, D, E or F or a number from 0 - 9. Each char

acter in the password can only be used once. What is the probability that a password has only one number?
A. 5/182
B. 10/91
C. 9/91
D. 9/364

2 answers:

Monica [59]3 years ago

7 0

Answer:

The answer is B!!!

Step-by-step explanation:

NON

motikmotik3 years ago

3 0

Answer:

B. 10/91

Step-by-step explanation:

Total passwords:

16C4 × 4!

43680

Passwords with exactly one digit:

6C3 × 10C1 × 4!

4800

Probability

4800/43680

10/91

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Use the properties you learned to show why (a+b)+c is equivalent to b+(a+c)

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Rearrange the following equation to solve for x. y=1/2x+10

maxonik [38]

In order to solve this we must first,

Subtract both sides of the equation by 10,
y-10=1/2x

Now we have to multiply both sides by 2 so that only x is left.

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3 years ago

During optimal conditions, the rate of change of the population of a certain organism is proportional to the population at time

Lana71 [14]

Answer:

The population is of 500 after 10.22 hours.

Step-by-step explanation:

The rate of change of the population of a certain organism is proportional to the population at time t, in hours.

This means that the population can be modeled by the following differential equation:

$\frac{dP}{dt} = Pr$

In which r is the growth rate.

Solving by separation of variables, then integrating both sides, we have that:

$\frac{dP}{P} = r dt$

$\int \frac{dP}{P} = \int r dt$

$\ln{P} = rt + K$

Applying the exponential to both sides:

$P(t) = Ke^{rt}$

In which K is the initial population.

At time t = 0 hours, the population is 300.

This means that K = 300. So

$P(t) = 300e^{rt}$

At time t = 24 hours, the population is 1000.

This means that P(24) = 1000. We use this to find the growth rate. So

$P(t) = 300e^{rt}$

$1000 = 300e^{24r}$

$e^{24r} = \frac{1000}{300}$

$e^{24r} = \frac{10}{3}$

$\ln{e^{24r}} = \ln{\frac{10}{3}}$

$24r = \ln{\frac{10}{3}}$

$r = \frac{\ln{\frac{10}{3}}}{24}$

$r = 0.05$

So

$P(t) = 300e^{0.05t}$

At what time t is the population 500?

This is t for which P(t) = 500. So

$P(t) = 300e^{0.05t}$

$500 = 300e^{0.05t}$

$e^{0.05t} = \frac{500}{300}$

$e^{0.05t} = \frac{5}{3}$

$\ln{e^{0.05t}} = \ln{\frac{5}{3}}$

$0.05t = \ln{\frac{5}{3}}$

$t = \frac{\ln{\frac{5}{3}}}{0.05}$

$t = 10.22$

The population is of 500 after 10.22 hours.

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Black_prince [1.1K]

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Step-by-step explanation

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tia_tia [17]

Answer:

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