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3 years ago

Find prime factorizations of 3,210 and 3,528. Show your work.

2 answers:

5 0

Find the prime factorization of 3210
3210 = 2 × 3 × 5 × 107

Find the prime factorization of 3528
3528 = 2 × 2 × 2 × 3 × 3 × 7 × 7

To find the GCF, multiply all the prime factors common to both numbers:

Therefore, GCF = 2 × 3

GCF = 6

ANSWER: 6

brilliants [131]3 years ago

4 0

9514 1404 393

Answer:

3210 = 2·3·5·107

3528 = 2³·3²·7²

Step-by-step explanation:

Divisibility rules help.

A number is divisible by 2 if it is even.

A number is divisible by 3 if the sum of digits is divisible by 3.

A number is divisible by 5 if it ends in 5 or 0.

A number is divisible by 7 if subtracting twice the 1s digit from the rest of the number results in a number divisible by 7.

Even, and ends in 0, so is divisible by 2·5

3210/10 = 321

Sum of digits is 6, so is divisible by 3

321/3 = 107

None of the divisibility rules applies, and √107 ≈ 10.3, so there are no prime factors of 107.

3210 = 2·3·5·107

Ends in 2 digits divisible by 4, so is divisible by 4

3528/4 = 882

Even, so is divisible by 2

882/2 = 441

Sum of digits is 9, so is divisible by 9

441/9 = 49

This is recognizable as the square of 7.

3528 = 2³·3²·7²

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A customer visiting the suit department of a certain store will purchase a suit with probability 0.22, a shirt with probability

Pachacha [2.7K]

Answer:

a. The probability that a customer purchase none of these items is 0.49

b. The probability that a customer purchase exactly 1 of these items would be of 0.28

Step-by-step explanation:

a. In order to calculate the probability that a customer purchase none of these items we would have to make the following:

let A represents suit

B represents shirt

C represents tie

P(A) = 0.22

P(B) = 0.30

P(C) = 0.28

P(A∩B) = 0.11

P(C∩B) = 0.10

P(A∩C) = 0.14

P(A∩B∩C) = 0.06

Therefore, the probability that a customer purchase none of these items we would have to calculate the following:

1 - P(A∪B∪C)

P(A∪B∪C) =P(A) + P(B) + P(C) − P(A ∩ B) − P(A ∩ C) − P(B ∩ C) + P(A ∩ B ∩ C)

= 0.22+0.28+0.30-0.11-0.10-0.14+0.06

= 0.51

Hence, 1 - P(A∪B∪C) = 1-0.51 = 0.49

The probability that a customer purchase none of these items is 0.49

b.To calculate the probability that a customer purchase exactly 1 of these items we would have to make the following calculation:

= P(A∪B∪C) - ( P(A∩B) +P(C∩B) +P(A∩C) - 2 P(A ∩ B ∩ C))

=0.51 -0.23 = 0.28

The probability that a customer purchase exactly 1 of these items would be of 0.28

6 0

3 years ago

Are is 16/14 and 64/60

zalisa [80]

Do you know how to solve this??

6 0

3 years ago

Find three consecutive interferes whose sum is 96

Ronch [10]

Answer:

31, 32, 33

Step-by-step explanation:

x + x + 1 +x + 2 = 96

3x + 3 = 96

-3 -3

3x = 93

/3 /3

x = 31

31 is the first number, so since they’re consecutive, the second two numbers are 32 and 33.

6 0

3 years ago

each side of an equilateral triangle measures 32 centimeters, as shown. What is the approximate height h of the triangle?

Neko [114]

32 square root 6
use the pythagoream theorum
the sides would be 32 and 16. 16^2+x^2=32^2

4 0

3 years ago

A 12 ounce mixture of window cleaner is 4% alcohol. How many ounces of the mixture is alcohol

nekit [7.7K]

0.48 ounce is alcohol
Because you have to divide 100% from 12 ounces which is equivalent to 0.12 ounces for 1% now you will have to multiply 0.12 x 4% WHICH is 0.48 ounce

6 0

4 years ago