a. A circular park of radius 14 m has a road of 7 m width all around on its outside. Find the area of the road.​

The given geometric progression's fourth, seventh, and ninth term is 24, 192, and 768 respectively.

In mathematics, a sequence known as a geometric progression (GP) is one in which each following term is generated by multiplying each preceding term by a constant integer, known as a common ratio. This progression is sometimes referred to as a pattern-following geometric sequence of numbers. Learn development in mathematics here as well. Here, each phrase is multiplied by the common ratio to generate the subsequent term, which is a non-zero value.

The given geometric progression: 3,6,12,24.......

The first term of GP is a = 3 and the Common ratio r = 2,

We know that the nth term of GP is,

[tex]T_n=ar^{n-1}[/tex]

We have to Find the 4, 7, and 9th terms of  above mentioned GP,

[tex]T_4\\\\T_4=ar^{4-1}\\\\T_4=3*2^3\\\\T_4=24\\\\\\T_7\\\\T_7=3*2^{7-1}\\\\T_7=192\\\\\\T_9\\\\T_9=3*2^{9-1}\\\\T_9=768[/tex]

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We estimated the margin of error for the population mean with 95% confidence using the given data and formula. The margin of error is approximately 3.32, providing a reasonable range for the true population mean.

To find the margin of error for estimating the population mean with 95% confidence, we can use the formula:

Margin of error = t(α/2) × (s/√n)

where t(α/2) is the critical value of the t-distribution with (n - 1) degrees of freedom and a significance level of α/2 (0.025 for 95% confidence), s is the sample standard deviation, and n is the sample size.

From the given data, we can calculate the sample mean and standard deviation as:

x = (10 + 8 + 12 + 15 + 13 + 11 + 6 + 5) / 8 = 9.75

s = √[((10-9.75)² + (8-9.75)² + (12-9.75)² + (15-9.75)² + (13-9.75)² + (11-9.75)² + (6-9.75)² + (5-9.75)²) / 7] = 3.36

Using a t-table or calculator, we can find the critical value t(0.025) with 7 degrees of freedom to be approximately 2.365.

Substituting these values into the formula, we get:

Margin of error = 2.365 × (3.36 / √(8)) ≈ 3.32

Therefore, with 95% confidence, the margin of error for estimating the population mean is approximately 3.32.

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A triangle has three straight sides that meet at a point. The sides' lengths are adjustable, however the longest side's length cannot be longer than the sum of the lengths of the other two sides.

A triangle has three straight sides that meet at a point. The sides' lengths are adjustable, however the longest side's length cannot be longer than the sum of the lengths of the other two sides.

In the triangle ΔFUN,

∠F is an angle formed by the vertices F, U, and N.

∠U is an angle formed by the vertices F, U, and N.

The included sides of ∠F and ∠U are:

The included side of ∠F is UN.

The included side of ∠U is FN.

The included angles of ∠F and ∠U are:

Therefore, The included angle of ∠ F is ∠FUN, which is formed by the sides FU and UN. The included angle of ∠U is ∠NUF, which is formed by the sides NU and UF.

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Answer:yo

Step-by-step explanation:

16 weeks is 277

3800 insects in about 27.4 weeks

The answer to the question is given below.An entomologist has an insect colony for an experiment. The population of insects is increasing at a continuous rate of 5.6 percent per week. The initial population of the insect colony was 100.The formula that represents the insect colony population after tt weeks is P(t) = 100 (1 + 0.056)^tUsing the formula from section (a), we can calculate that the insect population after 16 weeks is 277. The nearest whole number is 277.After how many weeks would the population of insects reach 3800?Let’s apply the formula P(t) = 100 (1 + 0.056)^t3800 = 100 (1 + 0.056)^t(1 + 0.056)^t = 38(1.056)^t = 38log 1.056^t = log 38t log 1.056 = log 38t = log 38 / log 1.056t ≈ 27.4 weeksThe insect population will reach 3800 insects in about 27.4 weeks. We rounded the answer to one decimal place.

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The solution for the given equation isθ = π/2, 5π/6, 13π/6.

The given equation is cos(θ) - sin(θ) = √2sin(θ/2)cos(θ/2).Use double-angle formula for sin to write sin(θ) in terms of cosθ as follows:sin(θ) = 2sin(θ/2)cos(θ/2).Substitute sin(θ) with the above equation. We have,cos(θ) - 2sin(θ/2)cos(θ/2) = √2sin(θ/2)cos(θ/2)cos(θ) - 3sin(θ/2)cos(θ/2) = 0(cosθ - 3sin(θ/2) = 0 or cosθ/3 = sin(θ/2)Squaring both sides of the equation gives us:cos2θ/9 = 1 - cos2(θ/2)cos2(θ/2) = (1 - cos2θ/9) / 2cos2(θ/2) = (9 - cos2θ) / 18sin2(θ/2) = 1 - cos2(θ/2)sin2(θ/2) = 1 - ((9 - cos2θ) / 18)sin2(θ/2) = (9 + cos2θ) / 18Therefore, the solution for the given equation isθ = π/2, 5π/6, 13π/6.

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Answer: y < 5x+6

Step-by-step explanation:

Thus, if the weather is warm, you can make a total of 20 combinations (5 shirts x 4 pants), and if the weather is cold, you can make a total of 40 combinations (5 shirts x 4 pants x 2 sweaters).

The total combination of clothing items you can wear is 5 shirts, 4 pants, and either 2 neckties or 2 sweaters. If the weather is warm, you can opt to omit the sweater and keep the two neckties. If the weather is cold, then you can omit the neckties and wear the two sweaters. To calculate the total number of clothing combinations you can make, you need to multiply the items you are allowed to wear. For example, if you are wearing a shirt and a pair of pants, you can make 5 x 4 = 20 combinations. If you are wearing a shirt, pants, and either a necktie or a sweater, you can make 5 x 4 x 2 = 40 combinations.

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In the number 7,326.64, the digit 2 appears in the thousands place, and its value is 200. Therefore, the answer is (Choice C) 7,326.64.

A number is a mathematical concept used to represent a quantity or value. Numbers can be used to count, measure, or calculate, and they are fundamental to many fields of mathematics, science, and everyday life. Numbers can be represented and manipulated using mathematical symbols, such as digits, operations, and functions. They are used in many applications, such as in finance, engineering, physics, and computer science.

Here,

To solve this problem, we need to find a number that has a digit 2 with a value that is 1/10 times as great as the digit 2 in the number 6,257.11.

In the number 6,257.11, the digit 2 appears in the thousands place, and its value is 2,000.

To find a number in which the digit 2 has a value that is 1/10 times as great, we need to divide 2,000 by 10, which gives us 200.

So, we need to look for a number in which the digit 2 appears in the thousands place and has a value of 200. The only option that satisfies this condition is (Choice C) 7,326.64.

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Therefore , the solution of the given problem of expressions comes out to be  students can develop their factoring abilities and avoid mistakes with practise and instruction.

Estimates that combine joining, disabling, and rather than randomly divide should be produced when variables are shifting. If they got together, they could solve a mental puzzle, provide some data, and instead software. A declaration of truth contains formulas, components, and mathematical processes like combination, subtraction, omission, and grouping. Both phrases and words can be assessed and analysed.

Here,

are some pointers to assist students B and C prevent incorrect factoring in the future:

Regularly practise factoring: Since factoring is a talent that must be honed, students should make sure to factor problems frequently. They will be better able to understand the procedure and spot trends in the expressions they are factoring as a result of this.

Verify the indications again because they are prone to error when factoring. Students should double-check their distribution of the signs and make sure no negative indicators are being left out.

Students should double-check their work by multiplying the factors back together after factoring an equation. They'll be able to correct any errors they may have made thanks to this.

If students need assistance with factoring, they should ask an instructor or tutor for assistance. Although factoring can be a challenging ability to master, students can develop their factoring abilities and avoid mistakes with practise and instruction.

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We can use the tangent function to solve this problem. Let h be the height of the skyscraper.

First, we need to find the length of the adjacent side of the right triangle formed by Sadie, the base of the skyscraper, and the point where she is standing. This length is the horizontal distance between Sadie and the base of the skyscraper, which is 275 meters.

Next, we can use the tangent of the angle of elevation to find the ratio of the opposite side (the height of the skyscraper) to the adjacent side:

tan(36°) = h/275

Solving for h, we get:

h = 275 tan(36°)

Using a calculator, we find:

h ≈ 198.64 meters

Therefore, the height of the skyscraper is approximately 198.64 meters.

Answer: 201.49

Step-by-step explanation:

The amounts due on December 31, 2026 are: Bond payable (09/30/2026 installment) = $29,897,000, Bond payable (other than 09/30/2026 installment) = $90,313,578.19,Interest payable = $622,578.19

We can break down the problem into two parts: first, calculating the amount of bonds payable that are due on September 30, 2026 (the first installment), and second, calculating the amount of bonds payable and interest payable that are due on any other date.

Bond payable due on September 30, 2026:

The total amount of bonds payable outstanding is $119,588,000. The installment due on September 30, 2026 is $29,897,000. Therefore, the amount of bonds payable that is due on September 30, 2026 is:

$29,897,000

Bond payable and interest payable due on any other date:

The total amount of bonds payable outstanding is $119,588,000. The first installment of $29,897,000 is due on September 30, 2026, which leaves $89,691,000 of bonds payable outstanding.

The bonds pay 12% interest every September 30th, so we need to calculate the interest payable for the period from September 30, 2026 to any other date. Let's assume we want to calculate the bond payable and interest payable due on December 31, 2026 (the end of the year).

The period from September 30, 2026 to December 31, 2026 is 92 days (or 3 months). The annual interest rate is 12%, so the daily interest rate is:

12% / 365 = 0.0328767%

The interest payable for 92 days is therefore:

$89,691,000 x 0.0328767% x 92/365 = $622,578.19

Adding this to the outstanding bonds payable gives:

Bond payable (other than 09/30/2026 installment) = $89,691,000 + $622,578.19 = $90,313,578.19

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Answer:

Area of white circle = 346.36 cm²

Step-by-step explanation:

Area of a circle = πr² where r is the radius

r = diameter/s

For the green circle, d = 42, r = 21

A = π(21)² = 1,385.44 cm²

The white circle has a diameter half of the green circle = 42/2 = 21 cm
So radius of white circle = 21/2 = 10.5 cm

Area of white circle = π (10.5)² = 346.36 cm²

Answer:

Increase both dimensions by 2 meters: (x+2)^2

Decrease both dimensions by 2 meters: (x-2)^2

Increase one dimension by 2 meters and decrease the other dimension by 2 meters: (x+2)(x-2)

Step-by-step explanation:

Let's label the regions in the Venn diagram as follows:

F: students who do only field events

T: students who do only track events

S: students who do only swimming events

FT: students who do both field and track events

ST: students who do both swimming and track events

FST: students who do all three events

From the information given in the problem, we can fill in some of the values in the Venn diagram:

F + FT + 15 = 33 (33 students do field events, and 15 do field events only)

T + FT + 14 = 40 (40 students do track events, and 14 do both field and track events)

S + ST + 10 = 23 (23 students do swimming, and 10 do both swimming and track events)

F + T + S + 2FT + ST + FST = 68 (there are 68 students in total)

We can simplify these equations to:

F + FT = 18

T + FT = 26

S + ST = 13

F + T + S + 2FT + ST + FST = 68

To solve for the remaining unknowns, we need to use some algebra. We can start by solving for FT:

F + FT = 18

T + FT = 26

Adding the two equations, we get:

F + T + 2FT = 44

Rearranging, we get:

FT = (44 - F - T) / 2

Now we can substitute this expression for FT into the equation for the total number of students:

F + T + S + 2FT + ST + FST = 68

F + T + S + 2((44 - F - T) / 2) + ST + FST = 68

F + T + S + 44 - F - T + ST + FST = 68

Simplifying, we get:

S + ST + FST = 26

Now we have two equations involving S, ST, and FST:

S + ST = 13

S + ST + FST = 26

We can solve for S and ST by subtracting the first equation from the second:

S + ST + FST = 26

(S + ST) + FST = 26

Substituting S + ST = 13:

13 + FST = 26

FST = 13

So there are 13 students who do all three events. Now we can use the equation S + ST = 13 to solve for S:

S + ST = 13

ST = 10 (given in the problem)

S = 13 - 10 = 3

So there are 3 students who do swimming only. Similarly, we can use the equation T + FT = 26 to solve for T:

T + FT = 26

FT = (44 - F - T) / 2

Substituting F + FT = 18:

T + (18 - F) / 2 = 26

Multiplying both sides by 2:

2T + 18 - F = 52

The dividends per share on preferred stock for four years is $0.12, $0.12, $0.12, $0.12 and for common stock is $0.057, $0.152, $0.220, $0.220.

To calculate the dividends per share for each class of stock, we need to first determine the total dividends paid in each year.

For the preferred stock, the dividends are cumulative, which means any unpaid dividends from previous years must be paid before any dividends can be paid to common stockholders. Therefore, we need to calculate the total amount of unpaid dividends for each year before we can determine the amount available for common stockholders.

To calculate the unpaid dividends for the preferred stock in each year, we need to multiply the number of shares of preferred stock by the dividend rate (3%) and subtract the dividends paid in that year.

Unpaid dividends for preferred stock:

1st year: (80,000 x $20 x 0.03) - $33,000 = $9,600

2nd year: (80,000 x $20 x 0.03) - $72,000 - $9,600 = $9,600

3rd year: (80,000 x $20 x 0.03) - $100,000 - $9,600 = $9,600

4th year: (80,000 x $20 x 0.03) - $100,000 - $9,600 = $9,600

Now we can calculate the total dividends available for common stockholders in each year by subtracting the unpaid dividends for preferred stock from the total dividends paid in that year.

Total dividends available for common stockholders:

1st year: $33,000 - $9,600 = $23,400

2nd year: $72,000 - $9,600 = $62,400

3rd year: $100,000 - $9,600 = $90,400

4th year: $100,000 - $9,600 = $90,400

Finally, we can calculate the dividends per share for each class of stock by dividing the total dividends by the number of shares outstanding.

Dividends per share:

Preferred stock:

1st year: $9,600 / 80,000 = $0.12 per share

2nd year: $9,600 / 80,000 = $0.12 per share

3rd year: $9,600 / 80,000 = $0.12 per share

4th year: $9,600 / 80,000 = $0.12 per share

Common stock:

1st year: $23,400 / 410,000 = $0.057 per share

2nd year: $62,400 / 410,000 = $0.152 per share

3rd year: $90,400 / 410,000 = $0.220 per share

4th year: $90,400 / 410,000 = $0.220 per share

Therefore, the dividends per share on each class of stock for each of the four years are as follows:

Preferred stock (dividends per share)

1st Year: $0.12 per share

2nd Year: $0.12 per share

3rd Year: $0.12 per share

4th Year: $0.12 per share

Common stock (dividends per share)

1st Year: $0.057 per share

2nd Year: $0.152 per share

3rd Year: $0.220 per share

4th Year: $0.220 per share

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The length of the ribbon used by Lilly Mae is 15.7 inches.

A circle is a two-dimensional shape made up of points that are equidistant from a center point.

The perimeter of a circle is also known as its circumference and the formula for perimeter of circle is given by  

                                  C = 2πr

Where 'r' is the radius of the circle.

Here we have

Lilly Mae measures the length of the radius of her bedroom clock

From the figure, the Radius of the clock is 2.5 inch

Here the length of the ribbon around clock will equal the perimeter of the circular clock

From the formula, the Perimeter of the circle = 2πr  

Length of the ribbon used = 2(3.14)(2.5) = 15.7 inches

Therefore,

The length of the ribbon used by Lilly Mae is 15.7 inches.

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7. The speed of the car is approximately 73.3 miles per hour. 10.  a. 7.07 ft/sec b. 9.87 feet from the center. c. the person on the outside is approximately 30 ft.

It is a fundamental concept in physics and is used to describe the motion of objects in both everyday life and scientific contexts. In addition to speed, other related concepts include velocity (which includes direction) and acceleration (the rate at which an object's speed or velocity changes).

7. The circumference of the wheel is given by C = πd, where d is the diameter of the wheel. Therefore, the circumference of each wheel is:

C = πd = π(22 in) = 22π in

Since the wheels are rotating at 600 rpm (revolutions per minute), the distance covered by each wheel in one minute is:

distance = circumference × revolutions = 22π in/rev × 600 rev/min = 13,200π in/min

To convert this to miles per hour, we need to convert inches to miles and minutes to hours. There are 12 inches in 1 foot and 5280 feet in 1 mile, so there are 63360 inches in 1 mile. There are 60 minutes in 1 hour, so:

distance = 13,200π in/min = (13,200π in/min) × (1 ft/12 in) × (1 mi/5280 ft) × (60 min/1 hr) ≈ 73.3 mi/hr

Therefore, the speed of the car is approximately 73.3 miles per hour.

10. a) The linear speed of a point on the carousel is given by v = rω, where r is the distance from the center of the carousel and ω is the angular velocity in radians per second. Since the carousel makes 3 revolutions per minute, the angular velocity is:

ω = (3 rev/min) × (2π rad/rev) × (1 min/60 sec) = π/10 rad/sec

The linear speed of a person riding a horse that is 22.5 ft from the center is:

v = rω = (22.5 ft) × (π/10 rad/sec) ≈ 7.07 ft/sec

b) Let d be the distance of the person on the inside from the center. Since the carousel makes 3 revolutions per minute, the angular velocity is still ω = π/10 rad/sec. The linear speed of the person on the inside is given as 3.1 ft/sec, so:

v = rω

3.1 ft/sec = d × (π/10 rad/sec)

d = (3.1 ft/sec) × (10/π rad/sec) ≈ 9.87 ft

Therefore, the person on the inside is approximately 9.87 feet from the center.

c) The linear speed of a point on the carousel is proportional to its distance from the center. Therefore, the ratio of the linear speeds of the person on the outside and the inside is equal to the ratio of their distances from the center:

v_outside/v_inside = r_outside/r_inside

We know that the linear speed of the person on the inside is 3.1 ft/sec and the distance of the person on the inside is approximately 9.87 feet. Therefore:

v_outside/3.1 ft/sec = r_outside/9.87 ft

v_outside = (r_outside/9.87 ft) × (3.1 ft/sec)

We can solve for r_outside by using the fact that the carousel makes 3 revolutions per minute:

v_outside = r_outsideω

v_outside = r_outside × (3 rev/min) × (2π rad/rev) × (1 min/60 sec)

v_outside = r_outsideπ/10 rad/sec

Combining these equations, we get:

r_outsideπ/10 rad/sec = (r_outside/9.87 ft) × (3.1 ft/sec)

r_outside ≈ 30.9 ft

Therefore, the person on the outside is approximately 30.

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Answer:

The answer is C.

Step-by-step explanation:

The midway point is (19/2, -6)

19/2 = 9.5

Hope this helps!

ps. you can type this in a calculator and ask it to find the midpoint, if that helps :)

To answer the question, let's start by preparing a scatterplot graphing the volume of oil changes (x-axis) against the company's monthly operating expenses (y-axis). From the data provided, the scatterplot appears as follows:

It appears that there is a fairly strong correlation between the number of oil changes performed and the company's operating expenses each month. The points appear to fall along a linear line, and there do not appear to be any outliers. This indicates that the company's operating costs are fixed.

Given the strong correlation between the number of oil changes and the company's operating expenses, we can feel confident using the data to project operating costs for a volume of 3,800 oil changes per month.

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Answer:

We can solve this system of equations using substitution or elimination.

Using substitution, we can solve for one variable in terms of the other in one equation and substitute that expression into the other equation. For example, we can solve the first equation for x in terms of y:

2x + 5y + 1 = 0

2x = -5y - 1

x = (-5/2)y - 1/2

Now we can substitute this expression for x into the second equation:

3x + 7y = 1

3((-5/2)y - 1/2) + 7y = 1

-15/2 y - 3/2 + 7y = 1

9.5y = 5

y = 5/9.5 = 1/1.9

Now we can substitute this value of y back into either equation to solve for x:

x = (-5/2)y - 1/2

x = (-5/2)(1/1.9) - 1/2

x = -2.632

So the solution to the system of equations is x = -2.632 and y = 1/1.9.

15 miles in 6 hours was covered, hence with the average speed formula we find that the average speed is 2.5 miles per hour.

To find the average speed, we can use the formula:

Average Speed = Total Distance / Total Time

In this case, the total distance covered is 15 miles, and the total time taken is 6 hours. Substituting these values into the formula, we get:

Average Speed = 15 miles / 6 hours

Average Speed = 2.5 miles per hour

Therefore, the average speed for the 15 miles covered in 6 hours is 2.5 miles per hour. Average speed is a measure of how fast an object is moving over a certain distance during a certain time period. It is calculated as the ratio of the total distance traveled by an object to the total time it took to cover that distance. The unit of measurement for average speed is distance divided by time, such as miles per hour (mph), kilometers per hour (km/h), or meters per second (m/s). Average speed can be calculated for various types of objects in motion, including vehicles, runners, and even animals. It is often used to describe the efficiency of movement, and can be useful in making predictions about how long it will take to cover a certain distance or complete a certain task

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(a) (65+5x)m², (b) 15+2+x+5+(15−x)+5+2=44m is the perimeter, (c) Rs.250(x+21) , (d) Rs.150(15−x) (e) 5x=35 ⇒x=7m

In an algebraic expression, variables are represented by letters or symbols, and constants are represented by numerical values. The variables can be used to represent unknown values that need to be solved for, while the constants provide fixed values.

Algebraic expressions are used extensively in algebra and other mathematical fields to represent relationships between variables and to solve equations.

(a)

length of bedroom =x m

Breadth of bedroom =5 m

And, length of kitchen =15−(x+2)=13−x m

Breadth of kitchen =5 m

So, Area of both kitchen and bedrooms =2× times of area of bedroom + area of kitchen

=2(5×x)+(13−x)×5

=10x+(65−5x)

=(65+5x)m²

(b)

From figure,

Perimeter of the living room

=15+2+x+5+(15−x)+5+2=44m

(c)

From figure,

Total area of both living the room and the bedrooms =(5×x)+(7×15)=(5x+105)m²

The cost of carpeting is Rs. 50/m²

Therefore, total cost of carpeting

=(5x+105)×50=Rs.250(x+21)

(d)

Total area, bathroom and kitchen

=(15−x)×5m²

The cost of tiling is Rs. 30/m²

Therefore, total cost of tilling

=(15−x)×5×30=Rs.150(15−x)

(e)

Given, Area of floor of each bedroom 35 m²

So, Area of one bedroom

=5xSq.m

∴5x=35

⇒x=7m

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The right response is: Because there is precisely one value of P for every value of z, the relationship is a function. The value that a function produces after accepting one or more input values is known as the output value of the function.

The right response is:

Because there is precisely one value of P for every value of z, the relationship is a function.

Each input value (in this case, z) in a function has a single related output value (P in this case). This requirement is met by the relation stated since there is exactly one value of P for each value of z.

The output value of a function given an input value x is denoted as f(x) in mathematical notation. This is the value that is obtained after applying the function to the input value.

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If Beef costs $4.30 per pound and chicken costs $3.40 per pound then the three pounds of chicken costs $10.20.

The cost of chicken is $3.40 per pound. To find the cost of 3 pounds of chicken, we can multiply the price per pound by the number of pounds:

Cost of 3 pounds of chicken = 3 pounds × $3.40/pound

Cost of 3 pounds of chicken = $10.20

Therefore, the cost of 3 pounds of chicken is $10.20.

Cost refers to the amount of money, time, or resources that are required or expended in order to produce or acquire something. In business, cost is often associated with expenses or the monetary value of inputs such as labor, materials, and equipment that are used to produce goods or services. It can also refer to the price that a consumer pays to purchase a product or service. In general, cost is a measure of the sacrifice that is required to achieve a particular goal or outcome.

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Answer:

Use a calculator for you to get an answer

Answer:

y=10x+24

Step-by-step explanation:

y-4=10(x-(-2))

y-4=10(x+2)

y-4=10x+20

y=10x+24

Answer:

y= -2x

Step-by-step explanation:

m=y2-y1/x2-x1

m=-6-4/3-(-2)

m=-2

y= mx+q

y= -2x+q

-6= -2(3)+q

-6+6= q

q= 0

Therefore y= -2x

Answer:72

Step-by-step explanation:

71+1=72