A bathtub is draining at a constant rate. After 2 minutes, it holds 30 gallons of water. Three minutes later, it holds 12 gallons of water. Write an equation that represents the number y of gallons of water in the tub after x minutes.

There are 11 colored pencils and 99 markers.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Mrs. O'Neill has 9 times as many markers as colored pencils.

Total number of markers and colored pencils = 110.

let the number of colored pencils be x.

Then, number of markers = 9x

Thus x+ 9x = 110

10x =110

x= 11

So, there are 11 colored pencils and 99 markers.

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Final answer:

Mrs. O'Neill has 11 colored pencils.

Explanation:

To solve the problem of how many colored pencils Mrs. O'Neill has, let's denote the number of colored pencils as x. According to the information given, Mrs. O'Neill has 9 times as many markers as she has colored pencils, so the number of markers is 9x.

The total number of markers and colored pencils is 110, represented by the equation x + 9x = 110.

Solving this equation will help us find the value of x:

Mrs. O'Neill has 11 colored pencils.

Answer:

[tex]\frac{28}{45}[/tex] of the book student read in 70 minutes

Step-by-step explanation:

A student reads 2⁄5 of a book in 45 minutes.

In 45 minutes the student reads 2/5 of a book

In 1 minute the student reads 2/5 divide by 45

[tex]\frac{\frac{2}{5}}{45} = \frac{2}{225}[/tex]

In 1 minute the student reads  [tex]\frac{2}{225}[/tex]

In 70 minutes the student reads [tex]70* \frac{2}{225}[/tex]

[tex]\frac{140}{225}[/tex]

Now simplify the fraction

divide both sides by 5

[tex]\frac{28}{45}[/tex]

The constant term in the function y=10x+25, representing the number of trading cards Sean has, is 25. This term is best interpreted as the number of cards Sean had when he started his collection, which corresponds to Option A.

The function y=10x+25 represents the number of trading cards Sean has over time, where y is the number of cards and x is the time in months since he began collecting. The constant term in this linear equation (the number 25) is the y-intercept, which is the value of y when x is zero. This term represents the number of cards that he had when he started his collection. It shows us that before any months have passed (when x=0), Sean already had 25 cards. Therefore, the best interpretation of the constant term in this function is Option A: the number of cards that he had when he started his collection.

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The solution to the system  2x + 7y = 1 and 2x - 4y = 12 is (- 1, 4).

In the elimination method of solving two or more than two equations, we make one variable of both equations the same by multiplying or dividing and then we add or subtract them.

Given, 2x + 7y = 1 and 2x - 4y = 12.

If we subtract (2x + 7y = 1) - (2x - 4y = 12) we'll have,

7y + 4y = 1 - 12.

11y = - 11.

y = - 1.

Now putting the value of y in any one of these equations we get,

2x + 7(-1) = 1.

2x - 7 = 1.

2x = 8.

x = 4.

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After calculating the hourly rates by dividing the total earnings by the hours worked, Elisa has a higher hourly rate of $16 per hour compared to Rida's $14 per hour.

To determine whose hourly rate is greater between Rida and Elisa, we need to calculate each person's hourly wage by dividing the total amount earned by the number of hours worked.

Rida's hourly rate calculation:

Elisa's hourly rate calculation:

Comparing the hourly rates, we find that Elisa's hourly rate is greater than Rida's.

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The product of a number and its reciprocal is always 1, because multiplying a number by 1 divided by itself simplifies to 1.

The product of a number and its reciprocal is always 1. This is because a reciprocal is defined as 1 divided by the number. For any non-zero number x, the reciprocal is [tex]\frac{1}{x}[/tex]. Therefore, when you multiply a number by its reciprocal, x × [tex]\frac{1}{x}[/tex], you are essentially multiplying the number by 1 divided by itself, which simplifies to 1.

For example, the reciprocal of 2 is [tex]\frac{1}{2}[/tex], and when you multiply 2 by [tex]\frac{1}{2}[/tex], the product is 2 × [tex]\frac{1}{2}[/tex] = 1. This concept is crucial in mathematics, as it underlies the operations of division and multiplication, where division by a number is the same as multiplying by its reciprocal.

Hello!  I know somebody might have already answered this question, but I figured I could add more to it. In order to help you know whenever a question shows up like this again, I'll make an ordered situation for you.

Let's go ahead and make the situation!

The Situation:  Let's call the person trying to figure this problem out by Alison.  Alison turns on the water and allows it to run in the tub for about 9 minutes. She then turns the water off while she runs to answer the front door. She soon comes back and allows water to run into the tub for a couple more minutes before she takes a short bath. After the bath, Alison allows the water to completely drain from the tub.  That's how the problem would've went, but your question.

When you're asking the question you're also trying to figure out how it would've gone.  So, since you tried following the paragraph I made for the picture/problem I can show how'd it help you comprehend it better.  After Alison turns on the water, turns it back off then comes back to run the water AGAIN.. She finally drains it from the tub, which is what the picture exactly shows.  BUT when did she turn it off?!!!

Look at the problem, at the point where the Water level(in) starts decreasing.  We know that we end with the Water level(in) at 0, but how'd it get there?  The point at 12 in time is when it starts decreasing! But, from there it continues until it's at 15(min)

THE FINAL ANSWER: At 12(min) it decreases until it hits 15(min) which is when the tub is empty.  So, if you do common math 15(min) - 12(min) is 3(min)  So, it took 3(min) to empty the tub when it was the most full.

0.625 inches on the map represents 1 mile.

To find how much distance on the map represents 1 mile when [tex]\frac{1}{2}\ inch[/tex] represents [tex]\frac{4}{5}\ mile[/tex], set up a proportion.

If [tex]\frac{1}{2}\ inch = \frac{4}{5} \ mile[/tex], then we can set up the equation:

x inches = 1 mile

First, we recognize that:

Next, using the proportion, we can set up and solve for x:

[tex]\frac{0.5\ inch}{0.8\ mile} =\frac{x\ inch}{1\ mile}[/tex]

Cross-multiplying gives:

0.5 * 1 = 0.8 * x

0.5 = 0.8x

Solving for x:

[tex]x = \frac{0.5}{0.8}[/tex]

x = 0.625 inches

Therefore, 0.625 inches on the map represents 1 mile.

Final answer:

The long division for 6,250 ÷ 5 results in 1,250. By dividing each place value by 5 methodically, you arrive at the total step by step.

Explanation:

Performing Long Division

To perform the long division for 6,250 ÷ 5, you divide 6,250 by 5. Here’s the step-by-step process:

First, you look at the thousands place. 6,000 divided by 5 gives you 1,200. So you write 1,200 above the division bar.

Next, since you accounted for 5,000 of the 6,250, you have 1,250 left. Then divide 1,000 by 5 to get 200, and write this under the 1,200.

Now you have accounted for 6,000 and only 250 remain. You divide 250 by 5 to get 50 and write this under the 200.

Add the totals above the division bar: 1,200 + 200 + 50 to get 1,250.

The answer to 6,250 ÷ 5 is 1,250. This is how you use long division to solve this problem.

The fractions that are less than (1/2) can be, 1/4, 1/6, 1/7, 1/8, and so on.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, A fraction (1/2).

Now, The fractions that are less than (1/2) can be obtained by multiplying such fractions which are less than 1.

For, Example, 1/4, 1/5, 1/6, etc.

Therefore, One such fraction that is less than (1/2) is (1/2)×(1/4),

= 1/8.

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Mrs. Gee should arrange the 24 carpet squares in a rectangle of 6 by 4 squares to achieve the smallest perimeter of 20 units.

Arranging Carpet Squares with the Smallest Perimeter

To minimize the perimeter when arranging 24 carpet squares, Mrs. Gee should create a shape that is as close to a square as possible. Since 24 is not a perfect square, we look for dimensions that are factors of 24 that are closest to each other, which are 6 and 4. This would create a rectangle that is 6 squares long and 4 squares wide. Arranging the carpet squares in this manner results in a perimeter of:

(6 + 4) x 2 = 20 units

This is the smallest possible perimeter for 24 squares with whole number side lengths.

The number with digits 2, 5, and 4 rounds to 200 when rounded to the nearest hundredh is 245.

We round off numbers to make them easier to remember and it also keeps their value approximately to the place it has been rounded off.

To round off any number to any place we'll look for the digit next to that place and if it is equal to or greater than 5 we'll add one to the previous digit and make all the digits after it zeroes and if the digit is less than 5 we do not add one to the preceding digit and simply make all the digit after it to zeroes.

Given, A number has the digits 2, 5, and 4. To the nearest 100, the number rounds to 200.

Now if it rounds to 200 the first digit must be 2 so the number is either

254 Or 245.

254 rounds to 300 and 245 rounds to 200.

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Answer:

it is 8 feet

Step-by-step explanation: