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Amiraneli [1.4K]
3 years ago
14

A lock has two digit numeric code, with the numbers 1 through 7 available for each digit of the code. Note that numbers can be r

epeated in the code so there are 7 possibilities for each two digits. Find the total number of possible codes for the lock.
Mathematics
1 answer:
lubasha [3.4K]3 years ago
7 0
If there is 2 digits and 7 numbers the combos would be:
1,1 2,1 3,1 4,1 5,1 6,1 7,1
1,2 2,2 3,2 4,2 5,2 6,2 7,2
1,3 2,3 3,3 4,3 5,3 6,3 7,3
1,4 2,4 3,4 4,4 5,4 6,4 7,4
1,5 2,5 3,5 4,5 5,5 6,5 7,5
1,6 2,6 3,6 4,6 5,6 6,6 7,6
1,7 2,7 3,7 4,7 5,7 6,7 7,7

Therefore there are 49 possible combinations :)
You might be interested in
Factor each of the following polynomial<br>lows.<br>1. 2x2 - 8x​
SVEN [57.7K]

Answer:

2x (x - 4)

Step-by-step explanation:

7 0
3 years ago
salma purchased a prepaid phone card for $20. long distance calls cost 24 cents a minute using this card. salma used her card on
suter [353]
We can set up an equation to solve this problem, but first we need to write out what we know.

$20 overall
$0.24 every minute
$13.52 remaining on the card

Now that we know our information, we can set it up in an equation. 

20 - 0.24x = 13.52

The 20 represents $20 overall when she first got the phone card.
We are then subtracting $20 from how must it costs a minute (which is 24 cents). The 'x' indicates the number we are trying to find (how many minutes her call lasted). Lastly, 13.52 is the result of everything, since she has $13.52 remaining on the card.

We can now solve the equation:

20 - 0.24x = 13.52
-0.24x = 13.52 - 20 /// subtract 20 from each side
-0.24x = -6.48 /// simplify
x = 27 /// divide each side by -0.24

Our solution is: x = 27.

-----

An easier way to solve this problem would be to first, subtract the total amount of money she had on the card when she first got it, and then the remaining total she ended up with.

$20 - $13.52 = $6.48

So, she spent a total of $6.48 on long distance calls, but since we are looking for how many minutes, we need to divide the total she spent and how much it costs per minute.

6.48 ÷ 24 = 27

We receive the same amount of minutes spent just like we did the last way we solved.

-----

Salma spent 27 minutes on the phone. 
3 0
3 years ago
In P2, find the change-of-coordinates matrix from the basis B = {1 − 3t 2 , 2 + t − 5t 2 , 1 + 2t} to the standard basis of P2.
Serjik [45]

Complete Question:

In P2, find the change-of-coordinates matrix from the basis B = {1 − 3t² , 2+t− 5t² , 1 + 2t} to the standard basis C = {1, t, t²}. Then, write t² as a linear combination of the polynomials in B.

Answer:

The change of coordinate matrix is :

M = \left[\begin{array}{ccc}1&2&1\\0&1&2\\-3&-5&0\end{array}\right]

U = t² = 3 [1 − 3t²] - 2 [2+t− 5t²] + [1 + 2t]

Step-by-step explanation:

Let U =  {D, E, F} be any vector with respect to Basis B

U = D [1 − 3t²] + E [2+t− 5t²] + F[1 + 2t]..............(*)

U = [D+2E+F]+ t[E+2F] + t²[-3D-5E]...................(**)

In Matrix form;

\left[\begin{array}{ccc}1&2&1\\0&1&2\\-3&-5&0\end{array}\right] \left[\begin{array}{ccc}D\\E\\F\end{array}\right] = \left[\begin{array}{ccc}D+2E+F\\E+2F\\-3D-5E\end{array}\right]

The change of coordinate matrix is therefore,

M = \left[\begin{array}{ccc}1&2&1\\0&1&2\\-3&-5&0\end{array}\right]

To find D, E, F in (**) such that U = t²

D + 2E + F = 0.................(1)

E + 2F = 0.........................(2)

-3D -5E = 1........................(3)

Substituting eqn (2) into eqn (1 )

D=3F...................................(4)

Substituting equations (2) and (4) into eqn (3)

-9F+10F=1

F = 1

Put the value of F into equations (2) and (4)

E = -2(1) = -2

D = 3(1) = 3

Substituting the values of D, E, and F into (*)

U = t² = 3 [1 − 3t²] - 2 [2+t− 5t²] + [1 + 2t]

3 0
3 years ago
Charlie is trying to cover the shape shown with paper. He will NOT be covering the top and the bottom. How much paper will he ne
DENIUS [597]

You need to determine how much paper you need to cover the lateral side of the cylinder shown in the picture. For this, you have to calculate the surface area of the cylinder, which you can do using the following formula:

A=2\pi rh

Where

A is the area

π is the number pi, for the calculations we usually use up to the first two decimal values of this number, 3.14

r is the radius

h is the height of the cylinder

The given cylinder has a height of h=15m and a diameter of d=6m

To calculate the lateral area you need to use the radius. The diameter is twice the radius, so to determine the radius of the cylinder you have to divide the diameter by 2

\begin{gathered} r=\frac{d}{2} \\ r=\frac{6}{2} \\ r=3 \end{gathered}

Now you can calculate the lateral area as follows:

\begin{gathered} A=2\pi rh \\ A=2\cdot3.14\cdot3\cdot15 \\ A=282.6m^2 \end{gathered}

Charlie will need 282.6 m² to cover the lateral side of the cylinder.

6 0
1 year ago
Determine as a linear relation in x, y, z the plane given by the vector function F(u, v) = a + u b + v c when a = 2 i − 2 j + k,
Ostrovityanka [42]

Answer:

2x - y - 3z = 0

Step-by-step explanation:

Since the set

{i, j}  = {(1,0), (0,1)}

is a base in \mathbb{R}^2

and F is linear, then

<em>{F(1,0), F(0,1)}  </em>

would be a base of the plane generated by F.

F(1,0) = a+b = (2i-2j+k)+(i+2j+k) = 3i+2k

F(0,1) = a+c = (2i-2j+k)+(2i+j+2k) = 4i-j+3k

Now, we just have to find the equation of the plane that contains the vectors 3i+2k and 4i-j+3k

We need a normal vector which is the cross product of 3i+2k and 4i-j+3k

(3i+2k)X(4i-j+3k) = 2i-j-3k

The equation of the plane whose normal vector is 2i-j-3k and contains the point (3,0,2) (the end of the vector F(1,0)) is given by

2(x-3) -1(y-0) -3(z-2) = 0

or what is the same

2x - y - 3z = 0

3 0
3 years ago
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