A bathtub holds about 2 hectoliters of water. If 25 liters of water are let down the drain, how many liters of water are still in the bathtub?

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

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The 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'.

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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Final answer:

The linear function to describe the cost of using the pencil as a function of the number of refill packs Jorge buys is C(x) = 8 + 2x, where C(x) is the total cost and x is the number of refill packs.

Explanation:

Jorge bought a mechanical pencil for $8, and each lead and eraser refill pack costs $2. To describe the cost of using the pencil as a function of the number of refill packs, we can write a linear function. The initial cost of the pencil is a fixed cost, and the cost of each refill pack is a variable cost.

Let's let x represent the number of refill packs, and C(x) represent the total cost of using the pencil. The linear function for the cost would then be:

C(x) = 8 + 2x

Here, $8 represents the fixed cost (the cost of the pencil), and $2 is the cost per refill pack, so 2x represents the variable cost (the cost of x refill packs).

Final answer:

The linear function that describes the cost of using the pencil as a function of the number of refill packs is Cost(x) = 8 + 2x.

Explanation:

To write a linear function that describes the cost of using the mechanical pencil as a function of the number of refill packs, we need to consider the initial cost of the pencil and the cost of each refill pack.

Let's assume x represents the number of refill packs.

The initial cost of the pencil is $8, which remains constant regardless of the number of refill packs.

The cost of each refill pack is $2, and it increases linearly as the number of refill packs increases.

Therefore, the linear function that describes the cost of using the pencil as a function of the number of refill packs is:

Cost(x) = 8 + 2x

To find the value of f(-7), substitute -7 into the function f(x) = 8x + 15. The value of f(-7) is -41.

To find the value of f(-7), we substitute -7 into the function f(x) = 8x + 15.

f(-7) = 8(-7) + 15 = -56 + 15 = -41.

Therefore, the value of f(-7) is -41.

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Jeff ate 2/5 of the entire pumpkin pie on Saturday, calculated by multiplying 1/2 by the 4/5 which was left in the refrigerator.

The question asks what fraction of the entire pumpkin pie Jeff ate on Saturday if he left 4/5 of it in the refrigerator and then ate 1/2 of what was left. To solve this, we'll calculate the fraction of the pie he consumed using multiplication.

He started with 4/5 of the pie left. Eating 1/2 of what was left means he consumed 1/2 of 4/5, which can be calculated as:

(1/2) times (4/5) = 4/10 = 2/5

Jeff ate 2/5 of the entire pumpkin pie on Saturday.

Answer:

i know what question this is, thw answer is D, or |-10.6 = -10.6

The correct answer for [tex]750[/tex]g as percentage of [tex]1.5[/tex]kg is  ,[tex]750[/tex]g is [tex]50[/tex]% of  [tex]1.5\\[/tex]kg.

To express 750g as a percentage of 1.5kg, convert both quantities to the same unit of measurement.

Since both grams (g) and kilograms (kg) are units of mass,

convert 1.5kg to grams:

[tex]1[/tex] kg = [tex]1000[/tex] g

=[tex]1.5*1000[/tex]

= [tex]1500[/tex] g

To express [tex]750[/tex]g as a percentage of [tex]1500[/tex]g,

Percentage = (Part / Whole) * 100

Percentage = [tex]\dfrac{750}{1500}*100[/tex]

Percentage =  [tex]0.5*100[/tex]

Percentage =  [tex]50[/tex]%

The correct answer is [tex]750[/tex]g is [tex]50[/tex]% of [tex]1.5[/tex]kg.

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Answer: The simplified answer is 15.

Explanation:

Since we have given that

[tex]5+1\times 10[/tex]

As we know about the BODMAS rule,

Where B stands for brackets

D stands for division

M stands fro Multiplication

A stands for addition

S stands for subtraction

So, in this expression, we first use the multiplication operation and then addition as shown below:

[tex]=5+1\times 10\\\\=5+10\\\\=15[/tex]

Hence , the simplified answer is 15.

Answer: The width of each section is [tex]3\frac{2}{3}\ inches[/tex] .

Step-by-step explanation:

Since we have given that

Length of a page = 11 inches

According to question, Flyers are folded into thirds before being stapled and mailed.

So, Width of each section is given by

[tex]\frac{11}{3}\\\\=3\frac{2}{3}\ inches[/tex]

Hence, the width of each section is [tex]3\frac{2}{3}\ inches[/tex] .

Answer:

The car completed 20% of the trip between the cities.

Step-by-step explanation:

The distance between Oswego and Syracuse = 40 miles

The car traveled from Oswego towards Syracuse = 8 miles

We have to calculate the percentage of the trip that the car completed.

8 miles out of 40 miles = [tex]\frac{8}{40}[/tex]

To calculate we have to multiply it by 100 and put the mark of percentage.

[tex]\frac{8}{40}[/tex] × 100

= 0.2 × 100 = 20%

The car completed 20% of the trip between the cities.

With the help of ratios, we know that 85 students are enrolled in the 7th grade and 115 students are enrolled in the 8th grade.

So, first, add the raions and then multiply the fractions with total students as follows:

7th grade:

8th grade:

So, with the help of ratios, we know that 85 students are enrolled in the 7th grade and 115 students are enrolled in the 8th grade.

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