An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 22 feet up. The ladder makes an angle of 77
∘
∘
with the ground. Find the length of the ladder.

Answer:

-------------------------------

Angles at vertex V and Y are of same measure since they intercept same arc WX:

Angle measure of V and Y is:

Arc measure of WX is double the inscribed angle:

the expressions that could be used to find the volume of the sculpture are A and B and  the volume of the sculpture is 364 cubic feet.

Part A:

To find the volume of the sculpture, we need to add the volumes of the two rectangular prisms: the original one and the one that was cut from it. We can express the volume of the original prism as:

9 × 7 × 8

And the volume of the cut prism can be expressed as:

7 × 7 × 4

So, the expressions that could be used to find the volume of the sculpture are A and B:

A. (7 × 8 × 2) + (7 × 7 × 4)

B. (8 × 2 × 7) + (9 × 4 × 7)

Part B:

Using expression A, we get:

(7 × 8 × 2) + (7 × 7 × 4) = 112 + 196 = 308 cubic feet

Using expression B, we get:

(8 × 2 × 7) + (9 × 4 × 7) = 112 + 252 = 364 cubic feet

Therefore, the volume of the sculpture is 364 cubic feet.

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You should invest $139.07 each month to end up with $17,000 in 8 years, assuming a guaranteed APR of 4.5%.

The annual interest rate (also known as the annual percentage rate or APR) is the amount of interest that is charged on a loan or investment over the course of one year.

To calculate the monthly deposit needed to reach the target amount of $17,000 in 8 years at a guaranteed APR of 4.5%, we can use the formula for future value of an annuity:

FV = P * ([tex](1 + r/n)^(n*t)[/tex] - 1) / (r/n)

where FV is the future value, P is the monthly payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, we want to find the monthly payment (P), and we know that:

FV = $17,000

r = 4.5% = 0.045 (decimal)

n = 12 (since we are making monthly deposits)

t = 8

When these values are added to the formula, we obtain:

$17,000 = P * ([tex](1 + 0.045/12)^(12*8)[/tex] - 1) / (0.045/12)

Simplifying and solving for P, we get:

P = $139.07

Therefore, you should invest $139.07 each month to end up with $17,000 in 8 years, assuming a guaranteed APR of 4.5%.

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The supplied question's response based on the savings account is A geometric sequence is the sequence f.

A geometric sequence is a set of numbers where each term is obtained by multiplying the one before it by a predetermined quantity known as the common ratio. The following is the generic formula for a geometric sequence:

[tex]a, ar, ar^2,ar^3,ar^4,...[/tex]

There are two types of geometric sequences: finite and endless. While an infinite geometric sequence has no end, a finite geometric sequence has a set number of terms.

Because each term is created by multiplying the term that came before by a constant ratio of 1.1, the sequence f is a geometric sequence. (which accounts for the interest that has accrued on the preceding balance using the formula 1 + 0.1).

The first term is for $70, and each succeeding term is equal to the first term times 1.1. As a result, the nth term of the series can be

written as: [tex]f(n)=\$ \times 1.1^{n-1}[/tex]

where n is how long it has been since the first year of saving.

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Answer:

The formula gives the circumference of a circle:

C = πd

Where d is the diameter of the circle.

Substituting the given values, we get:

C = (22/7) x 21 cm

C = 66 cm (approx)

Therefore, the circle's circumference with a diameter of 21 cm, approximated using π equals 22/7, is 66 cm.

So, the correct option is (C) 66 cm.

Answer:  Therefore, at the start of the game, Peter had 80 marbles and Jack had 80 marbles.

Step-by-step explanation:

The measure of the angles in triangle ARST are: 28 degrees, 28 degrees, 124 degrees, 124 degrees. The measure of the angles in triangle ANSP are: 28 degrees, 51 degrees, 101 degrees, 129 degrees.

An angle is a geοmetric figure fοrmed by twο rays οr lines with a cοmmοn endpοint, called the vertex. Angles are typically measured in degrees οr radians and are used tο describe the amοunt οf turn οr rοtatiοn between twο intersecting lines οr οbjects. Angles can be acute (less than 90 degrees), right (exactly 90 degrees), οbtuse (greater than 90 degrees), straight (exactly 180 degrees), οr reflex (greater than 180 degrees).

Here,

To find the measure of the angles in each triangle, we need to solve for the value of x in both equations.

For the first equation, we can simplify it as follows:

x + 14 = 2x

Subtracting x from both sides, we get:

14 = x

For the second equation, we can simplify it as follows:

3x + 9 = 2x + 23

Subtracting 2x and 9 from both sides, we get:

x = 14

Now that we know x = 14, we can find the measure of the angles in each triangle.

In triangle ARST, we have:

angle A = x + 14

= 14 + 14

= 28 degrees

angle R = 2x

= 2(14)

= 28 degrees

angle S = 180 - (angle A + angle R)

= 180 - (28 + 28)

= 124 degrees

angle T = 180 - (angle A + angle R)

= 180 - (28 + 28)

= 124 degrees

In triangle ANSP, we have:

angle A = x + 14

= 14 + 14

= 28 degrees

angle N = 3x + 9

= 3(14) + 9

= 51 degrees

angle S = 180 - (angle A + angle N)

= 180 - (28 + 51)

= 101 degrees

angle P = 180 - (angle N)

= 180 - 51 = 129 degrees

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Answer:

It must be greater than 4

Step-by-step explanation:

We know that 36 ÷ 9 = 4.

Therefore, if the denominator is less than 9 and the numerator is greater than 36, the quotient would only increase since the numerator increases while the denominator decreases.

Therefore, it must be greater than 4.

Answer:

The length of the flower bed is 11.4 feet.

Step-by-step explanation:

If the ratio of width to length of the flower bed is 10:19, this means that for every 10 units of width, there are 19 units of length.

Let's call the width of the flower bed "W" and the length "L". We know that W is 6 feet, so we can write:

W:L = 10:19

Substituting the value of W, we get:

6:L = 10:19

To solve for L, we can cross-multiply to get:

10L = 6 x 19

10L = 114

L = 11.4

Therefore, the length of the flower bed is 11.4 feet.

To find the mean of the number of stamps for these four friends, we need to add up the total number of stamps and divide by 4 (the number of friends). 
Samir has 60 stamps. Lisa has 2 1/2 times as many stamps as Samir, which can be calculated as follows: 2 1/2 * 60 = 150 

Kwame has 443 stamps. 
Jake has 159 fewer stamps than Kwame, which can be calculated as follows: 443 - 159 = 284 To find the total number of stamps, we add up the number of stamps each friend has: 60 + 150 + 443 + 284 = 937 

To find the mean, we divide by 4: 937 / 4 = 234.25 

Therefore, to the nearest whole number, the mean of the number of stamps for these four friends is 234. 
Therefore, the answer is K. 234.

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Mean age: 16.1 years, Sample variance: 50.47 square years and Sample standard deviation: 7.10 years for the given problem.

To estimate the mean age, we need to find the midpoint of each age range and multiply it by the number of individuals in that range. Then we add up these products and divide by the total number of individuals:

Mean age = [(1+10)/2 x 35 + (11+20)/2 x 22 + (21+30)/2 x 20 + 35.5 x 7] / 84

= (5.5 x 35 + 15.5 x 22 + 25.5 x 20 + 35.5 x 7) / 84

= 16.1

Therefore, the estimated mean age of this extended family group is 16.1 years.

To calculate the sample variance, we need to find the deviation of each age from the mean, square each deviation, and add up these squared deviations. Then we divide this sum by the total number of individuals minus one:

s2 = [(1-16.1)2 x 35 + (11-16.1)2 x 22 + (21-16.1)2 x 20 + (35.5-16.1)2 x 7] / (84-1)

= (2254.05 + 537.08 + 220.89 + 253.68) / 83

= 50.47

Therefore, the estimated sample variance is 50.47 square years.

We simply take the square root of the sample variance to calculate the sample standard deviation:

s = [tex]\sqrt{s2}[/tex]

= s[tex]\sqrt{50.47}[/tex]

= 7.10

Therefore, the estimated sample standard deviation is 7.10 years.

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The total weight of the dog toys that weighed 1/8 of a pound or 3/8 of a pound is 1 3/8 pounds.

A line plot is a graphical representation of data that involves placing X's or other symbols above a number line to show the frequency of each value in a data set.

Each X represents one occurrence of the data value on the number line. Line plots are useful for quickly visualizing the distribution of a data set, especially when there are only a few unique values in the data set.

Based on the line plot, we can see that there are 2 dog toys that weigh 1/8 of a pound and 3 dog toys that weigh 3/8 of a pound.

To find the total weight of the dog toys that weigh 1/8 of a pound or 3/8 of a pound, we need to add the weights of these toys.

The total weight of the dog toys that weigh 1/8 of a pound is 2/8 of a pound, which simplifies to 1/4 of a pound.

The total weight of the dog toys that weigh 3/8 of a pound is 3 x 3/8 = 9/8 of a pound.

Adding these weights together, we get:

1/4 + 9/8 = 11/8 of a pound

This simplifies to 1 3/8 pounds.

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Answer: 3/20 and 15%

Step-by-step explanation:

The x intercept of the function f(x) = x√(x + 4) is at

(-4, 0) and (0, 0)

The x-intercept is the point where a graph or a line crosses the x-axis. In other words, it is the point where the value of the dependent variable (usually represented on the y-axis) is zero.

In an equation, the x-intercept is the value of x when y is equal to zero. It is often denoted by the point (x, 0) on a graph.

The plotted graph shows that the x intercept is at

(-4, 0) and (0, 0)

Graph is attached

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The total change in value is $45,000 - $12,000 = $33,000. The annual rate of change is 0.0495. Converting the rate of change to a percentage is 4.95%. Assuming the car value continues to drop by the same percentage, the value of the car in 2003 is $10,850.

A percentage is a way of expressing a number as a fraction of 100. Percentages are typically expressed using the symbol "%".

In the given question,

A) The total change in value is $45,000 - $12,000 = $33,000. The time period is 9 years (2000 - 1991). Therefore, the annual rate of change is:

r = [tex](Change in value / Initial value) ^ (1/Time period)[/tex] - 1

r = [tex]($33,000 / $45,000) ^ (1/9)[/tex] - 1

r = 0.0495

Rounding this to 4 decimal places, the annual rate of change is 0.0495.

B) Converting the rate of change to a percentage:

r = 0.0495 * 100

r = 4.95%

Therefore, the answer to part A in percentage form is 4.95%.

C) Assuming the car value continues to drop by the same percentage, we need to calculate the value of the car in the year 2003. The time period from 2000 to 2003 is 3 years. Therefore, the value of the car in 2003 can be calculated as follows:

Value in 2003 = $12,000 * [tex](1 - r) ^ 3[/tex]

Value in 2003 = $12,000 * [tex](1 - 0.0495) ^ 3[/tex]

Value in 2003 = $10,840.09

Rounding this to the nearest 50 dollars, the value of the car in 2003 is $10,850.

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Trigonometric ratios connect angles and sides of right triangle. The cofunction of sinθ = cosecθ.

Trigonometric ratios are mathematical proportions that connect the angles and sides of a right triangle. The hypotenuse, adjacent, and opposing sides are the three sides of a right triangle, which is a triangle having one angle of 90 degrees.

For example, imagine a triangle made up of wires of length L.

The same wire can be used to create a square if all sides are the same length.

The length covered by the perimeter of the shape is called the perimeter. Therefore, the units of circumference are the same as the units of length.

As we can say, the surroundings are one-dimensinal. As a result, you can measure in meters, kilometers, millimeters, etc.

Inches, feet, yards, and miles are other globally recognized units of circumference measurement.

Hence, The function equivalent to sinθ = cosecθ.

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Mathematics is a field that involves primarily abstract reasoning and mental calculations, but there are still several types of equipment that mathematicians may use to aid in their work.

What are different equipments use in mathematics?

1.) Calculator: A calculator is an electronic device that performs arithmetic operations quickly and accurately. It is often used by mathematicians to check their calculations, solve equations, and perform more complex calculations.

2.) Protractor: A protractor is a tool used to measure and draw angles. It is commonly used in geometry and trigonometry to draw and measure angles of various shapes.

3.) Compass: A compass is a tool used to draw circles and arcs. It is commonly used in geometry to draw circles, bisect angles, and construct various geometric shapes.

4.) Ruler: A ruler is a straightedge tool used to measure lengths and draw straight lines. It is commonly used in geometry and algebra to draw graphs, construct figures, and measure distances.

5.) Graph paper: Graph paper is a type of paper that has a grid of small squares printed on it. It is often used in algebra and geometry to draw graphs, plot data, and make calculations.

The question doesn't contain any table and is incomplete, below is the complete question -

Fill in the table with equipment measurements.

Equipment Code: The required field for the primary key.

Standard for equipment: The kind of equipment. confirmed by the listing of equipment standards.

Use of Equipment: Describe how the piece of equipment is used in this field.

categorization: Select a categorization for this piece of equipment using the field provided. The Condition Assessment programme organises and categorises your data using this classification.

Equipment state: To characterise the equipment's condition, select one of the values from the list box: new, good, fair, or poor.

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The number that must row 2 in the matrix be multiplied for the matrix to be changed to B. -2.

What are row operations?

Row operations are mathematical operations that can be performed on the rows of a matrix to manipulate its properties or solve systems of linear equations.

To solve this problem, we need to perform row operations on the matrix until row 2 is transformed into the desired row. Each row operation involves multiplying a row by a scalar, adding or subtracting one row from another, or swapping two rows.

Starting with the given matrix:

20 -2

1 1 1 1 1 6 -14

We can perform the following row operations:

Subtract row 1 from row 2:

20 -2

1 1 1 -19 -19 4 -6

Multiply row 2 by -3:

20 -2

-3 -3 -3 57 57 -12 18

Subtract 2 times row 2 from row 1:

26 4

-3 -3 -3 57 57 -12 18

Divide row 1 by 13:

2 4/13

-3 -3 -3 57 57 -12 18

Therefore, we see that row 2 in the matrix must be multiplied by -3 to transform it into the desired row.

So the answer is: B. -2

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Answer:331

Step-by-step explanation:

7360.3097-7029.415≈330.8947

Santiago could have $81 more than Ella after 18 years.

To calculate the amount of money each person can have after 18 years, we are able to use the formulation for compound interest:

[tex]A = P(1 + r/n)^{(nt)[/tex]

Wherein:

For Ella's investment:

P = $4,800

r = 2.28125% = 0.0228125

n = 4

t = 18

[tex]A = 4800(1 + 0.0228125/4)^{(4*18)[/tex]

A = $8,481.48

For Santiago's investment:

P = $4,800

r = 2.28333% = 0.0228333

n = 365 (compounded daily)

t = 18

A = 4800(1 + 0.0228333/365)^(365*18)

A = $8,562.02

The distinction of their final amounts is:

$8,562.02 - $8,481.48 = $80.54

Therefore, Santiago could have $81 more than Ella after 18 years.

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The distance between Toby and Meg are approximately 95 feet apart.

We can solve this problem using the Pythagorean theorem, which relates the lengths of the sides of a right triangle.

The distance between Toby and Meg is the hypotenuse of a right triangle with legs 57 feet and 76 feet.

So we can use the Pythagorean theorem to find this distance:

distance^2 = 57^2 + 76^2

distance^2 = 3249 + 5776

distance^2 = 9025

distance = sqrt(9025)

distance = 95

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y=200(0.5)2t  this functiοn represents decay, y=12(2.5)t6 this functiοn represents grοwth and y=(0.65)t4 this functiοn represents decay.

In mathematics, a functiοn is a relatiοnship between twο sets οf elements, called the dοmain and the range, such that each element in the dοmain is assοciated with a unique element in the range.

In general, we can determine whether a functiοn represents grοwth οr decay by examining the base οf the expοnential term.

If the base is greater than 1, the functiοn represents grοwth.

If the base is between 0 and 1, the functiοn represents decay.

Here are the classificatiοns fοr each οf the given functiοns:

y=200(0.5)2t

The base οf the expοnential term is 0.5, which is between 0 and 1. Therefοre, this functiοn represents decay.

y=12(2.5)t6

The base οf the expοnential term is 2.5, which is greater than 1. Therefοre, this functiοn represents grοwth.

y=(0.65)t4

The base οf the expοnential term is 0.65, which is between 0 and 1. Therefοre, this functiοn represents decay.

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Complete Question:

Select "Growth" or "Decay" to classify each function.

Function Which ones are growth or decay

f(x)=(1.05)t4

y=100(0.4)t

f(x)=14(10)t12

The equation of the line L is y = -8x + 35.

What is the slope?

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

To find the equation of the line L that passes through the points (5,-5) and (4,3), we need to use the point-slope form of a linear equation:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is one of the given points.

First, we need to find the slope of the line L:

m = (y2 - y1) / (x2 - x1)

m = (3 - (-5)) / (4 - 5)

m = 8 / (-1)

m = -8

Now we can use either point to write the equation of the line. Let's use (5, -5):

y - (-5) = -8(x - 5)

y + 5 = -8x + 40

y = -8x + 35

Therefore, the equation of the line L is y = -8x + 35.

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A)  The annual rate of change or APR between 1991 and 2000 is approximately -0.1091.

B) The correct answer to part A in percentage form is approximately -10.91%.

C) The value of the car in 2003 is $7,750.

What is annual rate?

The car depreciated from $45,000 to $12,000 in 9 years. Using the formula for annual rate of change or annual percentage rate (APR):

r = [tex](Vf/Vi)^{1/n}[/tex] - 1

where Vf is the final value, Vi is the initial value, n is the number of years, and r is the annual rate of change or APR.

Substituting the given values:

r = [tex]($12,000/$45,000)^{1/9}[/tex] - 1

r ≈ -0.1091

Therefore, the annual rate of change or APR between 1991 and 2000 is approximately -0.1091.

B) The correct answer to part A in percentage form is approximately -10.91%.

What is APR?

To express the answer as a percentage, multiply the annual rate of change by 100 and round to the nearest 0.01%:

r = -0.1091 × 100

r ≈ -10.91%

Therefore, the correct answer to part A in percentage form is approximately -10.91%.

C) The value of the car in 2003 is $7,750.

What is the value?

To find the value of the car in 2003, we need to use the same percentage rate of decrease from 2000 to 2003. Since 2003 is 3 years after 2000, the value will be:

value = $12,000 × (1 + r)³

value ≈ $7,729.18

Rounding to the nearest 50 dollars, the value of the car in 2003 is $7,750.

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The correct area models are 4e and none of the given models for 4d and 4c.

What is the quadratic equation?

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

The area model of 4c is incorrect because the last term of the polynomial, which is 40, is represented by the bottom right box of the area model. However, in the given area model, the box representing 40 is in the upper row.

The area model of 4e is correct because it represents the polynomial as the product of two binomials, where the factors are (x-5) and (x-8).

When multiplied using the distributive property, the resulting polynomial is x² - 13x + 40, which matches the given polynomial form.

The area model of 4d is incorrect because it does not properly represent a factorable polynomial.

It only includes three boxes, representing the three terms of the polynomial, but it does not show how the terms can be factored into binomials.

Therefore, the correct area models are 4e and none of the given models for 4d and 4c.

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Answer:

[tex]100\pi \text{ in}^3[/tex]

Step-by-step explanation:

Volume of a Cone Equation:

[tex]v = \frac{1}{3}\times \pi \times r^2 \times h[/tex]

1) Find h

Use the Pythagorean Theorem to find h

[tex]a^2 \times b^2 = c^2[/tex]

Change diameter to radius. (10 in ---> 5in)

a = 5

[tex]1) 5^2 + b^2 = 13^2\\\\2) 25 + b^2 = 169\\\\3) b^2 =144\\\\4) 12[/tex]

Step 2) Subtract 25 on both sides so [tex]b^2[/tex] is alone

Step 3) Square root both sides

Step 4) h = 12

2) Plug in known variables:

h = 12 in

r = 5 in;

Equation now:

[tex]v = \frac{1}{3} \times \pi \times 5^2 \times 12[/tex]

3) Solve:

[tex]1) \frac{1}{3} \times \pi \times 5^2 \times 12\\\\2) \frac{\pi}{3} \times 5^2 \times 12\\\\3) \frac{\pi}{3} \times 25 \times 12 \\\\4) \frac{\pi}{3} \times 300\\\\5) \frac{300\pi}{3} \\\\\text{Simplify:}\\100\pi[/tex]

As f(3) is not equal to zero, 3 is not a zero of the polynomial f(x) = -x⁴ -8x²-x-5.

Given the polynomial in the question;

f(x) = -x⁴ -8x²-x-5

Given number: 3

To check if 3 is a zero of the polynomial f(x) = -x⁴ -8x²-x-5, we need to substitute x = 3 into the polynomial and see if the result will give zero.

f(x) = -x⁴ -8x²-x-5

plug i x = 3

f(3) = -3⁴ - 8(3)² - 3 - 5

= -81 - 72 - 3 - 5

= -161

Therefore, 3 is not a zero of the polynomial f(x) = -x⁴ -8x²-x-5.

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The profit function for a furniture company introducing a new line of lounge chairs is P(x) =[tex]-8.32x^2 + 1,248x - 36,400[/tex], where x represents the number of chairs to be manufactured and sold.

The problem provides the revenue function and cost function for a furniture company introducing a new line of lounge chairs. To find the profit function, we need to subtract the cost function from the revenue function.

The revenue function R(x) is given as 1,248x - [tex]8.32x^2[/tex], where x represents the number of chairs manufactured and sold. This function calculates the total revenue obtained by the company by multiplying the number of chairs sold (x) by the price of each chair (1,248 - 8.32x).

The cost function C(x) is given as 36,400 - 83.2x. This function calculates the total cost incurred by the company to manufacture x chairs, which includes both fixed and variable costs.

To find the profit function for the furniture company, we need to subtract the cost function C(x) from the revenue function R(x):

P(x) = R(x) - C(x) = (1,248x - [tex]8.32x^2[/tex]) - (36,400 - 83.2x)

Simplifying this expression, we get:

P(x) =[tex]-8.32x^2[/tex] + 1,248x - 36,400

Therefore, the profit function for the furniture company is P(x) = [tex]-8.32x^2[/tex] [tex]+ 1,248x - 36,400[/tex].

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Answer:

$43.96

Step-by-step explanation:

We first need to find the area of the patio which is 12-foot by 14-foot

12 ft * 14 ft = 168 sq ft

next, we need to know how many quarts are needed to cover the entire area of the patio, and we know a quart cover 53 square feet, so we divide the total area of the patio by 53:

168 sq ft ÷ 53 sq ft/quart ≈ 3.17 quarts

We'll need to buy 4 quarts of paint to cover the entire patio.
The cost of 1 quart of paint is $10.99, so the total cost of 4 quarts will be:

4 quarts x $10.99/quart = $43.96

Therefore, the estimated cost of painting the concrete patio will be around $43.96.