In an effort to eat healthier, Bridget is tracking her food intake by using an application on her phone. She records what she eats, and then the


application indicates how many calories she has consumed. One Monday, Bridget eats 10 medium strawberries and 8 vanilla wafer cookies as an


after-school snack. The caloric intake from these items is 192 calories. The next day, she eats 20 medium strawberries and 1 vanilla wafer cookie as an after-school snack. The caloric intake from these items is 99 calories.



a. Write a system of equations for this problem situation. Let S represent the number of calories in one strawberry and let W represent the number of calories in one vanilla wafer cookie.



The equation _____ represents the calories Bridget ate on Monday and the equation _____ represents the calories she ate the next day.



b. Solve the system of equations using the substitution method. Check your work.



The number of calories in each strawberry is ____


And the number of calories in each vanilla wafer cookie is ____. The solution is ____.



PLEASE HELP ME

If two prisms are similar, their corresponding dimensions are proportional.

Let's assume that the ratio of the corresponding lengths of the smaller prism to the larger prism is k:1, where k is a constant.

Then the ratio of the corresponding surface areas of the smaller prism to the larger prism is [tex](k^2):1[/tex], because the surface area of a prism is proportional to the square of its length.

In this problem, the surface area of the smaller prism is not given.

However, we can find the ratio of the corresponding lengths of the smaller prism to the larger prism using the fact that they are similar.

The height of the smaller prism can be found as follows:

[tex]7/5 = h/L[/tex]

where h is the height of the smaller prism and L is the length of the larger prism.

Solving for h, we get:

[tex]h = (7/5)L[/tex]

The ratio of the corresponding lengths of the smaller prism to the larger prism is 7:5.

The ratio of the surface areas of the smaller prism to the larger prism is:

[tex](7/5)^2 : 1 = 49/25 : 1[/tex]

We know that the surface area of the larger prism is [tex]90 m^2.[/tex]

Let's denote the surface area of the smaller prism by A. Then we can set up an equation:

(49/25)A = 90

Solving for A, we get:

A = (25/49) * 90 = 45/7 ≈ 6.4

The surface area of the smaller prism is approximately [tex]6.4 m^2.[/tex]

(Note: The units of the surface area are not provided for the smaller prism, so I assumed the same units as the larger prism.

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Using the given sample data, the data values are:

Range 24

Q1 52

Q3 69

IQR 17

1. Arrange the data in ascending order:
52, 52, 52, 54, 58, 61, 62, 64, 67, 69, 69, 73, 76

2. Calculate the range (highest value - lowest value):
Range = 76 - 52 = 24

3. Find the first quartile (Q1) - the median of the first half of the data:
Since there are 13 data points, we'll take the median of the first 6 numbers: (52 + 52) / 2 = 52

Q1 = 52

4. Find the third quartile (Q3) - the median of the second half of the data:
We'll take the median of the last 6 numbers: (69 + 69) / 2 = 69

Q3 = 69

5. Calculate the interquartile range (IQR) by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 69 - 52 = 17

So, the requested values are:
Range = 24
Q1 = 52
Q3 = 69
IQR = 17

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The income statement and Accounting Information System, along with the balance sheet and cash flow statement, help you understand your company's financial health.

MIS employs non-financial data, but AIS exclusively uses financial data.

MIS indirectly to other external users.

The income management account is most likely affected by Selling, General, and Administrative Expenses.

In accounting, an instrument that provides the data needed to effectively manage an organization and make decisions is a management information system (MIS).

It is used to locate, collect, process, and distribute economic data about a company to a variety of users (AIS).

MIS concentrates on the financial and accounting aspects of a business, diagnosing problems and proposing solutions. The former management system, that occasionally relied on intuition and unscientific approaches and was arbitrarily constructed, has been replaced with MIS.

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The sum of the first 10 terms of the given series  8,20/3,50/9... is 140.

Given series: 8,20/3,50/9...

The given series is not in a standard form, but it appears to be an arithmetic sequence with a common difference of  4/3. To check this, we can find the difference between consecutive terms:

20/3-8=4/3

50/9-20/3=4/3

Thus, the common difference is indeed [tex]\frac{4}{3}[/tex].

We notice that each term of the series can be written as:

a_n=a+(n-1)d

a_n=8+(n-1)(4/3)

where n is the index of the term, and 4/3  is the common difference between the consecutive terms.

To find the sum of the first 10 terms of the series, we use the formula for the sum of an arithmetic series:

S=(n/2)[2a_1+(n-1)d]

where S is the sum of the series, a_1 is the first term of the series, d is the common difference, and n is the number of terms to be added.

Substituting the given values, we get:

S=(10/2)[2*8+(10-1)(4/3)]

Simplifying the expression:

S=5[16+9(4/3)]

S=5[16+12]=5(28)=140

Therefore, the sum of the first 10 terms of the series is 140.

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Answer:

radius is 50.95

area is 8158.55

Step-by-step explanation:

cirumference = 2pi×r

or,320.28=2×(22/7)×r

or, r=320.28/(2×(22/7))

r=50.95 cm

area=(22/7)r^2

=8158.55

The amount of water that leaks from the bucket each hour is 38 ounces/hour.

The amount of water in the bucket at 8 am would have been 380 ounces. The bucket will be empty after 8 hours, or at 6 pm.

To find the amount of water that leaks from the bucket each hour, we can use the information that the leak is at a constant rate. We can find the total amount of water that leaked out of the bucket from 10 am to 3 pm, which is 304 - 114 = 190 ounces.

This is over a time period of 5 hours (from 10 am to 3 pm), so the amount of water that leaks from the bucket each hour is:

190 ounces ÷ 5 hours = 38 ounces/hour

To find how many ounces of water were in the bucket at 8 am, we need to estimate the amount of water that leaked out from 8 am to 10 am. We know that the bucket loses 38 ounces of water every hour, so from 8 am to 10 am (2 hours), the amount of water that leaked out would be:

38 ounces/hour x 2 hours = 76 ounces

Therefore, the amount of water in the bucket at 8 am would have been:

304 ounces + 76 ounces = 380 ounces

To find at what time the bucket will be empty, we can assume that the leak rate remains constant at 38 ounces/hour. We know that the bucket starts with 304 ounces, so we can set up the equation:

y = 304 - 38x

where y is the amount of water in the bucket and x is the time in hours since the leak began. When the bucket is empty, y will be zero, so we can solve for x:

0 = 304 - 38x

38x = 304

x = 8

Therefore, the bucket will be empty after 8 hours, or at 6 pm.

The equation for the amount of water in the bucket as a function of time can be written in slope-intercept form as:

y = -38x + 304

where the slope (m) is -38 (the rate at which water is leaking out of the bucket) and the y-intercept (b) is 304 (the initial amount of water in the bucket).

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The least number of packages of plates, napkins, and cups Maria has to buy is 15 packages .

To find the least number of packages, we need to find the least common multiple (LCM) of the three package sizes: 8 (plates), 10 (napkins), and 12 (cups).

The prime factors of 8 are 2x2x2, of 10 are 2x5, and of 12 are 2x2x3. To find the LCM, we multiply the highest powers of each prime factor: 2³x3x5 = 120.

This means Maria needs 120 of each item. She will buy 120/8 = 15 packages of plates, 120/10 = 12 packages of napkins, and 120/12 = 10 packages of cups.

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The percentage of evergreen trees from the total combination of trees is 79%

The percentage of evergreen trees will be calculated using the formula -

Percentage of evergreen trees = number of evergreen trees/total number of trees × 100

Total number of trees = number of evergreen + deciduous trees

Total trees = 3160 + 840

Total trees = 4000

Percentage of evergreen trees = 3160/4000 × 100

Cancelled common zeroes in numerator and denominator and performing division

Percentage = 79%

Hence, the percentage of evergreen trees is 79%.

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The value of the expression  a+b = 45+8 = 53

To write (3x)² (5x⁶) in the form of ax^b, we need to simplify the expressions and multiply the coefficients and the variables separately:

(3x)² (5x⁶) = 9x² × 5x⁶ = 45x^(2+6) = 45x^8

So, the expression (3x)² (5x⁶) can be written as 45x^8 in the form of ax^b, where a=45 and b=8.

Therefore, a+b = 45+8 = 53

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The maximum height reached by the rocket is approximately 504.6 feet.

To find the maximum height reached by the rocket, we need to determine the vertex of the parabola represented by the given quadratic equation: y = -16x^2 + 180x + 63.

The x-coordinate of the vertex can be found using the formula x = -b / 2a, where a = -16 and b = 180.

x = -180 / (2 * -16) = 180 / 32 = 5.625

Now, we'll plug the x-coordinate back into the equation to find the y-coordinate (maximum height).

y = -16(5.625)^2 + 180(5.625) + 63

y ≈ 504.6

The maximum height reached by the rocket is approximately 504.6 feet.

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The intersection of a plane and a cylinder can result in the following polygons when the plane is either parallel or perpendicular to the base:

Oa Rectangle

Oc Square

Od Triangle

The angle and position of the plane relative to the cylinder intersect determines a myriad of shapes not limited to just one. Herein are the descriptions for a few that may arise:

Rectangle: If a plane intersects the cylinder but remains parallel to its base, the resulting outline shall be rectangular. This is due to the aforementioned plane cutting through the lateral surface of the circumference, forming two equal lines--thereby shaping a closed loop in an angular fashion.

Square: The intersection of a plane perpendicularly bisecting the base of a cylindrical object will conjure up a square shape congruent to the cylinders. In other words, a perfectly squared compartment matching with the pre-existing edges of the bottom curve of the cylinder.

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Inflation is an important factor to consider when planning future purchases.

The Inflation Calculator does not provide the inflation-adjusted price for a fancy leather couch 10 years from now because it relies on historical data and cannot predict future inflation rates accurately.

Inflation rates are influenced by various economic factors and can fluctuate over time.

Therefore, it's difficult to determine the exact future cost of items with certainty. However, you can use historical trends as a general guide to estimate potential increases in cost due to inflation.

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To find the polynomial closest to another polynomial in an inner product space, you can follow these steps:

Choose an inner product on the space of polynomials. One common inner product on this space is the L2 inner product, which is defined as:

<f,g> = ∫a^b f(x)g(x) dx,

where a and b are the endpoints of the interval on which the polynomials are defined.

Let P be the space of polynomials of degree at most n, where n is the degree of the polynomial you want to approximate. Let f be the polynomial you want to approximate, and let g be an arbitrary polynomial in P.

Define the error between f and g as e = f - g.

Compute the inner product of e with itself:

<e,e> = ∫[tex]a^b (f(x) - g(x))^2 dx.[/tex]

Minimize this inner product with respect to g. This can be done by setting the derivative of <e,e> with respect to g equal to zero and solving for g.

The polynomial that minimizes the error is the polynomial closest to f in the L2 sense.

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Approximately 21.3 percent of the total items sold were baseball items.

Out of the 300 items sold, 5 of them were football items, so the number of non-football items sold is:

300 - 5 = 295

We know that 20% of the non-football items sold were baseball items, so the number of baseball items sold is:

0.20 * 295 = 59

Therefore, the total number of baseball and football items sold is:

59 + 5 = 64

The percentage of total items sold that were baseball items is:

(64 / 300) * 100% = 21.3%

Therefore, approximately 21.3 percent of the total items sold were baseball items.

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The radius of the circle of equation x² + y² = 19² is given as follows:

r = 19 units.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle.

The equation of the circle in this problem is given as follows:

x² + y² = 19².

Hence the radius is obtained as follows, comparing to the general equation:

r² = 19²

r = 19 units.

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To find the probability of p(m) given the information provided, we can use the formula:
p(m) = p(m cap c') + p(m cap c)
where c' represents the complement of c, or everything that is not c.

First, we need to find the probability of c' by using the formula:
p(c') = 1 - p(c)
p(c') = 1 - 0.048

p(c') = 0.952
Next, we can find the probability of p(m cap c') by using the formula:
p(m cap c') = p(m) - p(m cap c)

p(m cap c') = p(m cup c) - p(c)
p(m cap c') = 0.524 - 0.048
p(m cap c') = 0.476

Finally, we can substitute these values into the formula for p(m) and solve:
p(m) = 0.476 + 0.044
p(m) = 0.52

Therefore, the indicated probability of p(m) is 0.52.

In simpler terms, p(m) is the probability of event m occurring. To find this probability, we first need to find the probability of event c not occurring, or c'. Then, we can use this information to find the probability of event m occurring but c not occurring, or m cap c'.

Finally, we add this probability to the probability of event m occurring and c occurring, or m cap c, to get the overall probability of event m occurring, or p(m). In this case, the indicated probability of p(m) is 0.52.

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[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ P(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad R(\stackrel{x_2}{-2}~,~\stackrel{y_2}{-4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -2 +x}{2}~~~ ,~~~ \cfrac{ -4 +y}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE Q} }{(-5~~,~~1)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ -2 +x }{2}=-5\implies -2+x=-10\implies \boxed{x=-8} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ -4 +y }{2}=1\implies -4+y=2\implies \boxed{y=6}[/tex]

Answer:

The answer is (-8,6)

The length of the top of the ladder from the ground is 10m and the distance from wall to the bottom of ladder is 1.5m

Given that an ladder leans against a wall.

We have to find the length of the top of the ladder from the ground.

We know that tan function is the ratio of opposite side and adjacent side

Let x be the opposite side

tan 68 = x/4

2.475 = x/4

x= 4×2.475

x=9.9 m

x=10 m

So, the  length of the top of the ladder from the ground is 10m.

Now let us find the distance from wall to the bottom of ladder

cosine function is the ratio of adjacent side and hypotenuse

Cos 68 = x/4

0.374 =x/4

x=0.374×4

x=1.5m

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The mass of the wire is 500.

To find the mass of the wire, we need to integrate the density function over the surface area of the wire.

First, we need to parameterize the curve. The equation of the circle with center at the origin and radius 5 is:

x^2 + y^2 = 25

We can parameterize this curve by letting:

x = 5cos(t)
y = 5sin(t)

where t varies from 0 to pi/2 (the first quadrant).

Next, we need to find the surface area element. We can do this using the formula:

dS = sqrt(1 + (dz/dx)^2 + (dz/dy)^2) dA

where dz/dx and dz/dy are the partial derivatives of the height function z = f(x,y) (in this case, z = 0 since the wire is a curve in the xy-plane).

Since dz/dx = dz/dy = 0, we have:

dS = dA

where dA is the area element in the xy-plane, which is given by:

dA = |(dx/dt)(dy/ds) - (dx/ds)(dy/dt)| dt ds

Plugging in our parameterization, we have:

dA = 5 dt ds

Now we can integrate the density function over the surface area of the wire:

m = ∫∫ 8(x,y) dS

= ∫∫ 2xy dA

= ∫[0,pi/2] ∫[0,5] 2(5cos(t))(5sin(t)) (5 dt ds)

= 500

Therefore, the mass of the wire is 500.

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The variance in the number of rainy days in Marina's city in two weeks during the month of August is approximately 3.96.

We know that the probability of rain on any given day is0.43, and we want to find the  friction in the number of  stormy days in two weeks, which is 14 days.  

The  friction of a binomial distribution is given by the formula  

Var( X) =  npq  

where n is the number of trials,

p is the probability of success on each trial,

and q is the probability of failure on each trial( q =  1- p).

 In this case, n =  14,

p = 0.43, and

q = 0.57.

Substituting these values, we get  

Var( X) =  npq  

Var( X) =  14 x0.43 x0.57  

Var( X) = 3.9642  

Rounding to three significant  numbers, we get   Var( X) = 3.96

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Let's start by assigning variables to the unknowns in the problem:

- Let j be Jim's speed in miles per hour (in other words, the rate at which he walks).

- Let s be Steve's speed in miles per hour (in other words, the rate at which he runs).

- Let m be Matt's speed on his bike in miles per hour.

From the first sentence of the problem, we know that:

s = m + 4   (Steve runs 4 miles per hour slower than Matt rides his bike)

And from the second sentence, we know that:

j = s - 3   (Jim walks 3 miles per hour slower than Steve runs)

We want to find out how long it takes Jim to walk 25 miles and how long it takes Matt to ride his bike x miles. We can use the formula:

time = distance / rate

For Jim, we have:

time = 25 / j

For Matt, we have:

time = x / m

We also know that Steve runs 16 miles in the same time that Matt rides his bike 24 miles, so we can write:

16 / s = 24 / m

Substituting s = m + 4 and solving for m, we get:

16 / (m + 4) = 24 / m

16m = 24(m + 4)

16m = 24m + 96

8m = 96

m = 12

So Matt rides his bike at a speed of 12 miles per hour.

Now we can use the equations we set up earlier to solve for j and x:

j = s - 3

s = m + 4

j = (m + 4) - 3

j = m + 1

j = 13

x / m = 25 / j

x / 12 = 25 / 13

x = (25 * 12) / 13

x = 300 / 13

x ≈ 23.08

So it takes Jim 25 / 13 ≈ 1.92 hours to walk 25 miles, and it takes Matt 23.08 hours to ride his bike x = 300 / 13 ≈ 23.08 miles.

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The given equation, V = 1/3 πr²h, solved for h is:

h = 3V / πr²

From the question, we are to solve the give equation for h

From the given information,

The given equation is

V = 1/3 πr²h

To solve the equation for h, we will isolate h

Solving the equation for h

V = 1/3 πr²h

Multiply both sides of the equation by 3

3 × V = 3  × 1/3 πr²h

3V = πr²h

Divide both sides of the equation by πr²

3V / πr² = πr²h / πr²

3V / πr² = h

This can be written as

h = 3V / πr²

Hence, the equation solved for h is:

h = 3V / πr²

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The equation that can be used to compute the number of pieces of jewellery is ($120 + $15q)/q = $20 .

Average cost is total cost divided by the quantity of jewellery sold.

Average cost = total cost / quantity

Total cost is the sum of fixed cost and variable cost.

Total cost = fixed cost + variable cost

The fixed cost is the cost of renting the stall. The variable cost is the cost of the materials.

Total cost = $120 + ($15 x q)

T = $120 + $15q

Average cost = ($120 + $15q)/q = $20

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The value of Isabel's investment after 5 years is 2512.08 euros.

To calculate the value,

The formula for calculating compound interest is:

A = P (1 + r/n)^(nt)

where:

A = the final amount

P = the principal (initial amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time (in years)

In this case, we have

P = 2000 euros

r = 0.043 (4.3% as a decimal)

n = 2 (compounded biannually)

t = 5 years

So, the formula becomes:

A = 2000 (1 + 0.043/2)^(2*5) = 2512.08 euros

Therefore, after 5 years, Isabel's investment will be worth 2512.08 euros.

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Answer:

m = -4

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (-3,12) (-2,8)

We see the y decrease by -4, and the x increase by 1, so the slope is

m = -4

So, the slope of the line representing by the data is -4.

Answer:

Step-by-step explanation:

A= 1/2 b h    b=6   h=2.5

= 7.5

Answer:

7.5 inches squared

Step-by-step explanation:

If only distances are provided, there are two methods to find the area of a triangle.  Which method to use depends on which lengths are provided:

Method 1: Base * Height

For any triangle, a line segment from one vertex that terminates perpendicularly to the leg across from it is considered a "height," and the leg that the "height" intersects is "base".  If both quantities are known, then the area of the triangle is base times height divided by 2 (sometimes stated as 1/2 times base times height).

In an equation format: [tex]Area_{triangle}=\frac{1}{2}base*height[/tex], often abbreviated as [tex]A_{triangle}=\frac{1}{2}bh[/tex]

For this example, the base at the bottom "6 in" has a corresponding height of "2.5 in", so

[tex]A_{triangle}=\frac{1}{2}(2.5~\text{in})(6~\text{in})[/tex]

[tex]A_{triangle}=7.5\text{ in}^2[/tex]

Method 2: Heron's Formula

If you are not provided any of the heights, but only the three legs of the triangle, Heron's formula provides a method of finding the area of the triangle.  It is significantly more complicated, and should only be used if one doesn't have one of the heights given.

Heron's formula gives the area of a triangle using the following formula:[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex] where a, b, and c, are the side lengths of the triangle, and "s" is the "semi-perimeter" (one half of the perimeter) of the triangle: [tex]s=\dfrac{a+b+c}{2}[/tex]

To be consistent, let's let a=3 in, b=5 in, and c=6 in.

Calculating the semi-perimeter of the given triangle first:

[tex]s=\dfrac{a+b+c}{2}=\dfrac{(3~\text{in})+(5~\text{in})+(6~\text{in})}{2}=\dfrac{14~\text{in}}{2}=7~\text{in}[/tex]

Calculating the area:

[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]

[tex]A=\sqrt{(7~\text{in})((7~\text{in})-(3~\text{in}))((7~\text{in})-(5~\text{in}))((7~\text{in})-(6~\text{in}))}[/tex]

[tex]A=\sqrt{(7~\text{in})(4~\text{in)(2~\text{in})(1~\text{in})}[/tex]

[tex]A=\sqrt{56~\text{in}^4}[/tex]

[tex]A=7.48331477355...~\text{in}^2[/tex]

[tex]A\approx7.5~\text{in}^2[/tex]

Side note:  The 2.5 inches that they gave you in the problem isn't exactly 2.5 inches.  They rounded to one decimal place there.

Answer: No they are not

Step-by-step explanation:

Distribute the 4 from the left equation into the parenthesis.

you would get 20k - 12

that is not equivalent to 14k - 8

The approximate area of the circular fenced-in section is 950.5 square meters.

The circumference of a circle is given by the formula 2πr, where r is the radius of the circle. We are given that the circumference of the fenced-in section is 55 meters, so we can set up the equation:

2πr = 55

We can solve for r by dividing both sides by 2π:

r = 55/(2π)

We are asked to find the area of the section, which is given by the formula A = πr². Substituting our expression for r, we get:

A = π(55/(2π))²

Simplifying, we get:

A = (55²/4)π

Using the approximation 22/7 for π, we get:

A ≈ (55²/4)(22/7)

A ≈ 950.5

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The inequality that represents the cost of each cookie is C ≤ $2, where C is the cost of each cookie.

An inequality is a mathematical expression that shows a relationship between two values that may not be equal. To represent the cost of each cookie using an inequality, we can first determine the cost per cookie by dividing the total cost of a box by the number of cookies in each box. In this case, that would be $16 divided by 8 cookies.

Let C represent the cost of an individual cookie. Since the most a box can cost is $16, the highest cost per cookie would be $16 / 8 = $2. To express this situation as an inequality, we can write:

C ≤ $2

This inequality indicates that the cost of each cookie (C) must be less than or equal to $2, ensuring that the total cost for a box of cookies does not exceed the maximum price of $16. By using this inequality, we can evaluate different cookie flavors and their respective costs to confirm that they meet Cindy's Sweet Treats' pricing requirements.

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To find the mean and mean absolute deviation of a data set, you need to follow these steps:

1. Find the mean: To find the mean of a data set, add up all of the values in the set and then divide that sum by the number of values in the set. For example, if your data set is {2, 4, 6, 8, 10}, you would add up all of the values (2+4+6+8+10=30) and then divide that sum by the number of values (5). So the mean of this data set is 30/5 = 6.

2. Find the mean absolute deviation:

To find the mean absolute deviation of a data set, you first need to find the absolute deviation of each value in the set from the mean.

To do this, subtract the mean from each value in the set (for example, if your data set is {2, 4, 6, 8, 10} and the mean is 6, you would subtract 6 from each value: 2-6=-4, 4-6=-2, 6-6=0, 8-6=2, 10-6=4).

Then, take the absolute value of each of these differences (|-4|=4, |-2|=2, |0|=0, |2|=2, |4|=4). Finally, find the mean of these absolute deviations by adding them up and dividing by the number of values in the set.

For the example data set above, the mean absolute deviation is (4+2+0+2+4)/5 = 2.4.

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