Which two of the following are appropriate methods to graph the line x + 4y = 8.

The domain of the relation S is the set of all x-values from the ordered pairs in the relation. In this case, the given ordered pairs are (3, p), (3, 0), (4, g), and (1, 4).

To find the domain, we collect all the unique x-values from these ordered pairs.

From the given pairs, we have x = 3, x = 4, and x = 1. However, note that (3, p) and (3, 0) have the same x-value of 3. When considering the domain, we only need to list unique x-values.

Therefore, the domain of the relation S can be expressed as:

domain = {1, 3, 4}

Moving on to the range of the relation S, it refers to the set of all y-values from the ordered pairs.

From the given pairs, we have y = p, y = 0, y = g, and y = 4. Similarly, we need to consider only unique y-values when determining the range.

Thus, the range of the relation S can be expressed as:

range = {0, 4, g, p}

It's important to note that the specific values of g and p are not given in the question. So, in the range, g and p are considered as distinct symbols representing unknown values.

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Answer:

Step-by-step explanation:

0.14x + 0.06(20,500 - x) = 2,670.00

0.14x + 1,230 - 0.06x = 2,670.00

0.08x + 1,230 = 2,670.00

0.08x = 2,670.00 - 1,230

0.08x = 1,440.00

x = 1,440.00 / 0.08

x = 18,000.00

invested $18,000.00 in the bond account and $2,500.00 (20,500 - 18,000) in the certificate of deposit account.

The percent amount base in this problem is 50.

To identify the percent amount base in the problem "what percent of 50 is 60%," we need to use the formula for finding the percentage:percent = (part/whole) × 100In this formula, the "part" is the amount we want to find as a percentage of the "whole." In this case, we want to find the percentage that 60% of 50 represents.To do this, we can rearrange the formula to solve for the "whole":whole = part/percent × 100In this case, the "part" is 60% of 50, or 0.6 × 50 = 30. And the "percent" we are trying to find is the percentage that 30 is of 50.

So, we plug in these values to get:whole = 30/(percent) × 100Now, we can solve for "percent" by cross-multiplying and simplifying:whole × percent = 30 × 100percent = (30 × 100)/wholeTo find the percentage that 30 is of 50, we plug in 50 for "whole":percent = (30 × 100)/50percent = 60Therefore, 60% of 50 is 30, and 30 is 60% of 50.

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The correlation coefficient between X and Y is Corr(X, Y) = 0.

To calculate the marginal distribution of X and Y, we need to integrate the joint probability density function (PDF) over the appropriate ranges.

a. Marginal distribution of X:

To find the marginal distribution of X, we integrate the joint PDF over the range of Y:

∫[0, 1] J(x, y) dy

Since the joint PDF is defined as J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1 and J(x, y) = 0 otherwise, the integral becomes:

∫[0, x] 1 dy = x, for 0 ≤ x ≤ 1

So, the marginal distribution of X is simply X(x) = x for 0 ≤ x ≤ 1.

b. Expectation of X:

The expectation (mean) of X can be calculated as the integral of x times the marginal PDF of X:

[tex]E(X) = ∫[0, 1] x * X(x) dx = ∫[0, 1] x^2 dx = [x^3/3] from 0 to 1 = 1/3[/tex]

Therefore, the expectation of X is E(X) = 1/3.

c. Variance of X:

The variance of X can be calculated using the formula:

[tex]Var(X) = E(X^2) - (E(X))^2E(X^2) = ∫[0, 1] x^2 * X(x) dx = ∫[0, 1] x^3 dx = [x^4/4] from 0 to 1 = 1/4Var(X) = 1/4 - (1/3)^2 = 1/4 - 1/9 = 5/36[/tex]

Therefore, the variance of X is Var(X) = 5/36.

d. Covariance of X and Y:

The covariance of X and Y can be calculated as:

Cov(X, Y) = E(XY) - E(X)E(Y)

Since the joint PDF J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1, the integral becomes:

[tex]E(XY) = ∫[0, 1] ∫[0, x] xy dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6[/tex]

[tex]E(X) = 1/3 (from part b)E(Y) = ∫[0, 1] ∫[0, x] y J(x, y) dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6[/tex]

Cov(X, Y) = 1/6 - (1/3)(1/6) = 0

Therefore, the covariance of X and Y is Cov(X, Y) = 0.

e. Correlation coefficient between X and Y:

The correlation coefficient can be calculated using the formula:

Corr(X, Y) = Cov(X, Y) / √(Var(X) * Var(Y))

Since the covariance of X and Y is 0, the correlation coefficient will also be 0.

Therefore, the correlation coefficient between X and Y is Corr(X, Y) = 0.

f. Conclusion based on the correlation coefficient:

The correlation coefficient of 0 indicates that there is no linear relationship between X and Y. In this case, the fraction of male runners (X) and the

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Given statement solution is :- The value of x is -33/4.

To find the value of x in the equation:

3√(-2) = 2√(x + 8)

Let's solve it step by step:

First, simplify the radicals:

3√(-2) = 2√(x + 8)

The cube root of -2 can be written as [tex](-2)^(1/3):[/tex]

[tex](-2)^(1/3) = 2√(x + 8)[/tex]

Now, let's eliminate the radicals:

[tex](-2)^(1/3)^3 = (2√(x + 8))^3[/tex]

-2 = 8(x + 8)

Expand the equation:

-2 = 8x + 64

Rearrange the terms:

8x = -2 - 64

8x = -66

Divide both sides by 8:

x = -66/8

Simplify the fraction:

x = -33/4

Therefore, the value of x is -33/4.

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Answer:

Step-by-step explanation:

3√( x− 2) = 2√( x+ 8)

Square both sides

9(x-2) = 4(x+8)

Expand

9x-18=4x+32

9x-4x=32+18

5x=50

x=10

Answer:

$0.21 per marble

Step-by-step explanation:

Answer:

$0.21 per marble

Step-by-step explanation:

The trigonometric identities used to evaluate the trigonometric expressions indicates;

4.6.1 sin(A + B) and sin(A - B) are conjugate identities, therefore;

sin(A + B) - sin(A - B) = 2·cos(A)·sin(B)

4.6.2 sin(5·x) - sin(x) = 2·cos(5·x)·sin(x)

4.6.3. x= (2·k + 1)·π/10 or x = k·π, where k is an integer

Trigonometric identities are equations involving trigonometric functions that are true for all values of the variable for which the left and right side of the equation are defined.

4.6.1 sin(A + B) - sin(A - B) can be found using the sum and difference for the sine function as follows;

sin(A + B) = sin(A)·cos(B) + cos(A)·sin(B)

sin(A - B) = sin(A)·cos(B) - cos(A)·sin(B)

Plugging in the value of sin(A + B) and sin(A - B) in the equation sin(A + B) - sin(A - B), we get;

sin(A + B) - sin(A - B) = sin(A)·cos(B) + cos(A)·sin(B) - (sin(A)·cos(B) - cos(A)·sin(B))

sin(A)·cos(B) + cos(A)·sin(B) - (sin(A)·cos(B) - cos(A)·sin(B)) = sin(A)·cos(B) + cos(A)·sin(B) - sin(A)·cos(B) + cos(A)·sin(B)

sin(A)·cos(B) + cos(A)·sin(B) - sin(A)·cos(B) + cos(A)·sin(B) = 2×cos(A)·sin(B)

Therefore; sin(A + B) - sin(A - B) = 2·cos(A)·sin(B)

4.6.2 sin(5·x) - sin(x) can be simplified to a monomial by using the previous identity, sin(A + B) - sin(A - B) = 2·cos(A)·sin(B), as follows;

Let (A + B) = 5·x, and let (A - B) = x, we get;

sin(5·x) - sin(x) = 2·cos(5·x)·sin(x)

4.6.3 The general solution of sin(5·x) - sin(x) = 0, can be found using the identity in 4.6.1, as follows;

sin(5·x) - sin(x) = 0 = 2·cos(5·x)·sin(x), therefore;

2·cos(5·x)·sin(x) = 0

cos(5·x) = 0, and sin(x) = 0

The general solution for cos(5·x) = 0 is 5·x = (2·k + 1) × π/2

Therefore; x = (2·k + 1) × π/10

The general solution of sin(x) = 0 is k·π, where k is an integer

Therefore, the general solution of sin(5·x) - sin(x) = 0 is x = (2·k + 1)·π/10 or x = k·π, where k is an integer

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Yes, deductive thinking does start with a given set of rules or premises that are already accepted as true.

Deductive thinking is a logical process of reasoning in which one starts with a general premise or set of premises, and then uses logic to draw a specific conclusion based on those premises. This type of thinking is often used in mathematics, science, and philosophy.

In deductive reasoning, the premises are considered to be true and the conclusion necessarily follows from the premises. For example, if the premise is "All mammals have fur" and the conclusion is "A dog is a mammal", then the conclusion necessarily follows from the premise.

The use of a set of rules or premises is an essential feature of deductive thinking because it allows for logical reasoning and inference to take place. By starting with a set of accepted premises, one can use logic to deduce new information or conclusions.

In summary, deductive thinking does start with a given set of rules or premises that are already accepted as true. These rules or premises are used to draw specific conclusions based on logical reasoning and inference.

Given statement solution is :- a) The equation for Lookout Banquet Hall Cost of Lookout Banquet Hall = $1500 + $75x.

b) The point of intersection for the linear system is x = 20.

c) This point represents the number of people attending the banquet where the total cost for both Primo Banquet Hall and Lookout Banquet Hall is the same.

a) Let's represent the number of people attending the banquet as "x."

For Primo Banquet Hall:

The total cost for Primo Banquet Hall is the sum of the base cost ($2000) and the cost per person ($50) multiplied by the number of people attending (x). Therefore, the equation for Primo Banquet Hall is:

Cost of Primo Banquet Hall = $2000 + $50x

For Lookout Banquet Hall:

The total cost for Lookout Banquet Hall is the sum of the base cost ($1500) and the cost per person ($75) multiplied by the number of people attending (x). Therefore, the equation for Lookout Banquet Hall is:

Cost of Lookout Banquet Hall = $1500 + $75x

b) To find the point of intersection (PoI) for the linear system, we need to solve the equations:

Cost of Primo Banquet Hall = Cost of Lookout Banquet Hall

$2000 + $50x = $1500 + $75x

We can simplify the equation by subtracting $50x and $1500 from both sides:

$2000 - $1500 = $75x - $50x

$500 = $25x

Now, divide both sides of the equation by $25 to solve for x:

$500 / $25 = x

x = 20

So, the point of intersection for the linear system is x = 20.

c) This point represents the number of people attending the banquet where the total cost for both Primo Banquet Hall and Lookout Banquet Hall is the same. In other words, if Angela's school has exactly 20 people attending the banquet, the total cost for both venues will be equal.

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Answer:

864

Step-by-step explanation:

80/100 simplified is 4/5

so you do 4/5 of 1080

which is 1080 divided by 5 that is 216

and then 216 x 4 which is 864

By using a statistical calculator, the actual sample mean and sample standard deviation are:

Actual sample mean = 46.1500.

Actual ample standard deviation = 8.6256.

In Mathematics and Geometry, the sample mean for any set of data can be calculated by using the following formula:

Mean = ∑x/(n - 1)

In Mathematics and Geometry, the sample standard deviation for any set of data can be calculated by using the following formula:

Standard deviation, δx = √(1/N × ∑(x - [tex]\bar{x}[/tex])²)

By using a statistical calculator, the actual sample mean and sample standard deviation are as follows;

Actual sample mean = 46.1500.

Actual ample standard deviation = 8.6256.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The actual distance represented by 23.7 cm on the map is 355.5 km.

To find the ratio of the amount of money Mabaso has to the amount of money Thabo has and the amount of money Ally has, we can divide each amount by the smallest amount (which is R35) to simplify the ratio.

Mabaso has R140, Thabo has R70, and Ally has R35.

The ratio of Mabaso's money to Thabo's money is:

R140 ÷ R35 = 4

The ratio of Mabaso's money to Ally's money is:

R140 ÷ R35 = 4

Therefore, the ratio of the amount of money Mabaso has to the amount of money Thabo has and to the amount of money Ally has is 4:1:1.

To calculate the percentage discount of a steel table, we need to find the difference between the original price and the discounted price, and then divide it by the original price. Finally, we multiply the result by 100 to get the percentage.

Original price: R750

Discounted price: R600

Discount: R750 - R600 = R150

Percentage discount: (R150 ÷ R750) × 100 = 20%

So, the table has a 20% discount on Black Friday.

To convert 125 grams to kilograms, we divide the amount in grams by 1,000 (since there are 1,000 grams in a kilogram).

125 g ÷ 1,000 = 0.125 kg

Therefore, 125 grams is equal to 0.125 kilograms.

If a green grocer packs 12 apples in a plastic bag and has 285 apples, we divide the total number of apples by the number of apples per bag to determine the number of bags needed.

Number of bags needed: 285 apples ÷ 12 apples/bag = 23.75 bags

Since we can't have a fraction of a bag, we round up to the nearest whole number. Therefore, the green grocer would need 24 bags.

If the scale of a map is 1,500,000 and the measurement on the map is 23.7 cm, we can use the scale to determine the actual distance.

1 cm on the map represents 1,500,000 cm in reality.

23.7 cm on the map represents x cm in reality.

x = 23.7 cm × 1,500,000 cm = 35,550,000 cm

To convert cm to km, we divide by 100,000 (since there are 100,000 cm in a kilometer).

35,550,000 cm ÷ 100,000 = 355.5 km

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The probability of selecting two Democrats from the political discussion group is 3/8 or approximately 0.375.

The probability of selecting two Democrats from the group can be calculated using the concept of probability. In this case, we have a total of 10 Democrats out of 16 total group members.

The probability of selecting the first Democrat is 10/16, since there are 10 Democrats out of 16 group members.

After selecting the first Democrat, there are 9 Democrats left out of 15 remaining group members. Therefore, the probability of selecting the second Democrat is 9/15.

To find the probability of both events occurring, we multiply the individual probabilities together.

So the probability of selecting two Democrats in succession is (10/16) * (9/15) = 3/8 or approximately 0.375.

In summary, the probability of selecting two Democrats from the political discussion group is 3/8 or approximately 0.375.

This means that there is a 37.5% chance of choosing two Democrats if two members are selected randomly and in succession.

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The volume of the given triangular prism is approximately 104.76075 cubic inches.

To calculate the volume of a triangular prism, you need to multiply the area of the triangular base by the height of the prism.

Given that the triangular base has sides measuring 9 inches each, we can find the area of the base using the formula for the area of an equilateral triangle:

Area = [tex](\sqrt(3) / 4) * side^2[/tex]

where "side" represents the length of one side of the triangle. In this case, the side length is 9 inches.

Area = [tex](\sqrt(3) / 4) * 9^2\\ = (\sqrt(3) / 4) * 81\\ = (1.732 / 4) * 81\\ = 1.732 * 81 / 4\\ = 139.681 / 4[/tex]

    = 34.92025 square inches

Now that we have the area of the triangular base, we can calculate the volume of the prism by multiplying it by the height of the prism:

Volume = Base Area * Height

      = 34.92025 square inches * 3 inches

      = 104.76075 cubic inches

Therefore, the volume of the given triangular prism is approximately 104.76075 cubic inches.

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The domain is all real numbers, and the range is all real numbers greater than or equal to -4.

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

f(x) = (x + 2)(x + 6)

The above equation is a quadratic function

The rule of this function is that

The domain is the set of all real numbers

For the range, we expand and calculate the vertex

So, we have

f(x) = x² + 8x + 12

The x-coordinate of the vertex is

x = -8/(2 * 1)

x = -4

The x-coordinate of the vertex is

f(-4) = (-4)² + 8(-4) + 12

f(-4) = -4

So, the range is

y ≥ -4

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Answer:

(5,6) (6,7)

Step-by-step explanation:

An irrational number is a number that cannot be expressed as a fraction or a ratio of two integers. Let's examine each option:

1. The number pi: Pi (π) is an irrational number. It is a mathematical constant representing the ratio of a circle's circumference to its diameter. Pi cannot be expressed as a fraction or a terminating decimal. It is an infinite, non-repeating decimal (approximately 3.14159...).

2. A whole number: Whole numbers are integers without any fractional or decimal parts. They include positive numbers (0, 1, 2, 3, ...) and their negatives (-1, -2, -3, ...). Whole numbers can always be expressed as fractions by setting the denominator as 1, making them rational numbers.

3. Fractions: Fractions are numbers expressed as the ratio of two integers. They can be written in the form a/b, where a and b are integers and b is not zero. All fractions are rational numbers because they can be expressed as the division of two integers.

4. A decimal that terminates: A terminating decimal is a decimal number that has a finite number of digits after the decimal point. Terminating decimals can always be expressed as fractions, making them rational numbers. For example, 0.25 can be written as 1/4.

Based on the explanations above, the only option that represents an irrational number is "The number pi."

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Answer:

{(0,0)}

Step-by-step explanation:

Since only (0,0) works, then the relation R in roster form must be {(0,0)}

Answer:

5x + y = 4

Step-by-step explanation:

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

Next, we can subtract 3x from both sides of the equation to isolate the variable y on one side:

2x + (y + x) - 3x = 4 - 3x

2x + y = 4 - 3x

Finally, we can rearrange the equation to have the variables followed by the constant on the right-hand side of the equation:

2x + 3x + y = 4

5x + y = 4

So, the equation is standard form is 5x + y = 4

2x + (y + x) = 4

When a + is found in front of an expression inside a parenthesis, the expression stays the same.

2x + y + x = 4

Group like terms. If a term has no coefficient, its coefficient is considered to be 1.

2x + 1x

We group like terms by adding their coefficients.

(2 + 1)x = 3x

3x + y4

The safe amount of dose to administer in this situation is 15mL

To solve this problem, we can use the following steps:

Calculate the amount of drug in 1 mL of the solution.

Divide the desired dose by the amount of drug per mL.

The amount of drug in 1 mL of the solution is:

The other options are not safe because they would either deliver too much or too little medication. 20 mL would deliver 1000 mg, which is twice the desired dose. 4 mL would deliver only 60 mg, which is not enough medication. 2 mL would deliver only 30 mg, which is also not enough medication.

Therefore, the correct answer is 15 mL.

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Answer:

b. 4

c. 90⁰

Step-by-step explanation:

a. is in the diagram

Answer: To determine if the ordered pair (x, y) is a solution of the given system of equations, you need to substitute the values of x and y into each equation and check if both equations hold true.

Given system of equations:

2x - y = 1

5x - 3y = 1

Let's substitute the values of x and y from the ordered pair (x, y) into each equation:

For equation 1:

2x - y = 1

Substituting x = 2 and y = -1:

2(2) - (-1) = 4 + 1 = 5

For equation 2:

5x - 3y = 1

Substituting x = 2 and y = -1:

5(2) - 3(-1) = 10 + 3 = 13

Now, compare the results of each equation with the right-hand side of the respective equation:

For equation 1: 5 (left side) ≠ 1 (right side)

For equation 2: 13 (left side) ≠ 1 (right side)

Since both equations do not hold true when substituting the values of x = 2 and y = -1, the ordered pair (2, -1) is not a solution of the given system of equations.

Step-by-step explanation: Hope this helps!

Answer:

0

Step-by-step explanation:

The slope of a horizontal line is 0

The equation of the line is y = 2

At any two points (x₁, y₁) and (x₂, y₂) on the line,

y₂ - y₁ = 2 - 2 = 0

slope m = (y₂ - y₁)/(x₂ - x₁) = 0/(x₂ - x₁) = 0

To find the cost per square foot of the wallpaper used to cover the rectangular prism storage box, we need to determine the total area covered by the wallpaper and divide it by the total cost.

Let's assume the dimensions of the rectangular prism are length (L), width (W), and height (H). The box has six faces, each of which needs to be covered with wallpaper.

The total surface area of the box is given by:

Surface Area = 2(LW + LH + WH)

Since all the sides of the box are covered with wallpaper, the total surface area is the area covered by the wallpaper. We can set up an equation using this information:

2(LW + LH + WH) = $860

Simplifying the equation, we have

LW + LH + WH = $430

Now, to find the cost per square foot, we need to divide the total cost by the total area covered by the wallpaper. The total area covered is LW + LH + WH.

Let's assume the cost per square foot is C dollars. The total cost is given as $860. Therefore, we can set up the equation:

C * (LW + LH + WH) = $860

Now we can solve for C:

C = $860 / (LW + LH + WH)

The resulting value will give us the cost per square foot of the wallpaper.

Note: If you provide specific dimensions for the length, width, and height of the box, we can calculate the exact cost per square foot.

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To find the height of the cylinder when the volume is given as 1500 in³ and the radius is 7 inches, we can use the formula for the volume of a cylinder:

Volume = π * r² * h

Substituting the given values, we have:

[tex]1500 = 3.14 * 7^2 * h1500 = 3.14 * 49 * h1500 = 153.86 * h[/tex]

To solve for h, we divide both sides of the equation by 153.86:

h = 1500 / 153.86

h ≈ 9.75

Rounding the answer to the nearest hundredth, the height of the cylinder is approximately 9.75 inches.

Therefore, the height of the cylinder is 9.75 inches.

Note: It is important to use the accurate value of π, which is approximately 3.14159, for precise calculations. However, in this case, since you specified to use 3.14 for π, I have used that approximation to calculate the height.

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Solving a system of equations, we can see that the grocer should mix approximately 2.88 pounds of the first kind of candy and 12.12 pounds of the second kind of candy to obtain a 15-pound mix selling for $2.05 per pound.

Let's assume the grocer mixes x pounds of the first kind of candy, which sells for $1.00 per pound, and y pounds of the second kind of candy, which sells for $2.30 per pound.

The total weight of the mix is 15 pounds, so we have the equation:

x + y = 15

The price of the mix is $2.05 per pound, so we have the equation:

(1.00x + 2.30y) / 15 = 2.05

To solve this system of equations, we can use substitution or elimination method. Let's use the substitution method:

From equation (1), we can solve for x in terms of y:

x = 15 - y

Substituting this value of x in equation (2), we have:

(1.00(15 - y) + 2.30y) / 15 = 2.05

Simplifying and solving for y:

(15 - y + 2.30y) / 15 = 2.05

(15 + 1.30y) / 15 = 2.05

15 + 1.30y = 30.75

1.30y = 30.75 - 15

1.30y = 15.75

y = 15.75 / 1.30

y ≈ 12.12

Substituting this value of y back into equation (1), we can find x:

x + 12.12 = 15

x ≈ 2.88

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The expression to calculate the quantity of pepper used is: p/9 = (¹/₄)/3

Algebraic word problems are defined as problems that require converting a sentence into an equation and solving that equation. The equations that need to be written contain only basic arithmetic. and a single variable. Usually in real-life scenarios variables represent unknown quantities.

Now, we are told that they use ¹/₄ teaspoon of pepper to prepare 3 potatoes.

Thus:

3 potatoes = ¹/₄ teaspoon of pepper

Thus:

9 potatoes will be:

3/(¹/₄) = 9/p

rewritten as:

p/9 = (¹/₄)/3

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Answer: Triangle C.

Step-by-step explanation:

We can find the area of the triangles by multiplying the base by the height and dividing by 2. The given formula is A = [tex]\frac{bh}{2}[/tex].

    A = [tex]\frac{bh}{2} =\frac{4}{2} =2[/tex]

    B = [tex]\frac{bh}{2} =\frac{4}{2} =2[/tex]

    C = [tex]\frac{bh}{2} =\frac{3}{2} =1.5[/tex]

    D = [tex]\frac{bh}{2} =\frac{4}{2} =2[/tex]

    E = [tex]\frac{bh}{2} =\frac{4}{2} =2[/tex]

We can see that the triangle with the different area is triangle C. It has an area of 1.5 units², while the rest have an area of 2 units².

The length of the final cut paving stone is 5 feet.

In this question, we have a sidewalk that is 54.5 feet long and the paving stones that will be used are 5.5 feet long.

The worker has to place 9 full paving stones and cut the final stone to fit.

We are required to find the length of the final cut paving stone.

To find the length of the final cut paving stone, we first need to find the total length covered by the 9 full paving stones. We can do this by multiplying the length of each stone (5.5 feet) by the number of stones placed (9).

Total length covered by 9 full paving stones = 5.5 feet × 9 = 49.5 feet Next, we can subtract this total length from the length of the sidewalk to find out how much length is left for the final stone.

Length left for final stone = Length of sidewalk - Total length covered by 9 full paving stones= 54.5 feet - 49.5 feet = 5 feet.

Finally, we know that the worker has to cut the final stone to fit, so the length of the final cut paving stone will be equal to the length of the remaining space. Length of final cut paving stone = Length left for final stone= 5 feet.

Therefore, the length of the final cut paving stone is 5 feet.

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Tyrone will pay approximately $21,195.80 in interest and a total amount of $56,796 over the 20-year period for his student loans.

To calculate the amount Tyrone will pay in interest and the total amount he will pay over 20 years for his student loans, we can use the formula for calculating the monthly payment on a loan.

The formula for calculating the monthly payment on a loan is:

M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

M = Monthly payment

P = Principal loan amount

r = Monthly interest rate

n = Total number of payments

In this case, Tyrone owes $28,000, the interest rate is 8.25% (or 0.0825 as a decimal), and he will make monthly payments for 20 years (or 240 months).

First, we calculate the monthly interest rate:

r = 8.25% / 12 = 0.006875

Next, we plug the values into the formula to calculate the monthly payment:

M = 28000 * (0.006875 * (1 + 0.006875)^240) / ((1 + 0.006875)^240 - 1)

M ≈ $236.65

To calculate the total interest paid over the 20-year period, we subtract the principal loan amount from the total amount paid:

Total interest = (Monthly payment * Total number of payments) - Principal loan amount

Total interest = (236.65 * 240) - 28000

Total interest ≈ $21,195.80

Finally, to calculate the total amount Tyrone will pay over the 20-year period, we multiply the monthly payment by the total number of payments:

Total amount = Monthly payment * Total number of payments

Total amount = 236.65 * 240

Total amount = $56,796

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