You would like to start saving for retirement. Assuming you are now 25 years old and you want to retire at age 55, you have 30 years to watch your investment grow. You decide to invest in the stock market, which has earned about 13% per year over the past 80 years and is expected to continue at this rate. You decide to invest $2,000 at the end of each year for the next 30 years.

The option which is not personally liable for any losses or damages is Shareholders in a public corporation, the correct answer is A.

We are given that;

Four options of damages

Now,

Shareholders in a public corporation are not personally liable for any losses or damages caused by the corporation, because they have limited liability. This means that they can only lose the amount they invested in the corporation, and their personal assets are protected from creditors or lawsuits12.

Owner of a sole proprietorship, shareholders in a private corporation, and partners in a partnership are all personally liable for any losses or damages caused by their business activities, unless they have some form of liability insurance or protection12. This means that they can be sued for their personal assets if the business cannot pay its debts or obligations.

Therefore, by unitary method the answer will be Shareholders in a public corporation

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Answer:

The second scatterplot does not suggest a linear relationship between x and y.

The description of function transformations and an example is highlighted below

To describe the transformation of the functions, we need to identify the image and the preimage of the functions to be transformed

Take for instance the function is y = x² transformed to the function y = (x + 3)²

This means that the parent function is y = x²

When compared, we can see that

x in y = x² is x + 3 in y = (x + 3)²

This means that y = x² is shifted left by 3 units to form y = (x + 3)²

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Answer:

5/2

Step-by-step explanation:

Slope is rise over run, or how far it goes in the y direction over how far it goes in the x direction. In this case, y increases by a value of 5 at the same time x is increasing by a value of 2. This makes the slope 5/2, and it is positive since the values are increasing. If there is a problem your stuck on like this try graphing the points, desmos has a good graphing calculator :)

Answer:

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Find the composition of the functions f(x) and g(x), which is written as f(g(x)).

Given functions:

Find f(g(x)):

Evaluate f(g(2)):

So, (f·g)(2) = 14.

The new surface area of the hemisphere-shaped mole would be = 102mm².

A hemisphere-shaped mole has a shape that has one surface that is curved and the other surface a flat circular base.

Since the surface area of one hemisphere has been given, the second hemisphere can be determined.

To calculate the new surface area of the hemisphere-shaped moles the following is carried out;

Radius of the initial mole = 5.7/2 = 2.85 mm

If 2.85mm radius = 51 mm²

2(2.85mm) radius = x

Make X the subject of formula;

X = 2×2.85 × 51/2.85

= 102 mm²

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Answer:45.3 miles/h

Step-by-step explanation

let 'x' be the speed of the car.

60 × 2/3 = 120/3 = 40

30 × 1/5 = 151/5

151/5 /40 = x / 60

151 / 200 = x / 60

=> x = (151×60) / 200

=> x = 45.3

The area of one face of the cube that has a volume of 3375 cubic inches is: 225 square inches.

A cube has equal edge length, and therefore has faces with the same area. The formula for finding the volume of a cube is given as:

Volume of cube = s³, where s is the side length of the cube.

Also, to find the area of one face of a cube, we would use the formula below:

Area of one face of a cube = s².

Given the following:

Volume of a cube = 3375 cubic inches

Find s as shown below:

s = ∛3375

s = 15 inches.

Therefore, we have:

Area of one face of a cube = 15² = 225 square inches.

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Answer:

Im pretty sure its the third one

Step-by-step explanation:

It all depends on the square root to find the nearest tenth and rounding it all up.

Check the picture below.

[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{ triangle }{\cfrac{1}{2}(26)(17)}~~ + ~~\stackrel{ rectangle }{(26)(9)}}\implies 221+234\implies \text{\LARGE 455}[/tex]

The drop down menu is used to match each situation as below.

1. The rocket reached its maximum  the x-value of the vertex

height in 5 s.

2. ground level                                    the y-intercept

3. The rocket launcher was                the y-value of the point containing

on the ground.                                     the x-intercept on the right

4. The rocket was in the air 10           the x-intercept on the right                                                                                    

5. The maximum height of the           the y-value of the vertex

rocket is 50 ft.

6. the time the rocket was                the x-value of the point containing the

launched                                          y-intercept

The key features of the curve such as the x intercept is the point the launcher and the rocket were on ground.

The vertex is the point the rocket had the maximum and height.

Generally, the curve traces a parabolic path

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The given statement "If data set A has a larger standard deviation than data set B, data set A is more spread out than data set B" is true.

The standard deviation is a measure of a data set's dispersion. It tells us how far the data values are from the mean.

A larger standard deviation means that the data points are more spread out, i.e., they are farther from the mean.

Therefore, if data set A has a standard deviation that is greater than data set B, it means that the values in data set A are more spread apart.

Hence, the given statement is true.

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The side AC corresponds to the side AC in the other triangle and the length of BC is 15 units

For two triangles to be similar, the corresponding sides of the triangles must be in proportion

Having said  that

The side AC corresponds to the side AC in the other triangle

The length BC is calculated as

BC/9 = 25/15

Express as products

So, we have

BC = 9 * 25/15

Evaluate the products

BC = 15

Hence, the length of BC is 15 units

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Answer:  C

Step-by-step explanation:

Think about y=[tex]x^{3}[/tex]     This is an odd function because the highest exponent(degree) is odd

A.  is wrong. Symmetry is where you can fold it and it would be the same.  If i folded y=[tex]x^{3}[/tex] along the y- axis it would not be the same.  

B is wrong. Transformations are where has it moved, which has nothing to do with odd functions in general

C.  is correct.  It is folded along y=x and flipped.

D. is wrong.  If folded y=x it's in the same quadrant but it's not the same, its' reversed.

The solution to the given system of equations is a = 6, b = 4.

The system of equations is given as follows:

a + b = 10  .....(i)

a - b = 2    .....(ii)

To solve this system of equations, we can use the method of elimination.

Adding the two equations, we get:

(a + b) + (a - b) = 10 + 2

2a = 12

a = 6

Substituting a = 6 into one of the equations, we get:

6 - b = 2

b = 4

Therefore, the solution to the system of equations is:

a = 6, b = 4.

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Answer:

  (b)  The data has a possible range of 19, which is a wide spread. This might mean that there is a large difference in the number of water-skiing trips taken by the students.

Step-by-step explanation:

You want the best description of the spread of data shown in the histogram.

The least data value that can be represented on the chart is 6. The greatest value the chart can represent is 25. This means the possible range of data values is ...

  range = max - min = 25 -6 = 19

This possible spread of 19 might mean there is a large difference in the number of trips taken by students, choice B.

__

Additional comment

The range must be at least 21 -10 = 11 trips, not an answer choice. The most common number appears to be in the range 16-20, so will likely not be 10. (This is referred to as the "mode range", as we cannot tell from the grouped data what the actual mode is.)

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Answer: A,E or F.

Step-by-step explanation: That's the only ones that have X's and then x is 0

The fourth term in the expanded form of (x - 1)⁶ is  -20x³.

The fourth term in the expanded form of (x - 1)⁶  using the binomial theorem is calculated as follows;

The expanded form of (x - 1)⁶ using the binomial theorem is;

(x - 1)⁶ = 1x⁶ + (-6)x⁵ + 15x⁴ + (-20)x³ + 15x² + (-6)x + 1

(x - 1)⁶ = x⁶ -6x⁵ + 15x⁴ -20x³ + 15x² -6x + 1

To find the fourth term, we look for the fourth term from the left side to right side, which is  -20x³.

Therefore, the fourth term in the expanded form of (x - 1)⁶ is  -20x³.

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Answer:

Length= 43.98 cm

Step-by-step explanation:

Circumference=2πr

r=7cm

C=2π(7)

C=43.98 cm

circumference is equal to the length of ribbon along the outside of the circular object

The requried equivalent fraction for the equivalent fraction to 3 3/4 and 1 2/3, is 45/12, and 20/12.

To find a common denominator for 4 and 3, we can multiply them together to get 12.

So, we can convert 3 3/4 as:

3 3/4 = 12/4 + 3/4 = 15/4

Similarly, we can convert 1 2/3 as:

1 2/3 = 5/3

Therefore, the equivalent fractions for 3 3/4 and 1 2/3 using a common denominator of 12 are:

15/4 = 45/12 and 5/3 = 20/12

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Answer: f(x)=x-2

Step-by-step explanation:

Linear function means a straight line so graph each one to find which is a straight line

The area of a rectangle is 14x² + 19x - 3 square units.

The degree of 4x² + 3y - 6x⁴y + 4 is 5.

The number of terms of 4x² + 3y - 6x⁴y + 4 is 4.

Adding, subtraction or multiplying two polynomials always results in another polynomial.

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LB

Where:

By substituting the given parameters into the formula for the area of a rectangle, we have the following;

Area of rectangle = (7x - 1) × (2x + 3)

Area of rectangle = 14x² + 21x - 2x - 3

Area of rectangle = 14x² + 19x - 3 square units.

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The relation that is not a function is relation 3, and the other 3 are functions.

A relation is a function if each point on its domain is mapped into a single point in the range.

So if you see an input that is mapped into two different outputs, then it is not a function.

Then the relation 3 is not a function, because h is mapped to different things, meaning that we have the same input being mapped to different outpouts. While the other 3 relations are all functions.

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The area of the given rectangle is 83.6cm²

We know that the area of a rectangle is equal to the product between the dimensions, here we can see that:

b = 11cm

h = 7.6cm

The formula for the area is:

A = b*h

Replacing the values we will get:

A = 11cm*7.6cm = 83.6cm²

that is the area.

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The possible dimensions (length and width) of the field which is rectangle are (26m, 5m) or (5m, 26m) and (28m, 4m) or (4m, 28m)

Let's assume the length of the rectangle be L and the width be W.

We know that we have three sides of the rectangle to fence, so the total length of the fence will be L+2W = 36m.

Also, we know the area of the rectangle = L×W = 154 sq.m

Using the two equations above, we can solve for L and W as follows:

L = 36 - 2W (from the first equation)

Substituting this value of L in the second equation:

(36 - 2W)W = 154

2W² - 18W + 77 = 0

We get two possible values of width: W = 5 or W = 4

For W = 5, L = 26

For W = 4, L = 28

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The three equivalent numerical expressions are  1/32, 0.03125, 3.125 x 10^-2

Using the exponential rules, we can simplify the expressions as:

(2^-3)(2^5)/2^7)

= 2^(5-3)/2^7

= 2^2/2^7

= 1/2^(7-2)

= 1/2^5

= 1/32

Therefore, three equivalent numerical expressions for the given expression are: 1/32, 0.03125, 3.125 x 10^-2

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The probability that both events will occur is 23.76%.

Given that, you have 100 tiles and 98 are letters and 2 are blank you randomly drawl 2 title the first is a consonant and the 2nd is a vowel.

Consonants (A) = 56

Vowels (B) = 42

Blank = 2

Total letters = 100

Two letters are drawn with replacement.

P(A) = 56/100 = 0.56

P(B) = 42/ (100-1) = 0.424

P(A).P(B) = 0.56*0.424 = 0.2376

Hence, the probability that both events will occur is 23.76%.

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Complete question is attached.

Based on the figure, we can see that triangles OHJ and OIX are similar because they share the same angle at O and HI and HJ are tangent to the circle. Thus, we can set up the following proportion:

OH / OI = HJ / (HJ + 9)

Substituting the given values:

6.5 / 3.9 = HJ / (HJ + 9)

Cross-multiplying:

6.5(HJ + 9) = 3.9HJ

Distributing:

6.5HJ + 58.5 = 3.9HJ

Simplifying:

2.6HJ = -58.5

HJ = -22.5

However, this answer doesn't make sense in the context of the problem. Since HJ represents a length, it cannot be negative. Therefore, we need to re-examine our work.

Looking back at our proportion, we can see that the ratio of OH to OI is greater than 1, which implies that HJ is greater than 9. This makes sense since HJ is a chord of the circle and thus must be longer than the radius.

Let's try the problem again, but this time we'll rearrange the proportion to solve for HJ:

HJ / (HJ + 9) = OI / OH

Substituting the given values:

HJ / (HJ + 9) = 3.9 / 6.5

Cross-multiplying:

6.5HJ = 3.9HJ + 35.1

Simplifying:

2.6HJ = 35.1

HJ = 13.5

Therefore, HJ is equal to 13.5.