A number is increased by 70% and the result is 42.5. What is the number?
A. 29.75
B. 27.5
C. 25
D. 17
E. 12.75

The system has infinitely many solutions, which can be written as (x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.

To solve the system of equations:

1x + 0y + 60z = 1

1x + 10y + 0z = 0

0x + 0y + 0z = 0

The third equation is an identity, implying that it does not give us any new information. The first two equations can be used to solve for x, y, and z:

From the first equation, we get x = 1 - 60z

From the second equation, we get y = 0 - 10x = -10(1 - 60z) = -10 + 600z

Therefore, the solution to the system can be written as a point in terms of z as:

(x, y, z) = (1 - 60z, -10 + 600z, z)

Since z can take on any value, there are infinitely many solutions to the system, which can be parameterized as:

(x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.

he system has infinitely many solutions, which can be written as (x, y, z) = (1 - 60s, -10 + 600s, s) where s is a parameter.

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The figures created are a square and a right triangle, and the perimeter of the entire figure is (13x/3) + x × sqrt(10).

When Namandu divides the top side of the square into three equal parts, he creates two segments of length x/3 each. By connecting the first point of division with the vertex of the parallel side, he creates a right triangle with legs of length x/3 and x, and hypotenuse of length y.

Using the Pythagorean theorem, we can solve for y:

y^2 = (x/3)^2 + x^2

y^2 = x^2/9 + x^2

y^2 = (10x^2)/9

y = x×sqrt(10)/3

Now we can find the perimeter of each figure that is created

Perimeter of the original square = 4x

Perimeter of the right triangle = x + x/3 + y = x + x/3 + xsqrt(10)/3

Perimeter of the entire figure = 4x + x + x/3 + xsqrt(10)/3 = (13x/3) + x×sqrt(10)

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The temperature of the cup of water is approximately 180°F after 6 minutes.

Using the given formula, we can write:

T = Ta + (To - Ta) * e^(-kt)

where Ta = 73°F (the temperature of the room), To = 201°F (the initial temperature of the water), and T = 189°F (the temperature of the water after 3 minutes).

We can solve for the decay constant k as follows:

(T - Ta) / (To - Ta) = e^(-kt)

ln[(T - Ta) / (To - Ta)] = -kt

k = -ln[(T - Ta) / (To - Ta)] / t

Substituting the given values, we get:

k = -ln[(189°F - 73°F) / (201°F - 73°F)] / 3 minutes

k = -ln[116 / 128] / 3 minutes

k ≈ 0.0434 minutes^-1 (rounded to the nearest thousandth)

Now we can use this value of k to find the temperature of the water after 6 minutes:

T = Ta + (To - Ta) * e^(-kt)

T = 73°F + (201°F - 73°F) * e^(-0.0434 minutes^-1 * 6 minutes)

T ≈ 180°F (rounded to the nearest degree)

Therefore, the temperature of the cup of water is approximately 180°F after 6 minutes.

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The length οf line FG is 12 cm, If  Figure EFGH is a parallelοgram.

A parallelοgram is a type οf quadrilateral with twο pairs οf parallel sides. The οppοsite sides οf a parallelοgram are equal in length and parallel tο each οther.

Since EFGH is a parallelοgram, we knοw that the οppοsite sides are parallel and equal in length. Therefοre, the length οf line FG is equal tο the length οf line EH.

We can find the length οf EH by using the Pythagοrean theοrem οn right triangle EFG:

[tex]EF^2 + FG^2 = EG^2[/tex]

Since EF = 5 cm, EG = 13 cm, and angle FEG is a right angle (as οppοsite angles in a parallelοgram are equal), we can sοlve fοr FG:

[tex]FG^2 = EG^2 - EF^2[/tex]

[tex]FG^2 = 13^2 - 5^2[/tex]

[tex]FG^2 = 144[/tex]

[tex]FG = \sqrt{(144)[/tex]

[tex]FG = 12 cm[/tex]

Therefοre, the length οf line FG is 12 cm.

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When the function d(x) = -x +(-3), then the value of d(0) is -3

In mathematics, a function is a relationship between two sets of numbers, called the domain and range. A function assigns each element of the domain to exactly one element of the range.

In the given problem, we are given a function d(x)=-x-3. The notation d(0) represents the value of the function d(x) when x = 0.

To find d(0), we need to substitute x = 0 in the function d(x)=-x-3, which gives:

d(0) = -(0) - 3

The first term -(0) is equal to zero, and the second term -3 is a constant value that remains the same regardless of the value of x. Therefore, we can simplify the expression as

d(0) = -3

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To compute the 90% confidence interval for the population proportion, large a sample should you draw to ensure that the sample proportion does not deviate from the population proportion by more than 0.05, 271 is the minimum sample

A confidence interval is a range of values where an unknown population parameter lies. The level of confidence is the likelihood of the interval containing the parameter.

The formula to calculate the sample size required to produce a specific margin of error with a known level of confidence for the estimation of a population proportion is given below: 95% confidence interval for population proportion using a sample size formula

[tex]\[n=\frac{z^{2}p(1-p)}{E^{2}}\][/tex]

Where

[tex]\[z\][/tex] is the z-score The formula is modified to calculate the sample size required to produce a specific margin of error with a known level of confidence as follows:

[tex]\[n=\frac{z^{2}}{4E^{2}}\][/tex]

Note: For this problem, the sample size needs to be large enough to ensure that the sample proportion does not deviate from the population proportion by more than 0.05.

Using a Z-score Table, the z-value that corresponds to 90% confidence interval is 1.645.

[tex]n=\frac{z^{2}}{4E^{2}}\ = \frac{1.645^{2}}{4(0.05)^{2}} = \frac{2.706225}{0.0100} = 270.6[/tex]

(rounded up to the next highest integer)Therefore, 271 is the minimum sample size required to compute a 90% confidence interval for the population proportion.

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(a) The present value of an annuity formula can be used to calculate the monthly payment: Payment is equal to (PV x I / (1 - (1 + i)(-n)).

Where PV is the loan's present value, I is its monthly interest rate (0.035 / 12), and n is the number of payments (15 years multiplied by 12 months every year = 180 months).

Applying the values provided, we obtain:

(136,000 x 0.002917) / (1 - (1 + 0.002917)(-180)) is the amount to be paid.

Amount paid: $1,054.63

Hence, the installment will be $1,054.63 per month.

(b) By deducting the loan amount (PV) from the total amount paid over the loan's lifetime, it is possible to get the total interest payment:

Total interest equals PV minus (Payment x n)

Applying the values provided, we obtain:

$1,054.63 multiplied by 180 equals $136,000 in interest.

Interest totaled $88,833.40.

The total interest payment will therefore be $88,833.40.

(c) The Turners will have paid 120 times over the course of 10 years (10 years x 12 months/year). To determine their equity, we can apply the formula for calculating a loan's remaining balance:

The remaining balance is calculated as follows: PV x (1 + i)n - Payment x (1 + i)n - 1)/i

Where n denotes how many payments are still due (180 - 120 = 60).

Applying the values provided, we obtain:

The remaining balance is calculated as follows: $136,000 x (1 + 0.002917)60 - $1,054.63 x (1 + 0.002917)60 - 0.002917

Balance remaining: $71,587.90

As a result, their equity will be $170,000 (the original purchase price) less $71,587.90 (the outstanding balance) = $98,412.10 after ten years.

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The coordinates of the point P is (-1,2) .

What is translation?

In mathematics, a translation is a geometric transformation that moves every point of a figure or a space by the same amount in a given direction. The amount and direction of the movement can be described using a vector, which is a mathematical object that has both magnitude and direction.

Finding the coordinates of the point P :

The coordinates of point P can be found by subtracting the vector from point Q.

To find the coordinates of point P, we need to subtract the vector [tex]\begin{pmatrix}4\\-3\end{pmatrix}[/tex] from the coordinates of point Q, which are (3, -1).

Subtracting the x-coordinate of the vector from the x-coordinate of point Q gives us:

3 - 4 = -1

Similarly, subtracting the y-coordinate of the vector from the y-coordinate of point Q gives us:

-1 - (-3) = 2

Therefore, the coordinates of point P are (-1, 2).

So, the correct answer is (C) (-1, 2).

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The dimensions of the triangle with maximum area are a base of 11 cm and a height of 11 cm.

We are given that the sum of the base and height of a triangle is 22 cm. Let's call the base of the triangle "b" and the height "h". Then we have the equation:

b + h = 22

We want to find the dimensions of the triangle that will give us the maximum area.

The formula for the area of a triangle is A = (1/2)bh.

We can use the equation b + h = 22 to solve for one of the variables in terms of the other.

we can solve for h:

h = 22 - b

Substituting this into the formula for the area, we get:

A = (1/2)b(22 - b)

The equation 0 = 11b - (1/2)b² can be rearranged to:

(1/2)b² - 11b = 0

We can then use the quadratic formula to solve for "b"

b = 11 ± 11

So the value of b that gives us the maximum area is b = 11 cm. Substituting this back into the equation h = 22 - b, we get:

h = 22 - 11 = 11 cm

Triangle has a base of 11 cm and a height of 11 cm.

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Answer:

36

Step-by-step explanation:

Answer:

Elise's average pay per hour for the year 2017 was £11.88.

Step-by-step explanation:

First, we need to calculate Elise's monthly salary in 2017 after the 3% increase:

3% of £2100 = 0.03 x £2100 = £63

Elise's new monthly salary in 2017 = £2100 + £63 = £2163

Next, we need to calculate her total earnings in 2017:

Total earnings = monthly salary x number of months worked

Elise worked for 45 weeks in 2017, which is approximately 10.4 months:

Total earnings = £2163 x 10.4 = £22,477.20

Finally, we can calculate her average pay per hour for the year:

Total number of hours worked = 42 hours/week x 45 weeks = 1890 hours

Average pay per hour = total earnings / total number of hours worked

Average pay per hour = £22,477.20 / 1890 hours = £11.88 per hour

Answer:

I got $13.73 per hour

Step-by-step explanation:

If you multiply 2100 by 12 months you get $25200 for an annual salary before percent increase.

Then you include the 3% salary increase each month 25200 x .03 = 756 then add the two 25200 + 756 = 25956 OR you can calculate the longer way by doing each individual month, either way it will be the same answer. 2100 x .03 = 63 then 2100 + 63 = 2163 then 2163 x 12 = 25956

Then you divide 25956 by the number of weeks worked in the year. 25956/45 = 576.8

So, each week $576.8 was earned.

Then to get an hourly rate, you divide this by the number of hours worked in each week. 576.8/42 = 13.73

So, the hourly rate is $13.73.

I hope this helped :)

The hotel served 306 gallons of orange juice this year.

To find the amount of orange juice served this year, we need to add 70% more of the amount served last year to the amount served last year. Let's denote the amount served last year as "x". Then we can set up the equation:

Simplifying this equation gives us:

We know from the problem that the amount served last year was 180 gallons. Plugging this into our equation, we get:

Simplifying this equation gives us:

Therefore, the hotel served 306 gallons of orange juice this year.

In summary, we used the information given in the problem to set up an equation and solve for the amount of orange juice served this year. We first found the amount served last year, and then added 70% more of that amount to get the total amount served this year.

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P(0 received correctly) = P(0 sent) × P(0 received correctly | 0 sent)= [tex](2/3) × 0.8= 0.5333[/tex] (rounded to 1 decimal place)Thus, the probability that a 0 is received is 0.5333 (rounded to 1 decimal place).

0.5333

A space probe near Neptune communicates with Earth using bit strings. Suppose that in its transmissions it sends a 1 one-third of the time and a 0 two-thirds of the time. When a 0 is sent, the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 1) is 0.2. When a 1 is sent the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 0) is 0.2.The probability that a 0 is received correctly is given in the problem as 0.8, and the probability that a 0 is sent is 2/3. Therefore, the probability that a 0 is received correctly

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The last two rows of the table should be completed as follows:

Input   Output

8       22.80

10      28.50

An algebraic expression is a mathematical phrase that contains numbers, variables, and operations. It is used to represent a single quantity or value, and can be written in terms of one or more variables.

The rule given is an algebraic expression, x, which is the input, multiplied by 2.85, which is the output. Using this information, we can determine the cost of 10 muffins.

To find the cost of 10 muffins, we can use the algebraic expression given. First, we will multiply 10, the number of muffins, by 2.85, the cost of one muffin. This gives us a total of 28.50. Therefore, the cost of 10 muffins is 28.50.

Using this same rule and process, we can also determine the cost of any number of muffins. For example, if we want to know the cost of 15 muffins, we can simply multiply 15 by 2.85, giving us a total of 42.75.

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Step-by-step explanation:

5x - 30 = 3x

2x = 30

x = 15

that's the answer

The coordinates of R are (-8,-1). To find the coordinates of R, we first need to find the length of PQ.

Using the distance formula, we have:

d(P,Q) = √((x2-x1)² + (y2-y1)²)

= √((-4-(-12))² + (-9-7)²)

= √(8² + (-16)²)

= √(320)

= 8 √(5)

Since PR:QR is 3:5, we can set up the following equation:

d(P,R)/d(R,Q) = 3/5

Let the coordinates of R be (x,y). We can use the midpoint formula to find the coordinates of the midpoint of PQ, which is also the coordinates of the point that divides PQ into two parts in the ratio of 3:5.

Midpoint of PQ = ((-12-4)/2, (7-9)/2) = (-8,-1)

Using the distance formula again, we can find the distance between P and R:

d(P,R) = (3/8) d(P,Q)

= (3/8) (8 √(5))

= 3 √(5)

Now we can use the ratio PR:QR = 3:5 to find the distance between R and Q:

d(R,Q) = (5/3) d(P,R)

= (5/3) (3 √(5))

= 5 √(5)

Finally, we can use the midpoint formula to find the coordinates of R:

x = (-12 + (3/8) (8))/2 = -8

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

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Complete Question:

The coordinates of the endpoints of bar (PQ) are P(-12,7) and Q(-4,-9). Point R is on bar (PQ) and divides it such that PR:QR is 3:5. What are the coordinates of R ?

Answer:

$196

Step-by-step explanation:

1 lb = 16oz

28 lbs x 16 = 448 ozs (in 28 lb bag)

448/8 = 56 (8 oz portions)

56 x $3.50= $196

Answer: 6.75

Step-by-step explanation:

45 x 0.15= 6.75

The soda can has an estimated volume of 1,026.72 cubic centimeters and an estimated surface area of 452.39 square centimeters.

To find the volume and surface area of a soda can with radius 6 cm and height 11 cm, we can use the formulas:

Volume of cylinder = πr²h

Surface area of cylinder = 2πrh + 2πr²

Substituting the given values, we get:

Volume = π × 6² × 11

Volume = 1,026.72 cubic centimeters (rounded to two decimal places)

Surface area = 2π × 6 × 11 + 2π × 6²

Surface area = 452.39 square centimeters (rounded to two decimal places)

Therefore, the volume of the soda can is approximately 1,026.72 cubic centimeters, and the surface area is approximately 452.39 square centimeters.

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Answer:

If the tires on Mavis’ car have to be replaced when they each have 160 000 km of wear, then the total distance Mavis can drive on a set of tires is:

4 tires * 160,000 km = 640,000 km

If Mavis drives 25,000 km in a year, she will need to replace her tires after:

640,000 km ÷ 25,000 km/year = 25.6 years

Since Mavis will need to replace her tires once every 25.6 years, the cost of the wear on her tires for a single year is:

$140.00/tire * 4 tires = $560.00

So the total cost of the wear on Mavis’ tires for a year in which she drives 25,000 km is $560.00.

Step-by-step explanation:

source: trust me bro

There are 48 toy soldiers, which is 6 x 8 of them.

The anger Eminem expresses in "Like Toy Soldiers" is a result of his personal beefs with rappers Ja Rule and Benzino, who was the editor of The Source at the time. The song, "Toy Soldiers," by Martika, was sampled on the 2004 release Encore.

Let's name Leo's collection of toy soldiers "x" the amount.

As a result of the problem statement, we are aware of:

There are no more when he arranges them in groups of four, proving that x is divisible by four.

Six remain after he divides them into groups of seven, proving that (x - 6) is divisible by seven.

He organizes them into fives. If there are still 3 after multiplying by 5, (x - 3) can be divided by 5.

We may create a system of equations based on these three conditions:

x = 4a (from the first condition)

x - 6 = 7b (from the second condition)

x - 3 = 5c (from the third condition)

where a, b, and c are integers.

4a - 6 = 7b

4a - 3 = 5c

Now we need to solve for a, b, and c.

7b = 4a - 6

7b + 6 = 4a

Since 7 and 4 are relatively prime, we know that (7b + 6) must be divisible by 4. Therefore, we can write:

7b + 6 = 4k

where k is some integer. Solving for b, we get:

b = (4k - 6) / 7

Since b is an integer, k must be 2, which gives us:

b = (4(2) - 6) / 7 = -1

We can try the next possible value of k, which is 3:

b = (4(3) - 6) / 7 = 0

x - 3 = 5c

6 - 3 = 5c

c = 1

6 divided by 4 is 1 with no remainder.

(6 - 6) divided by 7 is 0 with a remainder of 0.

(6 - 3) divided by 5 is 1 with a remainder of 0.

Therefore, the answer is 48, which is 6 times 8.

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The probability that at least 2 people believe that they have seen a ufo is 0.1937102445. The probability that exactly 1 person believes that he or she has seen a ufo is problem: P(X = 1) = 10C₁ (0.10) (0.90)⁹= 0.3874204890.

The probability that at least 2 people believe that they have seen a UFO would be 0.1937102445. For this we use the binomial distribution formula.

P(X ≥ 2) = 1 − P(X = 0) − P(X = 1)P(X = 0) = (9/10)¹⁰

P(X = 1) = 10C₁ (0.10) (0.90)⁹= 0.3874204890 (rounded to 10 decimal places)

P(X ≥ 2) = 1 − 0.3874204890 − 0.3486784401 = 0.1937102445 (rounded to 10 decimal places)

The probability that 2 or 3 people believe that they have seen a UFO would be 0.1937102445. Using the formula of binomial distribution again we can solve for the probability of this event.

P(2 ≤ X ≤ 3) = P(X = 2) + P(X = 3)P(X = 2) = 10C₂ (0.10)² (0.90)⁸= 0.1937102445 (rounded to 10 decimal places)

P(X = 3) = 10C₃ (0.10)³ (0.90)⁷= 0.0573956280 (rounded to 10 decimal places)

P(2 ≤ X ≤ 3) = 0.1937102445 + 0.0573956280 = 0.2511058725 (rounded to 10 decimal places)

The probability that exactly 1 person believes that he or she has seen a UFO would be 0.3874204890. Using the binomial distribution formula to solve this problem:

P(X = 1) = 10C₁ (0.10) (0.90)⁹= 0.3874204890 (rounded to 10 decimal places)

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The true statement is, Parameter values can be used within the method code block. (option e).

In computer programming, methods are used to group a set of instructions together that can be executed repeatedly. Parameters are used to pass values to a method so that the method can perform specific actions based on the values passed. Let's discuss the given statements one by one to determine which ones are true.

Parameter values can be used within the method code block.

This statement is true. Parameter values can be used within the method code block to perform specific actions. The parameter values can be manipulated or combined with other values to produce the desired result.

In summary, methods can be written with any number of parameters, and parameter values can be used within the method code block to perform specific actions. The number of parameters needed will depend on the specific task the method is designed to perform.

Hence the option (e) is correct.

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The answers to the questions (a) the proportion who graduated in the top 25 percent of their high school class will be 0.672 and (b) the ratio in favor of having graduated in the top 25 percent of their high school class is 2:3.

(a) For first-time college students, the proportion who graduated in the top 25 percent of their high school class (rounded to three decimal places) is 0.672.

(b) For transfer students, the ratio in favor of having graduated in the top 25 percent of their high school class is 0.67:1. It is said that 0.666666666666667 proportion graduated in the top 25 percent of their high school class. This can be simplified as follows:0.666666666666667=20/30=10/15=2/3. Therefore, the ratio in favor of having graduated in the top 25 percent of their high school class is 2:3.

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The sum of the angles of an N-sided convex figure is (n-2)*180 - a simple proof of which is just to decompose the figure into triangles, each of which has all of its vertices the same as three of the vertices of the original figure. (Cut a quadrilateral into two triangles along a diagonal, for instance).

So, a 7-sided figure has angles totaling 5*180 = 900. Now set up a simple equation:

3x + 4(x+15) = 900

7x + 60 = 900

7x = 840

x = 120

The figure has three angles of 120 degrees, and four angles of 135 degrees.

The total number of ways of selecting the committee is, therefore,40 x 39 x 38 x 37= 7,903,040

A class of 40 students select a committee from the class that consists of a president, a vice president, a treasurer, and a secretary in the following way:Step-by-step explanation:The number of ways that a class of 40 students can choose a committee consisting of a president, vice president, treasurer, and a secretary can be found by using the permutation formula.If we assume that the positions of the committee members are different, the number of ways can be calculated as follows:The number of ways of selecting the president from 40 students is 40.The number of ways of selecting the vice president from the remaining 39 students is 39.The number of ways of selecting the treasurer from the remaining 38 students is 38.The number of ways of selecting the secretary from the remaining 37 students is 37.The total number of ways of selecting the committee is, therefore,40 x 39 x 38 x 37= 7,903,040Thus, secretary.

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The cost of one small crate of apples is $12 and the cost of one large crate of peaches is $8. The cost of 7 small cates of apples and 5 large containers of peach is $126.

The system of equations that describe the question is:

3s + 10l = 116 equation 1

11s + 20l = 292 equation 2

Where:

s = cost of one small crate of apples

l = cost of one large crate of peaches

The elimination method would be used to determine the values of s and l.

Multiply equation 1 by 2

6s + 20l = 232 equation 3

Subtract equation 3 from equation 2:

5s = 60

Divide both sides of the equation by 5

s = 60 / 5

s = $12

Substitute for s in equation 1:

3(12) + 10l = 116

36 + 10l = 116

10l = 116 - 36

10l = 80

l = 80 / 10

l = 8

Cost of 7 small crates of apples and 5 large containers of peaches = (7 x 12) + (8 x 5) = $124

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Answer:

A=100

B= 80

C=80

D=100

E=80

F=80

G=100

Step-by-step explanation:

Answer:28

Step-by-step explanation:

Answer: 28

Explanation:  Look for a pattern or reason for the following number in the sequence. In this case 3+1=4, 4+3=7, 7+5=12, 12+7=19, so the probable answer is to add the following odd number to the last one in the line to get the next. (19+9=28)

Answer: Yes Sofia will have enough money

=======================================================

Explanation:

Refer to the drawing below. I've split the hexagon into two pieces. The bottom is a rectangle and the top is a trapezoid.

The area of the rectangle is 16*7 = 112 square meters.

The trapezoid has 16 as one of the parallel sides. The other side is x meters. We'll use the perimeter 54 to determine what x must be

sum of the exterior sides = perimeter

6+7+16+7+6+x = 54

42+x = 54

x = 54-42

x = 12

The top most side is 12 meters. This is the missing side of the trapezoid. The hexagon has a height of 12.66 meters, so the trapezoid's height must be 12.66-7 = 5.66 meters. Refer to the blue segment I marked in the drawing below.

area of the trapezoid = 0.5*height*(base1+base2)

area = 0.5*5.66*(16+12)

area = 79.24 square meters

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

Recap so far

The total area of the entire hexagon is therefore 112+79.24 = 191.24 square meters.

Let's convert that to square decimeters.

Recall that 1 decimeter = 10 centimeters

Multiply both sides by 10

1 decimeter = 10 centimeters

10*(1 decimeter) = 10*(10 centimeters)

10 decimeters = 100 centimeters

10 decimeters = 1 meter

Then,

[tex]191.24 \text{ sq m}= 191.24 \text{ sq m} * \frac{10 \text{ dm}}{1 \text{ m}} * \frac{10 \text{ dm}}{1 \text{ m}}\\\\= \frac{191.24*10*10}{1*1} \text{ sq dm}\\\\= 19124 \text{ sq dm}\\\\[/tex]

The entire lawn is 19124 square decimeters.

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We have one final block of calculations to determine the total price.

x = number of rolls

1 roll covers 90 square decimeters

x rolls cover 90x square decimeters

90x = 19124

x = 19124/90

x = 212.489 approximately

Round up to the nearest integer to get x = 213. It doesn't matter that 212.489 is closer to 212. We round up to clear the hurdle. It means we'll have leftover grass that isn't used (perhaps it could be handy to have some back up grass just in case mistakes are made, and some patches need to be redone).

In short, Sofia needs 213 rolls.

1 roll costs $4.50

213 rolls will cost 213*4.50 = 958.50 dollars.

This is under the $1000 threshold (with 1000-958.50 = 41.50 dollars to spare).

Sofia will have enough money to pay for all of the grass.