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
Kipish [7]
2 years ago
7

How many area codes (abc) would be possible if all three digits could be any vaiue 1-9

Mathematics
1 answer:
kifflom [539]2 years ago
3 0

Answer:

<u>The total number of area codes that would be possible if all three digits could be any value from 1 to 9 is 729.</u>

Step-by-step explanation:

1. Let's start our reasoning to get this answer:

From 000 to 999, we have 1,000 possible area codes.

But for this question, we should find out the answer without considering the digit 0, therefore we must exclude:

A. From 000 to 099, that are 100 possible area codes.

B. We also have to exclude, from 100 to 110, 120, 130, 140, 150, 160, 170, 180 and 190. Those are 19 area codes more.

C. We also have to exclude these same options of code areas, for 200 - 210 and 2x0, and 19 more for each subset that starts with 3, 4, 5, 6, 7, 8 and 9. In total, 19 multiplied by 8, 152 numbers more.

<u>Therefore, the total number of area codes that would be possible if all three digits could be any value from 1 to 9 is:</u>

<u>1,000 - 100 - 19 - 152 = 729</u>

<u>The simplest way to find it, is:</u>

<u>For 000 to 999 = 1,000 or 10³</u>

<u>Excluding the digit zero = 729 or 9³</u>

You might be interested in
Find the area of the bedroom with the shape shown in the figure, in square feet.
maksim [4K]

I think the answer is C

6 0
3 years ago
Read 2 more answers
4/5 of 75 shared in ratio 2:3
Vika [28.1K]
4/5*75=60
ratio will be 24:36
4 0
2 years ago
Read 2 more answers
If X - A = B, what is X?
sineoko [7]

Answer:

x=a+b

Step-by-step explanation:

Just move a to the other side (by adding it)

6 0
2 years ago
Read 2 more answers
How much greater is this week’s median temperature than last week’s median temperature?
Scrat [10]

Answer:

5 degrees

Step-by-step explanation:

5 0
2 years ago
Derivative of tan(2x+3) using first principle
kodGreya [7K]
f(x)=\tan(2x+3)

The derivative is given by the limit

f'(x)=\displaystyle\lim_{h\to0}\frac{f(x+h)-f(x)}h

You have

\displaystyle\lim_{h\to0}\frac{\tan(2(x+h)+3)-\tan(2x+3)}h
\displaystyle\lim_{h\to0}\frac{\tan((2x+3)+2h)-\tan(2x+3)}h

Use the angle sum identity for tangent. I don't remember it off the top of my head, but I do remember the ones for (co)sine.

\tan(a+b)=\dfrac{\sin(a+b)}{\cos(a+b)}=\dfrac{\sin a\cos b+\cos a\sin b}{\cos a\cos b-\sin a\sin b}=\dfrac{\tan a+\tan b}{1-\tan a\tan b}

By this identity, you have

\tan((2x+3)+2h)=\dfrac{\tan(2x+3)+\tan2h}{1-\tan(2x+3)\tan2h}

So in the limit you get

\displaystyle\lim_{h\to0}\frac{\dfrac{\tan(2x+3)+\tan2h}{1-\tan(2x+3)\tan2h}-\tan(2x+3)}h
\displaystyle\lim_{h\to0}\frac{\tan(2x+3)+\tan2h-\tan(2x+3)(1-\tan(2x+3)\tan2h)}{h(1-\tan(2x+3)\tan2h)}
\displaystyle\lim_{h\to0}\frac{\tan2h+\tan^2(2x+3)\tan2h}{h(1-\tan(2x+3)\tan2h)}
\displaystyle\lim_{h\to0}\frac{\tan2h}h\times\lim_{h\to0}\frac{1+\tan^2(2x+3)}{1-\tan(2x+3)\tan2h}
\displaystyle\frac12\lim_{h\to0}\frac1{\cos2h}\times\lim_{h\to0}\frac{\sin2h}{2h}\times\lim_{h\to0}\frac{\sec^2(2x+3)}{1-\tan(2x+3)\tan2h}

The first two limits are both 1, and the single term in the last limit approaches 0 as h\to0, so you're left with

f'(x)=\dfrac12\sec^2(2x+3)

which agrees with the result you get from applying the chain rule.
7 0
3 years ago
Other questions:
  • What's the answer to -5-r=1+2r
    15·2 answers
  • Please show your work!<br> 25% of 80
    14·2 answers
  • The measure of the supplementary of an angle is 40 more than 2 times the measure of the complement of an angle. Find he measure
    12·1 answer
  • A group of friends went on a holiday to a hill station. It rained for 15 days. But when it rained in the morning, the afternoon
    5·2 answers
  • Can someone help me with 3 4 and 5?? WILL MARK BRAINLIEST!! PLZZ helpppp meee :(((
    6·2 answers
  • Simplify (9+7i)/(-10+8i)
    5·1 answer
  • Right any equation in slope intercept for the line that passes through (0,-2) And is parallel to the line whose equation is 3x+5
    11·1 answer
  • I need help what is 3-2y+(-8y)+7.8
    9·2 answers
  • Points plz plz plz awnser​
    13·2 answers
  • Please help me, I am so confused. Thanks​
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!