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3 years ago

What time does the clock show?

Mathematics

1 answer:

Gelneren [198K]3 years ago

6 0

Answer:

12:43

Step-by-step explanation:

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A computer system uses passwords that are six characters, and each character is one of the 26 letters (a–z) or 10 integers (0–9)

Blababa [14]

First of all, since we have 36 characters available per spot (26 letters and 10 digits), and we have 6 spots, we have a total of

$36^6$

possible passwords.

Event A happens if the password starts with either a, e, i, o or u. If we fix the first character, we're left with 36 characters available for each of the remaining 5 spots, leading to a total of

$5\cdot 36^5$

possible passwords.

So, the probability of event A, computed as the ratio between "good" cases and all possible cases, is

$\dfrac{5\cdot 36^5}{36^6}=\dfrac{5}{36}$

Event B works exactly the same, since we're fixing the last spot, leaving 36 characters available for each of the first 5 spots. So, we have

$P(A)=P(B)=\dfrac{5}{36}$

As for the intersection, we want the first character to be a vowel, and the last character to be an even digits. There are 25 passwords satisfying this request:

$axxxx0,\ axxxx2,\ axxxx4,\ axxxx6,\ axxxx8$

$exxxx0,\ exxxx2,\ exxxx4,\ exxxx6,\ exxxx8$

$ixxxx0,\ ixxxx2,\ ixxxx4,\ ixxxx6,\ ixxxx8$

$oaxxxx0,\ oxxxx2,\ oxxxx4,\ oxxxx6,\ oxxxx8$

$uxxxx0,\ uxxxx2,\ uxxxx4,\ uxxxx6,\ uxxxx8$

Where x can be any of the 36 characters.

So, we have 25 cases with 4 vacant slots, leading to a probability of

$P(A\cap B)=\dfrac{25\cdot 36^4}{36^6}=\dfrac{25}{1296}$

Finally, you can compute the probability of the union using the formula

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

Since we already computed all these quantities.

7 0

3 years ago

Carol drives her daughter to school at an average rate of 30 miles per hour, but only goes an average rate of 20 miles per hour

Ivahew [28]

<span>24 mph

</span>P.S. please vote this as the brainliest answer :)

6 0

3 years ago

The domain of the function <br> g(x) = √(x2−3x−4) is? Use the fishball method

frosja888 [35]

Result:
{x<= -1 or x>= 4 and x belongs to real numbers}

6 0

3 years ago

To demonstrate probabilities, a mathematics teacher had students draw marbles from a bag which contained 9 yellow marbles and 8

kolbaska11 [484]

Answer:

The loss of marbles did not change the probability.

Step-by-step explanation:

This is because the loss was even you lost 2 marbles from both category which keeps them equal similar to when you set two equations equal to one another and then you subtract 2 from each side the sides are still equal.

7 0

3 years ago

Frank invests $5100 for 8 years at a simple interest rate of 5%. How much interest will he earn? What will his total value be?

Westkost [7]

Answer:

A = P(1 + r)t

Step-by-step explanation:

Or this formula:

$A = P(1 + \frac{r}{n} )$

3 0

3 years ago