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pochemuha
2 years ago
9

What number must you add to complete the square?

Mathematics
1 answer:
Travka [436]2 years ago
7 0
B=9 (x+3)^2= x^2+6x+9
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Of the 9-letter passwords formed by rearranging the letters AAAABBCCC (4 A's, 2 B's, and 3 C's), I select one at random. Determi
Tanya [424]

Answer:

a) 3

b) (8!/9!)-(7!/9!)

c) (1-(8!/9!))*(7!/9!)

Step-by-step explanation:

a)With 4 As ;  2Bs and 3Cs it is possible to get a palindrome if you fixed the  letters C according to: (2) in the extremes of the word and the other one at the center therefore you only have palindrome in the following cases

<u>C</u> (       ) <u>C</u> (       ) <u>C</u>

To fill in the gaps we have  4 letters  A and 2 letters B, wich we have two divide in two palindrome gaps,  

AAB         and    BAA the palindrome is  C  AAB C BAA C

BAA         and    AAB    "           "           is  C  BAA C AAB C  

ABA         and    ABA    "           "           is  C  ABA C ABA C

b) 4 A  ;   2B  ; 3C

We have the total number of elements  9, so the total number of possible outcomes is : 9!

Total events: 9!

if we fixed 3 C we have (the group of 3 Cs becoming one element) so the total amount of events with 3 adjacent Cs is: 7!

Therefore the probability of having 3 adjacent Cs is: 7!/9!

If we fixed only 2 Cs we have:

4 A  ; 2 B  ; 2C  : 1C

Total number of words (events) in this case is 8! (2C becomes 1 element)

so the total numbers of events is 8! the probability in this case is 8!/9!(this value includes cases of adjacent 3 Cs previous calculated ) so this value minus the case of 3 adjacent Cs ) give us 2 adjacent C and the other no next to them

Probability (of words with 2 adjacent Cs and the other no next to them is); 8!/9! - 7!/9!

c) Probability of B apart from each other is the whole set of events minus those where 2 B are adjacent or (become 1 element)

4 A ; 2B ; 3C

Total of events 9! and events with adjacent B is 8!/9!

Therefore the probability of words with 3 adjacent Cs and 2 B separeted is

the probability of 3 adjacent Cs (7!/9!) times probability of words with no adjacent Bs wich is (1-(8!/9!))*(7!/9!)

5 0
3 years ago
The vertices of a polygon are shown below.
stiv31 [10]

Answer:

The Answer is C

Step-by-step explanation:

This applies to your exam.

6 0
2 years ago
Read 2 more answers
The table shows the ratio between the number of books ordered and their cost: Find equivalent ratios when the number of books or
Nana76 [90]

Answer:

The answer is below

Step-by-step explanation:

The table shows the ratio between the number of books ordered and their cost: Number of Books Cost (dollars) 7 21 8 24 9 27 Find equivalent ratios when the number of books ordered is 1, 2, and 3. Write them as ordered pairs in the form (x-coordinate, y-coordinate). Starting from the origin, explain how to plot the three equivalent ratios on a coordinate grid.

Answer: Let the number of books be represented as x and the cost (dollars) be represented as y. From the table the ordered pairs in the form (x, y) can be gotten. (7, 21), (8, 24), (9, 27). To get the relationship between the number of books and the cost, we can use the formula of a straight line.

Using point (7, 21) and (8, 24):

y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-21=\frac{24-21}{8-7}(x-7)\\ \\y-21=3(x-7)\\\\y=3x-21+21\\\\y=3x

When the number of books ordered is 1, 2, 3 the following pairs are:

For x = 1.     y = 3x = 3(1) = 3

For x = 2     y=3x = 3(2) = 6

For x = 3     y = 3x = 3(3) = 9

The ordered pairs are (1, 3), (2, 6), (3, 9)

The graph is attached

To plot the ordered pairs, the number of books are plotted on the x coordinate and the cost on the y coordinate  

8 0
3 years ago
Hows your day i just want to know: Who are your top 3 favorite rappers? And give me your or one of your favorite songs by each o
Doss [256]

Answer:

um mm

Brent fayiyz

all his songs

and ummm

4 0
2 years ago
Read 2 more answers
Patrick and his brother each start a savings account. Patrick begins with $200
skad [1K]

Answer:

Both brothers will have the same amount of money is their saving accounts after six months.

Step-by-step explanation:

I worked this out by finding out the first 8 months of savings for both brothers:

Patrick:               His brother:

200                     150

225                     185

250                     220

275                     253

300                     290

325                     325

375                     360

400                     395

I then looked across my results to see that at 6 months both brothers had $325.

Hope this helped.

7 0
3 years ago
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