what is the domain and range

The solution is : the measure of angle A is 150°.

We have,

First a diagram which looks like a 12 sided figure where all the sides are equal.

Now draw 2 consecutive radii.

There are 12 such triangles in a 12 sided polygon.

These triangles have an apex angle of 360 / 12 = 30 degrees.

The other two angles making up the triangle are both equal.

Therefore x + x + 30 = 180

2x = 150

x = 75

But 75 is 1/2 of the interior angle.

There are 2 such angles making up the interior angle 75 + 75 = 150.

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The example of systematic sampling is option c) in a population of 1000 at a school, every 64th person is chosen.

In systematic sampling, the population is first divided into a sampling frame (for example, a list or a map) and then every kth individual is selected from the list. In this example, every 64th person is chosen from the list of 1000 individuals, which is an example of systematic sampling. In the example given, there is a list of 1000 individuals, and every 64th person is chosen from the list. This means that the sampling interval k is 64, and the first individual is selected randomly from the first 64 individuals in the list. From then on, every 64th individual is selected to be included in the sample. For instance, if the first individual selected is number 8, then the individuals selected for the sample would be 8+64=72, 8+264=136, 8+364=200, and so on.

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The magnitude of the vector is 435 units.

The direction of the vector is  173.3⁰ .

The magnitude of the vector -3u is calculated as follows;

The new vector - 3u is determined as;

u = 144i - 17j

-3u = -3(144i - 17j )

= -432i + 51j

The magnitude of the vector is calculated as;

|u| = √ (-432² + 51²)

|u| = 435 units

The direction of the vector is calculated as follows;

θ = tan⁻¹ (uy / ux)

θ = tan⁻¹ (-51/432)

θ = -6.7⁰ = 173.3⁰

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The volume of the parallelepiped is 80 cubic inches.

To find the volume of the parallelepiped, we need to multiply the area of the base by the height. We are given that two parallel sides of the base are 5 inches long and 2 inches apart, which means that the base is a parallelogram with base length of 5 inches and height of 2 inches. The area of the base is therefore:

Area of base = base length x height = 5 inches x 2 inches = 10 square inches

The height of the parallelepiped is given as 8 inches. Therefore, the volume of the parallelepiped is:

Volume = area of base x height = 10 square inches x 8 inches = 80 cubic inches

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LCL and UCL values of both scenarios are (158.61,161.39),(69.65,70.35) respectively.

To calculate the lower confidence limit (LCL) and upper confidence limit (UCL) for each given scenario, you'll need to use the following formula:

LCL = X - (z * (sigma / √n))
UCL = X+ (z * (sigma / √n))

where X is the sample mean, n is the sample size, sigma is the population standard deviation, and z is the z-score corresponding to the desired confidence level (1 - alpha).

First Scenario:
X = 160, n = 436, sigma = 30, alpha = 0.01

1. Find the z-score for the given alpha (0.01).
For a two-tailed test, look up the z-score for 1 - (alpha / 2) = 1 - 0.005 = 0.995.
The corresponding z-score is 2.576.

2. Calculate LCL and UCL.
LCL = 160 - (2.576 * (30 / √436)) ≈ 158.61
UCL = 160 + (2.576 * (30 / √436)) ≈ 161.39

First Scenario Result:
LCL = 158.61
UCL = 161.39

Second Scenario:
X= 70, n = 323, sigma = 4, alpha = 0.05

1. Find the z-score for the given alpha (0.05).
For a two-tailed test, look up the z-score for 1 - (alpha / 2) = 1 - 0.025 = 0.975.
The corresponding z-score is 1.96.

2. Calculate LCL and UCL.
LCL = 70 - (1.96 * (4 / √323)) ≈ 69.65
UCL = 70 + (1.96 * (4 / √323)) ≈ 70.35

Second Scenario Result:
LCL = 69.65
UCL = 70.35

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The solution to the equation 4⁽⁻ˣ ⁺ ¹⁾ = 2²ˣ is x = 1/2.

Given the equation in the question:

4⁽⁻ˣ ⁺ ¹⁾ = 2²ˣ

To solve the equation 4⁽⁻ˣ ⁺ ¹⁾ = 2²ˣ using the equal base method, we can rewrite the right side with base 4, since 4 is a power of 2:

4⁽⁻ˣ ⁺ ¹⁾ = 2²ˣ

2²⁽⁻ˣ ⁺ ¹⁾ = 2²ˣ

Now both sides have the same base, so we can equate their exponents and solve for x:

2( -x + 1 ) = 2x

-2x + 2 = 2x

2x + 2x = 2

4x = 2

x = 1/2

Therefore, the value of x is 1/2.

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The requried, (6x10¹) + (9x10¹) in scientific notation is 1.50x10²

To add (6x10^1) + (9x10^1) in scientific notation, we need to first make sure that the exponents of 10 are the same.

Now we can add the two numbers:

6.0x10¹ + 9.0x10¹ = 15.0x10¹

To express the result in scientific notation, we need to write 15.0 as 1.50 and move the decimal point one place to the left, which gives:

1.50x10²

Therefore, (6x10¹) + (9x10¹) in scientific notation is 1.50x10².

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The kicker's ability to punt the ball any distance from the goal line means that the domain is unlimited in range.

As a transformation of f(x), g(x) carries the same infinity of values within its range as well with a limit up to 25.

Decidedly opening downwards, f(x)'s parabola possesses a vertex located at (30, 25). For playing according to territory: representing the kicker’s goal line, x = 30 houses the vertex of f(x) , so punting happens closer there.

In sum, while f(x) equips football players to strategically understand their field posisioning ranging  across all heights, trajectory of direction & ranges, executing effective plays based on the available resources; along with g(x) which offers a modified visual representation- they both obey the constraints of physics-based rules.

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Answer:

(681) 20.115

I think that's the answer

The tangent of G is given by the trigonometric relation tan G = √24 / 3

Given data ,

Let the triangle be represented as ΔFGH

Now , the measure of side GH = 3 units

The measure of side GF = √33 units

So , the measure of side HF = √ ( √33 )² - ( 3 )²

HF = √ ( 33 - 9 )

HF = √24 units

Now , from the trigonometric relations , we get

tan θ = opposite / adjacent

tan G = HF / GH

tan G = √24 / 3

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61

Why my answer is sixty one Because the Triangle ls the same size Of the other sixty one

Answer:

61

Step-by-step explanation:

Based on th mentioned iinformations, we would be requiring about 157 pens (rounded up) in order to exceed the weight of 1 kilogram.

There are 1000 grams in a kilogram. To find out how many pens are needed to exceed 1 kilogram, we need to divide 1000 grams by the weight of one pen:

1000 g / 6.4 g = 156.25 pens

Therefore, we would need 157 pens (rounded up) to exceed 1 kilogram.

Dividing 1000 grams by the weight of one pen gives us the number of pens that would weigh 1000 grams or 1 kilogram, which turns out to be 156.25 pens. Since we cannot have a fractional part of a pen, we round up to 157 pens to ensure that their total weight exceeds 1 kilogram.

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The complete question is :

A pen weighs 6.4 g. How many pens do we need to exceed the kilogram?

[tex]\blue{\boxed{\bold{\mathbb{SOLUTION}}}}[/tex]

Area of the biggest circle:

[tex]\pi r^{2}=\pi \times 6^{2}=\pi \times 36 \ cm^2[/tex].

Area of the rectangle:

[tex]4 \times (2+2+2+2) = 4 \times 8 = 32 \ cm^2[/tex].

Area of the 6 semicircles:

[tex]6 \times \dfrac{1}{2} \times \pi \times r^2 = 3 \times \pi \times 2^2 = \pi \times 12 \ cm^2.[/tex]

Total shaded area:

Biggest circle area - rectangle area - 6 semicircles area

[tex]= \pi \times 36 - 32 - \pi \times 12\\= \pi \times (36-12) - 32\\= \pi \times 24 - 32\\= 3.14 \times 24 - 32\\= 75.36 - 32\\= \boxed{43.36 \ cm^2}[/tex]

Therefore, the shaded part area is [tex]43.36 \ cm^2[/tex].

[tex]\aqua{\boxed{\mathfrak{Thank \: You}}}\\\aqua{\boxed{\bold{answered \: by: \: akbarsdtazm}}}[/tex]

The length of the rectangular prism is 15 feet.

A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.

The volume of a rectangular prism is expressed as;

V = w × h × l

Where w is the width, h is height and l is length

Given that:  the volume of the rectangular prism is 7800 cubic feet, the width is 40 feet, and the height is 13 feet.

We can substitute these values into the formula and solve for the length:

V = w × h × l

7800 = 40 × 13 × l

7800 = 520 × l

l = 7800 / 520

l = 15 ft

Therefore, the measure of the length is 15 feet.

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The dependent variable in the regression analysis that will be conducted is the salary offered (W) to university graduates.

It is considered the dependent variable because it is the variable that is predicted or explained by the Grade Point Average (G), which is the independent variable. The regression analysis will help to determine how much the salary offered varies with changes in the Grade Point Average, and the mathematical equation derived from the analysis will be used to predict the salary offered based on a given Grade Point Average.

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The absolute error is 2 ounces, and the relative error is approximately 11.76%.

The absolute error is the difference between the claimed weight and the true weight of the steak, which is:

Absolute error = |15 - 17| = 2 ounces

The relative error is the absolute error divided by the true weight of the steak, which is:

Relative error = (2/17) x 100% = 11.76%

So, the absolute error of the claimed weight is 2 ounces, and the relative error is 11.76%.

To find the absolute error, you'll need to subtract the true value (17 ounces) from the claimed value (15 ounces):

Absolute error = |True value - Claimed value| = |17 - 15| = 2 ounces

Now, to find the relative error, you'll divide the absolute error by the true value, and then multiply by 100 to get a percentage:

Relative error = (Absolute error / True value) x 100 = (2 / 17) x 100 ≈ 11.76%

So, the absolute error is 2 ounces, and the relative error is approximately 11.76%.

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False.

It is not possible to find a 3 by 3 matrix A which is not invertible, but where no two columns are scalar multiples of each other, and no two rows are scalar multiples of each other.

It is not possible to find a 3 by 3 matrix A which is not invertible, but where no two columns are scalar multiples of each other, and no two rows are scalar multiples of each other.

This is because if no two columns of A are scalar multiples of each other, then the columns are linearly independent, and the rank of A is at least 3. Similarly, if no two rows of A are scalar multiples of each other, then the rows are linearly independent, and the rank of A is also at least 3. Since A is a 3 by 3 matrix, it follows that the rank of A is at most 3. Therefore, the only way for A to have rank 3 is for A to be invertible.

So, any 3 by 3 matrix A that is not invertible must have either two columns that are scalar multiples of each other, or two rows that are scalar multiples of each other.

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Answer:

BCDE= 100+ 80+100+80 = 360 degree

BAC = 20 degree

DBC = 100 degree

BDE = 80 degree

Step-by-step explanation:

Shows all is correct

We associate isosceles trapezoid in this question, this helps us prove with angle A in the triangle vertices how we can find one of the adjacent angles from the trapezoid by subtraction when all angles within one single trapezoid = 360 degrees. We can use 20 degree angle A to subtract and find each alternative angle easier.

Step-by-step explanation:

The semi circle shows 9 stones

Where angles are interior to the trapezoid

Where all 4 sided shapes add up to 360 degree

We draw a line of symmetry on BCED angle

To make midway points BC  and DE = 90 degree

The two new formed shapes are still 4 sided and add up to 360 degree.

BC + DE = 180 degree

BDE = Triangle 180 -20/2 = 160/2 = 80

BCDE = Trapezoid = 360

Trapezoid angle DBC = 360-80-80/2 = 360-160/2 = 200/2 = 100 degree  

Finding interior angle A (BAC)

BAC = 180/9 = 20 degree

BAC * (2) = 360 degree circle

BAC = 360/18 = 20 degree

Proves BAC = 20 degree

20 degree is used in BAC workings above in bold and proves all trapezoid angles are correct. We now know this is an isosceles trapezoid and that is why symmetry and midway points can help us find the angles without any given length.

There are 6 different types of products sold in AR. Among these products, the one that sold the most is IPA (India Pale Ale). IPA is a popular choice among consumers due to its distinct flavor and versatility.

AR, or Arkansas, is known for its growing craft beer scene, so it's no surprise that there are many different types of products sold in the state. According to recent data, there are a total of six different types of products sold in AR.

The answer is imperial stout, which is a type of beer known for its high alcohol content and rich, roasted flavors. While pale ale and IPA are also popular choices among beer enthusiasts in AR, imperial stout seems to be the clear winner in terms of sales.

In conclusion, if you're looking to try some of the most popular products sold in AR, be sure to give imperial stout a try. Its complex flavors and high alcohol content make it a perfect choice for those who appreciate a strong and bold beer.

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Based on the mentioned informations, the farmer is calculated to have 143 chickens left after selling 2/5 and 5/6 of the initial 1800 chickens and 37 chickens died.

The farmer starts with 1800 chickens.

He sells 2/5 of the total, which is:

(2/5) x 1800 = 720 chickens.

So he has 1080 chickens left.

He then sells 5/6 of the remaining chickens, which is:

(5/6) x 1080 = 900 chickens.

So he has 180 chickens left.

Unfortunately, 37 chickens die, so the final number of chickens he has left is:

180 - 37 = 143 chickens.

Therefore, the farmer has 143 chickens left after selling 2/5 and 5/6 of the initial 1800 chickens and 37 chickens died.

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The complete question is :

A farmer has to sell 1800 chickens, first he sells 2/5 of the total, then 5/6 of the rest and if 37 chickens die, how many chickens does he still have left?

The required value of (8.8 × 10⁻⁴) × (7.4 x 10¹¹) in standard form is 6.512 × 10⁸.

The expression is given as follows:

(8.8 × 10⁻⁴) × (7.4 x 10¹¹)

When multiplying numbers in scientific notation, we can multiply the coefficients and add the exponents of 10.

(8.8 × 10⁻⁴) × (7.4 x 10¹¹)

= (8.8 × 7.4) × 10⁽⁻⁴⁺¹¹⁾

= 65.12 × 10⁷

To convert to standard form, we can write 65.12 as 6.512 × 10¹:

= 6.512 × 10¹ × 10⁷

= 6.512 × 10⁸

Therefore, the value of (8.8 × 10⁻⁴) × (7.4 x 10¹¹) in standard form is 6.512 × 10⁸.

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a) a = 2.72 makes the statement P(x ≤ a) = 0.24 true.

b)a = 3.77 makes the statement P(x > a) = 0.41 true.

c) a = 3.37 makes the statement P(2.29 ≤ x ≤ a) = 0.36 true.

Part A:

For a uniform probability distribution with range [2,5], the probability density function is:

f(x) = 1/(5-2) = 1/3 for 2 <= x <= 5

a) To find the value of a such that P(x ≤ a) = 0.24, we need to solve the following equation:

∫[2,a] f(x) dx = 0.24

Simplifying the equation, we get:

(a-2)/(5-2) = 0.24

a-2 = 0.72

a = 2.72

Therefore, a = 2.72 makes the statement P(x ≤ a) = 0.24 true.

b) To find the value of a such that P(x > a) = 0.41, we need to solve the following equation:

∫[a,5] f(x) dx = 0.41

Simplifying the equation, we get:

(5-a)/(5-2) = 0.41

5-a = 1.23

a = 3.77

Therefore, a = 3.77 makes the statement P(x > a) = 0.41 true.

c) To find the value of a such that P(2.29 ≤ x ≤ a) = 0.36, we need to solve the following equation:

∫[2.29,a] f(x) dx = 0.36

Simplifying the equation, we get:

(a-2.29)/(5-2) = 0.36

a-2.29 = 1.08

a = 3.37

Therefore, a = 3.37 makes the statement P(2.29 ≤ x ≤ a) = 0.36 true.

Part B:

Let D be the event that a family owns a dog, and let C be the event that a family owns a cat.

Given information:

P(D) = 0.35

P(C | D) = 0.20

P(C) = 0.32

We need to find:

P(D)

P(D | C)

Using Bayes' theorem, we can write:

P(D | C) = P(C | D) * P(D) / P(C)

Substituting the given values, we get:

P(D | C) = (0.20 * 0.35) / 0.32 = 0.21875

Therefore, the conditional probability that a randomly selected family owns a dog given that it owns a cat is 0.21875.

To find P(D), we can use the following formula:

P(D) = P(D | C) * P(C) + P(D | C') * P(C')

where C' represents the complement of C, i.e., the event that a family does not own a cat.

Since the probability of owning a cat or not owning a cat covers all possibilities, we have:

P(D) = P(D | C) * P(C) + P(D | C') * (1 - P(C))

Substituting the given values, we get:

P(D) = (0.20 * 0.35) + P(D | C') * (1 - 0.32)

We do not have enough information to directly calculate P(D | C'), so we need to use the fact that the probabilities must add up to 1. Thus:

P(D | C') = 1 - P(C' | D)

Using Bayes' theorem, we can write:

P(C' | D) = P(D | C') * P(C') / P

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The distance from Point A to Point B is

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

distance between points  (4, 6) and (-5, 5) is calculated by

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

substituting the values

d =√{(4 - (-5))² + (6 - 5)²}

d =√{81 + 1}

d = √82

d = 9.055 units

d = 9.1 units (to the nearest tenths)

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Answer: 43 - x =25

Step-by-step explanation:

43 - x = 25

so 43 - 25 = x

x = 18

There are several methods that can be used to verify the normality conditions for a scenario where a normal model is used to represent the distribution of sample means.

One common method is the visual inspection of a histogram or a normal probability plot. Another method is to use statistical tests such as the Shapiro-Wilk test or the Kolmogorov-Smirnov test to assess the normality of the sample data. Additionally, the sample size and the presence of outliers can also impact the normality conditions and should be taken into consideration when verifying normality.
Hi! To verify the normality conditions for the distribution of sample means, you should consider the following criteria:

1. Randomness: The sample data must be collected randomly to ensure independence of observations.
2. Sample size: The sample size should be sufficiently large (typically, n ≥ 30) to allow the Central Limit Theorem to apply.
3. Underlying distribution: If the population distribution is known to be normal, the sample means will also be normally distributed regardless of sample size.

These criteria help ensure the use of a normal model is appropriate in representing the distribution of sample means.

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The linear function f(x) and g(x) have different intercept and slope.

To find what true or false about the given statements, we need to write out the equations for both functions.

f(x) = x + 9

To find the function g(x), we need to find the slope and y-intercept.

The slope of the function is given as;

m = y₂ - y₁ / x₂ - x₁

Taking two points from the table;

m = 14 - 10 / 3 - 1

m = 4 / 2

m = 2

Using the slope, we can find the y - intercept with any one point;

y = mx + c

10 = 2(1) + c

10 = 2 + c

c = 10 - 2

c = 8

The equation is y = 2x + 8

Now, we can write out the functions again;

f(x) = x + 9

g(x) = 2x + 8

Let's observe each of the given statements;

a. f(x) has a greater y - intercept than g(x) which is true because f(x) has intercept at 9 and g(x) has intercept at 8.

b. f(x) has greater x -intercept than g(x). This is false as f(x) has a lower x-intercept than g(x)

c. f(x) has a greater slope than g(x). This is also false as g(x) has a slope of 2 and f(x) has a slope of 1

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The expression does not have any variable term (n) in it, the sequence converges to a constant value. The limit of the sequence as n approaches infinity is: Limit = 1/(sqrt(80))

To find the limit of the sequence n/(sqrt(16n^2 5)), we can simplify the expression by dividing both the numerator and denominator by n:

n/(sqrt(16n^2 5)) = 1/(sqrt(16*5/n^2)) = 1/(4sqrt(5/n^2))

As n approaches infinity, 5/n^2 approaches zero. Therefore, the denominator of the expression approaches infinity, and the whole expression approaches zero.

Therefore, the limit of the sequence is 0.
To find the limit of the given sequence n/(sqrt(16n^2 * 5)), we'll apply some algebraic simplification and use the properties of limits.

First, simplify the expression:

n/(sqrt(16n^2 * 5)) = n/(sqrt(80n^2))

Now, divide both the numerator and denominator by n:

n/(sqrt(80n^2)) = 1/(sqrt(80))

Since the expression does not have any variable term (n) in it, the sequence converges to a constant value. The limit of the sequence as n approaches infinity is:

Limit = 1/(sqrt(80))

This is the final answer.

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To calculate the reorder point, we need to consider the lead time (6 days) and the average daily usage of the product. Assuming a 30-day month, the average daily usage can be calculated as:
Product used per day = Total product used in a month / Number of days in a month
Product used per day = Inventory / 30

To determine the reorder point, we need to know the daily consumption rate of the product and the lead time (number of days it takes for the order to arrive).

1. Calculate the daily consumption rate: Since we have a 30-day month, we will divide the monthly consumption by 30.
Total consumption in a month = X gallons (Information not provided)
Daily consumption rate = X gallons / 30 days

2. Calculate the lead time demand: Since it takes 6 days for the order to arrive, we need to find out how many gallons are consumed during this time.
Lead time demand = Daily consumption rate * Lead time
Lead time demand = (X gallons / 30 days) * 6 days

3. Determine the reorder point: The reorder point is the level of inventory at which the product should be reordered to ensure that there is enough stock to cover the lead time demand.
Reorder point = Lead time demand
Reorder point = (X gallons / 30 days) * 6 days

Let's assume that the reorder point is the level of inventory at which we need to place a new order to avoid running out of stock. So, the reorder point can be calculated as:

Reorder point = Lead time demand + Safety stock

Here, the lead time demand is the product used during the lead time (6 days) and the safety stock is the buffer inventory kept to avoid stockouts. Let's assume a safety stock of 50 gallons.

Lead time demand = Product used per day * Lead time
Lead time demand = (Inventory / 30) * 6
Lead time demand = Inventory / 5

Reorder point = (Inventory / 5) + 50

We need to solve for the inventory level at which we should reorder. Let's assume the answer is X.

X / 5 + 50 = X
X - X/5 = 50
4X/5 = 50
X = (5/4) * 50
X = 62.5

So, the reorder point is 62.5 gallon. Therefore, the correct answer is "none of the above".

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Answer:

Step-by-step explanation:

m = 32g

The mean number of golf balls ordered by customers is 8.22 (rounded to 2 decimal places).

To find the mean number of golf balls, we need to multiply each possible value of X by its corresponding probability, and then sum up the products. That is:

Mean number of golf balls = E(X) = Σ[X*P(X)] where Σ is the summation symbol.

Using the given probability model, we have:

E(X) = 30.14 + 60.29 + 90.36 + 120.11 + 15*0.10

E(X) = 0.42 + 1.74 + 3.24 + 1.32 + 1.50

E(X) = 8.22

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