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3 years ago

How many different phone numbers are possible in the area code 503, if the first number cannot start with a 0 or 1

Mathematics

2 answers:

ElenaW [278]3 years ago

7 0

Answer:

8 X 10^(9)

Step-by-step explanation:

Originally we have 10 digit phone numbers excluding the area code.

For each face value we have these in store: 0,1,2,3,4,5,6,7,8,9 (total 10)

But if we exclude 1 and 0 for the first digit, we are left with 8 digits.

8P1 X .......

In a phone number, digits can repeat so we can choose out of these 10 numbers freely after this.

8P1 X 10P1 X 10P1 X...

Adding the area code while assuming 10P1 is just 10...we get:

1 X 1 X 1 X 8 X 10^(9)

= 8000000000

Very interesting question, thanks for the opportunity!

stealth61 [152]3 years ago

3 0

Answer:

8000000

Step-by-step explanation:

503-xxx-xxxx

for the last 7 digit: 2-9 .... 8 for first digit

0-9 .... 10 for digit 2 to digit 7

Total: 8*10*10*10*10*10*10 = 8000000

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Philip made a total of 9 bracelets and necklaces from 120 inches of cord. He used 8 inches of cord for each bracelet and 20 inch

Viktor [21]

Answer:

So Philip made 5 bracelets and 4 necklaces.

Step-by-step explanation:

Let x = number of bracelets and y = number of necklaces.

Since we have a total of 9 bracelets and necklaces,

x + y = 9 (1)

Also, we have 8 inches of cord for each bracelet and 20 inches of cord for each necklace, then the total length for the bracelet is 8x and that for the necklace is 20y.

So, the total length for both is 8x + 20y. Since the total length of cord used is 120 inches,

8x + 20y = 120 (2)

Simplifying it we have

2x + 5y = 30 (3).

Writing equations (1) and (3) in matrix form, we have

$\left[\begin{array}{ccc}1&1\\2&5\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}9\\30\end{array}\right]$

Using Cramer's rule to solve for x and y,

$x = det \left[\begin{array}{ccc}9&1\\30&5\end{array}\right] /det \left[\begin{array}{ccc}1&1\\2&5\end{array}\right] \\$

x = (9 × 5 - 30 × 1) ÷ (1 × 5 - 1 × 2)

x = (45 - 30) ÷ (5 - 2)

x = 15 ÷ 3

x = 5

$y = det \left[\begin{array}{ccc}1&9\\2&30\end{array}\right] /det \left[\begin{array}{ccc}1&1\\2&5\end{array}\right] \\$

y = (30 × 1 - 9 × 2) ÷ (1 × 5 - 1 × 2)

y = (30 - 18) ÷ (5 - 2)

y = 12 ÷ 3

y = 4

So Philip made 5 bracelets and 4 necklaces.

3 0

3 years ago

Write a number of your choice, using the following clues:

guapka [62]

Answer:

Step-by-step explanation:

90÷2= 45

90÷3=30

8 0

3 years ago

Read 2 more answers

I don’t understand how to do this

schepotkina [342]

Answer:

The solution is $x =0.$

Step-by-step explanation:

The equation

$\bold{(1).}\: sin(\dfrac{3\pi }{2} +x)+sin(\dfrac{3\pi }{2} +x) =-2$

can be rewritten as

$2* sin(\dfrac{3\pi }{2} +2) =-2$

and can be further simplified to

$sin(\dfrac{3\pi }{2}+x ) =-1$ .

Now, taking the inverse sine of both sides we get:

$sin^{-1}(sin(\dfrac{3\pi }{2} +x) =sin^{-1}(-1)$

$\bold{(2).}\: \dfrac{3\pi }{2} +2 =sin^{-1}(-1)$

The value of the right side on the interval $[0,2\pi)$ is

$sin^{-1}(-1) = \dfrac{3\pi}{2} \: \:( \text{or }270^o)$ ,

which makes the equation (2)

$\dfrac{3\pi }{2}+x =\dfrac{3\pi}{2}$

solving for $x$ gives

$\boxed{x = 0}$

which is our solution.

4 0

3 years ago

A 6am one morning the temperature was -14 degrees by noon it rose 8 degrees and then rose another 2 degrees by 3pm. By 6pm the t

valentina_108 [34]

Answer:

-9 degrees

Step-by-step explanation:

-14 + 8 = -6

-6 + 2 = -4

-4 - 5 = -9

3 0

2 years ago

PLEASE HELP it should be easy for someone but I can’t do it

-Dominant- [34]

Answer:

Total crackers on the plate are 12

Step-by-step explanation:

Manuel ate crackers = $\frac{1}{3}$

His brother ate crackers = $\frac{1}{4}$

Crackers left on the plate = 5

We need to find how many crackers were there on the plate.

Let x be the total crackers on the plate

So, we can write the equation

$x-\frac{1}{3}x-\frac{1}{4}x=5$

Because 1/3 and 1/4 crackers are eaten and 5 are left so, we subtract 1/3x and 1/4x from x and equal it to 5

$\frac{12x-4x-3x}{12}=5\\\frac{12x-7x}{12}=5\\\frac{5x}{12}=5\\x=\frac{5*12}{5}\\x=12$

So, we get x = 12

Therefore, total crackers on the plate are 12

8 0

3 years ago