Jordan knits a square blanket that has an area of 1,500 square inches. What is the approximate length of each side of the blanket?
O 16 inches
O 27 inches
O 39 inches
O 42 inches

To prove that the sum of the first n odd numbers is n^2 using induction, we need to show that the statement holds true for the base case (n = 1) and then prove the induction step.

Base case (n = 1):

When n = 1, we have 1 as the only odd number, and indeed, 1 = 1^2. So the statement is true for the base case.

Induction step:

Assume that the statement is true for some positive integer k, i.e., 1 + 3 + 5 + ... + (2k - 1) = k^2.

We need to prove that the statement holds for k + 1, i.e., 1 + 3 + 5 + ... + (2k - 1) + (2(k + 1) - 1) = (k + 1)^2.

Starting from the left-hand side of the equation:

1 + 3 + 5 + ... + (2k - 1) + (2(k + 1) - 1)

Using the assumption that 1 + 3 + 5 + ... + (2k - 1) = k^2:

= k^2 + (2(k + 1) - 1)

= k^2 + (2k + 2 - 1)

= k^2 + 2k + 1

= (k + 1)^2.

Therefore, if the statement is true for k, it is also true for k + 1.

By the principle of mathematical induction, we have shown that the sum of the first n odd numbers is indeed n^2 for all positive integers n.

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Answer:

\( {(2x + y)}^{3} + {(2x - y)}^{3} \\ \\{(2x + y)}^{2}(2x + y)\: + (2x - y)^{2}(2x - y) \\ \\ (4 {x}^{2} + 4xy + {y}^{2} )(2x + y) + (4 {x}^{2} - 4xy + {y}^{2} )(2x - y) \\ \\ (8 {x}^{3} + 12 {x}^{2} y + 6x {y}^{2} + {y}^{3} ) + (8 {x}^{3} - 12 {x}^{2} y + 6x {y}^{2} - {y}^{3} ) \\ \\ = 16 {x}^{3} + 12x {y}^{2} \)

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Answer:

\(45^{o}\)

Step-by-step explanation:

The intersection of two straight lines forms two sets of opposing angles, with each set of opposing angles having the same value.  Angles A and B will have the same value.  If angle A is \(45^{o}\), then angle B will also be  \(45^{o}\).

Answer:

2.5

Step-by-step explanation:

EG = EF + FG;

5x-8 = 2 + 3x-5

2x = 5

x = 2.5

FG = 3x-5 = 2.5

The interval of I₁ or I₂ or I₄ is  (2.5 ,10].

The interval of I₁ and I₂ is  [3 , 5.5] .

The interval of I₁ and I₃ is  [5.5]

The interval of I₁ and I₄ is (5.6 , 7]

(a) because the all 3 intervals square measure connected by or which suggests they're going to all embrace the quantity lying from interval one to three and is given by (2.5 ,10].

(b) because the interval square measure connected by and which suggests the common numbers lying in interval one and a couple of and is given by [3 , 5.5] .

(c) because the interval square measure connected by and which suggests the common numbers lying in interval one and three and is given by [5.5]

(d)As the interval square measure connected by and which suggests the common numbers lying in interval one and four and is given by (5.6 , 7] .

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The complete question is given below :

Given the intervals I₁ = (2.5, 5.5], I₂ =[3, 6], I₃=[5.5, 7] and I₄ = (5.5, 10]. Find

(a) I₁ or I₂ or I₄

(b) I₁ and I₂

(c) I₁ and I₃

(d) I₁ and I₄

Answer:

a = 7

Step-by-step explanation:

Expand the brackets

2 + 5a + 15 = 6a + 10

Rearrange by collecting the like terms

17 - 10 = 6a - 5a

7 = a

Answer:

Choice A

The ratio of the rise to the run of the given triangle is \(\frac{1}{4}\)

The ratio of the rise to the run of the image triangle is \(\frac{1}{4}\)

Answer:

slope = 25

y -intercept = 525

equation : y = 25x + 525

Step-by-step explanation:

An investor invests $525 in stock

It means the initial price of stock is $525

In 1 month increase in value of stock = $25

thus,

In x month increase in value of stock = $25x

Total cost of stock in x months = initial investment + increase in value of stock in x months

Total value of stock in x months = 525 + 25x

as Total value of stock in x months = f(x)

f(x) = 525 + 25x

it can be also written as

y =  25x   + 525

____________________________________________

we know that slope intercept form of linear relationship is

y = mx + c

where m is the slope

and c is the y intercept

thus

comparing  y =  25x   + 525 with y = mx + c

we have m = 25

c = 525

The region we are interested in is the part of the annular region between the two circles that lies within the sector between the two rays.

To sketch the region in the plane consisting of points whose polar coordinates satisfy the given conditions, we first need to understand what the conditions mean in terms of polar coordinates.

In polar coordinates, a point in the plane is represented by an ordered pair (r, θ), where r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line segment connecting the origin to the point.

The condition 2 < r < 5 means that the distance from the origin to the point is between 2 and 5 units. The condition 11/6 ≤ θ ≤ 13/6 means that the angle between the positive x-axis and the line segment connecting the origin to the point is between 11/6 and 13/6 of a full rotation (i.e., between 330° and 390°).

To sketch the region, we start by drawing the polar axis (the positive x-axis) and the origin. Then, we draw two concentric circles centered at the origin with radii of 2 and 5 units, respectively. Next, we draw two rays emanating from the origin and making angles of 11/6 and 13/6 of a full rotation, respectively, with the positive x-axis. These rays divide the region between the two circles into two parts, one with angles between 11/6 and 13/6, and one with angles between 0 and 11/6 or between 13/6 and 2π.

The region we are interested in is the part of the annular region between the two circles that lies within the sector between the two rays.

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Answer:

Step-by-step explanation:

They make it sound like it is 23 miles one way.

2(23)5(52)

11960 miles

The pool can contain 10492 gallons of water

What is volume of cylinder?

The capacity of a cylinder, which determines how much material it can carry, is determined by the cylinder's volume. There is a formula for the volume of a cylinder that is used in geometry to determine how much of any quantity, whether liquid or solid, may be immersed in it uniformly. A cylinder is a three-dimensional structure having two parallel, identical bases that are congruent.

Right circular cylinder: A cylinder with circular bases and a lateral curved surface with each line segment perpendicular to the bases.

Oblique Cylinder: A cylinder with sides that are inclined over the base at a different angle than a right angle.

An elliptic cylinder is a cylinder with ellipses at its bases.

Two right circular cylinders tied together inside of one another form a right circular hollow cylinder.

volume of cylinder= (π)\(r^2h\)

diameter= 18feet

radius = 9 feet

height = 5.5 feet

volume= 3.14*(\(9^2\))*5.5

     = 1398.87 \(feet^3\)

volume in gallons = 1398.87 * 7.5

                 = 10492 gallons

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In binary representation, each bit can be either 0 or 1. Using five binary bits, we can obtain 32 different numbers. Therefore, the correct answer is (B).

With five binary bits, we have five positions, and each position can have two possibilities (0 or 1). To calculate the total number of different numbers we can obtain, we need to raise 2 to the power of the number of bits. In this case, we have \(2^5,\) which equals 32. Therefore, we can obtain 32 different numbers using five binary bits. To understand this concept, we can think of each binary bit as a switch that can be either on (1) or off (0). With five switches, we have a total of 32 different combinations or numbers that can be represented. These numbers range from 0 (all switches off) to 31 (all switches on). Therefore, the correct answer is (B), which states that we can obtain 32 different numbers using five binary bits.

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A The amount of money in a savings account with an annual interest rate of 1.5%

Answer:

1 and 2

and the greatest common divisor is 2

The floating-point literal that correctly represents the scientific notation value: 2.3 x 10^7 will be A. 2.3e^7.

It should be noted that scientific notation simply means. way that's used to express numbers that are either too large or too small to be written in decimal form.

Therefore, it should be noted that the floating-point literal that correctly represents the scientific notation value: 2.3 x 10^7 will be:

= 2.3 × 20^7

= 2.3 × e^7

= 2.3e7

The correct option is A.

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Which floating-point literal correctly represents the scientific notation value: 2.3 x 10^7?

a. 2.3e^7

b. 2.3 × 10e^7

c. 2.3e × 10^7

d. 2.3 × e^7

Answer:

i cant see anything

Step-by-step explanation:

.

The inverse of the given matrix is not defined.

To find the inverse of a matrix, we need to check if the matrix is invertible or non-singular. For a square matrix to be invertible, its determinant must be non-zero.

Let's calculate the determinant of the given matrix:

Det(Matrix) = (1 * 0 * 2) + (2 * 2 * 1) + (1 * 3 * 8) - (2 * 0 * 1) - (1 * 2 * 8) - (1 * 3 * 0)

= 0 + 4 + 24 - 0 - 16 - 0

= 12

Since the determinant of the given matrix is non-zero (12 ≠ 0), it implies that the matrix is invertible.

Next, we can proceed to find the inverse of the matrix by using the formula:

Matrix^(-1) = (1/Det(Matrix)) * Adjoint(Matrix)

However, before calculating the adjoint of the matrix, let's check for any possible errors in the matrix elements. The elements of the matrix you provided are not consistent, and it seems there might be a mistake. The matrix you provided (121, 302, 182) does not conform to the standard 3x3 matrix format.

In conclusion, based on the given matrix, the inverse is not defined. Please make sure to provide a properly formatted 3x3 matrix to find its inverse.

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The best description of the transformation for the image being projected on the retina is A. A dilation with a scale factor between 0 and - 1 and center at the nodal point.

An mage is inverted and reversed as it passes through the lens of the eye, and is then projected upside down and reversed onto the retina. The process of transforming the image is called "rectification."

In mathematical terms, a dilation would have taken place because the object was shrunken by the eyes at the nodal point. When an object shrinks , then the scale factor is between 0 and 1 but because this image is inverted, the scale factor is between 0 and - 1.

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Answer:

A = 6 + 0.25j

Step-by-step explanation:

Answer:

0.25(j)=A+6

Step-by-step explanation:

Even if R is anti-reflexive, R2 may not necessarily be anti-reflexive. It depends on the specific properties and composition of the relation R.

Let R be a relation that is reflexive and transitive. We want to prove that R2 = R for any relation R with these two properties.

To prove this, we need to show that for any ordered pair (a, b), (a, b) ∈ R2 if and only if (a, b) ∈ R.

First, let's consider (a, b) ∈ R2. By definition, (a, b) ∈ R2 means that there exists an element c such that (a, c) ∈ R and (c, b) ∈ R.

Since R is reflexive, we know that (a, a) ∈ R and (b, b) ∈ R.

By the transitivity of R, if (a, c) ∈ R and (c, b) ∈ R, then (a, b) ∈ R.

Therefore, (a, b) ∈ R2 implies (a, b) ∈ R.

Now, let's consider (a, b) ∈ R. Since R is reflexive, we have (a, a) ∈ R and (b, b) ∈ R.

By the definition of R2, (a, a) ∈ R2 and (b, b) ∈ R2.

Since R is transitive, if (a, a) ∈ R2 and (a, b) ∈ R2, then (a, b) ∈ R2.

Therefore, (a, b) ∈ R implies (a, b) ∈ R2.

We have shown that for any ordered pair (a, b), (a, b) ∈ R2 if and only if (a, b) ∈ R. Hence, R2 = R.

If the relation R is anti-reflexive, it is not necessarily true that R2 is anti-reflexive.

To understand why, let's consider an example. Let R be a relation defined on the set of integers such that R contains the ordered pairs (a, b) where a < b.

In this case, R is anti-reflexive because for any integer a, (a, a) is not in R.

Now, let's consider R2. R2 is the composition of R with itself. If (a, b) ∈ R and (b, c) ∈ R, then (a, c) ∈ R2.

In our example, if we take a = 1, b = 2, and c = 3, we have (1, 2) ∈ R and (2, 3) ∈ R. Therefore, (1, 3) ∈ R2.

However, (1, 1) is not in R2 because (1, 1) is not in R. Therefore, R2 is not anti-reflexive in this case.

This example demonstrates that even if R is anti-reflexive, R2 may not necessarily be anti-reflexive. It depends on the specific properties and composition of the relation R.

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Boolean expressions are mathematical equations that are used to represent logic in digital circuits.

These expressions are made up of Boolean operators such as AND, OR, and NOT, and are used to determine how digital circuits should behave in response to various inputs.
It is important for Boolean expressions to be minimized in the design of digital circuits for several reasons. First, minimizing these expressions can reduce the complexity of the circuit, making it easier to design and maintain. This is because smaller expressions require fewer components and are less likely to result in errors.
Additionally, minimizing Boolean expressions can improve the efficiency and speed of the circuit. This is because smaller expressions require less processing power to execute, which can reduce the overall time it takes for the circuit to respond to inputs.
Overall, minimizing Boolean expressions is an important part of designing efficient and effective digital circuits. By reducing complexity and improving efficiency, circuits can perform more reliably and efficiently, which is essential for many applications.

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Answer:

46

Step-by-step explanation:

4+3x(8-2)+4

=7x6+4

=42+4

=46

The total cost before the sales tax was 19.828 pounds.

For a party, Jordan purchased 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad.

We have to determine the total cost before sales tax.

As per the question, we have prices as:

cost of turkey = 3.95 per pound

cost of egg cheese = 1.3 per pound

cost of egg salad = 0.89 per pound

The total cost of turkey = 3.8 × 3.95  = 15.01 pounds

The total cost of cheese = 2.2 × 1.3 = 2.86 pounds

The total cost of egg salad = 2.2 × 0.89 = 1.958 pounds

The total cost before sales tax = 15.01 + 1.958 +2.86

Apply the addition operation, and we get

The total cost before sales tax = 19.828 pounds

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The question seems to be incomplete the correct question would be:

Jordan bought 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad for a party. If prices are 3.95 per pound turkey, 1.3 per pound cheese and 0.89 per pound egg salad What was the total cost before sales tax?

Answer:

heres your answer 1.3333

a) Not possible to determine the percentage of the length of seashells collected by Jaya that were between 3.5 and 7 inches.

b) 25% of the length of seashells collected by Jaya were between 2 and 3.5 inches.

c) It is not possible to determine the percentage of the length of seashells collected by Jaya that were more than 5 inches based on the information provided.

d) The range of lengths of seashells collected by Jaya was = 4.2 inches.

In statistics, the range is the difference between the highest and lowest values for a particular data collection.

For instance, if the provided data set is 2,5,8,10,3, the range is 10 - 2 = 8.

As a result, the range may alternatively be defined as the difference between the highest and lowest observations.

a) It is not possible to determine the percentage of the length of seashells collected by Jaya that were between 3.5 and 7 inches based on the information provided.

b) 25% of the length of seashells collected by Jaya were between 2 and 3.5 inches.

c) It is not possible to determine the percentage of the length of seashells collected by Jaya that were more than 5 inches based on the information provided.

d) The range of lengths of seashells collected by Jaya was 6.2 - 2 = 4.2 inches.

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Answer: 21/5x+12

Step-by-step explanation:

3*7/5x+3*4

21/5x+12

Answer:

y=-3x-1

Step-by-step explanation:

Use point-slope form:

(y-2)=-3(x+1)

y-2=-3x-3

y=-3x-1