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3 years ago

What is the sum of all even numbers between 1 and 1000

1 answer:

4 0

There are 500 even numbers from 1 to 1000 starting with 2 and ending with 998. The sequence of even numbers is an arithmetic sequence with a common difference of 2. Using the equation for the arithmetic series,

S = (a1 + an)(n/2)
and substituting,

S = (2 + 998)(500/2)
we get,

S = 250,000

Therefore, the sum of all even numbers between 1 and 1000 is 250,000.

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Identify the ordered pair that represents the vector from a(1,6) to b(2,-3) and the magnitude of ab

aliina [53]

Answer: magnitude ab = 9.06

Step-by-step explanation:

The vector coordinates will be represented with ( X , Y )

Magnitude of ab will be

ab^2 = (X2 -X1)^2 + (Y2 -Y1)^2

ab^2 = (2 -1)^2 + (-3 -6)^2

ab^2 = 1^2 + 9^2

ab^2 = 1 + 81

ab = 9.06

3 0

3 years ago

Suppose you toss a fair coin 10 times, let X denote the number of heads. (a) What is the probability that X=5? (b) What is the p

zubka84 [21]

Answer: The required answers are

(a) 0.25, (b) 0.62, (c) 6.

Step-by-step explanation: Given that we toss a fair coin 10 times and X denote the number of heads.

We are to find

(a) the probability that X=5

(b) the probability that X greater or equal than 5

(c) the minimum value of a such that P(X ≤ a) > 0.8.

We know that the probability of getting r heads out of n tosses in a toss of coin is given by the formula of binomial distribution as follows :

$P(X=r)=^nC_r\left(\dfrac{1}{2}\right)^r\left(\dfrac{1}{2}\right)^{n-r}.$

(a) The probability of getting 5 heads is given by

$P(X=5)\\\\\\=^{10}C_5\left(\dfrac{1}{2}\right)^5\left(\dfrac{1}{2}\right)^{10-5}\\\\\\=\dfrac{10!}{5!(10-5)!}\dfrac{1}{2^{10}}\\\\\\=0.24609\\\\\sim0.25.$

(b) The probability of getting 5 or more than 5 heads is

$P(X\geq 5)\\\\=P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)\\\\=^{10}C_5\left(\dfrac{1}{2}\right)^5\left(\dfrac{1}{2}\right)^{10-5}+^{10}C_6\left(\dfrac{1}{2}\right)^6\left(\dfrac{1}{2}\right)^{10-6}+^{10}C_7\left(\dfrac{1}{2}\right)^7\left(\dfrac{1}{2}\right)^{10-7}+^{10}C_8\left(\dfrac{1}{2}\right)^8\left(\dfrac{1}{2}\right)^{10-8}+^{10}C_9\left(\dfrac{1}{2}\right)^9\left(\dfrac{1}{2}\right)^{10-9}+^{10}C_{10}\left(\dfrac{1}{2}\right)^{10}\left(\dfrac{1}{2}\right)^{10-10}\\\\\\=0.24609+0.20507+0.11718+0.04394+0.0097+0.00097\\\\=0.62295\\\\\sim 0.62.$

(c) Proceeding as in parts (a) and (b), we see that

if a = 10, then

$P(X\leq 0)=0.00097,\\\\P(X\leq 1)=0.01067,\\\\P(X\leq 2)=0.05461,\\\\P(X\leq 3)=0.17179,\\\\P(X\leq 4)=0.37686,\\\\P(X\leq 5)=0.62295,\\\\P(X\leq 6)=0.82802.$

Therefore, the minimum value of a is 6.

Hence, all the questions are answered.

3 0

3 years ago

Factor of 169 and 5x

krok68 [10]

Answer:

Step-by-step explanation:

3 0

2 years ago

What is the order from least to greatest? <br> -3, 1 1⁄4, -1 3⁄4, 1⁄10

Marianna [84]

Answer:

11/4 1/10/3/4 -/-3

Step-by-step explanation:

3 0

3 years ago

I need answer ASAP plz!!!

ANTONII [103]

It’s B I hope this helps :)

6 0

2 years ago