A prime number is a natural number greater than 1 that is not the sum of two lesser natural numbers (or a prime). Any natural number greater than one that is not prime is referred to as a composite number. For instance, the product 1 5 and 5 1 are the only two ways to write the number 5, making it a prime. The fact that it is the sum of two smaller integers (2 x 2), 4, however, makes it composite. Primes play a significant role in number theory because of the fundamental theorem of arithmetic, it states that any natural number greater than one is either a prime number itself or may be factored as a unique prime product up to the order of the primes. the prime number (or a prime).

The number of primes reduces almost exponentially as we move up the number line. The prime numbers between 0 and 100 are therefore far more numerous than those between 101 and 200. It is crucial to understand this general number theory point, but it may also be rapidly illustrated by attempting to find some primes in these two groups.

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6 0

2 years ago

Calculate the variance of the following set of data. 3, 33, 303, 233, 3, 73, 83, 63

andrew-mc [135]

Answer:

12083.929

Step-by-step explanation:

First step: find the mean of the data.

mean = 3+33+303+233+3+73+83+63

= 794

= 99.25

Second step: Now we calculate each dog's difference from the Mean.

Example : 3–99.25=96.25

Answer: (-96.25)+(-66.25)+203.75+133.75+(-96.25)+(-26.25)+(-16.25)+(36.25)

Third step: To calculate the Variance, take each difference, square it, and then average the result.

s² = (-96.25)²+(-66.25)²+203.75²+133.75²+(-96.25)²+(-26.25)²+(-16.25)²+(36.25)²

8–1

= 9264.063+4389.063+41514.063+17889.063+9264.063+689.063+264.063+1314.063

= 84587.5

= 12083.929

Variance Formula:

Variance = s² =Σ(xi− x )²

n−1

4 0

3 years ago

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A standard showerhead dispenses 21 gallons of water in 30 mins. At this rate, how many gallons of water will a standard showerhe

inysia [295]

Answer:

9.1 gallons of water.

Step-by-step explanation:

A standard showerhead dispenses 21 gallons of water in 30 mins. At this rate, how many gallons of water will a standard showerhead dispenses in 13 minutes?

30 minutes = 21 gallons

13 minutes = x gallons

Cross Multiply

30 minutes × x = 13 minutes × 21 gallons

x = 13 minutes × 21 gallons/30 minutes

x = 9.1 gallons of water

Therefore, a standard showerhead dispenses 9.1 gallons of water in 13 minutes.

7 0

3 years ago