You buy two tickets to an escape room using a coupon for $5 off your entire purchase. You pay a total of $45. 15 which includes 7% sales tax. What is the original price of one ticket?

The correct answer is:p = 3 × 4

Let's write the equation for the given statement:

Randy baked 4 pies

Let the number of pies that Liza baked be p

Liza baked 3 times as many pies as Randy.

Thus, the equation for the above statement can be written as:

p = 3 × 4Simplifying the above equation we get:p = 12Thus, Liza baked 12 pies.

So, the equation that can be used to find how many pies Liza made is:

p = 3 × 4The equation can be simplified to p = 12.

Therefore, the correct answer is:p = 3 × 4

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Use the expression to complete the statements: (0.5)^(10) is the exponentiation of (0.5) and 10 is the base of (0.5)^10.

In the given expression, (0.5)^(10), we have a base of 0.5 and an exponent of 10.

Exponentiation is the mathematical operation of raising a base to a certain power. In this case, we are raising 0.5 to the power of 10.

To calculate the value, we multiply the base (0.5) by itself 10 times:

(0.5)^(10) = 0.5 * 0.5 * 0.5 * 0.5 * 0.5 * 0.5 * 0.5 * 0.5 * 0.5 * 0.5

When we perform the calculation, we find that (0.5)^(10) is equal to 0.0009765625.

Now let's move on to the second statement. The statement "10 is the base of (0.5)^10" means that the base of the expression (0.5) raised to the power of 10 is 10.

However, this statement is not correct. The base of the expression (0.5)^10 is actually 0.5, not 10. The base is the number that is raised to the exponent. In this case, 0.5 is being raised to the power of 10.

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To find the missing angles, we have to use the fact that the sum of the angles of a triangle is 180°. So, we add up the known angles, and then subtract the sum from 180°. For problem 3:Let x be the measure of the missing angle at the bottom right corner of the triangle.

We know that the other two angles are 65° and 43°.Therefore,x + 65° + 43° = 180°x + 108° = 180°x = 72°So the measure of the missing angle is 72°.For problem 4:Let y be the measure of the missing angle at the bottom left corner of the triangle. We know that the other two angles are 70° and 50°.Therefore,y + 70° + 50° = 180°y + 120° = 180°y = 60°So the measure of the missing angle is 60°.Hence, the measures of the missing angles for problems 3 and 4 are 72° and 60°, respectively.

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The price of a 40-pound bag of chicken feed would be approximately $23.98.

Yes, we can use proportional reasoning to find the price of a 40-pound bag of chicken feed based on the given information.

Let's set up a proportion to determine the price of the 40-pound bag:

50 pounds of chicken feed = $29.98

25 pounds of chicken feed = $15.49

Let's assume the price of the 40-pound bag is x dollars. We can set up the proportion as:

50 pounds / $29.98 = 40 pounds / x

To find the value of x, we can cross-multiply and solve for x:

50 * x = 40 * $29.98

50x = 1199.2

Dividing both sides of the equation by 50:

x = 1199.2 / 50

x = 23.98

Therefore, using proportional reasoning, the price of a 40-pound bag of chicken feed would be approximately $23.98.

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One and one/third times four and two/fifths` is equal to `88/15`.

To find the value of `one and one/third times four and two/fifths`, lets convert these mixed numbers to improper fractions, then multiply them and simplify the result :

Step 1: Converting mixed numbers to improper fractions`one and one/third` can be written as:

$$1\frac13 = \frac{3}{3}+\frac{1}{3}=\frac{4}{3}$$`

four and two/fifths` can be written as:

$$4\frac{2}{5}=4+\frac{2}{5}=\frac{20}{5}+\frac{2}{5}=\frac{22}{5}$$

Step 2: Multiplying the improper fractions$\frac43\times\frac{22}{5}=\frac{4\times 22}{3\times 5}=\frac{88}{15}$

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The answer to the expression "One and one-third times four and two-fifths" is 6/5.

To multiply fractions, follow these steps:

Step 1: Multiply the numerators together.

Step 2: Multiply the denominators together.

Step 3: Simplify the result obtained in step 1 and step 2 by reducing it to the lowest term possible.

Let's calculate the given expression:

One and one-third can be converted to an improper fraction by multiplying the denominator 3 by 1 and adding the numerator 1 to the product, which gives 4/3.

The same can be done with four and two-fifths. 5 is multiplied by 4, resulting in 20. Then, 2 is added to 20, resulting in 22/5.

Now we have:

One and one-third times four and two-fifths = 4(4) + 2 / 5(3) = 16 + 2 / 15 = 18/15 = 6/5

Therefore, the answer to the expression "One and one-third times four and two-fifths" is 6/5.

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The carnival is in town for 21 days, and to determine how many weeks it is in town, we use the equation 21 days ÷ 7 days/week = 3 weeks.

To find the number of weeks the carnival is in town, we need to divide the total number of days (21) by the number of days in a week (7). This can be represented by the equation of division operation:

Number of weeks = Total number of days ÷ Number of days in a week

Plugging in the values, we have:

Number of weeks = 21 days ÷ 7 days/week

Dividing 21 days by 7 days/week, we get:

Number of weeks = 3 weeks

Therefore, the carnival is in town for 3 week

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the correct answer is 2.39 ft, which corresponds to option 2.

To determine the height of the cylindrical rain barrel, which has a radius of 2 feet and holds 30 cubic feet of water, we need to solve for the height using the given information and the formula for the volume of a cylinder. The answer choices provided are: 1. 58 ft, 2. 39 ft, 3. 57 ft, and 4. 78 ft.

The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height. In this case, we are given the radius as 2 feet and the volume as 30 cubic feet.

Substituting the given values into the formula, we have:

30 = 3.14 * 2² * h

Simplifying the equation:

30 = 12.56 * h

h = 30 / 12.56

h ≈ 2.39 ft

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The correct inequality for the given condition is,

⇒ x + 75 ≥ 200

We have,

Minimum amount to be saved = $200

And, She has $75 saved.

Let x is the amount needed to reach her good.

Hence, The correct inequality for the given condition is,

⇒ x + 75 ≥ 200

Therefore, Option A is correct.

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Complete question is shown in attached image.

Marcus ends up paying $37.70 for the two shirts.

To calculate the final price, we need to follow these steps:

1. Calculate the discounted price of each shirt:

  - Shirt 1: $28.99 - 30% = $20.29

  - Shirt 2: $30.29 - 30% = $21.20

2. Apply the additional 10% off the already reduced prices:

  - Shirt 1: $20.29 - 10% = $18.26

  - Shirt 2: $21.20 - 10% = $19.08

3. Calculate the total cost of the shirts before tax:

  - Total cost = $18.26 + $19.08 = $37.34

4. Add the 6% sales tax:

  - Sales tax = 6% of $37.34 = $2.24

5. Calculate the final price including tax:

  - Final price = $37.34 + $2.24 = $39.58

Therefore, Marcus ends up paying $39.58 for the two shirts. None of the provided options match the calculated amount, so none of the given options are correct.

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The 11.43 minutes is less than 12 minutes, Jillian has a good chance of making the team. Therefore, Jillian might make the cross country team.

Jillian is trying for the cross country team. To make it she must run 3 1/2 miles in less than 40 minutes.

To find out if Jillian will make the cross country team, we must check if she can run 3 1/2 miles in less than 40 minutes. The time required for Jillian to run one mile is found by dividing 40 minutes by 3.5:40 / 3.5 = 11.43Jillian must complete one mile in 11.43 minutes to be eligible for the cross country team.

Since ,11.43 minutes is less than 12 minutes, Jillian has a good chance of making the team. Therefore, Jillian might make the cross country team.

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The circle in the equation p<-18 is open. In mathematical notation, the symbol "<" represents "less than." Therefore, the inequality p<-18 means that the value of p is less than -18.

When graphing this inequality on a number line, we use an open circle to represent the endpoint, which in this case is -18. An open circle indicates that the value of p cannot equal -18.

To understand this concept, consider the inequality p<5. In this case, the graph would show an open circle at 5, indicating that p can be any value less than 5 but not equal to 5. Similarly, in p<-18, the open circle at -18 signifies that p can take on any value less than -18 but cannot be equal to -18. This distinction is crucial when interpreting inequalities and their graphs.

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The function f(x) = 2x2 - x + 2 is continuous at x = 2, the correct option is C. Yes, because the function is defined at x = 2 and approaches y = 8 on the left and right sides of x = 2.

A continuous function is a type of function in mathematics that has no abrupt changes or breaks in its graph. It is a function where the values change smoothly as the input values vary. In other words, a function is continuous if its graph can be drawn without lifting the pen from the paper.

Given the function f(x) = 2x² - x + 2.

Determine whether the function is continuous at x = 2.

Explanation: For a function to be continuous at x = a, it must satisfy the following conditions:

1. The function must be defined at x = a.

2. The limit of the function at x = a must exist.

3. The limit of the function at x = a must be equal to the value of the function at x = a.

Let us verify these conditions for the given function

f(x) = 2x² - x + 2 at x = 2.

1. The function is defined at x = 2.

2. We need to calculate the left-hand limit and the right-hand limit of the function as x approaches 2.

Let us first calculate the left-hand limit:

lim f(x) as x → 2- = lim (2x² - x + 2)

as x → 2- = 2(2)² - 2 + 2

= 6

Now, let us calculate the right-hand limit:

lim f(x) as x → 2+ = lim (2x² - x + 2)

as x → 2+ = 2(2)² - 2 + 2

= 6

Since both the left-hand limit and the right-hand limit of the function exist and are equal to 6, the limit of the function at x = 2 exists and is equal to 6.

3. We need to verify whether the limit of the function at x = 2 is equal to the value of the function at x = 2.

Let us calculate the value of the function at x = 2:

f(2) = 2(2)² - 2 + 2

= 8

Since the limit of the function at x = 2 is equal to the value of the function at x = 2,

we can say that the given function f(x) = 2x² - x + 2 is continuous at x = 2.

Thus, the correct option is C.

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Davidson has just arrived at the foothills of the Rockies and is on a cross-country motorcycle trip. He intends to take an hour longer on the east side of the 245 km trip than on the west side of the 225 km trip. On the downhill side, he intends to average 20 km/h more to achieve this. The trip through the Rockies will take approximately 17.375 hours.

Let the speed of the motorcycle on the west side of the trip be x km/h.

So, the time required to complete the 225 km trip will be:

Time for the west side of the trip = 225/x

Let the speed of the motorcycle on the east side of the trip be x + 20 km/h.

So, the time required to complete the 245 km trip will be:

Time for the east side of the trip = 245 / (x + 20)

We know that the time Davidson takes on the east side of the trip will be an hour longer than on the west side. Therefore, we can form the following equation:

245/(x + 20) = 225/x + 1

Multiplying both sides by x(x + 20),

we get:245x = 225(x + 20) + x(x + 20)

Simplifying the equation:20x = 400x = 20 km/h

Time taken on the west side of the trip is 225/20 = 11.25 hours

Time taken on the east side of the trip is 245/40 = 6.125 hours

So the total time for the trip through the Rockies is 11.25 + 6.125 = 17.375 hours, or about 17 hours and 22.5 minutes (rounded to the nearest minute).

Therefore, the trip through the Rockies will take approximately 17.375 hours.

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Based on the information given, the combination of loaves of zucchini bread and banana bread that Hayley can make is option D: 4 loaves of zucchini bread and 6 loaves of banana bread.

To determine the possible combinations, we need to ensure that Hayley has enough sugar and butter for each loaf. Let's analyze the options:

Option A: 8 loaves of zucchini bread and 4 loaves of banana bread

This combination requires a total of 8 cups of sugar and 8 sticks of butter, which exceeds Hayley's available supply.

Option B: 6 loaves of zucchini bread and 8 loaves of banana bread

This combination requires a total of 14 cups of sugar and 12 sticks of butter, which exceeds Hayley's available supply.

Option C: 2 loaves of zucchini bread and 12 loaves of banana bread

This combination requires a total of 16 cups of sugar and 16 sticks of butter, which exceeds Hayley's available supply.

Option D: 4 loaves of zucchini bread and 6 loaves of banana bread

This combination requires a total of 12 cups of sugar and 10 sticks of butter, which can be accommodated within Hayley's available supply.

Hence, option D is the correct combination based on the given quantities of sugar and butter.

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The range of the function g(x) = x^2 - 2, when the domain is {-2, -1, 1, 3}, is C. {-7, -2, -1, 1}.

To find the range of the function g(x) = x^2 - 2, we need to substitute each value from the given domain into the function and observe the corresponding outputs.

For x = -2, g(-2) = (-2)^2 - 2 = 4 - 2 = 2.

For x = -1, g(-1) = (-1)^2 - 2 = 1 - 2 = -1.

For x = 1, g(1) = (1)^2 - 2 = 1 - 2 = -1.

For x = 3, g(3) = (3)^2 - 2 = 9 - 2 = 7.

Thus, when the domain is {-2, -1, 1, 3}, the corresponding range values are {-7, -2, -1, 1}. Therefore, the correct option is C. {-7, -2, -1, 1}.

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The specific solutions to the equation cos θ = sin θ on the interval [0, 2π) are θ = 0, π, 2π, 3π.

To find the specific solutions to the equation cos θ = sin θ on the interval [0, 2π), we can use trigonometric identities and properties.

Let's rewrite the equation cos θ = sin θ as sin θ - cos θ = 0.

We know that sin θ = cos (π/2 - θ) from the complementary angle identity.

So, we can rewrite the equation as sin θ - sin (π/2 - θ) = 0.

Using the identity sin A - sin B = 2 sin((A - B)/2) cos((A + B)/2), we get:

2 sin((θ - (π/2 - θ))/2) cos((θ + π/2 - θ)/2) = 0.

Simplifying further:

2 sin(θ/2) cos(π/4) = 0.

Since cos(π/4) = 1/√2 is a nonzero constant, the equation reduces to:

sin(θ/2) = 0.

Now, we need to find the values of θ/2 that make sin(θ/2) = 0.

Sin(θ/2) = 0 when θ/2 = 0, π, 2π, 3π, ...

So, θ = 0, π, 2π, 3π are the specific solutions to the equation cos θ = sin θ on the interval [0, 2π).

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The length of AD, denoted as x, is less than 3/2.

Let's denote the length of AD as x.

According to the given information:

AB is 4 times as large as AD, so AB = 4x.

AC is 3 more than AD, so AC = x + 3.

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Applying this rule to triangle ABC, we can set up the following inequalities:

AD + AC > AB

x + (x + 3) > 4x

Simplifying the inequality:

2x + 3 > 4x

Subtracting 2x from both sides:

3 > 2x

Dividing both sides by 2:

3/2 > x

Therefore, the length of AD, denoted as x, is less than 3/2.

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A polynomial in standard form with a degree of 6 and only complex solutions can be represented as P(x) = (x - z₁)(x - z₂)(x - z₃)(x - z₄)(x - z₅)(x - z₆), where z₁, z₂, z₃, z₄, z₅, and z₆ are complex numbers.

A polynomial in standard form with a degree of 6 is written as P(x) = a₆x⁶ + a₅x⁵ + a₄x⁴ + a₃x³ + a₂x² + a₁x + a₀, where a₆ ≠ 0 and a₀, a₁, a₂, a₃, a₄, a₅, and a₆ are coefficients.

To ensure that the polynomial has only complex solutions, we need to make sure that all of its roots are complex numbers.

Complex numbers have the form a + bi, where a and b are real numbers and i is the imaginary unit (√(-1)).

By factoring the polynomial into linear factors, we can ensure that each factor (x - zᵢ) contributes a complex root.

Here, z₁, z₂, z₃, z₄, z₅, and z₆ represent complex numbers.

Since the polynomial has a degree of 6, we need six complex factors to form the polynomial.

The product of these factors will give us the desired polynomial with complex solutions.

Therefore, the polynomial in standard form with a degree of 6 and only complex solutions can be represented as P(x) = (x - z₁)(x - z₂)(x - z₃)(x - z₄)(x - z₅)(x - z₆), where z₁, z₂, z₃, z₄, z₅, and z₆ are complex numbers.

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The cost of a carton of milk is a) $0.35.

To find the cost of a carton of milk, we can set up a system of equations based on the given information.

Let's assume the cost of a hamburger is "h" and the cost of a carton of milk is "m".

From the information given, we can create the following equations:

Equation 1: 2h + 1m = 2.85 (from Monday's purchase)

Equation 2: 3h + 2m = 4.45 (from Tuesday's purchase)

We can solve this system of equations to find the value of "m", the cost of a carton of milk.

Multiplying Equation 1 by 2 and Equation 2 by 1, we can eliminate "h" and solve for "m":

4h + 2m = 5.70

3h + 2m = 4.45

Subtracting Equation 2 from Equation 1, we get:

(4h + 2m) - (3h + 2m) = 5.70 - 4.45

h = 1.25

Now, we can substitute the value of "h" back into Equation 1 or Equation 2 to find the value of "m":

2(1.25) + 1m = 2.85

2.50 + m = 2.85

m = 2.85 - 2.50

m = 0.35

Therefore, the cost of a carton of milk is $0.35.

The correct answer is option a) $0.35.

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Answer: The given function is y = f(x), defined as follows:

f(x) = x^2 * sin(4x) + 36, if x ≠ 0

f(x) = 0, if x = 0

The function f(x) combines the quadratic function x^2 with the sinusoidal function sin(4x), and then adds a constant term of 36.

For x ≠ 0, the function f(x) is determined by the product of x^2 and sin(4x), with an additional constant term of 36.

For x = 0, the function f(x) is simply equal to 0.

The domain of the function is (-∞, ∞), meaning it is defined for all real numbers.

If you have any specific questions or require further analysis of the function, please let me know and I'll be glad to assist you.

To calculate the earnings per share, we need to divide the company's profit by the number of outstanding shares. The given information includes the company's profit of $117,667,008 and the share price of $56.97.

To determine the earnings per share, we need to know the number of outstanding shares. Since the number of outstanding shares is not provided in the given information, it is not possible to calculate the earnings per share with the given data alone.

The earnings per share (EPS) is calculated by dividing the company's profit by the number of outstanding shares. It represents the portion of the company's profit that is allocated to each outstanding share. By dividing the profit by the number of shares, we can determine how much profit is attributable to each individual share.

However, without the number of outstanding shares, we cannot calculate the exact earnings per share. The market capitalization and current share price do not provide enough information to determine the number of shares outstanding. Additional information, such as the number of shares issued by the company, is needed to calculate the earnings per share accurately.

In summary, the earnings per share cannot be determined with the given information alone. The calculation requires the number of outstanding shares, which is not provided. The earnings per share is a measure of the company's profitability allocated to each share, obtained by dividing the company's profit by the number of outstanding shares. To calculate the earnings per share accurately, the number of shares outstanding must be known.

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To find out the total combined area of the living room and deck of the Bain's house, we first need to know the area of the living room and the deck. Once we have found out the areas of both, we can then add them up to get the total combined area.

Area of the living room: The area of a rectangle is calculated by multiplying its length by its width. If the length and width of the living room are 20 feet and 15 feet respectively, then the area of the living room will be: Area of the living room = Length × Width= 20 ft × 15 ft= 300 ft²Area of the deck: The area of a rectangle is calculated by multiplying its length by its width. If the length and width of the deck are 12 feet and 10 feet respectively, then the area of the deck will be: Area of the deck = Length × Width= 12 ft × 10 ft= 120 ft²Total combined area of the living room and deck: Now that we know the area of the living room and the deck, we can add them together to get the total combined area of the living room and deck .Total combined area of the living room and deck= Area of the living room + Area of the deck= 300 ft² + 120 ft²= 420 ft²Therefore, the total combined area of the living room and deck of the Bain's house is 420 square feet.

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To identify the beverage that consistently yielded the highest profit according to the Smith's BBQ Report, we need to compare the profit margins of liquor, beer, and wine. By analyzing the profit margins over time, we can determine which beverage consistently had the highest margin, indicating the highest profit.

To determine which beverage consistently yielded the highest profit, we need to analyze the data provided in the Smith's BBQ Report. The report likely includes information on the sales and profits generated from liquor, beer, and wine. By comparing the profit margins of each beverage over a period of time, we can identify the one that consistently yielded the highest profit.

1. Analyzing profit margins: To determine the beverage with the highest profit, we examine the profit margins for liquor, beer, and wine. Profit margin is calculated by subtracting the cost of goods sold (COGS) from the revenue and dividing the result by the revenue. By comparing the profit margins of each beverage, we can identify which one consistently had the highest margin.

For example, if the profit margin for beer is consistently higher than that of liquor and wine across different time periods, it suggests that beer consistently yielded the highest profit. The profit margin analysis would provide insights into the beverage that generated the most profit for Smith's BBQ consistently.

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Emma is using x fence panels along the width of her garden. We need to find expressions for f(x), the width of her garden in feet, and g(x), the length of her garden in feet.

To find an expression for f(x), the width of Emma's garden, we need to determine how the number of fence panels (x) relates to the width. Assuming each fence panel has a fixed width, we can express f(x) as:

f(x) = x * width of each fence panel

The width of each fence panel may vary depending on the specific measurements provided. For example, if each fence panel has a width of 4 feet, then the expression for f(x) becomes:

f(x) = 4x

To find an expression for g(x), the length of Emma's garden, we need additional information or assumptions. The given information does not specify how the number of fence panels along the width relates to the length of the garden. Without this information, we cannot determine a specific expression for g(x).

In summary, we can express the width of Emma's garden, f(x), by multiplying the number of fence panels (x) by the width of each fence panel. However, we cannot determine a specific expression for the length of her garden, g(x), without additional information or assumptions.

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Complete question:

Emma wants to enclose her rectangular garden with fence panels. If she uses x fence panels along the width of her garden, find an expression for f(x), the width of her garden in feet.

f(x) = ?

"Next, find an expression for g(x), the length of her garden, in feet.

g(x) = ?

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The area of the figure is given by 34cm²

The figure is made up of  triangle and a square.

The area of the figure is given by area of the square + area of the triangle

The area of a triangle is the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 b h. This formula is applicable to all types of triangles, whether it is a scalene triangle, an isosceles triangle, or an equilateral triangle

area of triangle = 1/2bh

Area of triangle = 1/2*10*6

Area = 30 com²

But the area of the square is S²

Where s = side

Area of square = 2*2 = 4cm²

therefore area of the shape is( 4+30)cm² = 34cm²

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The 27th term of the arithmetic sequence with the first term [tex]\(a_1 = -13\)[/tex] and a common difference of 4 is 91.

To find the 27th term of an arithmetic sequence, we can use the formula:

[tex]\[a_n = a_1 + (n - 1)d\][/tex]

where [tex]\(a_n\)[/tex] represents the [tex]\(n\)[/tex]th term, [tex]\(a_1\)[/tex] is the first term, [tex]\(d\)[/tex] is the common difference, and [tex]\(n\)[/tex] is the term number.

Given that [tex]\(a_1 = -13\)[/tex] and the common difference [tex]\(d = 4\)[/tex], we will simply substitute these values into the given formula:

[tex]\[a_{27} = -13 + (27 - 1) \cdot 4\][/tex]

Simplifying the equation, we have:

[tex]\[a_{27} = -13 + 26 \cdot 4\][/tex]

Calculating the expression, we get:

[tex]\[a_{27} = -13 + 104\][/tex]

Finally, evaluating the sum, we find:

[tex]\[a_{27} = 91\][/tex]

Therefore, the 27th term of the arithmetic sequence with the first term [tex]\(a_1 = -13\)[/tex] and a common difference of 4 is 91.

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The length of the midsegment LM in Trapezoid ABCD is 85.5 units. The length of the midsegment is equal to the average of the lengths of the two bases.

In a trapezoid, the midsegment is a line segment that connects the midpoints of the two non-parallel sides. The length of the midsegment is equal to the average of the lengths of the two bases.

Given that AB = 46 and DC = 125, we can find the length of the midsegment (LM) by calculating the average of these two values.

LM = (AB + DC) / 2

LM = (46 + 125) / 2

LM = 171 / 2

LM = 85.5

Therefore, the length of the midsegment LM in Trapezoid ABCD is 85.5 units.

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To determine the missing term in the perfect square trinomial, we need to look at the pattern and properties of perfect square trinomials.

A perfect square trinomial has the form (a ± b)^2 = a^2 ± 2ab + b^2. In this case, we have x^2 + 40x + 100, which fits the form of a perfect square trinomial.

We can identify the missing term by finding the square of half of the coefficient of the linear term, which in this case is 40. Half of 40 is 20, and squaring 20 gives us 400.

So, the missing term is 400. The complete perfect square trinomial is:

x^2 + 40x + 400

Therefore, the missing term in the perfect square trinomial x^2 + 40x + 100 is 400.

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In 175 graduants, 100 could be expected to seek higher education

From the question, we have the following parameters that can be used in our computation:

Rate = 4 out of every 7 graduating seniors

Graduating seniors = 175

using the above as a guide, we have the following:

Higher education seeker = Rate * Graduating seniors

Substitute the known values in the above equation, so, we have the following representation:

Higher education seeker = 4/7 * 175

Evaluate

Higher education seeker = 100

Hence, 100 could be expected to seek higher education

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After comparing the two sets, we find that 6 and 12 are the common elements of A and B. Therefore, the intersection of A and B is {6, 12}.

The set A is the set of multiples of 3 between 1 and 15 inclusive which are 3, 6, 9, 12, and 15.  The set B is the set of even natural numbers up to and including 20. The set B is {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}.To find A ∩ B, we must determine the elements that A and B have in common. The common elements of A and B are 6 and 12. Thus, the intersection of A and B, A ∩ B, is {6, 12}. To find the intersection of sets A and B, we look for the common elements in the two sets. The set A is the set of multiples of 3 between 1 and 15, while the set B is the set of even natural numbers up to and including 20.

Therefore, we have A = {3, 6, 9, 12, 15} and B = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}. The intersection of the two sets A and B is the set of elements they share in common. Therefore, we have to look for elements that appear in both sets. After comparing the two sets, we find that 6 and 12 are the common elements of A and B. Therefore, the intersection of A and B is {6, 12}.

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