The perimeter of square A is 28 feet less than the perimeter of square B. The area of square A is 161 square feet less than the area of square B. If x and y are the side lengths of square A and square B, respectively, what is the value of x + y?

The width of the porch will be 32 feet, the same as the parlor. However, to calculate the amount of building materials needed, additional specifics are required such as the porch's length, location of posts, and number of boards.

To answer the question related to designing a porch that matches the width of the parlor, we first understand that the parlor is of a rectangular shape with a width of 32 feet. Considering that the porch will have the same width, it means the porch will also have a width of 32 feet.

From this point, specifics such as the desired length of the porch, location of posts, number of boards or rails, and other related factors would come into play in the calculating of building materials needed for the construction. There may also be the need to consider factors like the ratio of width to length in the design, akin to the mathematical relation mentioned in the statement 'X = Y x 2 + 1'.

So, while we know the width of the porch because it matches the parlor, the exact amount of materials that will be required would depend on further specifics of the porch design, similar to the steps in a stoichiometry problem in chemistry where one calculates the amount of reactants or products in a chemical reaction based on known ratios.

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To get a percentage off of a total without a calculator, multiply the total by the percentage as a decimal. To calculate the total amount including tax, multiply the total by the tax percentage as a decimal and then add the result to the total.

To calculate a percentage off a total without using a calculator, you can multiply the total by the percentage as a decimal. For example, to find 66% off of a total, multiply the total by 0.66. To calculate the total amount including tax, you can add the tax amount to the original total. For a 7.5% tax, multiply the total by 0.075 and then add the result to the total.

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Final answer:

To solve for v in the equation y = v²/2a, multiply both sides by 2a and then take the square root of both sides which gives v = √(2ay).

Explanation:

The question requires us to solve the equation y = v²/2a for the velocity v. To isolate v, we multiply both sides of the equation by 2a, then take the square root of both sides.

This mathematical process makes v the subject of the equation based on the given formula from kinematics. It's important to note that v will have two values, one positive and one negative, since taking the square root of a number yields both a positive and negative result.

The cost of spoon is £1.84 and therefore the cost of one knife is £5.52.

Given :

Solution :

Now let x be the cost of spoon. Than the cost knife is 3x. It is given that 9 spoons and 12 knives costs £82.80.

[tex]9x + 12\times(3x)= 82.80[/tex]

[tex]9x + 36x = 82.80[/tex]

[tex]45x =82.80[/tex]

[tex]x = 1.84[/tex]

Therefore the cost of 1 knife = [tex]1.84\times 3 = 5.52[/tex].

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The average rate of change of the function over the given interval is 3.

To find the average rate of change of the function over the given interval, we need to calculate the change in the function values and divide it by the change in the input values.

Step 1: Calculate the function values for the two endpoints of the interval.

f(0) = 3(0) - 2 = -2

f(5) = 3(5) - 2 = 13

Step 2: Calculate the change in the function values.

Change in function values = f(5) - f(0) = 13 - (-2) = 15

Step 3: Calculate the change in the input values.

Change in input values = 5 - 0 = 5

Step 4: Divide the change in function values by the change in input values.

Average rate of change = (Change in function values) / (Change in input values) = 15 / 5 = 3

The properties that justify steps b and d, is 1. Multiplication Property of Equality; Subtraction Property of Equality.

Understanding these properties is crucial in solving equations properly.

Key Properties of Equality:

Multiplication Property of Equality: This property states that if you multiply both sides of an equation by the same non-zero number, the two sides remain equal.

Example: If [tex]a = b[/tex], then [tex]a \times c = b \times c[/tex].

Subtraction Property of Equality: This property indicates that if you subtract the same number from both sides of an equation, the two sides will also remain equal.

Example: If [tex]a = b[/tex], then (a - c = b - c.

Division Property of Equality: Similar to multiplication, this property states that if you divide both sides of an equation by the same non-zero number, the two sides remain equal.

Example: If [tex]a = b[/tex] and [tex]c \neq 0[/tex], then [tex]\frac{a}{c} = \frac{b}{c}[/tex].

Justification Steps b and d:

Given the context, let's assume step b involves subtracting a term from both sides of an equation, and step d involves multiplying both sides by a number.

For step b (subtracting x):

This step is justified by the Subtraction Property of Equality because the same amount [tex]x[/tex] is subtracted from both sides, which keeps the equality balanced.

For step d (multiplying by a number):

This step is justified by the Multiplication Property of Equality as you are multiplying both sides of the equation by the same non-zero number, thus preserving the equality.

The total interest earned in 45 days when the emergency fund is evenly split between a savings account and a CD is approximately $29.17. If 1 month's worth of emergency funds were in the savings account and the rest in a CD, the total interest would be approximately $38.05. The difference between the two scenarios is approximately $8.88.

Calculating Interest for Emergency Funds in Savings and CDs

To answer the student's question about the interest earned in 45 days on the emergency fund invested half in a savings account and half in a 45-day CD, as well as the comparison with an alternative investment scenario, we need to perform several calculations using the given interest rates and time periods.

Answer to Question 3

Firstly, the student's fixed expenses are $1,500.45/month, so for a 4-month emergency fund coverage, the total amount saved would be $1,500.45 x 4 = $6,001.80.

Half of this amount goes into the savings account and the other half into the CD, so each gets $3,000.90.

The interest in the savings account with an APR of 3.15% for 45 days (1.5 months) would be calculated using the formula for simple interest: Interest = Principal x Rate x Time.

So the interest earned on the savings account would be: $3,000.90 x (3.15% per year / 12 months) x 1.5 months ≈ $11.85.

The interest in the 45-day CD with an APR of 4.65% would be calculated similarly: $3,000.90 x (4.65% per year / 12 months) x 1.5 months ≈ $17.32.

Therefore, the total interest earned in 45 days would be approximately $11.85 + $17.32 = $29.17.

Answer to Question 4

If only 1 month's worth of emergency fund ($1,500.45) was invested in the savings account and the remainder in the CD, the interest from the savings account would not change, but the interest from the CD would, as it would be calculated on a larger principal of $4,501.35.

The new interest for the CD investment would be $4,501.35 x (4.65% per year / 12 months) x 1.5 months ≈ $26.20.

So the new total interest would be $11.85 (from savings) + $26.20 (from CD) = $38.05.

The difference in interest between the two scenarios would be $38.05 - $29.17 = $8.88.

The probability that the student is a junior, given that soccer is the favorite sport listed is 0.354.

The percentage of student on Junior level who like soccer will be:

= 33% × 45%

= 0.1485

The total percentage of students who like soccer is 42%. Therefore, probability that the student is a junior, given that soccer is the favorite sport listed will be:

= 0.1485/0.42

= 0.354

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Answer:

The probability that a point chosen at random in the rectangle is also in the blue triangle is:

1/2

Step-by-step explanation:

We are given a figure

We have to find the probability that a point chosen at random in the rectangle is also in the blue triangle.

Area of rectangle= 4×5 sq. in.

                            = 20 sq. in.

The area of blue triangle=[tex]\dfrac{1}{2}\times 4\times 5[/tex]

                                         = 10 sq. in.

P(that a point chosen at random in the rectangle is also in the blue triangle)

 = area of blue triangle/whole area of the rectangle

= 10/20

= 1/2

Answer: the answer is 1/2

Step-by-step explanation:

Given :[tex] 2log_{5} x^{2} =log_{5} 2^{2} [/tex]

To solve for x we use the logarithm rule for powers.

The log rule for powers states:

[tex] mlog_{a}n =log_{a} n^{m} [/tex]

We apply this rule to the left side of the equation.

[tex] log_{5} x^{2} =log_{5} 4

Both sides have log with same base so it can be eliminated.

Eliminating log from both sides we have:

[tex] x^{2} =4

To solve for x we take root of both sides

x=2,-2.