Which of these will have an effect on the GDP of the country?
Sam loses $10.00 in a bet with Kurt.
Sally buys a new patio furniture set.
Hershey makes 1,000 chocolate bars to export to Brazil.
Jack's grandpa fixes his car light.

Answer:

x = 42

y = 21

Step-by-step explanation:

Since its a right triangle, we have:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

[tex]sin (60) = \frac{21\sqrt{3} }{x} \\\\x= \frac{21\sqrt{3} }{sin (60)} \\\\x= \frac{21\sqrt{3} }{\frac{\sqrt{3} }{2} } \\\\x = \frac{21\sqrt{3} *2 }{\sqrt{3} } \\\\x = 21*2\\\\x = 42[/tex]

[tex]cos (60) = \frac{y}{x}\\\\cos (60) = \frac{y}{42}\\\\y = cos (60)*42 \\\\y = \frac{1}{2} * 42\\\\y = 21[/tex]

A 15-lb mixture, she should use 1.256 pounds of dried-fruit mixture and 13.744 pounds of nuts.

Based on the given information, we can set up the following system of equations:
Equation 1: x + y = 15 (since the total weight of the mixture is 15 pounds)
Equation 2: (5.90 * x) + (14.75 * y) = 9.44 * 15 (since the total cost of the mixture is the cost per pound multiplied by the weight of each component)
Now, let's convert this system of equations into matrix form:
| 1  1 |   | x |   | 15 |
| 5.90  14.75 |   | y | = | 9.44 * 15 |
To solve for x and y, we can use matrix algebra. We can multiply the inverse of the coefficient matrix by the right-hand side matrix to get the solution matrix:
| x |   | 1  1 |^-1   | 15 |
| y | = | 5.90  14.75 |      | 9.44 * 15 |
Using matrix calculations, we find that the inverse of the coefficient matrix is:
| 0.0877  -0.0576 |
| -0.0059   0.0678 |
Now, multiplying the inverse matrix by the right-hand side matrix gives us:
| x |   | 0.0877  -0.0576 |   | 15 |
| y | = | -0.0059   0.0678 | * | 9.44 * 15 |
Simplifying the multiplication gives us:
x = 1.256
y = 13.744
Therefore, the saleswoman should use 1.256 pounds of dried-fruit mixture and 13.744 pounds of nuts to get a 15-pound mixture.

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Rounded to the nearest tenth of a percent, the probability is approximately 27.8%.

To determine if the event of rolling a pair of dice and getting doubles or a sum of 6 is mutually exclusive, we need to assess whether the two outcomes can occur simultaneously or if they are mutually exclusive.

Let's analyze the two outcomes separately:

1. Getting doubles: When rolling a pair of dice, getting doubles means that the numbers on both dice are the same. The possible outcomes for getting doubles are (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6). There are a total of 6 outcomes that satisfy this condition.

2. Getting a sum of 6: To get a sum of 6, the numbers on the two dice should add up to 6. The possible outcomes for this condition are (1,5), (2,4), (3,3), (4,2), and (5,1). There are a total of 5 outcomes that satisfy this condition.

Now, to determine if the two outcomes are mutually exclusive, we need to check if there are any outcomes that satisfy both conditions. In this case, the outcome (3,3) satisfies both conditions (doubles and sum of 6).

Since there is one outcome that satisfies both conditions, we can conclude that the event of rolling a pair of dice and getting doubles or a sum of 6 is not mutually exclusive.

To find the probability of this event, we need to determine the total number of possible outcomes when rolling a pair of dice. Each die has 6 sides, so there are 6 possible outcomes for each die, resulting in a total of 6 * 6 = 36 possible outcomes when rolling a pair of dice.

The probability is calculated by dividing the number of favorable outcomes (satisfying the condition) by the total number of possible outcomes.

Favorable outcomes = 6 (for doubles) + 5 (for sum of 6) - 1 (for the overlapping outcome) = 10

Probability = Favorable outcomes / Total number of outcomes = 10 / 36 ≈ 0.2778

Rounded to the nearest tenth of a percent, the probability is approximately 27.8%.

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the statement “Zero is included in the range of the relation” is correct and the statement “5 is included in the domain of this relation” is also correct.

if we observe the given ordered pairs we can easily determine that,The domain is the set of all x-values from the ordered pairs in the relation.

So, the domain of the given relation is {−4,0,5} because we have only three unique x-values from the given ordered pairs.

The range is the set of all y-values from the ordered pairs in the relation.

So, the range of the given relation is {−7,−3,2,6} because we have four unique y-values from the given ordered pairs.

Also, we can conclude that the given relation is not a function since we have the same x-value (5) corresponding to two different y-values (−3,2).

And it is true that the zero is included in the range of the relation since we have the ordered pair (0,6) which gives the y-value of 6.

So, the statement “The given relation is a function” is incorrect. But the statement “Zero is included in the range of the relation” is correct and the statement “5 is included in the domain of this relation” is also correct.

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Hello!

Answer:

11/12

Step-by-step explanation:

To solve this problem, we would need to find the denominator of the 2 numbers. In this case, it is 12. We will now convert the fractions to twelfths.

2/3 = 8/12

1/4 = 3/12

After we add 8/12 and 3/12, we get our answer 11/12.

Based on the Pythagorean theorem, in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side. So, we can use this to find the possible values of the third side of the triangle.

The two given sides are 15 cm and 17 cm. We can label the unknown side as "x". Then, we can set up an equation:

15^2 + 17^2 = x^2

Simplifying this equation, we get:

225 + 289 = x^2

514 = x^2

x = sqrt(514)

Therefore, the possible value of the third side that would make it a right triangle is approximately 22.72 cm.

The sequence of transformations that maps ABC to A’B’C is a reflection across the line y = x followed by a translation of 10 units right and 4 units up.

The equivalent vertices C and C' are given as follows:

Considering the change in the orientation of the figure, it was reflected over the line y = x, for which the rule is given as follows:

(x,y) -> (y,x).

Hence:

(-4,2) -> (2,-4)

To go from (2,-4) to (12,0), the translation rule is given as follows:

(x,y) -> (x + 10, y + 4)

Hence the translation is defined as follows:

10 units right and 4 units up.

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The expression (3 - 11/5) ÷ (3 / -9/5) simplifies to -12/25.

To simplify the expression (3 - 11/5) ÷ (3 / -9/5), we can follow the order of operations, which is commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division - from left to right, Addition and Subtraction - from left to right).

First, let's simplify the numerator:

3 - 11/5 = 15/5 - 11/5 = 4/5

Next, let's simplify the denominator:

3 / -9/5 = 3 * -5/9 = -15/9 = -5/3

Now we have:

(4/5) ÷ (-5/3)

To divide fractions, we can multiply by the reciprocal of the divisor. So, we have:

(4/5) * (-3/5)

Multiplying across the numerators and denominators, we get:

(4 * -3) / (5 * 5) = -12/25

The simplified expression is -12/25.

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the period of y = 3cot(x) remains as π. the period of y = 3cot(4x - 3x) is also π.

To find the period of the function y = 3cot(4x - 3x), we need to determine the length of one complete cycle of the function.

First, let's simplify the expression inside the cotangent function: 4x - 3x = x.

Now, the cotangent function has a period of π, which means it repeats every π units.

To find the period of the given function y = 3cot(x), we need to determine how the variable x affects the period. Since the coefficient of x is 1, it means that the period is not affected by any scaling or stretching.

In summary, the period of the function y = 3cot(4x - 3x) is π, which means the function repeats every π units along the x-axis.

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The diagram to the right BC is parallel to DE.

Here, AD=15,

DB=12,

AE=10, and

EC=8.

We need to determine if BC||DE or not.

angle ADE = 180 - 90  = 49.106 degree.

Now, using the triangle BDC, we can find the value of sin[angle CDB] as follows.

angle CDB = angle DAB = angle ABD = 180 - angle ADE - angle EDC

To determine if BC is parallel to DE, we can use the concept of proportional sides of the triangle.

From the information given, AD = 15, DB = 12, AE = 10, and EC = 8.

If BC is parallel to DE, then by the intercept theorem (also known as Thales' theorem), the Die segments AD/DB and AE/EC must be the same.

Let's calculate these ratios:

AD/DB = 15/12 = 5/4

AE/EC = 10/8 = 5/4

AD/DB = AE/EC = 5/ 4, so we can conclude that: BC is parallel to DE.

The reason for this is that if two ratios are equal, it means that the corresponding sides of the triangle formed by the intersecting lines are proportional, which is a characteristic of parallel lines.

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The triangles EFG and WVU are similar by SSS

from the question, we have the following parameters that can be used in our computation:

Triangle EFG and WVU

The triangles in this figure are

EFG and WVU

These triangles are similar because:

The triangles do have similar corresponding sides

i.e. Ratio = 525/252 = 875/420 = 825/396

Evaluate

Ratio = 2.083 = 2.083 = 2.083

Hence, the triangles EFG and WVU are similar

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Among the 80 customers, 64 individuals choose to order drinks at the restaurant.

To find the number of people who order drinks at the restaurant, we can start by calculating the percentage of customers who do not order drinks.

Given that 20% of the customers do not order drinks, we can calculate the number of customers who do not order drinks by multiplying 80 (total customers) by 0.20 (20% expressed as a decimal):

Number of customers who do not order drinks = 80 * 0.20 = 16.

Since the total number of customers is 80, and 16 customers do not order drinks, we can subtract the number of customers who do not order drinks from the total number of customers to find the number of customers who do order drinks:

Number of customers who order drinks = 80 - 16 = 64.

Therefore, 64 people order drinks at the restaurant.

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They can buy 140 vans, 70 small trucks, and 70 large trucks.

The truck company plans to spend 14 million on 280 vehicles. Each commercial van cost 55,000 dollars. Each small truck 20,000 dollars and each large truck 70,000 dollars. They needed twice as many van as small truck

Therefore,

let

s = number of small truck

number of van = v

let

l = number of large truck

v + s + l = 280

55,000(v) + 20,000(s) + 70,000(l) = 14,000, 000

11v + 4s + 14l = 2800

Hence,

v = 2s

So,

26s+ 14l = 2800

26s + 14l = 2800

3s + l = 280

multiply equation(ii) by 14

26s + 14l = 2800

42s + 14l = 3920

subtract the equation

16s = 1120

s = 70

Therefore, they can buy the following:

number of small truck = 70

number of van = 140

number of large truck = 280 - 140 - 70 = 70

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The amount that is equal to 24 pints can be determined by using the conversion factors between different units of volume. The following amounts are equal to 24 pints:

A. 48 cups: There are 2 cups in 1 pint. Therefore, 24 pints = 24 × 2 cups = 48 cups.

B. 192 fluid ounces: There are 8 fluid ounces in 1 cup, and 2 cups in 1 pint. Therefore, 24 pints = 24 × 2 cups = 48 cups = 48 × 8 fluid ounces = 384 fluid ounces. Hence, 192 fluid ounces are equal to 24 pints.

C. 3 gallons: There are 8 pints in 1 gallon. Therefore, 24 pints = 24/8 gallons = 3 gallons.

D. 48 quarts: There are 2 pints in 1 quart. Therefore, 24 pints = 24/2 quarts = 12 quarts. Hence, 48 quarts are not equal to 24 pints.

Therefore, the correct answers are A, B, and C.

the sequence g is a decreasing sequence.

Here is the step-by-step solution to the problem based on the information given in the question:

Wanahton purified a portion of water with 900 grams of contaminants. Each hour, a third of the contaminants was filtered out.Let g(n) be the amount of contaminants (in grams) that remained by the beginning of the nth hour. g is a sequence. We need to determine the kind of sequence.The amount of contaminants in the beginning

= 900 grams

Amount of contaminants filtered out

= (1/3) * 900 = 300

grams Amount of contaminants left after first

hour = 900 - 300 = 600

gramsAmount of contaminants filtered out in the second

hour = (1/3) * 600 = 200

grams Amount of contaminants left after the second

hour = 600 - 200 = 400 grams

Amount of contaminants filtered out in the third

hour = (1/3) * 400 = 133.33 grams

(rounded to two decimal places)Amount of contaminants left after the third

hour = 400 - 133.33 = 266.67 grams

(rounded to two decimal places)In this way, the sequence will continue. We can observe that the amount of contaminants in the beginning is decreasing and the sequence is decreasing as well

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The difference between the observed and expected number of late departures is statistically significant, we need to perform a binomial test by calculating the probability of observing 16 or more late departures out of 300 flights assuming the null hypothesis is true. If the resulting p-value is less than 0.05, we can conclude that the difference is statistically significant.

Based on the given information, an airline with a 95% on-time departure rate has 16 out of 300 flights with late departures. The question asks whether the difference between what occurred (16 late departures) and what you would expect by chance is statistically significant.
To determine if the difference is statistically significant, we need to conduct a hypothesis test. In this case, we can use a binomial test since we are dealing with two possible outcomes: on-time departure or late departure.
The null hypothesis (H0) assumes that the observed number of late departures is equal to what would be expected by chance. The alternative hypothesis (Ha) assumes that there is a significant difference between the observed and expected values.
In this case, the expected number of late departures can be calculated by multiplying the total number of flights (300) by the expected on-time departure rate (95%). This gives us an expected value of 300 * 0.05 = 15.
To perform the binomial test, we can calculate the probability of observing 16 or more late departures out of 300 flights, assuming the null hypothesis is true. This probability can be calculated using the binomial probability formula or by using statistical software.
If the resulting probability (also known as the p-value) is less than the significance level (usually 0.05), we can reject the null hypothesis and conclude that the difference between what occurred and what would be expected by chance is statistically significant. Otherwise, if the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that the difference is not statistically significant.
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1) 10% stock dividend: Increase in shares, no change in equity value.

2) 2 for 1 stock split: Doubles shares, no change in equity value.

3) 1 for 5 reverse stock split: Decreases shares, no change in equity value.

The decisions made by Mahmud Mahtab regarding stock dividend, stock split, and reverse stock split would result in the following changes to the accounts:

1) 10% Stock Dividend:

A stock dividend is a distribution of additional shares of stock to existing shareholders. In this case, a 10% stock dividend means that for every 10 shares held, shareholders will receive an additional share. As a result, the following changes would occur:

- Common stock: The number of shares would increase by 10% (3,000 additional shares).

- Additional paid-up capital: There would be no change.

- Retained earnings: There would be a reduction of the amount equal to the market value of the shares issued as dividends.

2) 2 for 1 Stock Split:

A stock split involves dividing existing shares into a larger number of shares. In a 2 for 1 stock split, each existing share would be split into two shares. The following changes would take place:

- Common stock: The number of shares would double (60,000 shares).

- Additional paid-up capital: There would be no change.

- Retained earnings: There would be no change.

3) 1 for 5 Reverse Stock Split:

A reverse stock split combines a number of existing shares into a smaller number of shares. In a 1 for 5 reverse stock split, every five shares would be consolidated into one share. The accounts would be affected as follows:

- Common stock: The number of shares would decrease by 80% (24,000 shares).

- Additional paid-up capital: There would be no change.

- Retained earnings: There would be no change.

Note: The above changes would affect the number of shares and their par value, but the total shareholders' equity (1,00,00,000 TK) would remain unchanged.

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Answer:4

Step-by-step explanation:1+1 is 2, so if you take 2+2 it is 4, same as 2×2 is 4.

Answer:

slope (m) = 2/3

Step-by-step explanation:

slope = change in x /change in y

Also, slope is y2 - y1 / x2 -x1. That is what I apply for this activity, hence:

slope = 3 - (-1) / 0 - (-6)

         = 3 + 1 / 0 + 6

         = 4 / 6

         = 2/3

∴ slope(m) = 2/3

In the first row, the ordered pair can be expressed as f(8) = -6 in function notation.

Of(3) is 18.

Of(x) = -5 when x is -2.

The given table represents a function, and we need to express the values in function notation and determine specific inputs that correspond to certain outputs.

In the table's first row, the ordered pair are shown which can be expressed as function notation:

f(8) = -6

This means that when the input (x) is 8, the corresponding output (f(x)) is -6.

f(x) = -5 when x is -2.

This means that when the input (x) is -2, the value of the function (f(x)) is -5.

In the table, the function is defined by the equation f(x) = 8x - 6. Each input value (x) is multiplied by 8 and then subtracted by 6 to determine the corresponding output (f(x)).

By substituting different values for x into the function, we can find the corresponding values for f(x) in the table.

when x = 3, we have:

f(3) = 8(3) - 6

f(3) = 24 - 6

f(3) = 18

So, f(3) is 18.

Similarly, when x = -2, we have:

f(-2) = 8(-2) - 6

f(-2) = -16 - 6

f(-2) = -22

Thus, when x is -2, f(x) is -22.

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True because corresponding sides and angles of the triangles are congrent.

Answer: C

Step-by-step explanation:

Point D is at -14 on the number line.

In Mathematics, the midpoint of a line segment with two end points can be calculated by adding each end point on a line segment together and then divide by two (2).

Since E is the midpoint of line segment CD, we can logically deduce the following relationship:

Line segment CD = Line segment C + Line segment D

Midpoint E = (point C + point D)/2

By substituting the given points into the equation above, we have the following:

-3 = (8 + D)/2

-6 = 8 + D

D = -6 - 8

D = -14

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The equation W = 32 - 0.05n represents the volume of water used, the glass tank's volume will be equal to W plus the volume occupied by the marbles.

In the given equation W = 32 - 0.05n, W represents the volume of water (in liters) Andrei uses, and n represents the number of marbles used. We can interpret this equation as follows: as Andrei increases the number of marbles used (n), the volume of water required (W) decreases.

To determine the glass tank's volume, we need to consider the relationship between the volume of water used and the number of marbles used. We can rearrange the equation to solve for n:

W = 32 - 0.05n

0.05n = 32 - W

n = (32 - W) / 0.05

The volume of the glass tank can be inferred from the equation, as the total volume will be the sum of the volume occupied by marbles and the volume occupied by water.

If we assume that the volume occupied by the marbles is constant, then the remaining volume in the tank will be filled with water. Therefore, the glass tank's volume can be represented as:

Glass Tank Volume = Volume of Water (W) + Volume of Marbles

The given equation W = 32 - 0.05n represents the volume of water used based on the number of marbles, but it does not directly provide information about the glass tank's volume. Further information about the marbles or the tank's dimensions is required to determine the glass tank's volume accurately.

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The probability that the 5 starting members of the basketball team are lined up from shortest to tallest is 1/120. Option A.

To calculate the probability that the 5 starting members of the basketball team are lined up from shortest to tallest, we need to determine the number of favorable outcomes (arrangements where the players are lined up from shortest to tallest) and divide it by the total number of possible outcomes.

Since the order matters and we want the players to be arranged from shortest to tallest, there is only one favorable outcome. The shortest player must be in the first position, followed by the second shortest, and so on, until the tallest player is in the last position.

The total number of possible outcomes is given by the number of permutations of 5 players, which is denoted as 5!.

Therefore, the probability is:

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

Probability = 1 / 5!

Probability = 1 / (5 * 4 * 3 * 2 * 1)

Probability = 1 / 120 Option A is correct.

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The expression that is equivalent to StartRoot [tex]8 x^7 y^8[/tex] EndRoot is ([tex]2 x^3 y^4[/tex] StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot [tex]8 x^7 y^8[/tex] EndRoot:

We can rewrite 8 as [tex]2^3[/tex], and since the square root can be split over multiplication, we have StartRoot [tex](2^3) x^7 y^8[/tex] EndRoot. Applying the exponent rule for square roots, we get StartRoot [tex]2^3[/tex] EndRoot StartRoot [tex]x^7[/tex] EndRoot StartRoot [tex]y^8[/tex] EndRoot.

Simplifying further, we have 2 StartRoot [tex]2 x^3 y^4[/tex] EndRoot StartRoot [tex]2^2[/tex] EndRoot StartRoot [tex]x^2[/tex] EndRoot StartRoot [tex]y^4[/tex] EndRoot. Finally, we obtain 2 [tex]x^3 y^4[/tex] StartRoot 2 x EndRoot, which is the expression in question.

([tex]2 x y^2[/tex] StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have [tex]2 x y^2[/tex]StartRoot [tex](2^3) x^3[/tex] EndRoot. Applying the exponent rule for square roots, we get [tex]2 x y^2[/tex] StartRoot [tex]2^3[/tex] EndRoot StartRoot [tex]x^3[/tex] EndRoot.

Simplifying further, we have [tex]2 x y^2[/tex] StartRoot 2 x EndRoot. Squaring the entire expression, we obtain ([tex]2 x y^2[/tex] StartRoot 2 x EndRoot)^2.

Therefore, the expression ([tex]2 x^3 y^4[/tex] StartRoot 2 x EndRoot)^2 is equivalent to StartRoot [tex]8 x^7 y^8[/tex] EndRoot.

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The missing values for the inverse matrix A⁻¹ are:

The solution is:

In Mathematics and Geometry, a square matrix refers to a type of matrix that is composed of an equal number of both rows and columns. Generally speaking, m × m matrix is typically referred to as a square matrix of order m.

Next, we would convert the system of three linear equations in standard form to matrix form as follows;

[tex]\left[\begin{array}{ccc}1&1&1\\10&-20&98\\5&10&-10\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}200\\250\\500\end{array}\right][/tex]

By using technology, the solutions to this system of three linear equations include the following:

x = -9200

y = 7025

z = 2375.

By using technology, the inverse of this matrix is given by;

[tex]A^{-1}=\left[\begin{array}{ccc}-78&2&11.8\\59&-1.5&-8.8\\20&-0.5&-3\end{array}\right][/tex]

Therefore, the missing values are as shown in the inverse of this matrix A⁻¹ above.

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Answer: 268

Step-by-step explanation:

Answer: All of the choices in the response would be correct.

Step-by-step explanation:

The standard error represents the average deviation of the sample means from the true population mean. Rounding this value to four decimal places, the standard error of X¯¯¯ is approximtely 0.6500 mpg.

A smaller standard error indicates that the sample means are more likely to be close to the population mean.To calculate the standard error of X¯¯¯, the mean from a random sample of 25 fill-ups by one driver, we can use the formula:

Standard Error (SE) = σ / sqrt(n),

where σ is the standard deviation and n is the sample size.

In this case, the standard deviation (σ) is given as 3.25 mpg, and the sample size (n) is 25.

Plugging in these values into the formula, we have:

SE = 3.25 / sqrt(25).

Calculating the square root of 25, we get:

SE = 3.25 / 5.

Performing the division, we find:

SE ≈ 0.65.

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