Find b: If a = 9 and c = 9
С
a
b

Note that the equation for the parent function y=x² stretched horizontally by a factor of 4 and shifted down 5 units is given as follows: y = (1/16)x² - 5

Note that a parent function is a simple, basic function from which other more complex functions can be derived by applying transformations.

To stretch the graph horizontally by a factor of 4, we divide x by 4, which gives:

y = (1/16)x²

To shift the graph down 5 units, we subtract 5 from the whole function, which gives:

y = (1/16)x² - 5

Therefore, the equation for the parent function y=x^2 stretched horizontally by a factor of 4 and shifted down 5 units is:

y = (1/16)x² - 5

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So the equation that can be used to find the number of cars that Mr. Diaz sold, c, is:

34c - 8 = 28

In algebra, a statement of mathematics that proves the equality of two mathematical expressions is known as an equation. Consider the equation 3x + 5 = 14, where the word "equal" is used to denote the relationship between the terms 3x + 5 and 14.

Let c be the number of cars that Mr. Diaz sold.

According to the problem statement, Ms. Wong sold 8 fewer cars than 34 times the number of cars Mr. Diaz sold, which can be written as:

Ms. Wong's cars sold = 34c - 8

We also know that Ms. Wong sold 28 cars, so we can set this expression equal to 28 to get:

34c - 8 = 28

To solve for c, we can add 8 to both sides and then divide both sides by 34:

34c - 8 + 8 = 28 + 8

34c = 36

c = 36/34

So the equation that can be used to find the number of cars that Mr. Diaz sold, c, is:

34c - 8 = 28

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Answer:

[tex]\csc \theta=\dfrac{\sqrt{61}}{6}[/tex]

[tex]\sin \theta=\dfrac{6}{\sqrt{61}}=\dfrac{6\sqrt{61}}{61}[/tex]

[tex]\cot \theta=\dfrac{5}{6}[/tex]

Step-by-step explanation:

Use Pythagoras Theorem to calculate the length of the hypotenuse of the given right triangle:

[tex]\implies a^2+b^2=c^2[/tex]

[tex]\implies 5^2+6^2=c^2[/tex]

[tex]\implies 25+36=c^2[/tex]

[tex]\implies c^2=61[/tex]

[tex]\implies c=\sqrt{61}[/tex]

Therefore:

[tex]\boxed{\begin{minipage}{8cm}\underline{Trigonometric ratios}\\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\\\$\sf\csc(\theta)=\dfrac{H}{O}\quad\sec(\theta)=\dfrac{H}{A}\quad\cot(\theta)=\dfrac{A}{O}$\\\\where:\\\phantom{ww}$\bullet$ $\theta$ is the angle.\\\phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle.\\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse.\\\end{minipage}}[/tex]

Substitute the given values into each ratio:

[tex]\csc \theta=\dfrac{\sqrt{61}}{6}[/tex]

[tex]\sin \theta=\dfrac{6}{\sqrt{61}}[/tex]

[tex]\cot \theta=\dfrac{5}{6}[/tex]

Note: The sin θ ratio can also be written as:

[tex]\implies \sin \theta=\dfrac{6}{\sqrt{61}}\cdot \dfrac{\sqrt{61}}{\sqrt{61}}[/tex]

[tex]\implies \sin \theta=\dfrac{6\sqrt{61}}{61}[/tex]

V = r²h where,

V is the volume of the cylinder

r is the radius of the cylinder

h is the height of the cylinder

in this case, h is the value we want to find, h, r is 3m and V is 155.43m³ !!

155.43 = × (3)² × h

17.27 = × h

h = 5.4972117...

= 5.50m (3.s.f) = height of cylinder

hope this helped, if you have any questions feel free to ask !! :D

We can use the formula for compound interest to find the time it will take to reach the target amount:

FV = PV * (1 + r)^t

where FV is the future value (target amount), PV is the present value (amount you have today), r is the interest rate, and t is the time (in years).

Substituting the given values, we get:

230000 = 31000 * (1 + 0.045)^t

Simplifying and solving for t, we get:

t = log(230000/31000) / log(1 + 0.045)

t ≈ 14.09

Therefore, it will take approximately 14.09 years to save enough to buy the Ferrari.

Using the graph of the line, we can see that the inequality, including the line which is the boundary of inequality, is:

 y + 2x ≥ -3

What is meant by inequality?

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using inequality symbols.

Given that the boundary line of equality has points (4,5) and (1,-1) on it.

So we can write the equation of the line.

Slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = -1-5 / 1-4 = 2

Equation of the line:

y - y1 = m (x-x1)

y - 5 = 2(x - 4)

y - 5 = 2x - 8

y = 2x - 3

y + 2x = -3

Point (−3, −5) makes the inequality false.

Substituting,

-5 + 2 * -3 = -5 - 6 = -11

y + 2x should not be -11

When graphing the line it should not include the point (−3, −5).

This point is present on the lower portion of the line.

So the upper portion of the line should be the inequality including the line itself.

Therefore using the graph of line, we can see that the inequality, including the line which is the boundary of inequality, is:

 y + 2x ≥ -3

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The solution for x in the given equation (x-c)/2 = d is x = 2d + c.

What is the solution for x in the given equation?

Given the equation in the question;

(x-c)/2 = d

x = ?

To solve for x, cross multiply and simplify.

(x-c)/2 = d

x - c = d × 2

x - c = 2d

Add +c to both sides

x - c + c = 2d + c

x = 2d + c

Therefore, the solution for x in the given equation (x-c)/2 = d is x = 2d + c.

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Intersection points for the lines are,

⇒ (3, 5) (1, 7) and (1, 5)

Line segment is the part of line which have two endpoint and bounded by two distinct end points and it contain every point on the line which is between its endpoint.

Given that;

The equation of lines are,

x + y = 8  .. (i)

y = 5 .. (ii)

x = 1  .. (iii)

Now, Intersect point for equation (i) and (ii);

x + y = 8  .. (i)

y = 5 .. (ii)

⇒ x + 5 = 8

⇒ x = 3

Hence, The intersection point = (3, 5)

And, Intersect point for equation (i) and (iii);

x + y = 8  .. (i)

x = 1  .. (iii)

⇒ x + y = 8

⇒ y = 8 - 1

⇒ y = 7

Hence, The intersection point = (1, 7)

And, Intersect point for equation (ii) and (iii);

⇒ (1, 5)

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Answer:

The answer to this question would be A

Step-by-step explanation:

I took the test one time before .

When the triangle's vertices are (2, 2), (4, 2), and (2, 2), its circumference is 28. (4,6).

An closed path that surrounds, distinguishes, or comprises a multiple shape or a three-dimensional length is spoken to as a boundary. The perimeter of either an ellipse or circle refers from its outermost area. The perimeter calculation had several practical uses. Discover how to determine the perimeter by adding the measurements of the vertices of various forms. You can still find the perimeter of a shape by multiplying its side lengths. The peripheral of an object is the space around it. At your house, a covered garden is one illustration. The circumference of anything is all area encircling it. For a 50 feet x 50 feet yard, a 200 yard fence is required.

given

d=√(x2−x1)2+(y2−y1)2

d1=√(4+1)2+(−5−6)2=√146≅12

For the second two;

d2=√(−2−4)2+(−4+5)2=√37≅6

And for the last pair;

d3=√(−2+1)2+(−4−6)2=√109≅10

So the sum of the three sides is roughly;

12+6+10=28

When the triangle's vertices are (2, 2), (4, 2), and (2, 2), its circumference is 28. (4,6).

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The values and heights obtained using the trigonometric ratios are as follows;

4. The six trigonometric ratios are;

5. The two other ways to write cot(θ) are;

6. The six trigonometric function values are;

7. The function for the height of the tree is; H = 100·tan(θ)

The completed table is presented as follows;

θ   [tex]{}[/tex]               10°                 15°              20°                 25°

H[tex]{}[/tex]               17.63             26.79          36.4               46.63

Trigonometric ratios are functions that relate the ratio of two of the sides of a right triangle to an interior angle of the right triangle.

4. The length of the adjacent side to the angle θ according to the Pythagorean Theorem is; Adjacent = √(17² - 8²) = 15

The six trigonometric ratios are;

cos(θ) = 15/17, sec(θ) = 17/15 = 1 2/15

sin(θ) = 8/17, csc(θ) = 17/8 = 2 1/8

tan(θ) = 8/15, cot(θ) = 15/8 = 1 7/8

5. The 2 other ways to write cot(θ) are;

cot(θ) = 1/(tan(θ))

cot(θ) = cos(θ)/sin(θ)

6. The location of the point on the terminal side of the angle is; (-3, -4)

Length of the hypotenuse side = √((-3)² + (-4)²) = 5

Let x represent the angle, we get;

The six trig functions of the angle are;

7. The length of the shadow of the tree = 100 m

Angle of elevation of the Sun = θ

Let h represent the height of the tree, we get;

tan(θ) = h/100

Therefore, the height of the tree, h = 100·tan(θ)

The values of the height of the tree at the different angle of elevation in the table are;

θ = 10°, h = 100 feet × tan(10°) ≈ 17.63 feet

θ = 15°, h = 100 feet × tan(15°) ≈ 26.79 feet

θ = 20°, h = 100 feet × tan(20°) ≈ 36.4 feet

θ = 25°, h = 100 feet × tan(25°) ≈ 46.63 feet

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The distance across the lake VW is 185m.

Triangles that are similar but not necessarily the same size are called similar triangles. This indicates that their sides are proportional and that their angles are the same.

We can see there are two similar triangles with interior parallel line.

So, apply the Side Angle Side (SAS) rule for ΔUVW ≈ ΔUXY;

⇒   [tex]\frac{VW}{XY} = \frac{UV}{UX}[/tex]

⇒   [tex]\frac{VW}{120.25}=\frac{(130+70)}{130}[/tex]

Cross multiply both sides,

⇒   VW  =  [tex]\frac{200}{130}*120.25[/tex]

⇒    VW = 185 m

Therefore, the value of VW is 185m.

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The Volume of Solid is 2,773.66 inch³ and Surface Area is

2,552.82 inch².

Surface area is the amount of space covering the outside of a three-dimensional shape.

Given:

Cylinder: Height = 30 inch, Radius = 5 inch

Semi sphere: radius = 5 inch

Cone: Height = 6 inch, radius = 5 inch, l= √r² + h² = 7.81 inch

Now, The Volume solid

= Volume of Semi sphere  + Volume of Cylinder + Vol. of Cone

= 2/3 πr³ + πr²H + 1/3 πr²h

= πr² (2/3 r + H + 1/3 h)

= 3.14 x 5 x 5 (2/3(5) + 30 + 1/3 (6))

= 78.5 x ( 10/ 3 + 30 + 2)

= 2,773.66 inch³

Now, the Surface Area of Solid

= SA (Cylinder+ S. Sphere + Cone)

= πr²H + 2πr² + 1/3 πrl

= πr (rH + 2r + 1/3l)

= 3.14 x 5 (150 + 10 + 2.60)

= 2,552.82 inch²

Now, the model is increased by 8 times then the dimensions are:

Cylinder: Height = 240 inch, Radius = 40 inch

Semi sphere: radius = 40 inch

Cone: Height = 48 inch, radius = 40 inch, l= √r² + h² = 62.48 inch

and, Now, The Volume solid after dilation

= Volume of Semi sphere  + Volume of Cylinder + Vol. of Cone

= 2/3 πr³ + πr²H + 1/3 πr²h

= πr² (2/3 r + H + 1/3 h)

= 3.14 x 40 x 40 (2/3(40) + 240 + 1/3 (48))

= 78.5 x ( 10/ 3 + 30 + 2)

= 1,420,117.33 inch³

Now, the Surface Area of Solid

= SA (Cylinder+ S. Sphere + Cone)

= πr²H + 2πr² + 1/3 πrl

= πr (rH + 2r + 1/3l)

= 3.14 x 5 (1200 + 80 + 20.82)

= 163, 382. 992 inch²

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The question you have indicated appears incomplete. However, here is a very similar example that uses the same logic and principles of probability and proportion. In this case, the proof is given below.

a.

Given: f(x) = 2(x+2)/5 , 0 <x< 1

Calculating P(0 <X< 1)

P(0 <X< 1) = ∫ f(x) dx {0.1}

Substitute 2(x+2)/5 for f(x)

P(0 <X< 1) = ∫ 2(x+2)/5 dx {0.1}

P(0 <X< 1) = 2/5 ∫(x+2) dx {0.1}

Integrate with respect to x

P(0 <X< 1) = 2/5 (x²/2+2x) {0.1}

P(0 <X< 1) = 2/5 (1²/2+2(1))

P(0 <X< 1) = 2/5 (½+2)

P(0 <X< 1) = 2/5 * 5/2

P(0 <X< 1) = 1 ----- Proved

b.

Here we're to solve for P(¼<X< ½)

P(¼<X< ½) = ∫ f(x) dx {¼,½}

Substitute 2(x+2)/5 for f(x)

P(¼<X< ½) = ∫ 2(x+2)/5 dx {¼,½}

P(¼<X< ½) = 2/5 ∫(x+2) dx {¼,½}

P(¼<X< ½) = 2/5 (x²/2+2x) {¼,½}

P(¼<X< ½) = 2/5 [ (½²/2+2(½)) - (¼²/2+2(¼))]

P(¼<X< ½) = 2/5 [(⅛+1)-(1/32 + ½)]

P(¼<X< ½) = 0.2375

The probability that more than ¼ but fewer than ½ of the people contacted will respond to this type of solicitation is 0.2375

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Full Question:

The proportion of people who respond to a certain mail-order solicitation is a continuous random variable X that has the density function f(x) = 2(x+2)/5 , 0 <x< 1, 0, elsewhere.

(a) Show that P(0 <X< 1) = 1.

(b) Find the probability that more than ¼ but fewer than ½ of the people contacted will respond to this type of solicitation.

Primary data is usually designed to collect original data which is required for a specific kind of research. This data is tailored according to what is the focus of the research and what outcome are the people looking for.

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Complete Question:

A marketing manager tells her assistant that she wants to use only primary data in her market research. Which of the following data would be most applicable for this research?

Interviews

Observation

Focus groups

Experiment

Surveys and Questionnaire

qualitative research

market research

The original length of each side of the square was 14 inches.

A square is a geometric form with two dimensions that has four equal sides and four angles that are each 90 degrees (also known as right angles). With all sides being the same length and all angles being right angles, it is a particular case of a rectangle and a parallelogram. A square's sides are all perpendicular to one another, and its diagonals are at right angles to one another. Squares exhibit rotational symmetry of order 4 because they are symmetrical in both their vertical and horizontal axes.

Let's assume that the original length of each side of the square was "x" inches.

When each side of the square is decreased by 2 inches, the new length of each side will be (x-2) inches.

The perimeter of the new square is given as 48 inches. Since a square has four equal sides, the perimeter of a square is given by the formula:

Perimeter = 4 * Side

So, for the new square, we have:

48 = 4 * (x-2)

Simplifying the above equation, we get:

12 = x-2

Adding 2 to both sides, we get:

x = 14

Therefore, the original length of each side of the square was 14 inches.

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3x - 8y = -19 would be -6x + 16y = 38. Option A is correct when we multiply the equation by factor -2

The systems of equation that would be equivalent to

3x - 8y = -19 can be gotten by using a common factor that can get us the solution

3x - 8y = -19 we would multiply this by 2

6x - 16y = -38 this is not in the solution

Then we have to multiply the first equation by -2

-2(3x - 8y = -19)

-6x + 16y = 38

Therefore the first option is equivalent to the first equation in the system

proof using 7 and 5

- 6 * 7 + 16 * 5 = 38

-42 + 80 = 38

Also 3x - 8y = -19

= 3 * 7 - 8 * 5 = -19

21 - 40 = -19

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The measure of angle 1 and the measure of angle 2 are 45° and 90°.

A square is a two-dimensional closed shape with 4 equal sides and 4 vertices. Its opposite sides are parallel to each other.

Given is a square,

We are asked to find the missing angles,

We know that, The diagonals of the square bisect each other at 90°,

The diagonal of a square bisects its internal angle,

Therefore, the measure of angle 1 = 45°

And,

The measure of angle 2 = 90°

Hence, the measure of angle 1 and the measure of angle 2 are 45° and 90°.

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The statement that are true are:

a) (Vx) (x+xzx). (R)

c) (3x) (3*=x²). (R)

d) (3) (3x). (R)

f) (Vx)(Vy) [x<y -> (3x<3y)]. (R)

a) (Vx) (x+xzx). (R) - This statement is true. It is a vacuously true statement, meaning it is true because the predicate (x+xzx) is never satisfied for any element x in the universe (R).

b) (3x) (2x+3=6x+7). (N) - This statement is false. There is no value of x in the universe (N) that satisfies the equation 2x+3=6x+7.

c) (3x) (3*=x²). (R) - This statement is true. For every value of x in the universe (R), 3 times x is equal to x squared.

d) (3) (3x). (R) - This statement is true. For any value of x in the universe (R), multiplying x by 3 will always result in a real number, which means 3x is also in the universe (R).

e) (3x) (3(2-x)=5+8(1-x)). (R) - This statement is false. There is no value of x in the universe (R) that satisfies the equation 3(2-x)=5+8(1-x).

f) (Vx)(Vy) [x<y -> (3x<3y)]. (R) - This statement is true. For any two elements x and y in the universe (R) where x<y, 3x is always less than 3y, so the implication (3x<3y) is true. Since this is true for all x and y, the universal quantifiers (Vx)(Vy) make the statement true.

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The height of the given triangle having an area of 13.5in.² and a base length of 6.75 in. is 4 in.

What is a triangle?

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total. Any three points in Euclidean geometry, when they are not collinear, produce a distinct triangle.

In a two-dimensional plane, a triangle's area is the area that it completely encloses. A triangle is a closed shape with three sides and three vertices, as is common knowledge. The entire area occupied by a triangle's three sides is referred to as its area. Half of the product of the triangle's base and height provides the general formula for calculating the area of the triangle.

In this question, we are given,

Area of triangle A = 13.5 in.²

Base of triangle b = 6.75 in.

We are asked to find the height h of the triangle.

Now formula of the area is:

A = 1/2 * b * h

13.5 = 1/2 * 6.75 * h

h = 13.5 *2 / 6.75 = 4 in.

Therefore the height of the given triangle is 4 in.

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Answer:

Step-by-step explanation:

up to beyond hald a milimeter in length

2mm

Answer:

Step-by-step explanation:

The expression "X divided by 5 multiplied by 12" can be written as:

( X / 5 ) * 12

To simplify this expression, we can first multiply 12 by X/5, which gives:

( X / 5 ) * 12 = X * (12/5)

So the simplified expression is:

X * (12/5)

or

(12/5)X

which is equivalent to "12/5 times X".

The interest to pay at the end of the first month C. $18.71.

To calculate the monthly interest rate, divide the annual percentage rate by 12. For excellent credit, the monthly rate is 4.75% / 12 = 0.3958%, and for good credit, the monthly rate is 5.00% / 12 = 0.4167%.

The total cost of the mobile home including sales tax is $92,738 ($89,000 x 4.2% sales tax). With a $3,000 down payment, the amount financed is $89,738.

For excellent credit, the monthly interest rate :

= 4.75% / 12

So, the interest charged in the first month is $89,738 x  4.75% / 12 = $355.21

For good credit, the monthly interest rate is 0.4167%. So, the interest charged in the first month is $89,738 x 0.004167 = $33.91.

The difference in interest charged between good and excellent credit is $373.91 - $355.21 = $18.71.

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The complete question is:

Your parents are purchasing a mobile home for $89,000. The sales tax is 4.2%, they make a $3,000 down payment. How much more interest do your parents have to pay at the end of the first month because their rating is good rather than excellent?

Secured Unsecured

Credit APR (%) APR (%)

Excellent 4.75 5.50

Good 5.00 5.90

Average 5.85 6.75

Fair 6.40 7.25

Poor 7.50 8.40

Options:

$29.39

$21.10

$18.71

$19.02

The Spirit Club makes $2.5 profit on each shirt at the end of the year.

What is profit?

Cost price and selling price are better ways to explain profit. Cost price is the actual cost of the good or service, whereas selling price is the price at which it is offered for sale. In this case, the business has made a profit if the selling price of the good is higher than the cost price. Consequently, the profit calculation formula is;

Selling price minus cost price equals profit or gain.

Given that the cost of a shirt for the Spirit Club is $8.

They mark up the shirts 75% to sell in the school store.

The amount that is up on each shirt is $8×75%

= $8×(75/100)

= $8×(3/4)

= $6.

The marked price of each shirt is  $8 + $6 = $14.

They sell the shirts for 25% off at the end of the year.

The discount amount is $14×25%

= $14×(25/100)

= $14×(1/4)

= $3.5

The selling price of each shirt at the end of the year is $14 - $3.5 = $10.5.

The profit is Selling price - cost price = $10.5 - $8 = $2.5

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By integration of monthly revenue we will get total revenue of the shop for a year is $51,600.

What is integration ?

Integration is a fundamental operation in calculus that involves finding the area under a curve, or the antiderivative of a function. It is the reverse operation of differentiation, which is used to find the rate of change of a function.

Integration is represented by the symbol ∫ (the integral sign), and the result of the operation is called the indefinite integral or antiderivative of the function. The antiderivative is a family of functions that differ only by a constant, known as the constant of integration.

Given by the question:

The monthly revenue can be calculated by multiplying the unit price and the quantity of goods sold in a given month. Therefore, the monthly revenue function is:

[tex]R(t) = P(t) * Q(t) = (t^2 + 9t + 36) * (t + 12)[/tex]

To find the total revenue over a year, we need to integrate the monthly revenue function over the interval [0,12] (since we are considering a year):

[tex]Total revenue = \int\limits^a_0 {R(t)} \, dt[/tex]

= [tex]\int\limits^a_b (t^2 + 9t + 36) * (t + 12) } \, dt[/tex]

= [tex]\int\limits^a_b {(t^3 + 21t^2 + 132t + 432) } \, dt[/tex]

=[tex][t^4/4 + 7t^3/3 + 66t^2 + 432t][/tex]evaluated from 0 to 12

=[tex](20736/4 + 12096 + 9504 + 5184) - (0 + 0 + 0 + 0)[/tex]

= [tex]51600[/tex]

Therefore, the total revenue of the shop for a year is $51,600.

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The required length of the parking lot is 75 meters.

Perimeter is the measure of the figure on its circumference.

Here,
Let's call the length of the parking lot "L". The perimeter of a rectangle is given by the formula:

Perimeter = 2 × (length + width)

We know that the width is 62 m and the perimeter is 274 m, so we can plug these values into the formula and solve for the length:

274 = 2 × (L + 62)

Dividing both sides by 2, we get:

137 = L + 62

Subtracting 62 from both sides, we get:

L = 137 - 62

L = 75

Therefore, the length of the parking lot is 75 meters.

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The measure of the segment OD is same as OE. Hence , OD = DE.

A straight line that only touches a circle once is said to be tangent to it. The term "point of tangency" refers to this point. At the point of tangency, the tangent to a circle is perpendicular to the radius.

Given: XY is the tangent to the circle with centre O at A and

∠CAX=∠BAY=60°

By Alternate Segment Theorem

∠BCA=∠BAY=60°

Similarly,

∠ABC=∠CAX=60°

Therefore, ΔABC is an equilateral triangle circumscribing the circle with centre O.

Thus, centre O is also the centroid.

⇒OA:OD=2:1

Also,

OA=OE            (Radii)

∴ OD=DE

Hence , OD = DE

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