A taste test asks people from Texas and California which pasta they prefer, brand A or brand B. This table shows the results. A person is randomly selected from those tested. What is the probability that the person is from California, given that the person prefers brand A? A. 0.55 B. 0.62 C. 0.60 D. 0.53

Step-by-step explanation:

6 x j = 78

j = 78 ÷ 6

j = 13

hope this helps

Answer:

the answer is d

Step-by-step explanation:

Answer:

The answer is A.

Step-by-step explanation:

The simplified answer is 3/4. A simplifies to 2/3. B simplifies to 3/4. C simplifies to 3/4. D simplifies to 3/4. To get my answer I divided  all of the fractions and saw which ones equalled .75 .

When a\(_{n}\) = \(2^{n}\)+ n,  a₀ = 1,  a₁ = 3,  a₂ = 6, and a₃ = 11  

When a\(_{n}\) = n^(n+1)!,  a₀ = 0,  a₁ = 2,  a₂ = 2⁶, and a₃ = 3²⁴  

When a\(_{n}\) =  [n/2], a₀ = 0,  a₁ = 1/2,  a₂ = 1, and a₃ = 3/2      

When a\(_{n}\) = [n/2] + [n/2], a₀ = 0,  a₁ = 1,  a₂ = 2, and a₃ = 3/2  

Number sequence

A number sequence is a progression or a list of numbers that are directed by a pattern or rule.

Here,

a₀, a₁, a₂, and a₃ are terms of a sequence

from option a, a\(_{n}\) = \(2^{n}\)+ n

⇒ a₀  = 2⁰+ 0 = 1+0 = 1

⇒ a₁  = 2¹+ 1 = 2+1 = 3

⇒ a₂, = 2²+ 2 = 4+2 = 6

⇒ a₃  = 2³+ 3 = 8 +3 = 11  

from option b, a\(_{n}\) = n^(n+1)!

⇒ a₀  = 0^(0+1)! = 0

⇒ a₁  = 1^(1+1)! = 2² = 2

⇒ a₂, = 2^(2+1)! = 2^(3)! = 2⁶          [ ∵ 3! = 6 ]

⇒ a₃  = 3^(3+1)! = 3^(4)! = 3²⁴         [ ∵ 4! = 24 ]

from option c, a\(_{n}\) =  [n/2]          

⇒ a₀  = [0/2] = 0

⇒ a₁  = [1/2] = 1/2

⇒ a₂, = [2/2] = 1

⇒ a₃  = [3/2] =  3/2  

from option d, a\(_{n}\) = [n/2] + [n/2]

⇒ a₀  =  [0/2] + [0/2] = 0

⇒ a₁  =  [1/2] + [1/2] = 1/2 + 1/2 = 1

⇒ a₂, = [2/2] + [2/2] = 1 + 1 = 2

⇒ a₃  =  [3/2] + [3/2] = 6/4 = 3/2

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The Complete Question is -

What are the terms a₀, a₁, a₂, and a₃ of the sequence {a\(_{n}\)}, where a\(_{n}\) is where a\(_{n}\) equals

a. \(2^{n}\) + n                    b. n^(n+1)!

c. [n/2]                      d. [n/2] + [n/2]

Answer:

False, false, true

Step-by-step explanation:

3/1 = 1/3 False

3/1 = 1 False

3/3 = 1 True

Step-by-step explanation:

3/1 = 1/3

3 = 1/3

3 ≠ 1/3 FALSE

3/1 = 1

3 = 1

3 ≠ 1 FALSE

3/3 = 1

3 ÷ 3 = 1

1 = 1 TRUE

We have shown that E(Z) = E(X) + E(Y) for nonnegative random variables X and Y.

The alphabetic character that expresses a numerical value or a number is known as a variable in mathematics. A variable is used to represent an unknown quantity in algebraic equations.

To show that E(Z) = E(X) + E(Y), we need to use the definition of the expected value of a random variable and some properties of max function.

The expected value of a random variable X is defined as E(X) = ∑x P(X = x), where the sum is taken over all possible values of X.

Now, let's consider the random variable Z = max(X, Y). The probability that Z is less than or equal to some number z is the same as the probability that both X and Y are less than or equal to z. In other words, P(Z ≤ z) = P(X ≤ z and Y ≤ z).

Using the fact that X and Y are nonnegative, we can write:

P(Z ≤ z) = P(max(X,Y) ≤ z) = P(X ≤ z and Y ≤ z)

Now, we can apply the distributive property of probability:

P(Z ≤ z) = P(X ≤ z)P(Y ≤ z)

Differentiating both sides of the above equation with respect to z yields:

d/dz P(Z ≤ z) = d/dz [P(X ≤ z)P(Y ≤ z)]

P(Z = z) = P(X ≤ z) d/dz P(Y ≤ z) + P(Y ≤ z) d/dz P(X ≤ z)

Since X and Y are nonnegative, we have d/dz P(X ≤ z) = P(X = z) and d/dz P(Y ≤ z) = P(Y = z). Therefore, we can simplify the above expression as:

P(Z = z) = P(X = z) P(Y ≤ z) + P(Y = z) P(X ≤ z)

Now, we can calculate the expected value of Z as:

E(Z) = ∑z z P(Z = z)

    = ∑z z [P(X = z) P(Y ≤ z) + P(Y = z) P(X ≤ z)]

    = ∑z z P(X = z) P(Y ≤ z) + ∑z z P(Y = z) P(X ≤ z)

Since X and Y are nonnegative, we have:

∑z z P(X = z) P(Y ≤ z) = E(X) P(Y ≤ Z) and

∑z z P(Y = z) P(X ≤ z) = E(Y) P(X ≤ Z)

Substituting these values in the expression for E(Z) above, we get:

E(Z) = E(X) P(Y ≤ Z) + E(Y) P(X ≤ Z)

Finally, we note that P(Y ≤ Z) = P(X ≤ Z) = 1, since Z is defined as the maximum of X and Y. Therefore, we can simplify the above expression as:

E(Z) = E(X) + E(Y)

Thus, we have shown that E(Z) = E(X) + E(Y) for nonnegative random variables X and Y.

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Answer:

Step-by-step explanation:

The area of a circle is A = πr², where r is the radius. That means in order to solve this we have to find the value of x, which is the diameter of the lake, and then divide it in half to get the radius. To find x we will use similar triangles and proportions. x is the height of the big triangle and 4.5 is the height of the smaller triangle; 15.3 + 7.4 is the hypotenuse of the big triangle and 7.4 is the hypotenuse of the smaller triangle. Setting up our proportion:

\(\frac{x}{4.5}=\frac{15.3+7.4}{7.4}\) which simplifies a bit to

\(\frac{x}{4.5}=\frac{22.7}{7.4}\) and cross multiply to solve for x:

7.4x = 102.15 so

x = 13.8  That is the diameter of the lake. Divide it in half to get 6.9, the radius. Applying the area formula for a circle:

A = (3.14)(6.9)² and

A = 3.14(47.61) so

A = 149.5 which rounds to 150, Choice C

Step-by-step explanation:

If we add these together, we get 2+3√3

The distance that Iker ride this week is 6√3 kilometers.

Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.

The process of doing addition is also called as finding the sum.

Given that,

Iker rode his bike on two trails this week.

Distance of first trail = 2√3 kilometers

Distance of second trail = 4√3 kilometers

Total distance = 2√3 kilometers + 4√3 kilometers

                        = 6√3 kilometers

Hence the total distance that Iker rode the bike is 6√3 kilometers.

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Answer:

3 pieces

Step-by-step explanation:

For T to be a normal operator on a finite-dimensional complex inner product space V,

(a) If Tⁿ is the zero map, then T is the zero map.

(b) U commutes with T if and only if U commutes with each eigenprojection of T.

(c) There exists a normal U such that U² = T.

(d) T is invertible if and only if lambda_j is nonzero for all eigenvalues λ_j of T.

(e) T is a projection if and only if lambda_j is either 0 or 1 for all eigenvalues λ_j of T.

(f) T = -T* if and only if each eigenvalue of T is imaginary.

(a) If Tⁿ = 0 for some n ∈ ℕ, then the characteristic polynomial of T is p_T(x) = xⁿ. But by the spectral decomposition, the characteristic polynomial of T is given by p_T(x) = (x - λ₁)(d₁) × ... × (x - λ_k)(d_k), where λ₁, ..., λ_k are the distinct eigenvalues of T and d₁, ..., d_k are the dimensions of the corresponding eigenspaces. Since T is normal, the eigenspaces are orthogonal and hence the dimensions add up to the dimension of V. Thus we must have n = dim(V), which implies that T is the zero map.

(b) Let U be a linear operator on V that commutes with T. By the spectral decomposition, we can write T = λ₁P₁ + ... + λ_kP_k, where P₁, ..., P_k are orthogonal projections onto the eigenspaces of T. Since U commutes with T, we have U(P_i(v)) = P_i(U(v)) for any eigenvector v of T. It follows that U commutes with each P_i. Conversely, suppose U commutes with each P_i. Then we have U(T(v)) = U(λ_i P_i(v)) = λ_i U(P_i(v)) = λ_i P_i(U(v)) = T(U(v)) for any eigenvector v of T. Since the eigenvectors span V, this implies that U commutes with T.

(c) Let T = λ₁P₁ + ... + λ_kP_k be the spectral decomposition of T. Define U = λ₁(1/2)P₁ + ... + λ_k(1/2)P_k. Since T is normal, the eigenspaces are orthogonal and hence the projections P₁, ..., P_k are also orthogonal. It follows that U is also an orthogonal operator, and hence a normal operator. Moreover, we have U² = λ₁P₁ + ... + λ_kP_k = T.

(d) By the spectral theorem for normal operators, we can write T = λ₁P₁ + ... + λ_kP_k, where λ₁, ..., λ_k are the distinct eigenvalues of T and P₁, ..., P_k are orthogonal projections onto the corresponding eigenspaces. Moreover, we have T⁻¹ = λ₁⁻¹P₁ + ... + λ_k⁻¹P_k if all the eigenvalues are nonzero. Indeed, if all the eigenvalues are nonzero, then T is invertible and hence bijective. It follows that each eigenspace has a dimension at most 1, and hence T has a unique decomposition into a sum of orthogonal projections onto its eigenspaces. It is then easy to check that T⁻¹ has the desired decomposition. Conversely, suppose that T⁻¹ has the desired decomposition. Then we have T(T⁻¹(v)) = v for any v ∈ V. It follows that each eigenspace has dimension at most 1, and hence T is bijective, and hence invertible.

(e) By the spectral theorem for normal operators, we can write T = λ₁P₁ + ... + λ_kP_k, where λ₁, ..., λ_k are the distinct eigenvalues of T and P₁, ..., P_k are orthogonal projections onto the corresponding eigenspaces. It follows that T is a projection if and only if T² = T, which is equivalent to the condition that λ_i ∈ {0, 1} for all i.

(f) By the spectral theorem for normal operators, we can write T = λ_1 P_1 + ... + λ_k P_k, where λ_1, ..., lambda_k are the distinct eigenvalues of T and P_1, ..., P_k are the orthogonal projections onto the corresponding eigenspaces. Note that T is self-adjoint if and only if T = T*, or equivalently, λ_j is real for all j. On the other hand, T = -T* if and only if λ_j = -λ_j × for all j, or equivalently, lambda_j is imaginary for all j. Thus, T = -T* if and only if each λ_j is imaginary, as desired.

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System of equations can be calculated using substitution method, and several  other ways

The system of equations has infinitely many solutions

The system of equations is given as:

\(8x -2y=18\)

\(y = 4x - 9\)

Substitute 4x - 9 for y in \(8x -2y=18\)

\(8x - 2(4x - 9) = 18\)

Open brackets

\(8x - 8x + 18 = 18\)

Subtract 8x from 8x

\(18 = 18\)

The above equation means that, the system of equations has infinitely many solutions

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Probabilities are used to determine the chances of an event.

The probability that both selections are boys is 0.1667

The given parameters are:

boys= 35

girls= 50

total= 85

Since two are chosen to sing a duet, then the selection is without replacement.

So, the probability that both selections are boys is

p=boys/ total * boys-1/ total -1

This gives

p= 0.4118*0.4048

Hence, the probability that both selections are boys is 0.1667

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All the true statements about the area of the park include the following:

(a)The park can be decomposed into two parallelograms.

(b)The formula A = bh can be used to find the area of each piece of the park.

(c)The park can be decomposed into a parallelogram, a triangle, and a trapezoid.

(d)The area of the park is 126 m².

In Mathematics and Geometry, a parallelogram refers to a four-sided geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that is composed of two (2) equal and parallel opposite sides.

By critically observing the image of the park, if it is split along the bottom of the first part, two (2) parallelograms would be created. Similarly, splitting the park along the side of the bottom parallelogram would create a trapezoid, triangle, and a parallelogram.

In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:

Area of a parallelogram, A = base area × height

Area of a park = (5 × 12) + (6 × 11)

Area of a park = 60 + 66

Area of a park = 126 m²

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Complete Question:

There is a park near Raphael’s home. To find its area, Raphael took the measurements shown. Select all the true statements about the area of the park.

(a)The park can be decomposed into two parallelograms.

(b)The formula A = bh can be used to find the area of each piece of the park.

(c)The park can be decomposed into a parallelogram, a triangle, and a trapezoid.

(d)The area of the park is 126 m2.

(e)The area of the park is 96 m2.

The recursive function of a ball with a 67% rebound is a(n) = 0.67a(n-1)

The rebound is given as:

r = 67%

Express as decimal

r = 0.67

So, the recursive function is:

a(n) = Previous height * r

This gives

a(n) = a(n-1) * 0.67

Evaluate

a(n) = 0.67a(n-1)

Hence, the recursive function is a(n) = 0.67a(n-1)

Basketball

The initial height is given as:

a(1) = 54

So, we have:

a(2) = 0.67 * 54 = 36.18

a(3) = 0.67 * 36.18 = 24.24

Tennis ball

The initial height is given as:

a(1) = 58

So, we have:

a(2) = 0.67 * 58 = 38.86

a(3) = 0.67 * 38.86 = 26.04

Table-tennis ball

The initial height is given as:

a(1) = 26

So, we have:

a(2) = 0.67 * 26 = 17.42

a(3) = 0.67 * 17.42 = 11.67

Hence, the complete table is:

Bounce               n             Height

First bounce       1               Basketball: 54 inches

                                           Tennis ball: 58 inches

                                           Table tennis ball: 26 inches

Second bounce   2            Basketball: 36.18 inches

                                           Tennis ball: 38.86 inches

                                           Table tennis ball: 17.42 inches

Third bounce       3            Basketball: 24.24 inches

                                           Tennis ball: 26.04 inches

                                           Table tennis ball: 11.67 inches

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Missing part of the question

A ball is dropped such that each successive bounce is 67% of the previous bounce's height.

The expressions for dz/du and dz/dv are as follows:

dz/du = 4x siny

dz/dv = -6y cosx

To find the expressions for dz/du and dz/dv, we need to differentiate the given function z = 2x^2 - 3y with respect to u and v, respectively.

1. dz/du:

Since u = x^2 siny, we can express z in terms of u by substituting x^2 siny for u in the original function:

z = 2u - 3y

Now, we differentiate z with respect to u while treating y as a constant:

dz/du = d/dx (2u - 3y)

      = 2(d/dx (x^2 siny)) - 0 (since y is constant)

      = 2(2x siny)

      = 4x siny

Therefore, dz/du = 4x siny.

2. dz/dv:

Similarly, we express z in terms of v by substituting 2y cosx for v in the original function:

z = 2x^2 - 3v

Now, we differentiate z with respect to v while treating x as a constant:

dz/dv = d/dy (2x^2 - 3v)

      = 0 (since x^2 is constant) - 3(d/dy (2y cosx))

      = -6y cosx

Therefore, dz/dv = -6y cosx.

In summary, the expressions for dz/du and dz/dv are dz/du = 4x siny and dz/dv = -6y cosx, respectively.

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Answer:

The plotting the points 1 and then you will be able to compare the materials and how they work in comparison to the other material

Answer:

Bar graph

Step-by-step explanation:

Cuz he will make bars in order to show the materi

Answer:

as per ur ques if we take x as number then we get algebraic expression as

2x - 4

brainliest?

The probability to get a 3 or 4 in the third toss and 6 in the fourth toss is 1/18.

The sample space for a six-sided die is

{1, 2, 3, 4, 5, 6}

Hence the total number of possibilities = 6

The rolling of a die is IID that is Independently and Identically distributed.

Hence,

the result of one toss will not affect the result of the successive tosses.

Probability

= n(E)/n

= no of favorable outcomes for any event /total no. of outcomes

Here,

n = 6

Let A be the event of getting a 3 or 4 in the third toss

Let B be the event of getting 6 on the fourth toss

E(A) = {3,4}

n(A) = 2

Hence,

P(A) = 2/6

= 1/3

B = {6}

n(B) = 1

P(B) = 1/6

Since these are IID,

P(A and B) = P(A) X (B) [Property of independent events]

Hence P(A∩B) = 1/3 X 1/6

= 1/18

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The number of small boxes purchased is 4.

The number of large boxes purchased is 2.

The number of nails in a small box is 50, and the number of nails in a large box is 450.

The total number of nails bought is 1100.

Let the number of large boxes be "x".

The number of small boxes is "2x".

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equal sign.

The equation can be formed as given below :

x*450 + 2x*50 = 1100

450x + 100x = 1100

550x = 1100

x = 2

The number of small boxes purchased is 2*x = 2*2 = 4.

The number of large boxes purchased is x = 2.

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Answer:

4 boxes of small nails.

2 boxes of large nails.

Step-by-step explanation:

Define the variables:

Given information:

Create a system of equations with the given information and defined variables:

\(\begin{cases}x=2y\\50x+450y=1100\end{cases}\)

Substitute the first equation into the second equation and solve for y:

\(\implies 50(2y)+450y=1100\)

\(\implies 100y+450y=1100\)

\(\implies 550y=1100\)

\(\implies \dfrac{550y}{550}=\dfrac{1100}{550}\)

\(\implies y=2\)

Substitute the found value of y into the first equation and solve for x:

\(\implies x=2(2)\)

\(\implies x=4\)

Therefore the contractor purchased:

The probability that a truck drives between 99 and 128 miles in a day is 0.7734 rounded to four decimal places.

Standard deviation is a statistical measurement that depicts the average deviation of each value in a dataset from the mean value. It tells you how much your data deviates from the mean value. It represents the typical variation between the mean value and the individual data points.

The formula for the probability that a truck drives between 99 and 128 miles in a day is:

\(Z = (X - \mu) /\sigma\)

where, X is the number of miles driven per day; μ is the mean of the number of miles driven per day; σ is the standard deviation of the number of miles driven per day. The value of Z for 99 miles driven per day is:

\(Z = (99 - 120) / 11 = -1.91\)

The value of Z for 128 miles driven per day is:

\(Z = (128 - 120) / 11 = 0.73\)

Using a standard normal distribution table or calculator, the probability of a truck driving between 99 and 128 miles per day is:

\(P(-1.91 < Z < 0.73) = 0.7734\)

Therefore, the probability that a truck drives between 99 and 128 miles in a day is 0.7734 rounded to four decimal places.

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Answer: Uncle Luke is at 50 years old

Step-by-step explanation: I went through trial and error first with simple t-charts.  In the first one, I simply implemented the piece of info that Luke was 5 times older than the nephew. But then, I realized that Luke would always be 5 years older than his nephew. Here was the info for that t-chart:

\(\left \{ {{N=1} \atop {L=5}} \right. \left \{ {{N=2} \atop {L=6}} \right. \left \{ {{N=3} \atop {L=7}} \right.\)

Next, I tried a chart starting with the nephew at 2 years of age, and got an age gap of 8. This helped me realize that I would have to start at 4 years of age in order to have an age gap of 16
\(\left \{ {{N=2} \atop {L=10}} \right.\)        |             \(\left \{ {{N=4} \atop {L=20}} \right. \left \{ {{N=5} \atop {L=21}} \right.\)  (remember there are 1 increments)

Next, I realized that N=4, L=20 was 40 years ago, so if now the nephew was 44, we can increment 16 to get 50
44+16=50

Answer: i believe the answer is 39

Step-by-step explanation:

sum divided by the terms

The left circle represents isosceles triangles.

An isosceles triangle is described as  a triangle that has two sides of equal length.

In the area of the organizer where the circles meet, an isosceles and obtuse triangle would be appropriate

A triangle is also described as  a three-sided geometric shape whose internal angles added together shouldn't be greater than 180°.

We should note that the two sides and the two sharp angles of an isosceles right triangle are equal.

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Therefore, f(w ∩ x) = {0} ≠ f(w) ∩ f(x), which shows that the statement f(w ∩ x) = f(w) ∩ f(x) is false in general.

Let's consider the function f: R -> R defined by f(x) = x^2 and the subsets w = {-1, 0} and x = {0, 1} of the domain R.

f(w) = {1, 0} and f(x) = {0, 1}, so f(w) ∩ f(x) = {0}.

On the other hand, w ∩ x = {0}, and f(w ∩ x) = f({0}) = {0}.

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Answer:

Exact Form: Y = 5/7

Decimal Form: 0.714285...

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

The average speed of the horse is 25.0m/s

Speed is the rate of change of distance over time

The given parameters are:

The average speed of the horse is then calculated as:

\(Speed = \frac{Distance}{Time}\)

This gives

\(Speed = \frac{800}{32.0}\)

Evaluate the quotient

\(Speed = 25.0\)

Hence, the average speed of the horse is 25.0m/s

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Answer:

∠ C = 100°

Step-by-step explanation:

since 2 sides of the triangle are congruent then the triangle is isosceles with base angles congruent.

consider the angle inside the triangle to the left of 140°

this angle and 140° are a linear pair and sum to 180°

angle + 140° = 180° ( subtract 140° from both sides )

angle = 40°

then the angle on the left of the triangle = 40° ( base angles congruent )

the sum of the angles in a triangle = 180° , so

∠ C + 40° + 40° = 180°

∠ C + 80° = 180° ( subtract 80° from both sides )

∠ C = 100°

Answer:

x = {2,3,4}    (if x can only be positive whole numbers)

Step-by-step explanation:

For a triangle exists, the side lengths of the triangle must be such that the sum of the two shorter sides must be greater than the third side.

This also is equivalent to any two sides must have a sum greater than the third side.

So

7+10 > x^2, => x^2 < 17 => x < sqrt(17)     (maximum)

7+x^2 > 10, => x^2 >3 => x > sqrt(3)

Therefore

sqrt(3) < x < sqrt(17)

If x must be an integer,

2< x < 4, or x = {2,3,4}

By walking 25 blocks in the east direction, Irfan will essentially retrace his steps, moving back towards his apartment building and ultimately reaching it.

In this problem, we are given the following information:

Irfan walked 20 blocks west.

Irfan walked an additional 5 blocks west.

To determine what Irfan must do to return to his apartment building, let's analyze the given information.

Irfan initially walked 20 blocks in the west direction, which means he moved away from his apartment building in the westward direction. Then, he walked an additional 5 blocks west, which implies he moved even farther away from his apartment building.

To return to his apartment building, Irfan needs to reverse the direction and head eastward. Therefore, to complete the statement, we would select the option "He must walk 25 blocks east."

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the coordinates (1,1), (7,3), (8,0) and (2,-2) are joined which shape is formed as Square

When the coordinates (1,1), (7,3), (8,0) and (2,-2) are joined, a square is formed. The sides are equal length and the angles are all 90 degrees.The coordinates (1,1), (7,3), (8,0) and (2,-2) are points on a two-dimensional plane. When the points are connected, a square is formed. A square is a four sided shape with four 90 degree angles and four equal length sides. The length of each side can be calculated by finding the distance between the two points. For example, the distance between (1,1) and (7,3) is 6 units. Therefore, the length of each side of the square is 6 units.

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