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3 years ago

Find the sum of the first 2,000 positive integers (the numbers 1 through 2000).

Mathematics

1 answer:

MAVERICK [17]3 years ago

6 0

According to Gauss, the formula to find the sum of a series is:

S=n(n+1)/2 where n is the number of terms in the series

Since n=2000, then:

S=2000(2000+1)/2

S=4002000/2

S=2001000

The famous mathematician Gauss had used this same method to find the sum of the digits 1 to 100 while in elementary school. So the sum of the first 2000 positive integers is 2,001,000

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Find the value of x if B is the midpoint of AC, AB = 2x + 9 and BC = 37.

Leno4ka [110]

Answer:

Step-by-step explanation:

B is the midpoint of AC, in other words it is the halfway point.

So A to B should be equal to B to C

Our expression is:

2x + 9 = 37

Subtract 9

2x = 28

Divide by 2

x = 14

5 0

3 years ago

Read 2 more answers

If nine is X percent of 45, what is X percent of 5

antoniya [11.8K]

Answer:

x percent of 5 is 1

Step-by-step explanation:

Nine is x percent of 45

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3 years ago

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3 years ago

The number 64 has the property that it is divisible by its units digit. How many whole numbers between 10 and 50 have this prope

sineoko [7]

Answer:

$\large \boxed{17}$

Step-by-step explanation:

Let's call the numbers "tu", where t is the tens digit and u is the units digit.

We can solve this by the "brute force" method — examining each number to see if it satisfies the conditions.

$\begin{array}{cccl}\mathbf{u}&\mathbf{tu}& \textbf{Divisible by u} & \\0 &20, 30, 40 & 0 & \text{Division by zero is impossible}\\1 & 11, 21, 31, 41 & 4& \text{All numbers are divisible by one}\\2 & 12, 22, 32, 42 & 4 & \text{All even numbers are divisible by two}\\3 & 13, 23, 33, 43 & 1 &\text{Only 33 is divisible by three}\\4 & 14, 24, 34, 44 & 2 & \text{Only 24 and 44 are divisible by four}\\5 & 15, 25, 35, 45 & 4 & \text{Numbers ending in 5 are divisible by five}\\\end{array}$

$\begin{array}{cccl}6 & 16, 26, 36, 46 & 1 & \text{Only 36 is divisible by six}\\7 & 17, 27, 37, 47 & 0 & \text{None of the numbers is divisible by seven}\\8 & 18, 28, 38, 48 & 1 & \text{Only 48 is divisible by eight}\\9 & 19, 29, 39, 49 & 0 & \text{None of the numbers is divisible by nine}\\& \textbf{TOTAL =} &\mathbf{17}& \\\end{array}\\\text{$\large \boxed{\mathbf{17}}$ numbers between 10 and 50 are divisible by their units digit}$

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3 years ago

On Monday, Jayla raised $30 and Carlos raised $50.

gayaneshka [121]

Answer:

84 days

Step-by-step explanation:

You would use the LCM to solve this.

12 and 7 don't share any common factors other than 1,

so you would multiply 12 x 7, which gets you 84.

After 84 days they would have raised the same amount.

8 0

3 years ago