Given the following equation, solve for x.<br> y = mx+b

Is the dilatation an enlargement or a reduction

Brilliant_brown [7]

Enlargement of 2.

if it were a reduction it'd be getting smaller..

5 0

3 years ago

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

Which statement is true?

serious [3.7K]

Answer:

b

Step-by-step explanation:

all squares have 4 sides which is a quadrilateral.

5 0

3 years ago

Round 13,046 to the nearest thousand.

Margaret [11]

Answer:

13,000

Step-by-step explanation:

When rounding, first:

Find the place value that you are looking for, in this case, being the thousands place value. It is a 3:

1<u>3</u>,046

When you round, you will look at the place value directly next to the one you are trying to find (which is the thousands place value). In this case, it will be the hundreds place value, which has the value of 0.

When the value of the number is 5 or greater, you round up.

When the value of the number is 4 or less, you round down.

In this case, it is 0, which is less than 4, so you round down.

13,046 to the nearest thousand place value is 13,000.

~

8 0

2 years ago

Read 2 more answers

Which point is located on the line represented by the equation y+4=-5(x-3)

Genrish500 [490]

The equation of a line that passes through (x1,y1) and has a slope of m is
y-y1=m(x-x1)
given
y-(-4)=-5(x-3)
the point is (3,-4)

3 0

3 years ago

Given the following equation, solve for x. y = mx+b