The parking garage has 9 rows with 10 parking spaces in each row. There are 8 empty spaces.
How many spaces are filled?

The situation that shows causation are:

Causation in mathematics can be desrcibed as the term used in indicating a relationship between two events where there is a relationship between the two events and one of the event is affected by the other.

It shoud be note that In statistics, when the value of one event, increases or decreases due to the relationship beteen them, the other events is affected, it is said there is causation.

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comlete question;

Which situation shows causation?

When the number of people in a bus increases, the number of animals in a zoo also increases.

When the number of hours worked each week by an hourly employee decreases, the amount of money earned

by the employee also decreases.

When the amount of a discount for a sale increases, the number of items sold during the sale decreases.

6 When the number of bike trails in a city decreases, the amount of rainfall in the city increases.

The smallest possible value of (a+b) is 2, and this value is attained when a = 1 and b = 1.

Let r and s be the roots of the equation x^2 + ax + 2b = 0, and let p and q be the roots of the equation x^2 + 2bx + a = 0. Since both equations have real roots, their discriminants are nonnegative:

a^2 - 8b ≥ 0

4b^2 - 4a ≥ 0

Simplifying the second inequality, we get:

b^2 - a ≥ 0

b^2 ≥ a

We want to minimize (a+b). Adding the two given equations, we get:

(x^2 + ax + 2b) + (x^2 + 2bx + a) = 0

2x^2 + (a+2b+2b)x + (a+2b) = 0

This equation has real roots if and only if its discriminant is nonnegative:

(a+2b+2b)^2 - 8(2x^2)(a+2b) ≥ 0

(a+4b)^2 - 16b(a+2b) ≥ 0

a^2 + 8ab + 12b^2 ≥ 0

This inequality is always true for positive a and b, so we can safely assume that a and b are positive. Therefore, we can divide both sides by 4b^2 to get:

(a/b)^2 + 8(a/b) + 12 ≥ 0

Letting t = a/b, we can rewrite this as a quadratic inequality:

t^2 + 8t + 12 ≥ 0

This inequality is true for all values of t, so there are no restrictions on the ratio a/b. Therefore, we can minimize (a+b) by choosing a and b to be as small as possible subject to the constraint that b^2 ≥ a. Since a and b are both positive, we can take a = 1 and b = 1 to achieve this minimum. This gives:

(a+b) = 1+1 = 2

Therefore, the smallest possible value of (a+b) is 2, and this value is attained when a = 1 and b = 1.

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The probability that the proportion of racially or ethnically mixed couples in a sample of 300 married couples is greater than 0.07 is approximately 0.2190.

In statistics, a sample is a subset of a larger population that we use to make inferences about the whole population. When we take a sample, we are often interested in estimating some parameter of the population, such as the proportion of individuals with a certain characteristic. The sample proportion is the number of individuals in the sample with the characteristic of interest divided by the sample size.

In the given question, we are interested in the proportion of racially or ethnically mixed married couples in a sample of 300 married couples. We know from the article that in the population of all married couples in the United States, 5% are mixed racially or ethnically.

To answer the question, we need to use the Central Limit Theorem (CLT). The CLT states that, under certain conditions, the distribution of the sample mean approaches a normal distribution as the sample size increases. One of these conditions is that the sample size is large enough, usually considered to be n ≥ 30.

Using the CLT, we can assume that the sample proportion of racially or ethnically mixed couples, denoted by p', follows a normal distribution with mean p = 0.05 and standard deviation σ = √(p(1-p)/n). Substituting the given values, we get:

σ = √(0.05(1-0.05)/300)

  = 0.0258

To find the probability that the proportion of mixed couples in the sample is greater than 0.07, we need to standardize the variable:

z = (0.07 - 0.05) / 0.0258

  = 0.7752

We can now look up the probability corresponding to a z-score of 0.7752 in a standard normal distribution table, we find that this probability is approximately 0.2190.

Therefore, the probability that the proportion of racially or ethnically mixed couples in a sample of 300 married couples is greater than 0.07 is approximately 0.2190.

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The retailer's average daily sales rate is approximately 142.5 bottles per day.

To arrive at this answer, we can use the inventory turnover formula:

Inventory turnover = Cost of goods sold / Average inventory

Since we don't have the cost of goods sold, we can use the number of units sold instead:

Inventory turnover = Units sold / Average inventory

We know that the inventory turnover is 48 times per year, so we can set up the equation:

48 = Units sold / 414

Solving for units sold, we get:

Units sold = 48 * 414 = 19,872

To find the average daily sales rate, we divide the total units sold by the number of days in a year:

Average daily sales rate = 19,872 / 365 = 54.4

Therefore, the retailer's average daily sales rate is approximately 142.5 bottles per day (rounded to 1 decimal place). This means that the retailer sells, on average, 142.5 bottles of soda every day throughout the year. This information can be useful for the retailer in managing its inventory levels and ensuring that it has enough stock on hand to meet customer demand. It can also be used to calculate revenue and profit margins based on the cost of goods sold.

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Angles a and 139 are corresponding angles thus a = 139°

Angles a and b are supplementary hence b = 41°

When a transversal connects two parallel lines, it creates corresponding angles, which are two angles in a pair. A transversal produces a total of eight angles when it crosses two parallel lines. Pairs of these angles that are at the same relative position at each intersection are said to be corresponding angles.

Angles that correspond to one another have the same measure and are therefore congruent. The characteristics of parallel lines and the angles that the transversal forms lead to this congruence.

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Susan most likely used angle facts related to the sum of angles in a triangle to calculate angle a and then used triangle angle-sum property to find angle b.

To answer your questions:

Susan likely used angles facts related to the sum of angles in a triangle to find the calculation of angle a. This principle states that the sum of all angles in a triangle is always equal to 180 degrees.

For angle b, she then used triangle angle-sum property, which states that the measure of an angle of a triangle is equal to the sum of the measures of the other two angles subtracted from 180 degrees.

For instance, if angle a was 41 degrees, and the third angle was known to be 100 degrees, she would subtract these two angles from 180, resulting in angle b being 39 degrees.

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The length and width of the rectangular patio are 9 yards and 3 yards.

Let's assume that the length of the rectangular patio is x yards.

Then, according to the problem statement, the width of the rectangular patio is one-third of its length. As a result, the width of the rectangular patio is:

width = (1/3)x

The area of the rectangular patio is given as 27 square yards. We know that the area of a rectangle may be calculated as follows:

area = length x width

Substituting the values of width and area, we get:

27 = x*(1/3)x

Multiplying both sides by 3, we get:

81 = x²

When we take the square root of both sides, we get:

x = 9

So the length of the rectangular patio is 9 yards, and the width of the rectangular patio is:

width = (1/3)x = (1/3)*9 = 3

Therefore, the length and width of the rectangular patio are 9 yards and 3 yards, respectively.

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Sydnie:

The solution is correct. The exact values of x are x = 1.62 and x = -0.62. Sydnie gets 5/5. Trevor: The solution is incorrect. To complete the square, z2 - 12z must add and subtract (12/2)2 = 36.

The correct steps are:

z2 - 12z - 27 = 0

z2 - 12z + 36 - 36 - 27 = 0

(z - 6)2 = 63

z = 6 + sqrt(63) and z = 6 - sqrt(63)

The exact values of z are z = 6 + sqrt(63) and z = 6 - sqrt(63). Trevor gets 3/5.

Brayden:

The solution is incorrect. The quadratic formula is being used correctly, but the square root of -56 should be simplified to 4i(sqrt(14)). The correct steps are:

x = (-2 ± sqrt(4 - 60)) / (2 * 3)

x = (-2 ± sqrt(-56)) / 6

x = (-2 ± 4i(sqrt(14))) / 6

x = (1 ± 2i(sqrt(14))) / 3

The exact values of x are x = (1 + 2i(sqrt(14))) / 3 and x = (1 - 2i(sqrt(14))) / 3. Brayden gets 3/5.

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sydnie The solution is correct. The exact values of x are x = 1.62 and x = -0.62. Sydnie gets 5/5. Trevor: The solution is incorrect. To complete the square, z2 - 12z must add and subtract (12/2)2 = 36.

The correct steps are:

z2 - 12z - 27 = 0

z2 - 12z + 36 - 36 - 27 = 0

(z - 6)2 = 63

z = 6 + sqrt(63) and z = 6 - sqrt(63)

The exact values of z are z = 6 + sqrt(63) and z = 6 - sqrt(63). Trevor gets 3/5.

Brayden:

The solution is incorrect. The quadratic formula is being used correctly, but the square root of -56 should be simplified to 4i(sqrt(14)). The correct steps are:

x = (-2 ± sqrt(4 - 60)) / (2 * 3)

x = (-2 ± sqrt(-56)) / 6

x = (-2 ± 4i(sqrt(14))) / 6

x = (1 ± 2i(sqrt(14))) / 3

The exact values of x are x = (1 + 2i(sqrt(14))) / 3 and x = (1 - 2i(sqrt(14))) / 3. Brayden gets 3/5.

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The median number of musical instrument played is 1.5.

First, we need to arrange the number of instruments in ascending order, along with their respective frequencies:

Number of instruments: 0, 1, 2, 3

Frequency: 2, 3, 2, 4

To find the median, we need to determine which value is in the middle when the data is arranged in order. Since we have an even number of data points (11 in total), the median will be the average of the two middle values.

The two middle values are the second and third values: 1 and 2.

So, the median number of musical instruments played is the average of 1 and 2, which is:

Median = (1 + 2)/2 = 1.5

Therefore, the median number of musical instruments played is 1.5.

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An estimator is said to be unbiased if the expected value of the estimator is equal to the true value of the parameter being estimated.

Unbiased estimators are useful because they provide an estimate that, on average, is equal to the true value of the parameter, making them desirable for making accurate inferences about a population.

In statistics, an estimator is a statistic used to estimate the value of an unknown parameter in a population. An estimator is said to be unbiased if, on average, it produces an estimate that is equal to the true value of the parameter. An unbiased estimator is desirable because it provides an estimate that is, on average, accurate, which is important for making inferences about a population.

Biased estimators, on the other hand, tend to consistently overestimate or underestimate the true value of the parameter, which can lead to incorrect conclusions. Therefore, unbiased estimators are useful because they provide more accurate estimates, which can lead to more reliable inferences about a population.

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Based on the given radius of the circle, the area of the circle is approximately 26.41 square ft.

Area of a circle = πr²

Where,

π = 3.14

Radius, r = 2.9 ft

Area of a circle = πr²

= 3.14 × 2.9²

= 3.14 × 8.41

= 26.4074 square ft

Approximately,

26.41 square ft

Hence, 26.41 square ft is the area of the circle.

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The sizes could be used are 5 cm by 3 cm.

All sizes that have dimensions proportional to 6 cm by 10 cm can be used. This means that the ratio of the length to the width of the copies must be the same as the ratio of the length to the width of the original.

This ratio is 10/6 = 5/3.

For example, a size of 15 cm by 9 cm can be used because the ratio of length to width is 15/9 = 5/3, which is the same as the ratio of length to width of the original.

Similarly, a size of 12 cm by 8 cm can be used, and so on, as long as the ratio of the dimensions is 5/3.

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Answer:

The answer is 1.632.

Step-by-step explanation:

First, you multiply 3.2 by 1, which gives you 3.2. Then you move the decimal point one place to the left to get 0.32. You write this as 16.0 under the line and align the decimal points.

Next, you multiply 3.2 by 0.5, which gives you 1.6. You write this under the line and align the decimal points.

Then you add the two partial products: 16.0 + 1.6 = 17.6.

Finally, you count the number of decimal places in both factors: 3.2 has one decimal place and 0.51 has two decimal places, so the product has three decimal places. You move the decimal point three places to the left in the final answer to get 1.632.

Answer:

Step-by-step explanation:

To prove the validity of a Boolean algebra identity, apply Boolean algebra theorems and axioms to manipulate the expression, simplify it, and compare the result to the original identity.

A method for proving the validity of a Boolean algebra identity is as follows.

1. State the given Boolean algebra identity:

Write down the specific identity you want to prove. For example, let's consider the identity A + AB = A.

2. Apply Boolean algebra theorems and axioms:

Utilize the various theorems and axioms of Boolean algebra, such as the Identity law, Commutative law, Associative law, Distributive law, Complement law, and De Morgan's law, to manipulate the given expression.

3. Simplify the expression:

In our example, A + AB, we can apply the Distributive law to factor out the common term A: A(1 + B).

4. Use known identities to simplify further:

Now, apply the Identity law (A + 1 = 1) to the expression within the parenthesis: 1 + B = 1. So, the simplified expression becomes A(1), which, according to the Identity law, is just A.

5. Compare the simplified expression to the original identity:

If the simplified expression matches one side of the original identity, then the Boolean algebra identity is valid. In our example, the simplified expression A is equal to the left side of the original identity, proving its validity.

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A hiker is standing on one bank of a river. The height of the tree is approximately 159.45 feet.

To solve this problem, we can use the concept of trigonometry and set up a right triangle with the tree height, the distance between the hiker and the tree, and the angle of elevation.

Let's denote the height of the tree as 'h' and the distance between the hiker and the tree as 'd.' We know that the angle of elevation is 12°, which means that the angle between the ground and the line of sight from the hiker's eyes to the top of the tree is 12°. Therefore, we can set up a right triangle as follows:

    /|

   / |

h /  |d

/   |

/θ___|

where θ represents the angle of elevation (12°).

We can use the tangent function to relate the height of the tree to the distance between the hiker and the tree:

tan θ = opposite/adjacent = h/d

Rearranging this equation gives:

h = d tan θ

Now, we know that the distance between the hiker and the tree is 750 ft, and the angle of elevation is 12°. Plugging these values into the equation above, we get:

h = 750 tan 12°

Using a calculator, we can find that tan 12° is approximately 0.2126. Therefore,

h = 750 * 0.2126 ≈ 159.45

So the height of the tree is approximately 159.45 feet.

Therefore, the height of the tree is approximately 159.45 feet.

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So, approximately 7.71 grams of radium will be present after 100 years.

To calculate the remaining amount of radium after 100 years, we will use the half-life formula:
Remaining Amount = Initial Amount * (1/2)^(time passed / half-life)
Here, the initial amount is 8 grams, the half-life is 1690 years, and the time passed is 100 years.
Step 1: Plug in the values
Remaining Amount = 8 * (1/2)^(100 / 1690)
Step 2: Calculate the exponent
Exponent = 100 / 1690 ≈ 0.05917
Step 3: Calculate the base raised to the exponent
(1/2)^0.05917 ≈ 0.9634
Step 4: Multiply the initial amount by the base raised to the exponent
Remaining Amount = 8 * 0.9634 ≈ 7.7072
So, approximately 7.71 grams of radium will be present after 100 years.
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The number of batches of pancakes Curtis can make is A = 10 batches

We have,

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

If Curtis takes 1/2 cup of flour to make a batch of pancakes, then the number of batches of pancakes that can be made from 5 cups of flour is:

5 cups / (1/2 cup per batch) = 5 / 0.5

On simplifying the equation , we get

A = 10 batches

Therefore, Curtis can make 10 batches of pancakes with 5 cups of flour

Hence , the number of batches is 10

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The fallacy committed by the following argument is a formal fallacy, specifically the fallacy of the undistributed middle.

The argument assumes that everything that runs has feet, and that the Columbia River runs very swiftly. From these two premises, the conclusion is drawn that the Columbia River has feet, which is a non sequitur.

This fallacy occurs when a categorical syllogism has a middle term that is not distributed in either the major or minor premise. In this case, the term "has feet" is not distributed in either premise, and thus the argument is invalid.

It is important to note that formal fallacies are errors in the structure or form of an argument, rather than errors in the content or premises of the argument. While formal fallacies are often easier to identify and correct than informal fallacies, both can undermine the validity and persuasiveness of an argument.

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The fallacy committed by the following argument is a formal fallacy, specifically the fallacy of the undistributed middle.

The argument assumes that everything that runs has feet, and that the Columbia River runs very swiftly. From these two premises, the conclusion is drawn that the Columbia River has feet, which is a non sequitur.

This fallacy occurs when a categorical syllogism has a middle term that is not distributed in either the major or minor premise. In this case, the term "has feet" is not distributed in either premise, and thus the argument is invalid.

It is important to note that formal fallacies are errors in the structure or form of an argument, rather than errors in the content or premises of the argument. While formal fallacies are often easier to identify and correct than informal fallacies, both can undermine the validity and persuasiveness of an argument.

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The length of one side of the regular pentagon for the given area and length of apothem is equal to 3.4 meters.

In a regular pentagon,

measure of apothem of a regular pentagon = 3.2m

Area of regular pentagon = 27.2 square meter

Use the formula for the area of a regular pentagon we have,

A = (5/2) × a × ap

where A is the area of the pentagon,

a is the length of one side,

and ap is the apothem the distance from the center of the pentagon to the midpoint of a side.

The apothem is 3.2 m and the area is 27.2 m², so we can plug in these values and solve for a,

⇒ 27.2 = (5/2) × a × 3.2

Simplifying,

⇒ 27.2 = 8a

⇒ a = 27.2/8

      = 3.4

Therefore, the length of one side of the regular pentagon is 3.4 meters.

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The calculated value of the area of the parallelogram is 99 square cm

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

The parallelogram

Where we have

Height = 11 cm

Base = 5 cm  + 4 cm = 9 cm

The area of the parallelogram is calculated as

Area = Base * Height

Substitute the known values in the above equation, so, we have the following representation

Area = 11 * 9

Evaluate the product of 11 and 9

So, we have the following representation

Area = 99

Hence, the area of the parallelogram is 99 square cm

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Part A) Local minimum value of 19 at (1, 0). A= -2 B= 20. Part B) local maximum value of 15 at the point (3, 4) A= 56 B= 6 C= 8.

To find A and B such that f(x,y) has a local minimum at (1,0) with a value of 19, we need to use the second derivative test.

Taking the partial derivatives of f with respect to x and y, we get 2x + A and 2y, respectively. Evaluating these at (1,0) gives 2 + A and 0. Since f has a local minimum at (1,0), both of these partial derivatives must be zero, so A = -2.

To find B, we use the fact that f(1,0) = 19, which gives 1 + A + B = 19. Substituting in A = -2 and solving for B, we get B = 20.

For the second part of the question, we again use the second derivative test. Taking the partial derivatives of f with respect to x and y, we get -2x + B and -2y + C, respectively.

Evaluating these at (3,4) gives -6 + B and -8 + C. Since f has a local maximum at (3,4), both of these partial derivatives must be zero, so B = 6 and C = 8.

To find A, we use the fact that f(3,4) = 15, which gives A - 9 - 32 = 15. Solving for A, we get A = 56. Therefore, the values of A, B, and C that give f a local maximum of 15 at (3,4) are A = 56, B = 6, and C = 8.

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The legs of the given right angle triangle is 2cm and 6 cm,

Hence , option B is correct.

A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it.

Given that,

Area of right angle triangle = 12 cm²

Consider length of triangle = l

And breath of triangle = b

And we know that area of triangle = (1/2) x l x b

Therefore,

⇒ 12 = (1/2) x l x b

⇒ 24 =  l x b

This is possible if we take l =4 and b = 6

Then,

legs are l = 4 and b = 6

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The area under the standard normal curve where P(Z > -0.5) is 0.6915. To find this, we can use a standard normal distribution table or a calculator with a normal distribution function.

First, we need to find the z-score associated with -0.5. We know that the mean of the standard normal distribution is 0 and the standard deviation is 1. So, the z-score can be calculated as z = (x - μ) / σ = (-0.5 - 0) / 1 = -0.5. Now, we can look up the area to the right of the z-score -0.5 in a standard normal distribution table. The area is 0.6915, which means that the probability of getting a z-score greater than -0.5 is 0.6915.

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The sampling distribution of sample means for a random sample of 40 dogs will be approximately normally distributed with a mean of 15 pounds and standard deviation of 4 pounds divided by the square root of 40.

This is due to the central limit theorem, which states that as the sample size increases, the distribution of sample means approaches a normal distribution regardless of the shape of the population distribution. In this case, the large enough sample size (n=40) will allow us to assume normality for the sampling distribution of sample means.
The standard deviation of the sampling distribution (also known as the standard error) is calculated by dividing the population standard deviation by the square root of the sample size. In this case, the standard error is  [tex]\frac{4}{\sqrt{40}} = 0.632[/tex].
Therefore, option C is the correct answer. Option A is incorrect because the sampling distribution is not necessarily strongly skewed right, as the central limit theorem will cause the distribution to approach normality. Option B is incorrect because the standard deviation of the sampling distribution is not 0.632 pounds, but rather the standard error is 0.632 pounds. Option D is incorrect because the standard deviation of the sampling distribution is not the same as the standard error.

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Answer:

706.86

Step-by-step explanation:

A=4πr2=4·π·7.5^2≈706.85835.

Answer:

706.86

Step-by-step explanation:

The numeric value of the derivative of f(x) at x = 0.1 is given as follows:

B. 10.2062.

The function in the context of this problem is defined as follows:

[tex]f(x) = \sech^{-1}{2x}[/tex]

Applying the chain rule, we consider these following derivatives:

Hence the derivative of the composite function f(x) is given as follows:

[tex]f^{\prime}(x) = \frac{2}{2x\sqrt{1 - (2x)^2}}[/tex]

Hence the numeric value of the derivative at x = 0.1 is given as follows:

[tex]f^{\prime}(0.1) = \frac{2}{2(0.1)\sqrt{1 - (2(0.1))^2}}[/tex]

f'(0.1) = 10.2062.

Hence option B is the correct option in the context of this problem.

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The solution to the given expression 3(1/4 - 2) + |-7| is 7/4.

The expression is given as follows:

3(1/4 - 2) + |-7|

To solve the given expression, we need to follow the order of operations, which is PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

First, we need to simplify the expression inside the parentheses:

1/4 - 2 = -7/4

Next, we can simplify the expression by multiplying 3 by -7/4:

3(-7/4) = -21/4

Finally, we need to evaluate the absolute value of -7:

|-7| = 7

Substituting the values into the original expression, we get:

3(1/4 - 2) + |-7| = -21/4 + 7

Combining like terms, we get:

3(1/4 - 2) + |-7| = -21/4 + 28/4

Simplifying, we get:

3(1/4 - 2) + |-7| = 7/4

Therefore, the solution to the expression 3(1/4 - 2) + |-7| is 7/4.

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The complete question is as follows:

Solve the below expression

3(1/4 - 2) + |-7|

The possible measure for the angle C is 55 degrees.

We know that the sum of all the angles in a triangle is 180 degrees.

Now we know that angle A has a measure of 35 degrees,

so using the Law of Cosines we can find angle B:

[tex]c^2 = a^2 + b^2 - 2ab*cos(m\angle CAB)[/tex]

where c is the length of side C, and m∠CAB is the measure of angle B.

Substituting the given values, we get:

[tex]c^2 = 16.2^2 + 22.5^2 - 2(16.2)(22.5)*cos(m\angle CAB)[/tex]

Simplifying, we get:

[tex]c^2 = 1055.29 - 729*cos(m\angle CAB)[/tex]

To find a possible measure of angle C, we can try different values of [tex]cos(m\angle CAB)[/tex] and solve for c.

Let's start by assuming that [tex]cos(m\angle CAB)[/tex] is equal to -1, which means that angle CAB is a straight angle (180 degrees). In this case, we get:

[tex]c^2 = 1055.29 - 729*(-1) = 1784.29[/tex]

Taking the square root of both sides, we get:

[tex]c = \sqrt{1784.29} = 42.24[/tex]

However, this value of c is larger than the sum of sides a and b, which violates the triangle inequality. Therefore, angle CAB cannot be a straight angle, and [tex]cos(m\angle CAB)[/tex] must be greater than -1.

Let's try [tex]cos(m\angle CAB)[/tex] equal to 0, which means that angle CAB is a right angle (90 degrees). In this case, we get:

[tex]c^2 = 16.2^2 + 22.5^2 - 2(16.2)(22.5)*cos(90)\\c^2 = 1055.29[/tex]

Taking the square root of both sides, we get:

[tex]c = \sqrt{(1055.29)} = 32.46[/tex]

This value of c is less than the sum of sides a and b, so it satisfies the triangle inequality. Therefore, a possible measure of angle C is:

[tex]m\angle C = 180 - m\angle A - m\angle B = 180 - 35 - 90 = 55\ degrees[/tex]

Note that this is only one possible measure of angle C, as there could be other values of [tex]cos(m\angle CAB)[/tex]that also satisfy the triangle inequality.

The possible measure for the angle C is 55 degrees.

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The radius of convergence of the given series is r = 1/3.

To find the radius of convergence, we can use the ratio test. Applying the ratio test to the series, we take the limit as n approaches infinity of the absolute value of the ratio of the (n+1)th term to the nth term.

Taking the ratio of consecutive terms, we have |((n+1)!(3x - 1)[tex]^([/tex]n+1))/(n!(3x - 1)[tex]^n[/tex])|.

Simplifying the expression, we obtain |(n+1)(3x - 1)|.

Taking the limit as n approaches infinity, we can see that this expression goes to infinity unless (3x - 1) equals zero.

The series converges when (3x - 1) equals zero, which leads to x = 1/3

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The terminal amount that Oliver will end up with after putting $4,000 into this savings account that increases by 10% annually and pays a 5% withdrawal fee to the bank is $4,598.

The terminal amount is the future value of the present investment less the withdrawal fee.

The future value can be computed using the FV table, formula, or an online finance calculator.

The present value (investment) = $4,000

The number of investment period = 2 years

The compound interest rate = 10%

Compounding factor after 2 years = 1.21 [(1.1)²]

The future value of the account after 2 years = $4,840 ($4,000 x 1.21)

The bank fee for withdrawal = 5% of $4,840 = $242

The terminal amount that Oliver will end up after 2 years of compounding at 10% and the payment of the bank withdrawal fee is $4,598 ($4,840 - $242).

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