henry gets pic 'n mix when at the cinema and makes his bag up with 3 types of sweet. He picks 3 times as many smarties as cola bottles. He also picks twice as many marshmallows as smarties. What proportion of the bag of sweets are marshmallows

The selling price of the novel would be Rs 375. The bookseller should sell the novel for Rs 375 to earn a profit of 25%. Profit percentage is a measure of the profit earned as a percentage of the cost price.

In this case, the bookseller earns a profit of 25%. To calculate the selling price, we need to determine the profit earned and add it to the cost price.

To find the profit earned, we multiply the cost price by the profit percentage. In this case, the cost price of the novel is given as Rs 300, and the profit percentage is 25%. To calculate the profit, we multiply Rs 300 by (25/100) or 0.25. The result is Rs 75, indicating that the bookseller earns a profit of Rs 75.

To obtain the selling price, we add the profit to the cost price. In this case, the cost price is Rs 300, and the profit is Rs 75. Adding them together, we get Rs 375 as the selling price of the novel.

To calculate the selling price, we need to determine the profit earned by the bookseller and add it to the cost price.

Given:

Profit percentage = 25%

Cost price of the novel = Rs 300

To calculate the profit, we multiply the cost price by the profit percentage:

Profit = 25% of Rs 300 = (25/100) * 300 = Rs 75

The selling price is obtained by adding the profit to the cost price:

Selling price = Cost price + Profit = Rs 300 + Rs 75 = Rs 375.

Therefore, the selling price of the novel is Rs 375.

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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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Based on the given information, it takes approximately 37 years for the balance to quadruple when depositing $400 in an account that pays 3.75% annual interest compounded monthly.

To determine the time it takes for the balance to quadruple, we can use the formula for compound interest:

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

Where:

A = final amount

P = principal amount (initial deposit)

r = annual interest rate (as a decimal)

n = number of times interest is compounded per year

t = time in years

In this case, we have:

P = $400

r = 3.75% or 0.0375 (as a decimal)

n = 12 (monthly compounding)

We want to find t, the time it takes for the balance to quadruple, so A = 4P.

4P = P(1 + r/n)^(nt)

Dividing both sides by P:

4 = (1 + r/n)^(nt)

Taking the natural logarithm of both sides:

ln(4) = nt * ln(1 + r/n)

Solving for t:

t = ln(4) / (n * ln(1 + r/n))

Plugging in the given values:

t ≈ ln(4) / (12 * ln(1 + 0.0375/12))

Calculating this, we find:

t ≈ 37 years

Therefore, it takes approximately 37 years for the balance to quadruple in this scenario.

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You deposit $400 in an account that pays 3.75% annual interest compounded monthly. About how long does it take for the balance to quadruple?

A. 26.2 years

B. 32.5 years

c. 37 years

The value of function at x = 36 is 34.12.

To find the cost of mailing an object that weighs 36 pounds, we can substitute the value of x into the function f(x) = 5.32 + 0.80x.

The function f(x) = 5.32 + 0.80x represents a linear relationship between the weight of the object (x) and the cost (f(x)) with a base cost of $5.32 and an additional cost of $0.80 per pound. By plugging in the value of 36 into the function, we can calculate the specific cost for that weight.

Plugging in x = 36, we have:

f(36) = 5.32 + 0.80 * 36

Simplifying the expression:

f(36) = 5.32 + 28.8

f(36) = 34.12

Therefore, f(36) is equal to 34.12. This means that it would cost $34.12 to mail an object weighing 36 pounds according to the given function.

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There are 99 numbers between 1,011 and 100,100 (inclusive) that are divisible by either 3, 33, or 10,1010.

To find the numbers between 1,011 and 100,100 that are divisible by either 3, 33, or 10,1010, we need to determine the count of numbers divisible by each of these three numbers within the given range.

For a number to be divisible by 3, the sum of its digits must be divisible by 3. Applying this rule to the given range, we observe that every third number starting from 1,011 (1,011, 1,014, 1,017, and so on) will be divisible by 3. Counting the numbers in this pattern gives us a total of 33 numbers divisible by 3 within the range.

Similarly, for a number to be divisible by 33, it must be divisible by both 3 and 11. Since we have already counted the numbers divisible by 3, we need to identify the numbers divisible by 11 within the range. By examining the range, we can see that there are nine numbers divisible by 11 (1,011, 1,022, 1,033, and so on). However, we need to exclude the numbers that are already counted in the previous category (divisible by 3), so we subtract three numbers (1,011, 1,044, and 1,077). This gives us a total of six additional numbers divisible by 33.

Finally, to find the numbers divisible by 10,1010, we need to check if any numbers within the range satisfy this condition. Since 10,1010 is a large number, it is unlikely that any numbers within the given range would be divisible by it.

Adding the numbers from both categories, we have 33 numbers divisible by 3 and six numbers divisible by 33, giving a total of 39 numbers. Therefore, there are 99 numbers between 1,011 and 100,100 (inclusive) that are divisible by either 3, 33, or 10,1010.

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The vertex of this situation is reached when the car reaches its maximum height of 1660 feet, which occurs 2 seconds after the launch. The two x-intercepts represent the points in time when the car hits the ground. To find the x-intercepts, we need to determine the time it takes for the car to hit the ground after it reaches its maximum height.

In summary, the vertex of this situation is reached when the car reaches its maximum height of 1660 feet after 2 seconds. The two x-intercepts represent the times when the car hits the ground.

Now, let's explain the answer in more detail. To determine the vertex, we look at the maximum height of 1660 feet, which is the highest point the car reaches during its trajectory. This occurs 2 seconds after the launch. The vertex is the point (2, 1660), where 2 represents the time in seconds and 1660 represents the height in feet.

Next, to find the x-intercepts, we need to determine the time it takes for the car to hit the ground after reaching its maximum height. Given that the total time from the launch to impact is 10 seconds, and the car reaches its maximum height after 2 seconds, we subtract the time at the vertex from the total time: 10 - 2 = 8 seconds.

Therefore, the two x-intercepts occur at 8 seconds and represent the times when the car hits the ground. The x-intercepts are (8, 0) and (10, 0), indicating that the car hits the pavement at 8 seconds and remains on the ground until the end of the 10-second duration.

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The sample statistic for the proportion of voters surveyed who said they'd vote for Brown is 0.528.

In this question, we need to find the sample statistic for the proportion of voters surveyed who said they'd vote for Brown. The given data is: N = 9600 (registered voters)Poll result: Brown = 243, Feliz = 217 ,Undecided = 40Total = 500.We can find the sample proportion of voters who said they'd vote for Brown by dividing the number of people who said they'd vote for Brown by the total number of people who responded to the poll (excluding those who were undecided).Therefore, the sample proportion for Brown is: 243/(243+217) = 0.528Sample proportion for Brown is 0.528.

Thus, the sample statistic for the proportion of voters surveyed who said they'd vote for Brown is 0.528. It is a decimal rounded to 3 decimal places.

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The original cost of the curling iron was approximately $90.82.

Jema had a 45% coupon for a new curling iron, which means she was eligible for a discount of 45% on the original cost of the curling iron. The final price she paid after the discount was $49.95. To find out the original cost of the curling iron, we can use the formula:

Original cost = Final price / (1 - Discount rate)

In this case, since the discount rate is 45%, or 0.45 as a decimal, the formula becomes:

Original cost = $49.95 / (1 - 0.45)

Original cost = $49.95 / 0.55

Original cost ≈ $90.82

Therefore, the original cost of the curling iron was approximately $90.82.

This calculation shows that Jema took advantage of a significant discount on the original cost of the curling iron. By using the coupon, she was able to save around $41.87 on the purchase. This demonstrates the importance of looking for discounts and deals when shopping, as they can help save money and get more value for your purchases.

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Bicarbonate ions are formed when carbon dioxide combines with water. This reaction neutralizes the hydrogen ions, keeping the pH within the proper range. In conclusion, the bicarbonate ion is formed when carbon dioxide reacts with water. The bicarbonate buffer system is important in maintaining the body's pH balance.

Bicarbonate is a polyatomic anion with the chemical formula HCO₃−. Bicarbonate can form by combining water with carbon dioxide (CO2). The bicarbonate ion, HCO₃-, is formed when CO2 reacts with water, which causes a small amount of it to become bicarbonate ions. This reaction is extremely important in maintaining the pH of blood, and thus the proper functioning of the body.Bicarbonate ions play a significant role in buffering the body's pH balance. They act as a pH regulator in blood and other bodily fluids. The body needs to maintain a pH between 7.35 and 7.45 in order to maintain optimal health. When carbon dioxide in the body mixes with water, it produces carbonic acid, which can lead to a decrease in pH. The bicarbonate buffer system maintains the pH within the healthy range. The system works by converting carbon dioxide into bicarbonate ions, which then bind with excess hydrogen ions to form carbonic acid. This reaction neutralizes the hydrogen ions, keeping the pH within the proper range.

Bicarbonate is a chemical that contains three atoms: carbon, hydrogen, and oxygen. Bicarbonate is a polyatomic anion with the chemical formula HCO₃−. Bicarbonate can form by combining water with carbon dioxide (CO2).The bicarbonate ion, HCO₃-, is formed when CO2 reacts with water, which causes a small amount of it to become bicarbonate ions. This reaction is extremely important in maintaining the pH of blood, and thus the proper functioning of the body.Bicarbonate ions play a significant role in buffering the body's pH balance. They act as a pH regulator in blood and other bodily fluids. The body needs to maintain a pH between 7.35 and 7.45 in order to maintain optimal health. When carbon dioxide in the body mixes with water, it produces carbonic acid, which can lead to a decrease in pH. The bicarbonate buffer system maintains the pH within the healthy range. The system works by converting carbon dioxide into bicarbonate ions, which then bind with excess hydrogen ions to form carbonic acid.

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If the sum of the fractions is less than 1, the denominator could be any number greater than 10. If the sum is equal to 1, the denominator must be 10. If the sum is greater than 1, the denominator must be less than 10.

To find a denominator that satisfies the given conditions, we can consider the fractions with numerators 8 and 2. If the sum of these fractions is less than 1, the denominator could be any number greater than 10. If the sum is equal to 1, the denominator must be 10. If the sum is greater than 1, the denominator must be less than 10.

To determine the possible denominators that satisfy the conditions, we need to consider the given numerators of 8 and 2. Since the fractions have the same denominator, let's denote it as 'd'. The fractions can be written as 8/d and 2/d.

If the sum of these fractions is less than 1, we have:

8/d + 2/d < 1

Combining the fractions, we get:

(8 + 2)/d < 1

Simplifying, we have:

10/d < 1

To satisfy this inequality, the denominator 'd' can be any number greater than 10. For example, if we choose d = 11, the fractions become 8/11 and 2/11, and their sum is 10/11, which is less than 1.

If the sum of the fractions is equal to 1, we have:

8/d + 2/d = 1

Combining the fractions, we get:

10/d = 1

Solving for 'd', we find that the denominator must be 10. For example, if we choose d = 10, the fractions become 8/10 and 2/10, and their sum is 10/10, which is equal to 1.

If the sum of the fractions is greater than 1, we have:

8/d + 2/d > 1

Combining the fractions, we get:

10/d > 1

To satisfy this inequality, the denominator 'd' must be less than 10. For example, if we choose d = 9, the fractions become 8/9 and 2/9, and their sum is 10/9, which is greater than 1.

In summary, if the sum of the fractions is less than 1, the denominator could be any number greater than 10. If the sum is equal to 1, the denominator must be 10. If the sum is greater than 1, the denominator must be less than 10.

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the correct inequality that shows Annika's spending in terms of h is 35h + 180 ≤ 400.To express Annika's spending in terms of h, the number of hours the DJ can be at the party, we can set up an inequality by considering the total cost.

Let's represent Annika's spending on the DJ as 35h, where h is the number of hours. Additionally, we know Annika plans to spend $180 on decorations. Therefore, the total cost should be no more than $400.

The inequality can be written as:

35h + 180 ≤ 400

This inequality states that the cost of hiring the DJ (35h) plus the cost of decorations ($180) should be less than or equal to $400.

Therefore, the correct inequality that shows Annika's spending in terms of h is 35h + 180 ≤ 400.

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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 given equation is I = -2OD where I is the intensity of light, O is the aperture of the lens and D is the distance between the lens and the object. This equation is known as the Inverse Square Law of Light.

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The correct polynomial product is indeed Option B: 6y^3 + 17y^2 + 22y + 15.

Let's break down the options to see why Option B is correct:

Option A: 15y^3 + 17y^2 + 22y + 15

This option does not match the given product as it includes an additional term, 15y^3, that is not present in the correct polynomial product.

Option B: 6y^3 + 17y^2 + 22y + 15

This option matches the given polynomial product exactly. It includes all the terms and coefficients mentioned: 6y^3, 17y^2, 22y, and 15.

Option C: 6y^3 + 20y^2 + 22y + 15

This option differs from the correct product in the coefficient of the second term. It includes 20y^2 instead of 17y^2.

Option D: 6y^3 + 17y^2 + 22y + 25

This option differs from the correct product in the coefficient of the last term. It includes 25 instead of 15.

Therefore, Option B, 6y^3 + 17y^2 + 22y + 15, is the correct polynomial product based on the given information.

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The expression that represents the width of the rectangle in yards, given the area and length, is option C: 4x^3y^4.

To determine the width of the rectangle, we divide the area by the length. In this case, the area is 36x^(7y^(5)) and the length is 9x^4y. Dividing the area by the length will cancel out the common factors and leave us with the remaining factors representing the width.

When we divide 36x^(7y^(5)) by 9x^4y, we divide the coefficients (36/9 = 4) and subtract the exponents of the variables (x^(7-4) = x^3, y^(5-1) = y^4). Therefore, the width of the rectangle is 4x^3y^4, which matches option C.

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The value of the variables for which ABCD must be a parallelogram include the following:

x = 4.

y = 5.

In order for any quadrilateral to be considered as a parallelogram, two pairs of its parallel sides must be equal (congruent). This ultimately implies that, the diagonals of a parallelogram would bisect one another only when their midpoints are the same:

Line segment AC = Line segment BD

Next, we would write an equation to model the length of the diagonals of this parallelogram as follows;

4x - 2 = 3y - 1  .........equation 1.

3y - 3 = 3x       .........equation 2.

From equation 2, we have the following:

y - 1 = x       .........equation 3.

By substituting equation 3 into equation 1, we have:

4(y - 1) - 2 = 3y - 1

4y - 4 - 2 = 3y - 1

4y - 3y = 6 - 1

y = 5.

For the value of x, we have:

x = y - 1

x = 5 - 1

x = 4

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Complete Question:

Find values of x and y for which ABCD must be a parallelogram.

He travels: (i) C is 4 km north of A. (ii) C is 6 km east of A.

(i) North of A:

The northward component from A to B is 8 km on a bearing of N30°E. To find the northward distance, we can use trigonometry. Since the bearing is N30°E, we can split it into two right-angled triangles: one facing north and one facing east.

In the northward triangle:

Opposite side = 8 km * sin(30°)

Opposite side = 8 km * 0.5

Opposite side = 4 km

Therefore, C is 4 km north of A.

(ii) East of A:

The eastward component from B to C is 6 km due East. Since this distance is directly east, it does not change the eastward position of C relative to A. Therefore, C is 6 km east of A.

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Let's denote the cost of each coffee as 'c'.Neveah bought a cupcake for $5, which we can represent as 5.

She also bought coffees for 5 coworkers, so the total cost of the coffees can be represented as 5c.

The total amount Neveah spent is $35.

Putting it all together, we can set up the equation:

5 + 5c = 35

To solve for 'c', we can isolate the variable by subtracting 5 from both sides:

5c = 30

Then, we divide both sides by 5 to solve for 'c':

c = 30/5

Simplifying the expression, we find that each coffee costs $6.

Therefore, each coffee was bought for $6.

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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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If Vangs drives for 2 hours at a speed of 65 miles per hour, we can calculate how far he will be from Fort Worth. Vangs will be 125 miles away from Fort Worth.

Given that Vangs drives at a speed of 65 miles per hour for 2 hours, we can calculate the distance traveled using the formula Distance = Speed × Time.

Distance = 65 miles/hour × 2 hours = 130 miles.

Since Vangs started 185 miles away from Fort Worth and traveled a distance of 130 miles, we subtract the distance traveled from the initial distance to find how far he will be from Fort Worth.

Distance from Fort Worth = Initial distance - Distance traveled = 185 miles - 130 miles = 55 miles.

Therefore, Vangs will be 55 miles away from Fort Worth after driving for 2 hours at a speed of 65 miles per hour.

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The daily revenue (R) is given by R = 4.15x, and the daily cost (C) is given by C = 3.20x + 798, where x is the number of scoops served in a day.

In more detail, the given equations represent a linear relationship between the number of scoops served (x) and both the revenue (R) and cost (C). The coefficient of x in the revenue equation, 4.15, represents the revenue generated per scoop served. Similarly, the coefficient of x in the cost equation, 3.20, represents the cost incurred per scoop served. The constant term 798 in the cost equation represents additional fixed costs.

To determine the daily profit, we can subtract the cost from the revenue: Profit = R - C = 4.15x - (3.20x + 798) = 0.95x - 798. This equation allows us to calculate the profit based on the number of scoops served.

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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.

Mr. Alvarez creates a walkway using 3 cement slabs, each with a volume of 4 cubic feet. The total volume used for the walkway is 14 cubic feet.

1. Each cement slab has a volume of 4 cubic feet, and Mr. Alvarez uses 3 slabs for the walkway.

2. Therefore, the total volume of the slabs used for the walkway is 4 cubic feet per slab * 3 slabs = 12 cubic feet.

3. However, we are given that the total volume used for the walkway is 14 cubic feet.

4. To account for the additional 2 cubic feet, Mr. Alvarez must have used some additional material, such as mortar or filler, to secure the slabs and fill any gaps.

5. Thus, the walkway consists of 3 cement slabs with a total volume of 12 cubic feet, and an additional 2 cubic feet of material were used to complete the walkway, bringing the total volume used to 14 cubic feet.

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(a) The road distance between Wrexham and Oswestry is 15 miles.

(b) The number of miles Sarah travels to and from work each week is 330 miles.

Given a chart of the road distances between various towns and cities.

(a) From the chart,

Distance the corresponds to Wrexham and Oswestry = 15 miles

Road distance between Wrexham and Oswestry is 15 miles.

(b) Distance between Ruthin and Oswestry = 33 miles

Total distance travelled to and from work in a day = 33 × 2 = 66 miles

She works 5 days a week.

Total distance travelled for 5 days = 66 × 5 = 330 miles

Hence, the number of miles travelled by Sarah in a week is 330 miles.

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The chart is given below.

"Your question is incomplete, probably the complete question/missing part is:"

The chart shows the distances, in miles, between some towns and cities.

Toby lives in Wrexham and works in Oswestry.

Wrexham

18

Ruthin

a) Use the chart to find the road distance

between Wrexham and Oswestry.

15

21

12

Corwen

15

33

23

Oswestry

Sarah lives in Ruthin and works in Oswestry for

5 days a week. Each day she travels to and

from work using the route shown on the map.

MOLD

ROTHEN

WRESTHAM

b) How many miles, in total, does she travel to

and from work each week? 231 miles

CORNEN

OSWESTRY

Choose CI​

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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The sum of f(x) = 3x^2 + 3x + 2 and g(x) = 2x^2 - 2x + 3 is 5x^2 + x + 5, while the difference is x^2 + 5x - 1. These results are obtained by adding and subtracting the corresponding terms of the two functions.



To find the sum and difference of the functions f(x) = 3x^2 + 3x + 2 and g(x) = 2x^2 - 2x + 3, we add and subtract the corresponding terms.

For the sum, we add the like terms: (3x^2 + 2x^2) + (3x - 2x) + (2 + 3) = 5x^2 + x + 5.

For the difference, we subtract the like terms: (3x^2 - 2x^2) + (3x + 2x) + (2 - 3) = x^2 + 5x - 1.

Therefore, the sum of the functions is given by f(x) + g(x) = 5x^2 + x + 5, and the difference of the functions is given by f(x) - g(x) = x^2 + 5x - 1.

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No, it is not possible for Suri and Juan to make the same amount of wages, y, by working the same number of hours, x, in one week.

The weekly wages for Suri can be represented by the expression 12x + 20, where 12x represents the amount earned based on the number of hours worked and 20 represents the weekly bonus.

Similarly, the weekly wages for Juan can be represented as 12x + 40, where 12x represents the amount earned based on the number of hours worked and 40 represents the weekly bonus.

Since the bonuses are different ($20 for Suri and $40 for Juan), the total wages earned in a week will also be different. Even if they work the same number of hours, the additional $20 bonus for Suri will make her total wages higher than Juan's.

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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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Kent will earn $553.12 in interest from his 18-month CD with an interest rate of 3.25%.

To calculate the interest earned, we can use the formula: Interest = Principal × Rate × Time. In this case, the principal (amount invested) is $8,500, the interest rate is 3.25% (or 0.0325 as a decimal), and the time is 18 months (or 1.5 years). Plugging in these values into the formula, we get: Interest = $8,500 × 0.0325 × 1.5 = $553.12. Therefore, Kent will earn $553.12 in interest from his CD.

It's important to note that the interest rate is typically expressed as an annual rate. In this case, the interest rate is 3.25%, which means that for a full year, Kent would earn 3.25% of the principal amount. However, since the CD term is 18 months (or 1.5 years), we need to adjust the formula accordingly. By multiplying the principal by the interest rate and the time, we can determine the total interest earned over the given period. In this case, the interest earned is $553.12.

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Tommy walks 2 miles to school each morning, and he sees a billboard every 1/5 of a mile.

To find out how many billboards he sees, we can divide the total distance he walks (2 miles) by the distance between each billboard (1/5 of a mile).

Number of billboards = Total distance / Distance between billboards

= 2 miles / (1/5 mile)

= 2 miles * (5/1)

= 10 billboards

Therefore, Tommy sees 10 billboards each morning.

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