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The volume of the given rectangular prism is 315[tex]cm^3[/tex]

We have the information from the question:

A right rectangular prism has a height of 17.5 cm.

The area of the base of the prism is 18 square cm.

To find the volume, in cubic cm of the right rectangular prism.

We know that the volume of a right rectangular prism is given by-

Volume = A × h

Volume = (18)(17.5)

Volume = 315[tex]cm^3[/tex]

So the volume of the given rectangular prism is 315[tex]cm^3[/tex]

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The binary number 0000 1010 can be expressed as 0A in hexadecimal. Hexadecimal is a base-16 numbering system that uses 16 digits, where 0-9 represent their respective values and A-F represents values 10-15, respectively.

To convert binary to hexadecimal, the binary number is grouped into four bits, starting from the right side, and each group is converted to its equivalent hexadecimal digit. In this case, the binary number 0000 1010 has two groups, 0000 and 1010. The first group is equal to 0 in hexadecimal, and the second group is equal to A in hexadecimal. Therefore, the binary number 0000 1010 can be expressed as 0A in hexadecimal. It is important to note that hexadecimal is often used in computer programming, as it is a convenient way to represent binary data.

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He sold 116 pencils (approx) in that period.

Assume the store owner made x sales of pencils during that month.

A profit of one rupee every pen

One pencil costs 30 paise = Rs. 0.3, in loss.

40 pens sold for a total profit of 40 x Rs 1 = Rs 40

Pencil loss as a whole = x x Rs 0.3 = Rs 0.3x

Given, he loses Rs 5 during that month.

So, 40 - 0.3x = 5

0.3x = 35

x = 35/0.3

x = 116.67

Therefore, he sold 116 pencils approx in that period.

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Answer:

[tex]x \approx 16.26\°[/tex]

Step-by-step explanation:

We can solve for angle x in this right triangle using the trigonometric ratio sine.

[tex]\sin(\theta) = \dfrac{\text{opposite}}{\text{hypotenuse}}[/tex]     ... This is the SOH part of SOH-CAH-TOA

↓ plugging in the given values

[tex]\sin(x) = \dfrac{7}{25}[/tex]

↓ taking the inverse sine of both sides

[tex]\sin^{-1}(\sin(x)) = \sin^{-1}\left(\dfrac{7}{25}\right)[/tex]

↓ canceling ...  [tex]\sin^{-1}(\sin(\theta)) = \theta[/tex]

[tex]x = \sin^{-1}\left(\dfrac{7}{25}\right)[/tex]

↓ plugging into a calculator

[tex]\boxed{x \approx 16.26\°}[/tex]

The h'(3) = h'(x)|x=3 = 22. We can see from the calculation that the value of h'(3) depends on the slopes of both f(x) and g(x) at x=3, as well as their values at x=3.

To evaluate h'(3) for h(x) = f(x) * g(x), we will use the product rule. The product rule states that if h(x) = f(x) * g(x), then h'(x) = f'(x) * g(x) + f(x) * g'(x).
Given the graphs of f(x) and g(x), we need to find the values of f(3), g(3), f'(3), and g'(3).
1. Locate the point x = 3 on the graph of f(x) and determine the value of f(3).
2. Locate the point x = 3 on the graph of g(x) and determine the value of g(3).
3. Determine the slope of the tangent line at x = 3 on the graph of f(x), which represents f'(3).
4. Determine the slope of the tangent line at x = 3 on the graph of g(x), which represents g'(3).
Once you have the values of f(3), g(3), f'(3), and g'(3), plug them into the product rule formula:
h'(3) = f'(3) * g(3) + f(3) * g'(3)
After calculating, you'll get the value of h'(3). Please refer to the graphs of f(x) and g(x) to obtain the necessary values and complete the evaluation.

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The cost of six dresses is $145.74.

Let's assign variables to represent the costs of the watches and dresses. Let w be the cost of one watch, and d be the cost of one dress.

From the given information, we can set up the following equations:

3w = 5d (Three ladies watches cost as much as five dresses)

(5w + 3d) / 8 = $148.75 (Average cost of 5 watches and 3 dresses is $148.75)

From the first equation, we can solve for w in terms of d:

w = (5d) / 3

Substituting this expression for w into the second equation, we can solve for d:

(5[(5d) / 3] + 3d) / 8 = $148.75

Simplifying the equation:

(25d + 24d) / 24 = $148.75 * 8

49d = $1190

Dividing both sides by 49, we find:

d = $24.29

The cost of six dresses would be:

6 * $24.29 = $145.74

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A hamburger costs $4. We can substitute this value into one of the original equations to solve for the cost of a hot dog. Carter charges $3 for a hot dog.

Let's represent the cost of a hamburger with "h" and the cost of a hot dog with "d". We can then set up two equations based on the information given:

30h + 25d = 195 (Equation 1)

15h + 20d = 120 (Equation 2)

We can solve this system of equations using either substitution or elimination. Let's use the elimination method.

First, let's multiply Equation 1 by 4:

120h + 100d = 780 (Equation 1 multiplied by 4)

Next, let's multiply Equation 2 by 5:

75h + 100d = 600 (Equation 2 multiplied by 5)

Now we can subtract Equation 2 from Equation 1 to eliminate the "d" variable:

(120h + 100d) - (75h + 100d) = 780 - 600

45h = 180

h = 4

We now know that a hamburger costs $4. We can substitute this value into one of the original equations to solve for the cost of a hot dog. Let's use Equation 1:

30h + 25d = 195

30(4) + 25d = 195

120 + 25d = 195

25d = 75

d = 3

Therefore, Carter charges $3 for a hot dog.

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The vector sum [tex]\mathbf{u}+\mathbf{v}[/tex]  is approximately equal to [tex]3.9\left < \cos 26^{\circ},,\sin 26^{\circ}\right > , 3.9⟨cos26∘, sin26∘⟩[/tex] in magnitude and direction form.

To find the sum of two vectors, we add their corresponding components. In this case, [tex]\mathbf{u}+\mathbf{v} = 7\left < \cos 0^{\circ},,\sin 0^{\circ}\right > + 4\left < \cos 135^{\circ},,\sin 135^{\circ}\right >[/tex]. Evaluating the x- and y-components separately, we get:

[tex]\mathbf{u}+\mathbf{v} = (7\cos 0^{\circ} + 4\cos 135^{\circ}),\mathbf{i} + (7\sin 0^{\circ} + 4\sin 135^{\circ}),\mathbf{j}[/tex]

[tex]\mathbf{u}+\mathbf{v} = 3.9,\left < \cos 26^{\circ},,\sin 26^{\circ}\right >[/tex]

To write the answer in magnitude and direction form, we can use the ormula [tex]\left|\mathbf{u}+\mathbf{v}\right| = \sqrt{(u_1+v_1)^2 + (u_2+v_2)^2}[/tex] for the magnitude, and [tex]\theta = \tan^{-1}\left(\frac{u_2+v_2}{u_1+v_1}\right)[/tex] for the direction. Plugging in the values, we get:

[tex]\left|\mathbf{u}+\mathbf{v}\right| \approx 3.9\theta \approx 26^{\circ}[/tex]

Therefore, the vector sum [tex]\mathbf{u}+\mathbf{v} is approximately equal to 3.9\left < \cos 26^{\circ},,\sin 26^{\circ}\right > , 3.9⟨cos26∘, sin26∘⟩[/tex] in magnitude and direction form.

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Answer:

  637 cm²

Step-by-step explanation:

You want the area of the larger of two similar pentagons, given that the area of the smaller is 13 cm². Corresponding side lengths are in the ratio 14 : 2.

The (14 cm) : (2 cm) ratio of corresponding sides in the two figures tells you the scale factor is 14/2 = 7. The area of the larger pentagon will be the area of the smaller, multiplied by the square of this scale factor:

  (13 cm²)×7² = 637 cm²

The area of pentagon S is 637 cm².

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(a) A range vector b that satisfies b1 = 5 and b2 = 2 can be expressed as: b = [5; 2; 0] + x3[-2; -2; 1]

(b) The family of solutions of the system ax = b is :

x = [5; 2; 0] + x3[-2; -2; 1], where x3 is any real number.

(a) In exercise 6, part (b), we are given matrix A as:

A = [1 2 3; 4 5 6; 7 8 9]

To find a range vector b in which b1 = 5 and b2 = 2, we can set up a system of equations using the row echelon form of A:

[1 2 3 | b1]    [1  2  3 | 5]
[0 1 2 | b2] => [0 -3 -6 | -8]
[0 0 0 | 0]     [0  0  0 | 0]

From the row echelon form, we can see that the pivot variables are x1 and x2, while the free variable is x3. Using the pivot variables, we can express b1 and b2 in terms of x1 and x2:

x1 + 2x2 + 3x3 = 5
x2 + 2x3 = 2

Solving for x1 and x2 in terms of x3, we get:

x1 = 5 - 2x2 - 3x3
x2 = 2 - 2x3

Thus, a range vector b that satisfies b1 = 5 and b2 = 2 can be expressed as:

b = [5; 2; 0] + x3[-2; -2; 1]

(b) Using the b vector we found in part (a), we can solve the system ax = b using Theorem 1, part (iv):

If a system of linear equations ax = b has a nontrivial solution, then the solution set is a translate of the solution set of the homogeneous system ax = 0.

The homogeneous system is given by:

[1 2 3 | 0]
[0 1 2 | 0]
[0 0 0 | 0]

From the row echelon form, we can see that the pivot variables are x1 and x2, while the free variable is x3. Using the pivot variables, we can express x1 and x2 in terms of x3:

x1 = -2x2 - 3x3
x2 = -2x3

Thus, the general solution of the homogeneous system is:
xh = x3[-2; -2; 1]

To obtain the general solution of the system ax = b, we add the particular solution we found in part (a) to the general solution of the homogeneous system:
xp = [5; 2; 0] + x3[-2; -2; 1]

Thus, the family of solutions of the system ax = b is:
x = [5; 2; 0] + x3[-2; -2; 1], where x3 is any real number.

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An equation that represents the graph include the following: C. y equals two thirds times x minus 3.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

3 -1 0 -3

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-3 + 1)/(0 - 3)

Slope (m) = -2/-3

Slope (m) = 2/3

At data point (0, -3) and a slope of 2/3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 3 = 2/3(x - 0)

y = 2x/3 - 3 i.e "y equals two thirds times x minus 3"

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The VAT for the year is Birr 75,600.

Here, we have,

The pharmacy makes 42,000 Birr in monthly sales, as stated in the problem.

We must divide the monthly sales by the number of months in a year in order to determine the overall annual sales:

Total annual sales are calculated as follows: Birr 42,000 multiplied by 12 months to equal Birr 504,000.

Now that we have the VAT rate that is in effect in the area where the pharmacy is located, we can calculate the VAT (Value Added Tax). The VAT is often calculated as a share of sales.

Assuming a 15% VAT rate, the VAT can be calculated as follows:

VAT = 15% of total annual sales, which equals 0.15 times Birr 504,000 ($75,600).

Therefore, the VAT for the entire year is 75,600 Birr.

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complete question:

Jessica pharmacy has monthly sales of Birr 42,000. If the pharmacy is open for a year , calculate TOT or VAT???

Answer:  The probability that a random chosen test taker will score between 400 and 550 is approximately 0.5328.

Step-by-step explanation:

From question 33, we know that the mean score is 500 and the standard deviation is 100.

To obtain the probability that a random test taker will score between 400 and 550, we need to standardise these scores using the formula:

z = (x - μ) / σ

where x is the score we are interested in, μ is the mean score, and σ is the standard deviation.

For x = 400:

z = (400 - 500) / 100 = -1

For x = 550:

z = (550 - 500) / 100 = 0.5

Using a standard normal distribution table or calculator, we can find the probability of z being between -1 and 0.5:

P(-1 < z < 0.5) = P(z < 0.5) - P(z < -1)

= 0.6915 - 0.1587

= 0.5328

Therefore, the probability that a random chosen test taker will score between 400 and 550 is approximately 0.5328.

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Carrie's number is 64.

Jen's number is 64 + 9 = 73.

And Fran's number is 73 - 3 = 70.

Let's define our variables:

Let x be Carrie's number.

Then Jen's number is x + 9.

And Fran's number is (x + 9) - 3.

We know that when we add their numbers together, we get 207:

x + (x + 9) + ((x + 9) - 3) = 207

Simplifying the equation:

3x + 15 = 207

3x = 207 - 15

3x = 192

x = 192/3

x = 64

So Fran's number is 70.

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[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"y" varies directly with "x"}}{y = k(x)}\hspace{5em}\textit{we also know that} \begin{cases} y=24\\ x=4 \end{cases} \\\\\\ 24=k(4)\implies \cfrac{24}{4}=k\implies 6=k\hspace{9em}\boxed{y=6x}[/tex]

The total revenue is $2600.

To calculate the revenue, we need to determine the total number of drinks and cookies sold and multiply them by their respective prices.

Number of drinks sold: 500 people

Number of cookies sold (assuming for every 5 drinks, 3 cookies are sold): (500 / 5) * 3 = 300 cookies

Price per drink: $4

Price per cookie: $2

Total revenue from drinks: Number of drinks sold * Price per drink = 500 * $4 = $2000

Total revenue from cookies: Number of cookies sold * Price per cookie = 300 * $2 = $600

Total revenue = Revenue from drinks + Revenue from cookies = $2000 + $600 = $2600

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The event that is not possible in the context of sock drawer with 5 black socks, 10 white socks, and 6 multicolored socks is (black socks, red socks). So, option(c) is right one.

We have a sock drawer, Number of blacks socks in drawer = 5

Number of white socks in drawer = 10

Number of multicolored socks in drawer = 2

Total number of socks in drawer = 17

Now, schaid will randomly pull out 2 socks without seeing in the drawer.

We have to determine the event that is not possible in this context.

a) If selected two socks are black and white, then we have sufficient that for this event and easily determine the probability, so it is an event.

b) If selected two socks are white and multicolor then we have sufficient details that for this event and easily determine the probability, so it is an event. Similarly, in case of option (d) is also an event in same reason.

But in case of optio(c), If selected two socks are black and multicolor, we have data of black socks but no idea about number red socks in drawer. That is no data related to this, so it not possible event in context. Hence, required answer is ( black socks, red socks).

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Complete question:

a sock drawer has 5 black socks, 10 white socks, and 6 multicolored socks. schaid will randomly pull out 2 socks without looking in the drawer. which answer describes an event that is not possible in this context?

a) ( black socks , white socks)

b)(white socks, multicolour socks)

c) ( black socks, red socks)

d) ( black socks , multicolour socks)

The occurrence (black socks, red socks) is not feasible in the context of a sock drawer containing 5 black socks, 10 white socks, and 6 multi-colored socks. So, choice (c) is the best one.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence.

We have a sock drawer, Number of blacks socks in drawer = 5

Number of white socks in drawer = 10

Number of multicolored socks in drawer = 2

Total number of socks in drawer = 17

Schaid will now take two socks out of the drawer at random.

The event that cannot occur in this situation must be identified.

a) If selected two socks are black and white, then we have sufficient that for this event and easily determine the probability, so it is an event.

b) If selected two socks are white and multicolor then we have sufficient details that for this event and easily determine the probability, so it is an event. Similarly, in case of option (d) is also an event in same reason.

But in case of option (c), If selected two socks are black and multicolor, we have data of black socks but no idea about number red socks in drawer. That is no data related to this, so it not possible event in context. Hence, required answer is ( black socks, red socks).

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Complete question:

a sock drawer has 5 black socks, 10 white socks, and 6 multicolored socks. schaid will randomly pull out 2 socks without looking in the drawer. which answer describes an event that is not possible in this context?

a) ( black socks , white socks)

b)(white socks, multicolour socks)

c) ( black socks, red socks)

d) ( black socks , multicolour socks)

Therefore, According to the given information: W = 30 J (x=4.0m to x=7.0m), W = 40 J (x=0 to x=7.0m and x=7.0m to x=2.0m)

To calculate work, we use the formula W = F * d * cos(theta), where F is the force applied, d is the distance moved, and theta is the angle between the force and displacement vectors. Since the force is parallel to the x-axis, theta = 0 and cos(theta) = 1.
For the first question, the force is constant between x=4.0m and x=7.0m, so we can use W = F * d = (10 N)(3.0 m) = 30 J.
For the second question, we need to split the distance into segments where the force is constant. From x=0 to x=2.0m, the force is 0 N, so no work is done. From x=2.0m to x=4.0m, the force is 5 N, so W = (5 N)(2.0 m) = 10 J. From x=4.0m to x=7.0m, the force is 10 N, so W = (10 N)(3.0 m) = 30 J. Adding these up gives W = 40 J.
For the third question, we use the same approach as the second question but in reverse. From x=7.0m to x=4.0m, the force is 10 N, so W = (10 N)(3.0 m) = 30 J. From x=4.0m to x=2.0m, the force is 5 N, so W = (5 N)(2.0 m) = 10 J. From x=2.0m to x=0, the force is 0 N, so no work is done. Adding these up gives W = 40 J.

Therefore, According to the given information: W = 30 J (x=4.0m to x=7.0m), W = 40 J (x=0 to x=7.0m and x=7.0m to x=2.0m)

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The proof that ABCD is a parallelogram is given below.

In a parallelogram, the opposite sides of the quadrilateral are parallel to each other. Therefore, there are two sets of parallel sides.

The diagram for the given condition can be made as shown below in the attached image.

Now, consider the ΔPQS. Since A and B are the midpoints of the sides PQ and PS, respectively. Therefore, according to the basic proportionality theorem, AB║QS.

Similarly, consider the ΔQRS. Since QD = DR and SC = CR, therefore, D and C are the midpoints of the sides QR and SR, respectively. Therefore, according to the basic proportionality theorem, QS║DC.

As per the two conclusions drawn above, AB║QS and QS║DC. It can be concluded that AB║QS ║DC, therefore, AB║DC.

Further, in a similar manner consider ΔPQR and ΔPSR.

In ΔPQR, A and D are the midpoints of PQ and QR, respectively. Therefore, as per the Basic proportionality theorem the AD║PS.

In ΔPSR, B and C are the midpoints of PS and SR, respectively. Therefore, as per the Basic proportionality theorem the BC║PS.

As per the two conclusions drawn above, AD║PS and BC║PS. It can be concluded that AD║PS║BC, therefore, AD║BC.

Thus, ABCD is a parallelogram because of AB║DC and AD║BC.

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Answer:

Step-by-step explanation:

The longer you study the more you can remember so if she studied for 3.50 hrs she is more likely to get a grade in the 90s

If wrong im sry

Based on the information provided, d and e represent different statistical hypotheses about a population mean, denoted by. Specifically, the hypothesis d states that the population mean is greater than or equal to 1000, while the hypothesis e states that the population mean is less than 1000.

To put this into context, let's say that we are interested in studying the average income of workers in a certain city. We can collect a sample of data from a random sample of workers in the city, calculate the sample mean, denoted by x, and use it to make inferences about the population mean,. If we want to test the hypothesis that the average income is at least 1000 dollars, we can set up the null hypothesis as d: 1000 and the alternative hypothesis as not d: 1000. This means that we assume the population mean is 1000 or greater, and we want to see if there is enough evidence in the data to reject this hypothesis in favor of the alternative.

On the other hand, if we want to test the hypothesis that the average income is less than 1000 dollars, we can set up the null hypothesis as e: 1000 and the alternative hypothesis as not e: 1000. In this case, we assume the population mean is less than 1000, and we want to see if the data provide enough evidence to reject this hypothesis in favor of the alternative.

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B = {2.5, 3.5, 4.5} will make the statement false.

Option B is the correct answer.

We have,

A is the set of all integers.

And,

B ⊆ A

This means,

B is a subset of A where all elements in B is in A.

Now,

B = {1, 2, 3}.

This is true.

B = {2.5, 3.5, 4.5}

This is not true.

2.5, 3.5, and 4.5 are not integers.

They are real numbers.

B = {0}

This is true.

B = {-4, -1, 0, 5, 10}

This is true.

Thus,

B = {2.5, 3.5, 4.5} will make the statement false.

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An increase in the exchange rate of the U.S. dollar relative to a trading partner can result from higher interest rates and higher inflation in the U.S. The correct answer is option (e).

This is because higher interest rates attract foreign investors to the U.S., increasing demand for the U.S. dollar and causing its value to rise relative to other currencies.

Higher inflation in the U.S. also makes the dollar less attractive to foreign investors, causing its value to decline.

The other options listed may affect trade and economic activity, but do not directly impact the exchange rate.

Therefore, the correct option is (e) higher interest rates and higher inflation in the U.S.

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Deli can make 515,625 sandwiches.

Given that a deli has 25 types of bread, 25 different kinds of meat, 15 kinds of cheese, and 55 types of condiments, we need to find that how many sandwiches it can make,

So, the number of sandwiches it can make = 25 x 25 x 15 x 55

= 515,625

Hence the deli can make 515,625 sandwiches.

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To find the distance d from y to the subspace of R4 spanned by v1 and v2, we can use the formula. The distance d from y to the subspace of R4 spanned by v1 and v2 is approximately 6.558.

d = ||y - proj_v(y)||

where proj_v(y) is the projection of y onto the subspace spanned by v1 and v2. We can find proj_v(y) as:

proj_v(y) = ((y · v1)/(v1 · v1)) v1 + ((y · v2)/(v2 · v2)) v2

where · represents the dot product. Plugging in the given values, we get:

proj_v(y) = ((-3)(3) + (5)(-4) + (0)(2) + (-4)(-1))/(3^2 + (-4)^2 + 2^2 + (-1)^2) [3 -4 2 -1] + ((-3)(-4) + (5)(1) + (0)(-2) + (-4)(-20))/((-4)^2 + 1^2 + (-2)^2 + (-20)^2) [-4 1 -2 -20]
         = (-26/30) [3 -4 2 -1] + (53/441) [-4 1 -2 -20]
         = [-34/35 77/210 -43/105 -617/441]

Then, we can calculate the distance d as:

d = ||y - proj_v(y)|| = ||[-3 5 0 -4] - [-34/35 77/210 -43/105 -617/441]|| = ||[77/35 -131/210 43/105 -1117/441]||
 = sqrt((77/35)^2 + (-131/210)^2 + (43/105)^2 + (-1117/441)^2)
 = 6.558

Therefore, the distance d from y to the subspace of R4 spanned by v1 and v2 is approximately 6.558.

To compute the distance d from y to the subspace of R4 spanned by v1 and v2, we first need to find the orthogonal projection of y onto the subspace. Let's denote the projection as p(y).

1. Find the coordinates of y with respect to the basis {v1, v2}. Solve the equation: c1 * v1 + c2 * v2 = y.
2. Calculate p(y) using the coordinates found in step 1: p(y) = c1 * v1 + c2 * v2.
3. Calculate the distance d using the formula d = ||y - p(y)||.

After following these steps, you will find the distance d from y to the subspace of R4 spanned by v1 and v2.

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All four sequences (an = 0, an = 1, an = (-4)n, and an = 2(-4)n + 3) are solutions of the recurrence relation an = -3an-1 + 4an-2.

a. an = 0

This is a solution of the recurrence relation an = -3an-1 + 4an-2. To show this, we can start by substituting an = 0 and an-1 = 0 into the recurrence relation. We get:

0 = -3(0) + 4(0)

0 = 0

Since this is true, it follows that an = 0 is a solution of the recurrence relation.

b. an = 1

This is also a solution of the recurrence relation an = -3an-1 + 4an-2. To show this, we can start by substituting an = 1 and an-1 = 0 into the recurrence relation. We get:

1 = -3(0) + 4(1)

1 = 4

Since this is true, it follows that an = 1 is a solution of the recurrence relation.

c. an = (-4)n

This is also a solution of the recurrence relation an = -3an-1 + 4an-2. To show this, we can start by substituting an = (-4)n and an-1 = (-4)n-1 into the recurrence relation. We get:

(-4)n = -3((-4)n-1) + 4((-4)n-2)

(-4)n = -12((-4)n-1) + 16((-4)n-2)

(-4)n = 16((-4)n-2) - 12((-4)n-1)

Since this is true, it follows that an = (-4)n is a solution of the recurrence relation.

d. an = 2(-4)n + 3

This is also a solution of the recurrence relation an = -3an-1 + 4an-2. To show this, we can start by substituting an = 2(-4)n + 3 and an-1 = 2(-4)n-1 + 3 into the recurrence relation. We get:

2(-4)n + 3 = -3(2(-4)n-1 + 3) + 4(2(-4)n-2 + 3)

2(-4)n + 3 = -6(-4)n-1 - 9 + 8(-4)n-2 + 12

2(-4)n + 3 = 8(-4)n-2 - 6(-4)n-1 + 12

Since this is true, it follows that an = 2(-4)n + 3 is a solution of the recurrence relation.

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The sign of the expression can be determined by examining the signs of the individual terms involved.

3/5: The sign of this term depends on the sign of the numerator (3) and the denominator (5). As both the numerator and denominator are positive, this term is positive.

(3/5) / (5/3): To simplify this expression, we can multiply the numerator and denominator of the second fraction by 3/5, resulting in (3/5) * (3/5) / 1. The numerator is positive as it is the product of two positive numbers, and the denominator is positive as well. Therefore, this term is positive.

Combining the two positive terms, the overall expression will have a positive sign.

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The total number of isomers with the formula [Pd(C2O4)2I2]2– is 3150.

There are two parts to this answer: the first part is to determine the coordination number of the central palladium (Pd) atom, and the second part is to determine the number of possible isomers based on the coordination number.

To determine the coordination number, we need to count the number of ligands (the molecules that bind to the central atom) attached to the Pd atom. In this case, we have four oxalate (C2O4) ligands, each of which contributes two atoms (a total of eight atoms), and two iodide (I) ligands, each of which contributes one atom (a total of two atoms). This gives us a total of 10 ligands attached to the Pd atom. Since each ligand can only form one bond with the Pd atom, the coordination number is 10.

Next, we need to determine the number of possible isomers. Isomers are molecules with the same chemical formula but different arrangements of atoms. For this complex ion, there are two types of isomers: geometrical and optical.

Geometrical isomers arise from the fact that the ligands can be arranged around the central atom in different ways. In this case, since there are 10 ligands, there are a total of 10!/[(4!2!2!)x2] possible geometrical isomers, or 3150.

Optical isomers arise when there are non-superimposable mirror images of the molecule. However, since this complex ion has a plane of symmetry, it is achiral and does not have optical isomers.

Therefore, the total number of isomers with the formula [Pd(C2O4)2I2]2– is 3150.

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The bearings of B from A in the given diagrams are shown to be :

To be able to tell the bearing of B from A, you need to Identify and mark two points on a map or diagram of the area. Proceed to draw a straight line between these two points demarcating them clearly.

Employ a protractor in measuring the angle created between the aforementioned line and the north-south axis; this calculated measurement will be referred to as your "bearing."

Then, from the North - south line going up from A, you check the degree measure clockwise to B. Doing this, the bearings of B from A would be 50 °, 115° and 223 ° respectively.

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