A city of 82,080 residents has a population density of 2,160 residents per square mile what is the area of the city

To obtain a 50% mixture, 2.4 quarts of water must be added to 4 quarts of an 80% mixture.

To solve this problem, we'll use the concept of mixtures.

Let's denote:

x = the number of quarts of water to be added.

We have 4 quarts of an 80% mixture. This means that in these 4 quarts, 80% is the actual substance (let's call it A) and 20% is water.

So, the amount of substance A in the 4 quarts is [tex]\(0.80 \times 4 = 3.2\)[/tex]quarts, and the amount of water is [tex]\(0.20 \times 4 = 0.8\)[/tex] quarts.

When we add \(x\) quarts of water, the total amount of water becomes 0.8 + x, and the total volume of the mixture becomes 4 + x quarts.

For the mixture to be 50%, the amount of substance A in the mixture should be equal to the amount of water. So, we set up the equation:

[tex]\[3.2 = 0.5 \times (4 + x)\][/tex]

Solving for x:

[tex]\[3.2 = 2 + 0.5x\]\[0.5x = 3.2 - 2\]\[0.5x = 1.2\]\[x = \frac{1.2}{0.5}\]\[x = 2.4\][/tex]

So, 2.4 quarts of water must be added to 4 quarts of an 80% mixture to obtain a 50% mixture.

Answer:

3 9/20

Step-by-step explanation:

3.45 is 69/20

60 goes into 20 3 times

which leaves you with 3 9/20

The number 5.38516 is greater than the square root of 29 or the square root of the number 29 is less than the number 5.7145.

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

It is given that:

The two numbers are:

5.7145 and √29

It is required to compare the numbers

The square root of the number 29 can be found using the division method.

The square root of the number 29 is 5.38516

As we know, the number line can be defined as the representation of the numbers on a straight line that goes infinitely on both sides.

Plotting the numbers 5.7145  and 5.38516 on a number line.

We will see the:

5.38516 < 5.7145  OR

5.7145  > 5.38516

Thus, the number 5.38516 is greater than the square root of 29 or the square root of the number 29 is less than the number 5.7145.

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To find the unit rate of $32.05 for 15 gallons, divide the total cost by the number of gallons, resulting in $2.14 per gallon. This unit rate helps to compare the cost per gallon with other price points.

The unit rate is a way to compare a quantity to one unit of another quantity. For the case of $32.05 per 15 gallons, we can calculate the unit rate by dividing the total cost by the number of gallons to find the cost per one gallon.

Step-by-step Calculation

This means the unit rate, or the cost for one gallon of gasoline, is $2.14 per gallon.

Comparing this with other unit prices provided: $2.20 per gallon, $2.00 per gallon, $1.80 per gallon, $1.60 per gallon, $1.40 per gallon, $1.20 per gallon, and $1.00 per gallon, we can observe how this unit rate fits within the broader range of prices and quantities.

Final answer:

To calculate the total distance Gabriella flew in four shows at the circus, add up the distances she covered in each performance.

Explanation:

The total distance Gabriella flew on Saturday can be calculated by adding up the distances she covered in each show:

Distance 1: 8.05 meters

Distance 2: 17.71 meters

Distance 3: 14.38 meters

Distance 4: 19.35 meters

By adding these distances together, you can find the total distance Gabriella flew that day i.e. 8.05+17.71+14.38+19.35 =  59.49 m

Answer:  the correct option is

(D) [tex]c=\dfrac{d+ab}{a}.[/tex]

Step-by-step explanation:  We are given to solve the following equation for the value of c :

[tex]a(c-b)=d~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To solve the given equation for c, we need to take c on one side and all other values on the other side of the equation.

The solution for c of equation (i) is as follows :

[tex]a(c-b)=d\\\\\Rightarrow ac-ab=d\\\\\Rightarrow ac=d+ab\\\\\Rightarrow c=\dfrac{d+ab}{a}.[/tex]

Thus, the required value of c is [tex]c=\dfrac{d+ab}{a}.[/tex]

Option (D) is CORRECT.

Volume is a measurement that quantifies the amount of three-dimensional space occupied by an object, substance, or region.

Volume is a fundamental physical quantity that describes the extent or size of an object in the context of its three dimensions: length, width, and height.

Volume is commonly expressed in cubic units, such as cubic meters (m³), cubic centimeters (cm³), cubic inches (in³), or cubic feet (ft³), depending on the system of measurement used. It can apply to various entities, including solid objects, liquids, gases, or even abstract concepts like the volume of data.

For solid objects, the volume represents the total amount of space enclosed within its boundaries. It is typically determined by measuring or calculating the product of the object's length, width, and height or through more complex mathematical formulas for irregular shapes.

In the case of liquids or gases, the volume refers to the amount of space occupied by the substance within a container. It can be measured directly using tools such as graduated cylinders or indirectly through displacement methods.

Understanding volume is essential in fields like physics, engineering, architecture, chemistry, and many others where knowledge of spatial quantities is required for designing, analyzing, or describing various objects or systems.

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Answer:

0.1111.... = [tex]\frac{1}{9}[/tex].

Step-by-step explanation:

Given  : 0.1 repeating

To find : Which rational number equals 0.1111......

Solution : We have given 0. 11111.........

We can see there is only one number is repeating , we will multiply it by 10

Let  x = 0.1111.......

Multiply both sides by 10

10x = 10 * 0.1111.......

10x = 1.1111.......

We can write it in terms of x

10x = 1. 000 + 0.11111....

10 x = 1 + x

On subtracting both sides by x

10 x -x = 1

9 x = 1

On dividing both sides by 9

x = [tex]\frac{1}{9}[/tex].

0.1111.... = [tex]\frac{1}{9}[/tex].

Therefore, 0.1111.... = [tex]\frac{1}{9}[/tex].

The rational number that equals 0.1 repeating is 1/9.

The rational number that equals 0.1 repeating can be represented as follows:

Let x = 0.1 repeating

To convert the repeating decimal to a fraction, we can use the following method:

Let's multiply both sides of the equation by 10 to shift the decimal point one place to the right:

10x = 1.1 repeating

Now, subtract the original equation from this new equation to eliminate the repeating part:

10x - x = 1.1 repeating - 0.1 repeating

9x = 1

Divide both sides of the equation by 9 to solve for x:

x = 1/9

Therefore, the rational number that equals 0.1 repeating is 1/9.

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The approximation of 89972 to three significant digits is 900

The number is given as:

89972

To round to three signficant digits, we simply count three digits from the left.

i.e. 899

Next, we start the approximation from the next digit

i.e. 7

Hence, the approximation of 89972 to three significant digits is 900

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The value of s from the equation 0.7(3s+4)−1.1s = 7.9 is 5.1.

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

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.

We have,

Equation:0.7(3s+4)−1.1s=7.9

Now, solving equation for s we get

2.1 s + 2.8 - 1.1 s = 7.9

1 s = 7.9- 2.8

s = 5.1

Thus, the value of s is 5.1

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The required expression is equivalent to −10+(−40)+(−90) is  −10+(−90)+(−40). Option D is correct.

Given that,
An equivalent expression to −10+(−40)+(−90)  is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,

= −10+(−40)+(−90)
= -10 -40 - 90
= -140

a
= −(10−40)+(−90)
= +30 - 90
= -60

b
= −10−(40−90)
=-10+50
= 40

c
= 10+40+90
= + 140

d
=−10+(−90)+(−40)
= -10 - 90 -40
=-140

Thus, the required expression is equivalent to −10+(−40)+(−90) is  −10+(−90)+(−40). Option D is correct.

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The side of the four-square court is 8.1 ft.

The area of a square is given as the square of its side. the are of a square whose side is a is given as,

Area of Square = a²

the area of a four-square court = 66 ft²

Let's assume that the side of the four-square court is x.

the area of a four-square court = area of square

[tex]66 = x^2\\x^2 = 66\\x = \sqrt{66}\\x=8.124[/tex]

Thus, the side of the four-square court is 8.124 ft. but we want the value to be the nearest tenth of a foot,

[tex]\rm{8.124\ ft \approx 8.1\ ft[/tex]

Hence, the side of the four-square court is 8.1 ft.

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