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
igor_vitrenko [27]
3 years ago
7

Use the estimate in the text based on the Prime Number Theorem to give approximate values of the following. (a) The number of pr

imes between 1 and 1030. (b) The number of primes between 1 and 1029.
Mathematics
1 answer:
ozzi3 years ago
5 0

Answer:

a)148.47

b)148.34

Step-by-step explanation:

Let π(x) be the prime-counting function that gives the number of primes less than or equal to x, for any real number x. For example, π(7) = 4 because there are four prime numbers (2, 3, 5, 7) less than or equal to 7.

We can see that π(7)=π(10) because there are four prime numbers (2,3,5,7) less than or equal to 10.

A good aproximation for π(x) is x / log x, where log x is the natural logarithm of x.

a)The number of primes between 1 and 1030.

1030/log(1030)=148.47

b) The number of primes between 1 and 1029.

1029/log(1029)=148.34

 Extra: π(1029)=π(1030) because 1030 is not a prime.

You might be interested in
Please help! Which box plot represents a set of data that has the greatest mean absolute deviation? (see attached image)
djyliett [7]

Answer:

the 2nd is the answer

Step-by-step explanation:

7 0
3 years ago
Helen bought a four-unit apartment building for $561,000. The property lost value at a rate of 4.1% per year. Helen rented out e
ra1l [238]

Answer:

The correct answer is B

Step-by-step explanation:

$45,700 loss

5 0
3 years ago
Read 2 more answers
In ΔKLM, k = 700 cm, l = 460 cm and ∠M=78°. Find the length of m, to the nearest centimeter.
pashok25 [27]

Answer:

753

Step-by-step explanation:

m^2 =700^2 +460^-2 −2(700)(460)cos78

m^2 = 490000+211600-2(700)(460)(0.207912)

m^2 = 490000+211600-133895.12889

m^2 = 567704.87111

m=753.462=753

6 0
3 years ago
Two wires, a = 90 ft apart, tether a balloon to the ground, as shown. How high is the balloon above the ground? (Round your ans
valentina_108 [34]

Answer:

180

Step-by-step explanation:

7 0
3 years ago
Evaluate the expression, using the given value of the variable.
natka813 [3]
-10 is the answer to the question above.
3 0
3 years ago
Read 2 more answers
Other questions:
  • Samantha had 8 balloons. Jacob has 1/2 as many. How many does Jacob have?
    10·2 answers
  • The function f(t)=t^2+12t-18 represents a parabola.
    11·1 answer
  • Five friends equally shared half of one large pizza and 1/4 of another large pizza. what fraction of each pizza did each friend
    15·1 answer
  • Show that (A − B) − C is not necessarily equal to A − (B − C).
    15·2 answers
  • How many halves are in 2/3
    5·1 answer
  • Part A Anna took a taxi home from the airport. ​ ​The taxi fare was \$ 2.1$2.1 per mile, she gave the driver a tip of \$ 5$5, an
    8·1 answer
  • You buy a hat for $12 and give the cashier a $20 bill. How much change do you receive?
    5·1 answer
  • Find the measure of angle 1
    13·2 answers
  • The vertex of the graph of fox) = |x-3+ 6 is located at
    7·1 answer
  • Mr. Stanford has a class of 6 girls and 9 boys. If he randomly chooses a student to do an errand what is the probability he choo
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!