1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alex
3 years ago
14

Current rules for telephone area codes allow the use of digits​ 2-9 for the first​ digit, and​ 0-9 for the second and third​ dig

its, but the last two digits cannot both be 1​ (to avoid confusion with area codes such as​ 911). How many different area codes are possible with these​ rules? That same rule applies to the exchange​ numbers, which are the three digits immediately preceding the last four digits of a phone number. Given both of those​ rules, how many​ 10-digit phone numbers are​ possible? Given that these rules apply to the United States and Canada and a few​ islands, are there enough possible phone​ numbers? (Assume that the combined population is about​ 400,000,000.)
Mathematics
1 answer:
Anna35 [415]3 years ago
5 0

Using the fundamental counting theorem, we have that:

  • 648 different area codes are possible with this rule.
  • There are 6,480,000,000 possible 10-digit phone numbers.
  • The amount of possible phone numbers is greater than 400,000,000, thus, there are enough possible phone numbers.

The fundamental counting principle states that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are ways to do both things.

For the area code:

  • 8 options for the first digit.
  • 9 options for the second and third.

Thus:

8 \times 9 \times 9 = 648

648 different area codes are possible with this rule.

For the number of 10-digit phone numbers:

  • 7 digits, each with 10 options.
  • 648 different area codes.

Then

648 \times 10^7 = 6,480,000,000


There are 6,480,000,000 possible 10-digit phone numbers.

The amount of possible phone numbers is greater than 400,000,000, thus, there are enough possible phone numbers.

A similar problem is given at brainly.com/question/24067651

You might be interested in
HHHHHHHHHEEEEEELLLLLLLLPPPPPPPP how do I do this
lyudmila [28]

Answer:

1/6

Step-by-step explanation:

2/3 times 1/4 is 2/12. 2/12 simplified is 1/6, so 1/6 is your answer.

7 0
3 years ago
How do you do inequalities
fgiga [73]
So some quick tips for inequalities:
**What you do to one side you HAVE TO do it to the other 2**
**If you ever divide a negative number past the inequality signs, the signs FLIP!!**
(e.g. 2>-5x>25)
-2/5 <x < -5

I hope that this has helped!
8 0
3 years ago
Let x and y be two positive numbers whose sum is 175 and (x+3)(y+4) is a maximum
Vaselesa [24]

Answer:

Step-by-step explanation:

x+y = 175

y = 175 - x

f(x) = (x+3)(y+4)

= x(175-x) + 3(175-x) + 4x + 12

= 175x - x² + 525 - 3x + 4x + 12

= -x² +176x + 537

f'(x) = -2x + 176

maximum when x = 88

y = 175-x = 87

4 0
3 years ago
I need help quick please
kenny6666 [7]
Volume is Length x width x height divided by 3. You have the length and the width. which equals 24. (6x4). The volume that is present is 72... the last thing you do in the equation is divide by three so multiply 72 by 3 and get 216. This is the LxWxH. Like I said before you have the L and the W, which is 24. You would divide 24 from 216. The Height is 9cm.
6 0
3 years ago
Read 2 more answers
Sketch the graph of y = (x + 3)2 – 4 and identify the axis of symmetry.
Sloan [31]

Answer: Thought I’d return the favor and help u with this question! But anyways, the axis of symmetry is at x = -3.

Explanatio: This can be found by looking at the basic form of vertex form:

y = (x - h)^2 + k

In this basic form the vertex is (h, k). By looking at what is plugged into the equation, it is clear that h = -3 and k = -4. This means the vertex is at (-3, -4).

It is a fact that the axis of symmetry is a vertical line of x = (vertex value of x). So we can determine that the axis of symmetry is at x = -3

i hope this helps u

4 0
3 years ago
Other questions:
  • The surface area of an oil spill gets 125% larger every day, represented by the function s(x) = (1.25)x _ 1. On the first day, i
    5·2 answers
  • What is meant by the term the ???end of the Cold War???.
    13·1 answer
  • What two numbers have a sum of 15
    5·1 answer
  • On Thursday, a restaurant serves iced tea to 65 of its 245 customers. What percent of the customer ordered iced tea? Round to th
    8·1 answer
  • Can someone please help me with this question?
    11·2 answers
  • What is the height (h) of the prism?<br> 3ft<br> 6ft
    10·2 answers
  • Sales tax in Rally County is 8%. What would the amount of tax be on a $50 restaurant bill? Express your answer in the form of a
    10·1 answer
  • Grant made a $2800 investment that piece is simple interest rate at 6% per year. To the nearest hundredth which of the following
    10·2 answers
  • What is 898995x10007766767
    11·2 answers
  • You are making a rectangular rug. You want the rug to be twice as long as it is wide. let w represent the width (in feet) of the
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!