A swimming pool holds 12,500 gallons of water at the start of the day. A valve at the bottom of the pool releases water into a cleaning tank at a constant rate of 20 gallons per hour. A hose is running water into the pool at a constant rate of 60 gallons per hour. On one day, the hose was running for 3 hours, and the valve was left open for 6 hours. How much water is in the pool at the end of the day?

To find 5/6 of 15, you convert the whole number 15 into a fraction (15/1) and then multiply the numerators and denominators. This results in the fraction 75/6 which simplifies to 12.5.

The subject of this question is finding 5/6 of 15. This is a simple multiplication problem that involves fractions.

To solve this, you must multiply the fraction with the whole number. The calculation is as follows:

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Final answer:

To find 5/6 of 15, multiply 5/6 by 15/1 to get 75/6, which simplifies to 25/2 or 12.5 in decimal form.

Explanation:

To find 5/6 of 15, we can approach the problem in a straightforward manner by multiplying 5/6 by 15. Here are the steps to do this:

The answer in simplest form is 25/2 or 12.5.

Final answer:

To find out how many 2/3 cup servings are in a 4 cup container, divide 4 by 2/3, resulting in 6 servings.

Explanation:

The question is about determining how many 2/3 cup servings are in a 4 cup container of food. To find the answer, you divide the total amount of the container by the serving size. So, you divide 4 cups by 2/3 cup.

Calculation:

1 cup / (2/3 cup) = 3/2 servings

4 cups * (3/2 servings) = 6 servings

Therefore, you can fit 6 servings of 2/3 cup each in a 4 cup container.

The area of the rectangle is 135 [tex]cm^{2}[/tex], and the perimeter is 48 cm, given that the width is 3 / 5 of the rectangle's length which is 15 cm.

To find the area and perimeter of a rectangle where the width is 3/5 of the length, we apply the formulas. First, calculate the width:

Width = 3 / 5 × Length

Width = 3 / 5 × 15

Width = 9 cm

Now, calculate the area:

Area = Length × Width

Area = 15 cm × 9 cm

Area = 135 cm²

Next, calculate the perimeter:

Perimeter = 2 x (Length + Width)

Perimeter = 2 x (15 cm + 9 cm) = 2 x (24 cm)

Perimeter = 48 cm

The area of the rectangle is 135 cm2, and the perimeter is 48 cm.

To determine how many 3/4 are in 7/8, you would divide the first fraction by the second, which involves multiplying 7/8 by the reciprocal of 3/4 (which is 4/3), resulting in approximately 1.17.

To find out how many 3/4 are in 7/8, you have to divide 7/8 by 3/4. Division in fractions requires the multiplication of the first fraction by the reciprocal of the second fraction.

So, the reciprocal of 3/4 is 4/3. Now, you multiply 7/8 by 4/3 to get:

(7/8) * (4/3) = 7*4 / 8*3 = 28/24

Simplify the fraction 28/24 by dividing both numbers by their greatest common divisor, which is 4, resulting in the fraction 7/6.

So, there are 7/6, or about 1.17 times of 3/4 in 7/8.

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Base of the Sail is 12 feet and Height of the Sail is 5 feet

A right triangle or right-angled triangle, or more technically an orthogonal triangle, historically known as a rectangled triangle, is a triangle with one right angle (that is, a 90-degree angle) and two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.

here, we have,

Solution:

According to the Question,

Let, Base = x and Height = y

x = 7 + y

Using the Pythagorous Theorem

a^2 + b^2 = c^2

Using the above mentioned relation

49 + y^2 + 14y + y^2 = 169

2y^2 + 14y - 120 = 0

Discriminant = 34

y = 5, -12

The length of a sail can not be negative, therefore y = 5

From the equation 1, x = 12

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Answer:

24 fossil kits

Step-by-step explanation:

30 fossil kits with 8 samples in each of them would have a total of :

[tex]30*8=240[/tex]  samples

The other one has 10 samples per kit, so to have 240 samples, the number of fossil kits needed would be:

[tex]\frac{240}{10}=24[/tex]  kits

The equation represents the given situation is h+h+2.5=22. Therefore, option C is the correct answer.

Given that, José worked 2.5 hours more than William. Together, they worked a total of 22 hours.

We need to find which equation represents this situation.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

William worked h hours.

Now, number of hours Jose worked = h+2.5

h+h+2.5=22

⇒2h+2.5=22

⇒2h=22-2.5

⇒2h=19.5

⇒h=9.75 hours

The equation represents the given situation is h+h+2.5=22. Therefore, option C is the correct answer.

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Answer:

a). Volume of the smaller vase = 320 cm³

b). Surface area of the larger vase = 567 cm²

Step-by-step explanation:

When we calculate the volume of any figure we multiply it's three dimensions either length, width, height or we do the cube of the radius (r×r×r=r³).

In other words volume is a three dimensional figure and surface area is two dimensional.

Therefore, ratio of volumes of two similar structures will be the ratio of cube of one side given.

a). [tex]\frac{V_{1}}{V_{2} }=(\frac{Side 1}{Side2})^{3}[/tex]

[tex]\frac{V_{1}}{V_{2} }=(\frac{3}{2})^{3}[/tex]

[tex]\frac{1080}{V_{2} }=(\frac{3}{2})^{3}[/tex]

[tex]\frac{1080}{V_{2} }=(\frac{27}{8})[/tex]

[tex]27V_{2}=8\times 1080[/tex]

[tex]V_{2}=\frac{8640}{27}[/tex]

[tex]V_{2}=320[/tex] cm³

b). Similarly ratio of the surface area of two vase will be

[tex]\frac{A_{1}}{A_{2} }=(\frac{Side 1}{Side2})^{2}[/tex]

[tex]\frac{A_{1}}{252}=(\frac{3}{2})^{2}[/tex]

[tex]\frac{A_{1}}{252}=(\frac{9}{4})[/tex]

[tex]A_{1}=\frac{9\times 252}{4}[/tex]

[tex]A_{1}=567[/tex] cm²

Answer:

The answer to this problem is 2.52.

The simplified form of the expression 3 + 4(10 - 8) is 11.

Here, we have,

To simplify the expression 3 + 4(10 - 8), you can follow the order of operations, which is often remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction):

Step 1:

Start by evaluating the expression inside the parentheses: 10 - 8 = 2.

Now, the expression becomes 3 + 4(2).

Step 2:

Next, perform the multiplication: 4 * 2 = 8.

The expression now becomes 3 + 8.

Step 3:

Finally, perform the addition: 3 + 8 = 11.

Therefore, the simplified form of the expression 3 + 4(10 - 8) is 11.

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The number of thirds in ( -4 2/3 ) is given by the equation A = -14

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.

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 data ,

Let the equation be represented as A

Now , the value of A is

Let the number be represented as n

And , the value of n = - 4 2/3

On simplifying the equation , we get

n = ( -12 -2 ) / 3

n = -14/3

Now , the number of thirds in the number n is A = n / ( 1/3 )

Substituting the values in the equation , we get

A = ( -14/3 ) / ( 1/3 )

On simplifying the equation , we get

A = -14

Hence , the equation is A = -14

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