Halp me this question

Step-by-step explanation:

You'll need to simplify the numerator and denominator.

First, I started by simplifying the numerator, which is a quadratic equation.

(Quadratic Equation is: a^2 + ba + c

For each factor, you'll need to find two numbers with a sum of b and a multiple of c.

Then, I simplified the denominator by expanding out the equation.

After, I simplified the numerator and denominator, I started to cancel out any numbers/variables that were the same.

Answer:

√(15^2 - 9^2) = √(225 - 81) = √144 = 12

√(15^2 + 9^2) = √(225 + 81) = √306

= 3√34

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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Liam volunteered for approximately 0.32 hours (or 19 minutes) during the first month.

Let's start by using algebra to solve the problem.

First, we'll use x to represent the number of hours Liam volunteered during the first month. Then, since he volunteered 123 times as many hours the second month as he did the first month, he volunteered 123x hours during the second month.

According to the problem, Liam volunteered a total of 40 hours over the two months. We can set up an equation to represent this:

x + 123x = 40

Simplifying this equation:

124x = 40

Dividing both sides by 124:

x = 0.3225806451612903

So Liam volunteered for approximately 0.32 hours (or 19 minutes) during the first month.

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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 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???

The portion of the net public debt held by foreign residents refers to the amount of a country's public debt owed to foreign creditors and can have implications on a country's financial stability and exchange rate.

the portion of the net public debt held by foreign residents, we first need to understand what net public debt is. Net public debt refers to the total amount of debt owed by a government to its creditors, including domestic and foreign residents.

The portion of the net public debt held by foreign residents is true of the following:

1. It represents the amount of a country's public debt that is owned by foreign individuals, companies, or governments.
2. It is considered a liability, as the country is obligated to pay interest and eventually repay the principal amount to these foreign creditors.
3. The portion of net public debt held by foreign residents can impact a country's exchange rate, as the repayment of debt may require converting the domestic currency into foreign currency.
4. A high level of foreign-held public debt can indicate a dependence on foreign financing and may raise concerns about the country's financial stability and creditworthiness.

In summary, the portion of the net public debt held by foreign residents refers to the amount of a country's public debt owed to foreign creditors and can have implications on a country's financial stability and exchange rate.

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The total number of permutations of the four digits is 4 x 3 x 2 x 1 = 24.

To calculate the probability that the password for the school's grading system is composed of a one, a two, a three, and a four, we need to use the formula for permutations. A permutation is the number of ways that objects can be arranged in a specific order. In this case, we want to know the number of permutations of the four digits that make up the password.

There are nine possible digits to choose from, but we need to choose four specific digits: one, two, three, and four. The first digit can be any of the four digits we need, so there are four choices. The second digit can be any of the remaining three digits, so there are three choices. The third digit can be any of the remaining two digits, and the fourth digit must be the remaining digit.

Therefore, the total number of permutations of the four digits is 4 x 3 x 2 x 1 = 24. However, this is only the numerator of the probability fraction. The denominator is the total number of possible 4-digit passwords, which is 9 x 8 x 7 x 6 = 4,536.

So the probability that the password for the school's grading system is composed of a one, a two, a three, and a four is 24/4,536, which simplifies to 1/189. This means that there is a very small chance of the password being composed of these specific digits.

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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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Answer:

x = -5 and x = -4 are the x-intercepts of this parabola.

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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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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Option B is correct i.e. given graph is of equation y = 9/x

If draw the graph of y = 9/x, we can start by making a table of values for x and y.

When x = 1, y = 9/1 = 9.

When x = 2, y = 9/2 = 4.5.

When x = 3, y = 9/3 = 3.

When x = 4, y = 9/4 = 2.25.

When x = 5, y = 9/5 = 1.8.

We can plot these points on a graph and connect them with a smooth curve to get the graph of y = 9/x.

The graph of y = 9/x is a hyperbola that passes through the points (1, 9), (2, 4.5), (3, 3), (4, 2.25), and (5, 1.8). The graph approaches the x-axis and the y-axis but never touches them. The x-axis is a horizontal asymptote. The y-axis is a vertical asymptote. The graph is symmetric with respect to the origin because y = 9/x is unchanged when x is replaced by -x and y is replaced by -y.

The graph of 9/x is same as given graph.

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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 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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The requreid surface area of the sphere with a radius of 19 cm is 4536.46 cm².

To determine the exact surface area of the sphere with a diameter of 19 cm.

The surface area of the sphere is given as,
Surface area of the sphere = 4πr²

Substitute the value of the radius, r = 19 in the above formula,
Surface area of the sphere = 4*3.14*19²
                                             = 4536.46 cm²

Thus, the requreid surface area of the sphere with a radius of 19 cm is 4536.46 cm².

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A computed p-value less than 0.001 provides very strong evidence to reject the null hypothesis in a hypothesis test.

If the computed p-value is less than 0.001 in a hypothesis test, there is very strong evidence to reject the null hypothesis.

The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true. It represents the strength of evidence against the null hypothesis. A small p-value means that it is very unlikely to observe such an extreme test statistic under the null hypothesis, and therefore provides evidence against the null hypothesis.

The significance level, usually denoted by α, is the maximum allowable probability of making a Type I error, which is rejecting the null hypothesis when it is actually true. The conventional significance level is 0.05, which means that we are willing to accept a 5% chance of making a Type I error.

If the computed p-value is less than the significance level, we reject the null hypothesis and conclude that the alternative hypothesis is supported by the data. A p-value less than 0.001 means that the observed result is highly unlikely to occur by chance alone, even at a very low significance level such as 0.1% or 0.01%. Therefore, we have strong evidence against the null hypothesis and can reject it in favor of the alternative hypothesis.

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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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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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It is not wise to use the correlation coefficient r to summarize the association between this new pair of variables, without first examining the data and considering the context of the problem.

The correlation coefficient r measures the strength and direction of the linear relationship between two variables. However, it assumes that the relationship between the variables is linear, and that there are no outliers or influential points that could affect the results.

If the relationship between the variables is not linear or there are outliers, then the correlation coefficient r may not accurately summarize the association between the variables. In this case, it would be more appropriate to use other measures, such as nonparametric correlation coefficients or regression analysis.

Therefore, before using the correlation coefficient r, it is important to carefully examine the data and consider any potential issues that could affect the results. Only then can we determine whether the correlation coefficient r is an appropriate measure for summarizing the association between the variables.

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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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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]

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 quantity that maximizes revenue is 1450.

The price of each item at this production level is $14.50.

The total revenue at this price is $21,025.

The revenue as a function of q can be found by multiplying the price (p) by the quantity (q):

R(q) = pq = q(29 - 0.01q) = 29q - 0.01q^2

To find the quantity that maximizes revenue, we take the derivative of R(q) with respect to q and set it equal to zero:

R'(q) = 29 - 0.02q = 0

0.02q = 29

q = 1450

Therefore, the quantity that maximizes revenue is 1450.

To find the price at this production level, we substitute q = 1450 into the demand equation:

p = 29 - 0.01(1450) = $14.50

So the price of each item at this production level is $14.50.

The total revenue at this price can be found by substituting q = 1450 and p = $14.50 into the revenue equation:

R(1450) = 1450(14.50) = $21,025

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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]

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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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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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 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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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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