Considering the definition of prime number, prime factorization and a property of the potentiation, this factorization is not a prime factorization. The prime factorization is expressed as: 2⁵× 3× 5⁴× 11²
In the first place, a prime number is a natural number greater than 1 that has only two different divisors: itself and 1. That is, a prime number is an integer greater than 1 that is only divided exactly by 1 and itself .
On the other side, the "factors" are the numbers that you multiply together to get another number.
So "factoring into primes" is figuring out what prime numbers you have to multiply together to get the original number.
That is, factoring in prime numbers is writing any number as the multiplication of prime numbers, regardless of the order of the factors.
In this case, you have the factorization: 2²× 3× 5⁴× 8× 11²
This factorization is not a prime factorization. 2,3,5 and 11 are prime numbers, but 8 is not a prime number. This last number can be factored as:
8= 2³
Then, the factorization is expressed as: 2²× 3× 5⁴× 2³× 11²
A property of the potentiation expresses that the product of powers of equal base results in the same base raised to the sum of the exponents of each factor. In this case, 2² and 2³ are two powers with the same base, so the power is expressed as:
2²× 2³= 2²⁺³= 2⁵
Finally, the prime factorization is expressed as: 2⁵× 3× 5⁴× 11²
Learn more:
https://brainly.com/question/11709591?referrer=searchResultshttps://brainly.com/question/10371102?referrer=searchResultshttps://brainly.com/question/13315667?referrer=searchResultsThe given number is not in prime factorization due to the presence of '8'. The correct prime factorization is '2^5 X 3 X 5^4 X 11^2'.
Explanation:The number given in the question is not expressed in its prime factorization due to the presence of '8' which is composite number and can be broken down further. In fact, the number '8' can be represented as '2^3'. So, if we modify this in the original expression, it would change to 2^2 X 3 X 5^4 X 2^3 X 11^2. Simplifying this, we get 2^5 X 3 X 5^4 X 11^2, which is the correct prime factorization. A prime factorization only includes prime numbers, which are numbers that have exactly two distinct positive divisors: 1 and the number itself.
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A square garden with a side length 150 m has a square swimming pool in very center with a side length 25 m .Calculate the area of the garden.
Final answer:
Calculate the area of a square garden with a swimming pool in the center.
Explanation:
The area of the garden can be calculated by finding the area of the square garden and subtracting the area of the square swimming pool.
Area of the square garden:
Area = side length × side length
= 150 m × 150 m = 22500 m²
Area of the swimming pool:
Area = side length × side length
= 25 m × 25 m = 625 m²
Area of the garden: 22500 m² - 625 m² = 21875 m²
Therefore, the area of the garden is 21875 m².
Niall owes $187 to his cousin. However, he doesn't have any money right now. He hopes to earn some money by painting a house. He gets paid $34 for every 2 hours he paints. Which equation of a line models y, the amount of money he will have after paying back his cousin, in terms of x, the number of hours he spends painting?
Answer:
[tex]y=17x-187[/tex] where x>11
Step-by-step explanation:
Niall gets $34 for 2 hours.
So, he gets [tex]34/2=17[/tex] dollars per hour.
Now, he owes $187 to his cousin.
Let the number of hours he works be = x
Let the money left with him after paying his cousin be = y
So, the equation forms:
[tex]y=17x-187[/tex]
Rather we can say it is :
[tex]y=17x-187[/tex] where x>11
If we want to know how many hours are needed to pay the debt, we can consider y = 0
[tex]17x-187=0[/tex]
[tex]17x=187[/tex]
[tex]x=187/17[/tex]
So, x = 11 hours
So, Niall needs 11 hours of work to pay back his cousin and after that all his earnings is 'y'. When x>11 then 'y' will have some money left.
What is 7/8-1/2 in simplest form
To subtract fractions like 7/8 - 1/2 and simplify the result, find a common denominator and perform the subtraction to get 3/8.
To subtract fractions with different denominators like 7/8 - 1/2 and express the result in simplest form, you need to find a common denominator. In this case, the common denominator is 8. So, we rewrite both fractions with a common denominator of 8:
7/8 - 4/8 = 3/8
Therefore, 7/8 - 1/2 = 3/8 in simplest form.
suzanne buys 6 paints sets. each set contains the same number of brushes. she buys 18 brushes.how many bruxhes are in each paint set?
four students spent $12 on school lunch at this rate find the amount 10 students would spend on the same school lunch
A textbook costs $65.49 before tax the tax on the text book is 6.5% what is the total cost of the textbook?
What is 1/3x -5/7 equal to
Write 5 hundred + 56 ones in standard form
Write 1,340,000,000,000 in expanded form with exponents
It cost $3.99 for 25 fl. oz. of detergent or $6.99 for 90 fl. oz. Which is a better buy?
$6.99 for 90 fl. oz of detergent is a better buy.
Arithmetic operations is a concept that concerns the study of mathematical operations like addition, subtraction, division, and multiplication.
The determination on the type which is a better buy can be estimated by finding the cost of each detergent in the two cases.
For the first case, we are being told that It cost $3.99 for 25 fl. oz. of detergent.
From that, the price for 1 fl. oz will be:
[tex]\mathbf{x = \dfrac{3.99 \times 1 }{25}}[/tex]
x = $0.1596
For the second case, if the price for 90 fl. oz is $6.99
For 1 fl.oz, we have:
[tex]\mathbf{x = \dfrac{6.99 \times 1 }{90}}[/tex]
x = $0.0777
Therefore, we can conclude that $6.99 for 90 fl. oz of detergent is a better buy since the amount of each detergent is lesser than that of 25 fl. oz.
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Solve in simplest form 2t=4/7
Please help me by those math problems!
what is the answer to 50.28 divided by 4 (long division) PLEASE SHOW YOUR WORK
I do not understand the question. Plz help!
Select True or False. The expression 4x − 2(5x − 1) is equivalent to the expression 2 + 6x.
Answer: The given statement is FALSE.
Step-by-step explanation: We are given to check whether the following statement is True of False :
"The expression 4x − 2(5x − 1) is equivalent to the expression 2 + 6x".
We will be using the following distributive property :
[tex]a(b+c)=ab+ac.[/tex]
We have
[tex]4x-2(5x-1)\\\\=4x-10x+2\\\\=-6x+2\\\\=2-6x\\\\\neq 2+6x.[/tex]
Therefore, expression 4x − 2(5x − 1) is NOT equivalent to the expression 2 + 6x.
Thus, the given statement is FALSE.
On Wednesday, Abby and Lauren could not practice together, so they practiced separately. Abby practiced for 11/12 of an hour and Lauren practiced for 2/3 of an hour. How long did they practice on Wednesday?
Abby and Lauren practiced for a total of approximately 1.58 hours on Wednesday.
Explanation:The subject of this question is Mathematics and it concerns the addition of fractions. It is aimed at Middle School grade level.
Abby practiced for 11/12 of an hour and Lauren practiced for 2/3 of an hour, and to find out how long they both practiced, we need to add these two fractions together. Converting these fractions into like fractions (with same denominator), we have Abby's time as 33/36 (since 11/12 = 33/36) and Lauren's time as 24/36 (since 2/3 = 24/36).
Adding together Abby's practice time (33/36) and Lauren's practice time (24/36), gives 57/36 or 1 21/36 hours which is approximately 1.58 hours.
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use the graph to find the capacity in quarts of a 2.5 container gallon
Mindy read 8 pages of her book the first day, 15 pages the second day, and 22 pages the third day. if the pattern continues , how many pages of her book will she read on the sixth day
What is -2 plus 2X equalsNegative X plus 2 plus x
Answer:
x=2
Step-by-step explanation:
-2 + 2x = -x + 2 + x
-2 + 2x = -x + x + 2
-2 + 2x = 2
+2 +2
2x = 4
Divide 4 by to 2 in order to isolate the variable and then you get the answer of 2.
Word problems for 5x=45
what is one third plus one fourth equal to a mixed number
The mixed number equivalent to 7/12 is 0 and 7/12.
To add one-third and one-fourth, we need to find a common denominator. The least common multiple of 3 and 4 is 12.
Converting both fractions to have a denominator of 12:
1/3 = 4/12
1/4 = 3/12
Now, we can add the fractions:
4/12 + 3/12 = 7/12
The sum of one-third and one-fourth is 7/12. To express this as a mixed number, we need to divide the numerator (7) by the denominator (12):
7 ÷ 12 = 0 remainder 7
Therefore, the mixed number equivalent to 7/12 is 0 and 7/12.
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41 2/3% as a fraction in simplest form
Jenny has 50 square tiles. She arranges the tile into a rectangular array of 4 rows.How many tiles will be left over?
$7.59 divided by 2.2 ?
The quotient of two numbers is $3.45.
What is the division?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
Given that, $7.59 divided by 2.2.
Now, 7.59 ÷2.2
= 7.59/2.2
= $3.45
Therefore, the quotient of two numbers is $3.45.
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Final answer:
The division of $7.59 by 2.2 results in approximately 3.45. This can be calculated using long division or a calculator after adjusting for the decimal in the divisor.
Explanation:
The student has asked how to divide the number $7.59 by 2.2. This is a basic arithmetic operation involving division. To perform this division, you can use long division or a calculator. When you divide $7.59 by 2.2, you will get approximately 3.45, which is the quotient. Here's a step-by-step breakdown:
Set up the division with $7.59 as the dividend and 2.2 as the divisor. Since we are dividing by a decimal, we can move the decimal point of the divisor (2.2) to the right to make it a whole number (22). Simultaneously, we also move the decimal point in the dividend (7.59) the same number of places to the right, changing it to 759. Now, divide 759 by 22 using long division or a calculator. The result is approximately 34.5, but since we moved the decimal one place to the right, we must move it back one place to the left in our answer, resulting in 3.45.A family pays $45 each month for cable television. The cost increases 7%.
a. How many dollars increases?
b. What is the new monthly cost?
Students at a high school filled out a survey. The results showed that out of 640 students, 331 speak more than one language. How many students speak only one language?
Answer:
309
Step-by-step explanation:
640 - 331 = 309
A book sold 32,500 copies in its first month of release. Suppose this represents 8.4% of the number of copies sold to date. How many copies have been sold to date?
Simplify. –2 • (4) – 3 • (–5) = A. 55 B. 7 C. –23 D. –120
Find the perimeter and area of this rectangle 12 in by 6.5 in
How do you solve a Rubik's Cube?