Find the measure of 4=

a. The function will have 4 zeros

b. There are 2 negative zeroes, 2 positive zeros and no complex zero.

c. The possible zeros are ±1, ±2, ±3, ±6

d. The zeros are -1, 1, -2 and 3

Given that

-x⁴ + x³ + 7x² - x - 6

The degree of the above polynomial is 4

This means that it will have 4 zeros

Here, we have

-x⁴ + x³ + 7x² - x - 6

There are two sign changes from negative to positive, and vice versa.

So, there are 2 negative zeroes, 2 positive zeros and no complex zero.

Here, we have

-x⁴ + x³ + 7x² - x - 6

In the above, we have

p = -1

q = -6

The possible zeros are calculated as

Zeros = ±Factor of q/Factor of p

This gives

Zeros = ±(1, 2, 3, 6)/1

This gives

Zeros = ±1, ±2, ±3, ±6

Here, we have

-x⁴ + x³ + 7x² - x - 6

Set x = 1

-(1)⁴ + (1)³ + 7(1)² - (1) - 6 = 0

This means that, we x - 1 is a factor

So, we have the following synthetic setup

1   |  -1  1   7   -1  -6

           -1   0   7  6

      -1   0   7   6  0

So, we have

(x - 1)(-x³ + 7x + 6)

When factored, we have

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

This means that the zeros are -1, 1, -2 and 3

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The width, in feet, of the border is,

⇒ x = 1.5 feet

We have to given that,

An artist paints a mural that measures 25 feet by 18 feet. The artist adds a border around the mural that increases the total area to 588 square feet.

Here, The area of the mural and border is modeled by the given equation,

⇒ (25 + 2x) (18 + 2x) = 588

where x represents the width of the border.

Now, WE can simplify as,

⇒ (25 + 2x) (18 + 2x) = 588

⇒ 450 + 50x + 36x + 4x² = 588

⇒ 4x² + 86x + 450 - 588 = 0

⇒ 4x² + 86x - 138 = 0

⇒ 2x² + 43x - 69 = 0

⇒ x = (- 43 ± √43² - 4×2×- 69) / 2×2

⇒ x = (- 43 ± √1849 + 552) / 4

⇒ x = (- 43 ± 49) / 4

This gives two solution,

⇒x = (- 43 + 49) / 4

⇒ x = 6/4

⇒ x = 3/2

⇒ x = ( -43 - 49) / 4

⇒ x = - 92 / 4

⇒ x = - 23

Since, Width is never negative.

Hence, the width, in feet, of the border is,

⇒ x = 1.5 width

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Answer:

Step-by-step explanation:

sd

Answer: 4191

Step-by-step explanation: i took the quiz

The estimated average number of miles traveled per person in 1961 is approximately 4567 miles.

The given table is

Year    1915   1925   1935   1945   1955   1965   1975   1985   1995   2005

Average

miles  194     1056   1796   1788   3650   4569   6147   7460   9099  10,181

traveled

The equation for the linear regression is:

y = -211.902x² + 779.914x - 8742.14

To estimate the average number of miles traveled per person in 1961, we use the equation with the input value of 61 (1961 since 1900):

y = -211.902(61)² + 779.914(61) - 8742.14

y ≈ 4567 miles

Therefore, the estimated average number of miles traveled per person in 1961 is approximately 4567 miles.

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Building an emergency fund may take time, but it can provide peace of mind and financial security in the event of an unexpected emergency.

The amount you should have in your emergency fund depends on your personal circumstances. Experts typically recommend having three to six months' worth of living expenses saved in an emergency fund.

However, if you have a high-risk job or irregular income, you may want to consider saving up to nine months' worth of expenses.

Additionally, if you have a lot of debt or dependents, you may want to have a larger emergency fund to ensure you can cover unexpected expenses or job loss.

It's important to regularly reassess your emergency fund and adjust it as needed based on changes in your financial situation

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The domain of the function is (-∝, 6/7) U (6/7, 1) U (1, 6/5) U (6/5, ∝)

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

f(x) = x/(x - 1)

g(x) = 13/(x² - 36)

The composite function (f o g)(x) is calculated as

(f o g)(x) = f(g(x))

Using the above as a guide, we have the following:

(f o g)(x) = 13/((x/(x - 1))² - 36)

Evaluate

(f o g)(x) = 13(x - 1)²/(-35x² + 72x - 36)

Set the denominator not equal to 0

So, we have

-35x² + 72x - 36 ≠ 0

Evaluate

[tex]x < \frac{6}{7}\quad \mathrm{or}\quad \frac{6}{7} < x < 1\quad \mathrm{or}\quad \:1 < x < \frac{6}{5}\quad \mathrm{or}\quad \:x > \frac{6}{5}[/tex]

Express as interval notation

(-∝, 6/7) U (6/7, 1) U (1, 6/5) U (6/5, ∝)

Hence, the domain of the function is (-∝, 6/7) U (6/7, 1) U (1, 6/5) U (6/5, ∝)

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The number of square feet tile he needs to purchase is 45.9 feet squared.

Kyle is going to retile the bottom of his pool. He first needs to drain the pool.  

The pool hold 321 cubic feet of water and has a height of 7 feet. Therefore, the number of square feet tile he needs to purchase can be calculated as follows:

Therefore,

volume of the pool = base area × height

321 = 7b

divide both sides of the equation by 7

b = 321 / 7

b = 45.85

b =   45.9 feet squared

Therefore,

amount of square feet tiles to purchase = 45.9 feet squared

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The equation of the line passing through the points (-2, -3) and (2, 5) is y = 2x + 1.

To find the equation of a line passing through the points (-2, -3) and (2, 5), we can use the point-slope form of a linear equation, which is:

y - y1 = m(x - x1)

where (x1, y1) represents one of the points on the line, and m represents the slope of the line.

First, let's calculate the slope (m) using the given points:

m = (y2 - y1) / (x2 - x1)

  = (5 - (-3)) / (2 - (-2))

  = 8 / 4

  = 2

Now, we have the slope (m) as 2. Let's choose one of the points, (-2, -3), and substitute its coordinates into the point-slope form equation:

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

y + 3 = 2(x + 2)

Simplifying further:

y + 3 = 2x + 4

y = 2x + 4 - 3

y = 2x + 1

Therefore, the equation of the line passing through the points (-2, -3) and (2, 5) is y = 2x + 1.

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Answer:

Step-by-step explanation:

The polynomial in descending order is:-6x^4 - 7x^3 + 5x + 3

Answer:

Step-by-step explanation:

follow the exponents little numbers

1. Triangle inequality theorem.

3. The missing lengths and angles are:

<B = 27.07, <C = 98 and c = 32.64.

1. According to triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

2. To determine the number of triangles that can be formed, we can use the given measurements and check if the triangle inequality theorem is satisfied.

3. We have,

a = 27, b = 15, and A = 55°,

Using the Law of Sines,

sin A/ a = sin B/ b

sin 55 /27 = sin B / 15

0.81915204428 / 27 = sin B /15

0.4550844690444 = sin B

<B = 27.07

Now, <C = 180 - <A - <B = 180 - 55 - 27.07 = 98

Now, Using the Law of Sines

sin A/ a = sin C/ C

0.81915204428 / 27 = sin 98 / c

0.030338964602963 = 0.99026807 /c

c = 32.64

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The nurse needs to prepare 0.8 ml of medication R to administer the correct dose of 4,000 units subcutaneously every 6 hours.

To calculate the correct dose of medication R, the nurse needs to use the formula:

dose (in units) = concentration (in units/ml) x volume (in ml)

In this case, the nurse received an order for 4,000 units of medication R and the medication label stated that the concentration of the medication is 5,000 units/ml.

To calculate the volume of medication that the nurse needs to prepare, the nurse can rearrange the formula:

volume (in ml) = dose (in units) / concentration (in units/ml)

Plugging in the values, we get:

volume (in ml) = 4,000 units / 5,000 units/ml = 0.8 ml
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Answer: 523.8 cubic inches

Step-by-step explanation:

Volume of the sphere, V = (4/3) * π * r^3

where r is the radius of the sphere.

Given, the diameter of the sphere (d) = 10 inches

Therefore, the radius of the sphere, r = d/2 =10/2 = 5 inches

Now, substituting the value of the radius to the volume formula,

V = (4/3) * π * (5^3)

= (4/3) * (22/7) * 125

≈ 523.8 cubic inches

The x-intercepts of the polynomial are -1/3, 2, and -2.

Given is a polynomial, we need to factor the polynomial, and identify the x-intercepts,

y = 15x³ + 5x² - 60x - 20

To factor the polynomial y = 15x³ + 5x² - 60x - 20, we can follow these steps:

Step 1: Factor out the greatest common factor (GCF) if possible.

In this case, the GCF of all the terms is 5:

y = 5(3x³ + x² - 12x - 4)

Step 2: Use factoring by grouping or other factoring techniques to factor the remaining polynomial.

Group the terms:

y = 5[(3x³ + x²) + (-12x - 4)]

Factor out common terms from each group:

y = 5[x²(3x + 1) - 4(3x + 1)]

Notice that we now have a common binomial factor of (3x + 1):

y = 5(3x + 1)(x² - 4)

Step 3: Factor any remaining quadratic expressions if possible.

The quadratic expression x² - 4 can be factored as the difference of squares:

y = 5(3x + 1)(x - 2)(x + 2)

Now we have factored the polynomial completely.

To find the x-intercepts (also known as zeros or roots), we set y = 0 and solve for x:

0 = 5(3x + 1)(x - 2)(x + 2)

Setting each factor equal to zero and solving for x, we get:

3x + 1 = 0 ⇒ x = -1/3

x - 2 = 0 ⇒ x = 2

x + 2 = 0 ⇒ x = -2

Therefore, the x-intercepts of the polynomial are -1/3, 2, and -2.

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Certainly! Here are the steps to prove the trigonometric identity :

Step 1: Start with the left-hand side of the equation:

[tex]\qquad\sf\:\frac{{\tan \theta}}{{\cos \theta}} \\[/tex]

Step 2: Use the identity $$\sf\:\tan \theta = \frac{{\sin \theta}}{{\cos \theta}}\\$$ to rewrite the numerator:

$$\sf\:\frac{{\frac{{\sin \theta}}{{\cos \theta}}}}{{\cos \theta}}\\$$

Step 3: Simplify the fraction by multiplying the numerator and denominator by $$\sf\:\cos \theta\\$$:

$$\large\sf\:\frac{{\sin \theta}}{{\cos \theta}} \cdot \frac{{\cos \theta}}{{\cos \theta}}\\$$

Step 4: Cancel out the $$\sf\:\cos \theta\\$$ terms in the numerator and denominator:

$$\sf\:\sin \theta\\$$

Step 5: Rewrite the right-hand side of the equation:

$$\sf\:\frac{{\sin \theta}}{{1 - \sin^2 \theta}}\\$$

Step 6: Replace $$\sf\:\theta with \delta\\$$ to represent delta:

$$\sf\:\frac{{\sin \delta}}{{1 - \sin^2 \delta}}\\$$

Therefore, the equation $$\sf\:\frac{{\tan \theta}}{{\cos \theta}} = \frac{{\sin \theta}}{{1 - \sin^2 \theta}} {\text{can be represented as}} \frac{{\tan \delta}}{{\cos \delta}} = \frac{{\sin \delta}}{{1 - \sin^2 \delta}}\\$$ when using delta $$\sf\:(\delta)\\$$ to represent the angle.

[tex]\huge{\mathcal{\colorbox{black}{\textcolor{lime}{\textsf{I hope this helps !}}}}}[/tex]

♥️ [tex]\large{\textcolor{red}{\underline{\texttt{SUMIT ROY (:}}}}[/tex]

To assure the random selection of a sample population for determining the percentage of students who bring their lunch to school, a method known as simple random sampling can be employed.

Simple random sampling is a technique that provides each member of the population an equal chance of being selected for the sample. Here's an explanation of how simple random sampling can be implemented in this scenario:

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The drinks are in ascending order based on the fraction of fruit they contain,

Smoothie: 1:0:0 < Squash: 3:0:1 < Lemonade: 1:0:3 < Soda: 1:3:1.

Given,

The ratios of fruit to sugar to water in the four drinks are:

Lemonade: 1:0:3

Smoothie: 1:0:0

Soda: 1:3:1

Squash: 3:0:1

To put the drinks in ascending order based on the fraction of fruit they contain, we need to compare the fraction of fruit in each drink.

Since the fraction of fruit is the ratio of fruit to the total amount of ingredients, we can calculate by,

Firstly,

For lemonade, the fraction of fruit is 1/(1+0+3) = 1/4.

Secondly,

For the smoothie, the fraction of fruit is 1/(1+0+0) = 1.

Then,

For the soda, the fraction of fruit is 1/(1+3+1) = 1/5.

Then,

And for the squash, the fraction of fruit is 3/(3+0+1) = 3/4.

Hence, based on these calculations, the drinks are listed in ascending order based on the percentage of fruit they contain.:

Smoothie: 1:0:0 < Squash: 3:0:1 < Lemonade: 1:0:3 < Soda: 1:3:1.

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Answer:

13.27 cm

Step-by-step explanation:

I am using (xy) to mean the length of the side xy

7^2 + (xy)^2 = 15^2

49 + (xy)^2 = 225

(xy)^2 = 225-49

(xy)^2 = 176

Side (xy) = sqrt(176) = 13.2664991614 = 13.27 cm

Sally drank 1 cup more than Tammy did.

To compare the amount of water Sally and Tammy drank, we need to convert the units of measurement so that they are both in the same units. There are 4 cups in a quart, so we can use this conversion factor to convert Tammy's 1.5 quarts to cups:

[tex]1.5 quarts \times 4 cups/quart[/tex]= 6 cups

Therefore, Tammy drank 6 cups of water.

To compare who drank more, we can see that Sally drank 7 cups of water, which is more than what Tammy drank (6 cups). Therefore, Sally drank more water than Tammy.

To find out how much more Sally drank than Tammy, we can subtract the amount Tammy drank from the amount Sally drank:

7 cups - 6 cups = 1 cup

In summary, while Tammy drank 1.5 quarts of water, Sally consumed 7 cups of water. We know that Sally drank more water because 7 is more than 6 (the number of cups Tammy drank). Sally drank 1 cup more than Tammy did.

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Answer:

-18.75

Step-by-step explanation:

Since the x is being multiplied by 4/5, we have to divide by 4/5 on both sides.

How to divide by 4/5? Take the reciprocal. The reciprocal to 4/5 is 5/4 (flip it).

Multiply both sides by 5/4.

5/4(4/5x)=5/4(-15)

x=-18.75

Answer:

[tex]x = -\frac{75}{4}[/tex]

Step-by-step explanation:

Question:

[tex]\frac{4}{5}x = -15[/tex]

Now, we multiply both sides by 5:

[tex]\frac{4}{5} x*5 = -15*5[/tex]

Simplify:

[tex]4x = -75[/tex]

Divide both sides by 4:

[tex]x = -\frac{75}{4}[/tex]

The domain of (s - t)(x) in interval notation is (-∞, -8) U (-8, 5) U (5, 8) U (8,

∞).

To find (s - t)(x), we subtract the function t(x) from s(x).

s(x) =[tex](x - 5)/(x^2 - 64)[/tex]

t(x) = (x - 8)/(5 - x)

To subtract the functions, we need a common denominator. In this case, we can use (x^2 - 64) as the common denominator.

(s - t)(x) =[tex][(x - 5)/(x^2 - 64)] - [(x - 8)/(5 - x)][/tex]

To simplify the expression, we need to factor the denominators and simplify further:

[tex](x^2 - 64) = (x - 8)(x + 8)[/tex]

(5 - x) = -(x - 5)

Substituting these into the expression, we get:

(s - t)(x) = [(x - 5)/(x - 8)(x + 8)] - [(x - 8)/-(x - 5)]

Next, we need to find a common denominator for the two fractions. The common denominator will be (x - 8)(x + 8)(x - 5).

(s - t)(x) = [(x - 5)(-(x - 5))/((x - 8)(x + 8)(x - 5))] - [(x - 8)(x + 8)/((x - 8)(x + 8)(x - 5))]

Simplifying further:

(s - t)(x) = [tex][-(x - 5)^2 - (x - 8)(x + 8)]/[(x - 8)(x + 8)(x - 5)][/tex]

The domain of the function (s - t)(x) is the set of values for which the denominator is non-zero, since division by zero is undefined.

The denominator (x - 8)(x + 8)(x - 5) will be non-zero as long as x is not equal to 8, -8, or 5.

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The equation that models the relationship between the amount of time Rita spends on the treadmill (t) and the distance she walks (d) is: d = 2t

To determine the equation that models the relationship between the amount of time Rita spends on the treadmill (t) and the distance she walks (d), let's analyze the given table.

Since the table displays the relationship between time and distance, we can observe the pattern and infer the equation. Let's assume that Rita walks at a constant speed.

Table:

Time (t) Distance (d)

10 2

20 4

30 6

40 8

50 10

From the table, we can see that the distance Rita walks is always twice the amount of time she spends on the treadmill. This implies that for every 10 units of time, Rita walks 2 units of distance. Therefore, we can conclude that the relationship between time and distance can be represented by a linear equation.

Let's define the equation:

d = m * t

In this equation, 'd' represents the distance, 't' represents the time, and 'm' represents the slope or rate at which Rita walks.

From the given table, we can observe that for every 10 units of time (t), the distance (d) increases by 2 units. This indicates that the slope (m) of the equation is 2.

Therefore, the equation that models the relationship between the amount of time Rita spends on the treadmill (t) and the distance she walks (d) is:

d = 2t

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Then x = -3.5, correct step to find x and y is to add the equations to eliminate x.

To find the values of x and y from the given equations, we need to use a method to eliminate one of the variables. In this case, we can use the method of adding the equations to eliminate x. Adding the two equations gives us:

y + y = x + 15 - x + 8

Simplifying the above equation gives us:

2y = 23

Therefore, y = 11.5

Substituting the value of y in any of the given equations, we can find the value of x. Using the equation y = x + 15, we have:

11.5 = x + 15

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From the data given, we do not have enough evidence to conclude that the hypothesized average production cost of P24.6 million is false.

To test the hypothesis that the average production cost in making a movie is P24.6 million, we can perform a hypothesis test using the sample data.

Let's define the null hypothesis (H₀) and the alternative hypothesis (H₁) as follows:

H₀: The average production cost is P24.6 million.

H₁: The average production cost is not P24.6 million.

We will use a t-test since we have a sample size smaller than 30 and the population standard deviation is unknown.

Given the sample information, the sample mean (x) is P28.3 million, the sample size (n) is 15, the hypothesized population mean (μ) is P24.6 million, and the sample standard deviation (s) is P9.5 million.

We can calculate the t-statistic using the formula:

t = (x - μ) / (s / √n)

Substituting the values:

t = (28.3 - 24.6) / (9.5 / √15)

t = 3.7 / (9.5 / √15)

t = 1.51

To determine whether the hypothesis is true at a 0.01 level of significance, we need to compare the calculated t-value to the critical t-value from the t-distribution table for a two-tailed test with 14 degrees of freedom (n - 1 = 15 - 1 = 14) and a significance level of 0.01.

The critical t-value for a two-tailed test with 14 degrees of freedom and a significance level of 0.01 is approximately ±2.977.

If the calculated t-value falls within the range of ±2.977, we fail to reject the null hypothesis; otherwise, we reject the null hypothesis.

Since the calculated t-value of 1.51 does not exceed the critical t-value of ±2.977 for a two-tailed test at a 0.01 level of significance, we fail to reject the null hypothesis.

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The image of the figure after rotating by counterclockwise about the origin is J' = (-1, -1), K' = (-2, -1), L' = (-1, 4,) and O' = (-3, -2)

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

The coordinates are

J = (-1, 1)

K = (-1, 2)

L = (4, 1)

O = (-2, 3)

The rule of rotating a figure 90 counterclockwise about the origin is

(x,y) = (-y,x)

So, we have

J' = (-1, -1)

K' = (-2, -1)

L' = (-1, 4,)

O' = (-3, -2)

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Question

What are the coordinates of the image R(90°,0)(JKLO)=J'K'L'O'

J = (-1, 1) K = (-1, 2) L = (4, 1) O = (-2, 3)

If cost price is Rs. 120, profit is Rs. 25 then the selling price is Rs.145.

We have to find the selling price

The formula for find the selling price is given below:

Selling Price = Cost Price + Profit

Given that the Cost Price (C.P.) is Rs 120 and the profit is Rs 25.

we can substitute these values into the formula:

Selling Price = 120 + 25

When one hundred twenty is added with twenty five we get One hundred twenty five.

Selling Price = 145

Therefore, the selling price is Rs 145.

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C.P. = Rs 120, profit = Rs 25​ then find the selling price?

The Modulus = 1 / √37, Argument ≈ -0.9828 radians

To find the modulus and argument of the expression (1+i)^2 / (1-√3i)^4, let's first simplify the expression.

(1+i)^2 can be expanded as follows:

[tex](1+i)^2 = (1+i)(1+i) = 1 + 2i + i^2 = 1 + 2i - 1 = 2i[/tex]

Similarly, (1-√3i)^4 can be expanded as:

(1-√3i)^4 = (1-√3i)(1-√3i)(1-√3i)(1-√3i)

Expanding this further requires using the properties of complex numbers, namely (a+b)(c+d) = ac + ad + bc + bd and i^2 = -1.

Simplifying the expression, we get:

(1-√3i)^4 = ([tex]1^4 - 4(1^3)(\sqrt{3i} ) + 6(1^2)(\sqrt{3i} )^2 - 4(1)(\sqrt{3i} )^3 + (\sqrt{3i} )^4)[/tex]

= (1 - 4√3i - 6(-3) + 4(√3i)(-√3) + (-3)^2)

= (1 - 4√3i + 18 + 4(-3) - 9)

= (10 - 4√3i)

Now, we can calculate the modulus and argument of the expression:

Modulus: The modulus of a complex number is calculated by taking the square root of the sum of the squares of its real and imaginary parts.

The modulus of (1+i)^2 / (1-√3i)^4 is the modulus of (2i) / (10 - 4√3i), which can be simplified as:

Modulus = √(([tex]2^2 + 0^2[/tex]) / (10^2 + (-4√3)^2))

= √(4 / (100 + 48))

= √(4 / 148)

= √(1 / 37)

= 1 / √37

Argument: The argument of a complex number is the angle it makes with the positive real axis in the complex plane.

The argument of (1+i)^2 / (1-√3i)^4 can be calculated as the argument of (2i) / (10 - 4√3i), which is the argument of 2i minus the argument of (10 - 4√3i).

The argument of 2i is π/2 (or 90 degrees), as it lies on the positive imaginary axis.

The argument of (10 - 4√3i) can be calculated using the inverse tangent function:

Argument = atan((-4√3) / 10)

= atan(-2√3 / 5)

≈ -0.9828 radians (or approximately -56.31 degrees)

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The equation P10i=1(xi − 2) = 30 represents the sum of the differences between each observation xi and 2, summed over 10 observations.

To find the arithmetic mean of these 10 observations, we need more information. The given equation only represents the sum of differences, but it doesn't provide the individual values or the actual arithmetic mean.

The arithmetic mean, also known as the average, is calculated by summing all the observations and dividing by the total number of observations. However, since we don't have the individual observations, we cannot directly calculate the arithmetic mean.

To determine the arithmetic mean, we would need the actual values of the observations, rather than just the sum of differences. Without further information, we cannot determine the arithmetic mean based solely on the given equation.

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