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What is 66 2/3% of 39

lys-0071 [83]

Number x percent turned into decimal

39 x 0.666666666 = 26

5 0

3 years ago

Read 2 more answers

Find the prime factorization of 30,031

Tcecarenko [31]

Answer:

30,031 is not a prime, is a composite number. Integer prime factorization, as a product of prime factors: 30,031 = 59 x 509.

Step-by-step explanation:

Let's learn by having an example, take number 220 and build its prime factorization.

0) We need the list of the first prime numbers, ordered from 2 up to, let's say, 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. Prime numbers are the building blocks of the composite numbers' prime factorization process.

1) Start by dividing 220 by the first prime number in our list, 2 (start with the smallest prime number). We could have skipped the division by 2 if our number were an odd number, ie. 221.

220 ÷ 2 = 110; remainder = 0 => 220 is divisible by 2 (2 | 220) => 2 is a prime factor of 220. => 220 = 2 × 110.

2) Divide the result of the previous operation, 110, by 2, again:

110 ÷ 2 = 55; remainder = 0 => 110 is divisible by 2 (2 | 110) => 2 is once again a prime factor of 220 => 220 = 2 × 2 × 55.

3) Divide the result of the previous operation, 55, by 2, again:

55 ÷ 2 = 27 + 1; remainder = 1 => 55 is not divisible by 2.

4) Move on, divide 55 by the next prime number, 3 (notice that the sum of digits of 55 is 5 + 5 = 10 is not divisible by 3, so 55 is not divisible by 3):

55 ÷ 3 = 18 + 1; remainder = 1 => as we already said, 55 is not divisible by 3.

5) Divide 55 by the next prime number, 5:

55 ÷ 5 = 11; remainder = 0 => 55 is divisible by 5 (5 | 55) => 5 is yet another prime factor of 220 => 220 = 2 × 2 × 5 × 11.

6) Notice that the remaining number, 11, is also a prime number, so we've got already all the prime factors of 220.

7) Conclusion, 220 prime factorization: 220 = 2 × 2 × 5 × 11.

This can be written in a condensed form, in the exponent notation: 220 = 22 × 5 × 11.

6 0

3 years ago

Consider writing onto a computer disk and then sending it through a certifier that counts the number of missing pulses. Suppose

vagabundo [1.1K]

Answer:

a) 0.222

b)0.037

c)0.549

Step-by-step explanation:

Let's start defining the random variable ⇒

X : ''The number of missing pulses''

X can be modeled as a Poisson random variable.

X ~ Po(λ)

In a Poisson distribution : μ = λ

Where μ is the mean of the variable.

X ~ Po(0.3)

The probability function for a Poisson random variable is :

In the equation I replace λ = m

$P(X=x)=\frac{e^{-m}m^{x}}{x!}$

Where P(X=x) is the probability of the random variable X to assume the value x

e is the euler number

m = λ is the mean of the variable

In this exercise :

$P(X=x)=\frac{e^{-0.3}0.3^{x}}{x!}$

is the probability function.

For a)

$P(X=1)=\frac{e^{-0.3}0.3^{1}}{1!}=0.222$

For b)

$P(X\geq 2)=1-P(X$

$P(X\geq 2)=1-[P(X=0)+P(X=1)]$

$P(X\geq 2)=1-(e^{-0.3}+0.222)\\P(X\geq 2)=0.037$

c)

Let's define A :''a disk doesn't contain a missing pulse''

We are looking for P(A1∩A2) of two different disk don't have a missing pulse.

Because of the independence we can write this probability as

P(A1∩A2)= P(A1).P(A2)

The probability of a random disk to don't have a missing pulse is P(X=0)

$P(X=0)=e^{-0.3}$ ⇒

$P(A1).P(A2)=[P(X=0)].[P(X=0)]$

$[P(X=0)].[P(X=0)]=(e^{-0.3})(e^{-0.3})=0.549$

6 0

3 years ago

At the local grocery store, cans of beans are arranged in rows. The number of cans in each row forms an arithmetic sequence. The

Helen [10]

It seems the cans are arranged in a sequence 93,88,83,78,73,68,68,58,53,48 so the row containing 48 cans is row 10

7 0

3 years ago

CARD #2:

aalyn [17]

Answer:

When a dilation in the coordinate plane has the origin as the center of dilation, you can find points on the dilated image by multiplying the x- and y-coordinates of the original figure by the scale factor. For scale factor k, the algebraic representation of the dilation is (x, y) → (kx, ky). For enlargements, k > 1.

5 0

3 years ago