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
ExtremeBDS [4]
3 years ago
10

18 points - Qu. If 16 whole numbers factor into 120. You will see how 32 whole numbers factor into 1200 what does the same princ

ipal apply in scale for other numbers are they x2 , You can try one or two different numbers to 120 ones. Not asking for the individual factors just how many for your example 2 numbers one must be x 10 of itself like 120:1200 is.
Mathematics
1 answer:
alexandr402 [8]3 years ago
7 0

Explanation:

<em>Your premise and conclusion are both incorrect</em>.

120 has the prime factorization ...

  120 = 2³ × 3 × 5

The exponents of the prime factors are {3, 1, 1}. The number of divisors of 120 is the product of the increments of these numbers: (3+1)(1+1)(1+1) = 4·2·2 = 16.

120 has 16 natural-number divisors

__

1200 has the same prime factor and two more: 2·5, so the factorization is ...

  1200 = 2⁴ × 3 × 5²

These exponents are {4, 1, 2} and the product of their increments is 5·2·3 = 30.

1200 has 30 natural-number divisors.

__

When a number is multiplied by 2, its number of natural-number divisors will be (n+1)/n times the previous number of divisors, where n is the increment of the exponent of 2 that is a factor of the original number.

For 120, 2^3 is the power of 2 that is a factor. So, multiplying the number by 2 multiplies the number of divisors by (4+1)/4 = 5/4.

240 will have 20 divisors versus the 16 that 120 has.

Likewise, multiplying this number (240) by 5 will multiply its number of divisors by (2+1)/(1+1) = 3/2, where 1 is the power of 5 that is a factor of 240.

1200 will have 20(3/2) = 30 divisors, versus the 20 that 240 has, or the 16 that 120 has.

__

<em>Summary</em>

The number of divisors of an integer is the product of the increments of the exponents of its prime factors.

_____

<em>For reference</em>

Here are the divisors of 120:

  1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

Here are the divisors of 240:

  1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240

Here are the divisors of 1200:

  1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200

You might be interested in
If a multiple choice test consists of ​questions, each of which with of which only 1 is​ correct, ​(a) in how many different way
oksian1 [2.3K]

Answer:

Step-by-step explanation:

From the given information.

suppose a multiple choice test consists of 5 questions, each with 4 possible answers of which 1 is correct.:

So, we can now suggest that a person can answer each question in 4 different ways given that there are 5 different questions.

Thus, the  students can check off one answer to each question in 4^5 \ different \  ways

= 4 × 34 × 4 × 4 × 4

= 1024 different ways.

From the 4 possible answers, since 1 will be correct, definitely 3 other answers will be incorrect.

Thus, the number of ways a student can check off one answer to each question and get all the answers wrong is = 3⁵

= 3 × 3 × 3 × 3 × 3

= 243 ways

3 0
3 years ago
The weight of a tree is doubling every 3 years and how many years will be way of the tree be 1600% of its weight now
BARSIC [14]
Doubling every 3 years, meaning 200% every 3 years.

1600 \div 200 = 8
8 \times 3 = 24
The answer is 24 years.

Hope this helps. - M
6 0
3 years ago
Quick question! Will give brainliest!
Sever21 [200]

Answer:

3

3 rectangles have vertices ABCD that lie on grid nodes

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Anyone help me please fast
lisabon 2012 [21]

Answer:

Step-by-step explanation:49

3 0
3 years ago
Read 2 more answers
Write an equation in slope-intercept form from the points (0, 3) and (-4,-1)
Bezzdna [24]

Answer:

y = x + 3

Step-by-step explanation:

Slope-intercept form is represented by the formula y = mx + b. We can write an equation in point-slope form first, then convert it to that form.

1) First, find the slope of the line. Use the slope formula  m = \frac{y_2-y_1}{x_2-x_1} and substitute the x and y values of the given points into it. Then, simplify to find the slope, or m:

m = \frac{(-1)-(3)}{(-4)-(0)} \\m = \frac{-1-3}{-4-0} \\m = \frac{-4}{-4} \\m = 1

Thus, the slope of the line must be 1.

2) Now, since we know a point the line intersects and its slope, use the point-slope formula y-y_1=m(x-x_1) and substitute values for m, x_1, and y_1. From there, we can convert the equation into slope-intercept form.

Since m represents the slope, substitute 1 in its place. Since x_1 and y_1 represent the x and y values of a point the line intersects, choose any one of the given points (either one is fine) and substitute its x and y values into the equation, too. (I chose (0,3).) Finally, isolate y to find the answer:

y-3=1(x-0)\\y-3 = x\\y = x + 3

8 0
3 years ago
Other questions:
  • Evaluate the expression - |7-9|
    6·1 answer
  • Use the ruler to calculate the distance between P which is at 7..........
    11·1 answer
  • Solve -6n+5=59 it’s a 2 step equation and I need to no how to do it step by step
    14·1 answer
  • Nina can ride her bike 63,360 feet 3,400 seconds and Sophia can ride her bike 10 miles in 1 hour what’s is Nina’s rate in miles
    5·1 answer
  • Explain why (–4x)0 = 1, but –4x0 = –4.
    13·1 answer
  • What is 7 9/13 as an improper fraction
    14·1 answer
  • Which number belongs to the solution set of the equation below? x - 7 = 35
    6·2 answers
  • An accounting firm is trying to decide between IT training conducted in-house and the use of the third party consultants. To get
    10·1 answer
  • 2 3/10 x-5/7 y-4 5/6 y-2 4/5 x
    11·1 answer
  • What is square root of 5x^4-6x^5+x^6+16x^3-8x^2-8x+4 ? <br>help me pleasee !​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!