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
Lisa [10]
4 years ago
7

For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusiv

e. If p is the smallest prime factor of h(100) + 1, then p is ____.
Mathematics
1 answer:
Ugo [173]4 years ago
7 0

Answer:

More than 50

Step-by-step explanation:

To solve, we need to first see that the function is h(n). Picking main points from the question statement:

  • h(n) is the product of all even integers (From 2 to n)
  • p is the smallest factor of h(100)+1
  • h(100)+1 , here n=100

From here, we can write h(100) as:

h(100) = 2 * 4 * 6 * 8 * ...... * 100

h(100) = 2^{50} * (1*2*3*......*50)= 2^{50} * 50!

so,

h(100)+1 =(2^{50} * 50! )+1

Now two numbers,

h(100) and h(100)+1 are consecutive integers and since they are consecutive so they are co-prime. Hence they only have common factor of 1. Example, 13 and 14 have only common factor of 1

As h(100) has all prime numbers from 1 to 50 and according to above statement h(100)+1 won't have any prime factor from 1 to 50, so the smallest prime factor p is greater than 50.

You might be interested in
Simplify the expression:<br> 2(5 + 5q) =<br> What’s the answer
Serggg [28]

Answer:

10 + 10q

Step-by-step explanation:

2(5 + 5q) =

Distribute

2*5 + 2*5q

10 + 10q

7 0
4 years ago
Read 2 more answers
Which best describes a triangle with side lengths of 6 inches 8 inches and 9 inches?
Tcecarenko [31]
The correct answer for this question is this one: "C).a unique,acute triangle"

The statement that best describes a triangle with side lengths of 6 inches 8 inches and 9 inches is that it is <u>a unique,acute triangle</u><span>
Hope this helps answer your question and have a nice day ahead.

</span>
3 0
3 years ago
Read 2 more answers
A bag of pppcron contains 483 calories and seeves 3.5 people . How many calories are in each serving
stiks02 [169]

Answer:

I think the answer is1,690.5 calories.

Step-by-step explanation:

483×3.5=1,690.5 calories

3 0
4 years ago
Can someone please help me on this math problem!!?
olasank [31]

check the picture below.


since we know all those interior points are midpoints, then those interior lines are midsegments, recall the midsegment is half the parallel base.

in this case, the green DF || AC, and since AC is 50, DF is half that, 50/2.

6 0
3 years ago
Can someone help with these and please show work
dsp73

Step-by-step explanation:

3.)

34 + 3√(4 • 6 ÷ 2)^2 + 5^2

34 + 3√(12)^2 + 25

34 + 3√144 + 25

34 + 3√169

34 + 3 × 13

34 + 39 = 73

4.)

|9 - 12 • 3| - 2 + 10/2^2 + 10 - 7

|9 - 36| + 8/4 + 10 - 7

9 + 36 + 8/7 = 53/7

3 0
3 years ago
Other questions:
  • Solve the equation. 20x-7=5+16x
    7·2 answers
  • Haylee hikes to the top of a 120-foot vertical cliff. From the top of the cliff, the angle of depression to her campsite is 10∘.
    9·1 answer
  • Admission to the museum is $12 for children and $15 for adults. On a certain day 2450 people go the the museum and $33,456 is co
    8·2 answers
  • A new process for producing a type of resin is supposed to have a mean cycle time of 3.5 hours
    11·1 answer
  • Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    8·1 answer
  • What is an equation for this line?
    13·1 answer
  • If you help me I'll make as brilliant​
    14·1 answer
  • Need help tomorrow due
    12·1 answer
  • Please please help me i’ll mark brainlist
    9·1 answer
  • Before your raise, you earned $1,100 a month. What is your<br> new monthly income?<br> Helpppp
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!