Use the Internet to briefly define each of the following terms and explain how they are examples of annuities.

a) RRSP

The length of LG in the plane is

To find the distance between two points in a 2D plane, we can use the distance formula:

distance = √((x2 - x1)^2 + (y2 - y1)^2)

Using this formula, we can find the distance between L(4,4) and G(9,9):

distance = √((9 - 4)^2 + (9 - 4)^2)

= √(5^2 + 5^2)

= √50

= 5√2

Therefore, the distance between L(4,4) and G(9,9) is 5√2, which is approximately 7.07 units.

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Domain and range of function is (D)=D={x|x≥2}, R={y|y≥0}.

In mathematics, the domain of a function is the set of all possible input values for which the function is defined. The range of a function is the set of all possible output values that the function can produce, based on its input values. In other words, the domain is the set of all x-values that the function can take, while the range is the set of all corresponding y-values that the function can take.

The given graph is oriented toward x direction

Domain of function =x≥2

For every value of x the y is always positive

So, range =y≥0

Hence, domain and range of function is (D)=D={x|x≥2}, R={y|y≥0}

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G. y = 37/24x

Direct variation means that the number of inches of rain (y) is directly proportional to the number of hours (x). In this case, 37 inches of rain fell in a 24-hour period. To find the constant of proportionality, divide the total inches of rain by the total hours:

k = 37 inches / 24 hours

Now, we can write the equation of direct variation:

y = kx

Substitute the value of k:

y = (37/24)x

The surface area is approximately 41.7 square units.

The rectangle has dimensions 18 units by 6 units, so its area is:

A(rectangle) = l x h = 18 x 6 = 108 square units

The semicircle has a radius of 5 units, so its area is half that of a full circle:

A(semicircle)

= 1/2 x π x r²

= 1/2 x π x 5²

= 1/2 x 25π

= 12.5π

To find the total surface area, we need to add the areas of the rectangle and the semicircle. However, since the semicircle is attached to the top of the rectangle, we need to subtract the area of the portion of the circle that overlaps with the rectangle. This overlapping area is equal to the width of the rectangle (18 units) times half the circumference of the circle (1/2 x π x r), or:

A(overlap)

= w x 1/2 x π x r

= 18 x 1/2 x π x 5

= 45π

Therefore, the total surface area is:

Surface area = A(rectangle) + A(semicircle) - A(overlap) = 108 + 12.5π - 45π ≈ 41.7 square units

Rounding to the nearest tenth, the surface area is approximately 41.7 square units.

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If 31.2 out of every 100 pregnant women in India deliver their babies by C-section.

First, we need to find the fraction of pregnant women who deliver by C-section

31.2 out of 100 = 31.2/100 = 0.312

Then, we can use this fraction to find the number of pregnant women out of 85,733 who would be expected to deliver by C-section.

0.312 x 85,733 = 26,723.896

Rounding to the nearest whole number, we get

26,724 pregnant women.

26,724 pregnant women out of 85,733 would be expected to deliver by C-section.

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Answer:

See the below process

Step-by-step explanation:

let the Unknown value be x.

Now

[tex] \frac{17}{24} + x = \frac{ - 5}{12} [/tex]

[tex]x = \frac{ - 5}{12} - \frac{17}{24}[/tex]

Taking LCM

[tex]x = \frac{ - 10 - 17}{24} [/tex]

[tex]x = \frac{ - 27}{24} \\ = \frac{8}{9} [/tex]

we should add 8/9 to 17/24 to get -5/12

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The height of the rectangular prism is 8 inches.

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:

Volume V = 241.92 in³

Length l = 5.6 in

Width w = 5.4 in

Height h = ?

Plug the given values into the above formula and solve for h

V = w × h × l

h = V / ( w × l )

h = 241.92 in³ / ( 5.4 in × 5.6 in )

h = 8 in

Therefore, the height is 8 inches.

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the correct answer is a reflection across the x-axis.

How to solve questions?

Based on the given image, the type of transformation shown is a reflection across the x-axis.

A reflection is a transformation that flips a figure over a line of reflection, in this case, the x-axis. The resulting image is a mirror image of the original figure, with corresponding points on either side of the line of reflection equidistant from it.

In the given image, polygon ABCD is the preimage, and polygon A'B'C'D' is the resulting image. We can see that the two polygons are mirror images of each other across the x-axis. For example, point A in the preimage is reflected across the x-axis to point A' in the resulting image, which is directly below point A. Similarly, point B in the preimage is reflected to point B', point C to C', and point D to D'.

A 90° clockwise rotation would result in a different orientation of the polygon, where point A would move to the position of point B, point B to C, point C to D, and point D to A. A horizontal or vertical translation would result in a shift of the polygon in the respective direction, which is not the case here.

Therefore, the correct answer is a reflection across the x-axis.

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The changes that Jason should make are:

1. Plan a trip not during the tourist season.

2. In place of renting car, use transportation services of the country.

3. He should go to other places to find a nice hotel.

The solution has been obtained by using cost planning.

What is cost planning?

Estimating expenses, establishing an agreed-upon budget, and managing actual and projected expenditures in relation to that budget are all parts of cost planning and control.

The changes that Jason should make are:

1. Plan a trip not during the tourist season. This is because during the tourist season prices are high.

2. In place of renting car, use transportation services of the country. This is because the local transport will cost him less that the rental.

3. He should go to other places to find a nice hotel. This is because central Turkey is costly and he might find a nice hotel in other areas in less price.

Hence, the required solution has been obtained.

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Here is an example of how to create an object model, UML diagrams, and contract obligations in general.

Let's have a look at a basic "Bank Account" system, where a customer may deposit money, withdraw it, and see the amount of their account. The following classes would be represented in the UML class diagram for this system:

Bank Account Client

The following characteristics would be included in the Bank Account class:

string Account Number

stability: float

and the subsequent techniques:

deposit(float amount) = None

withdrawal(float :amount) = None

float: check Balance()

The following characteristics would apply to the Customer class:

string name

list of accounts[Bank Account]

and the subsequent techniques:

account: Bank Account; add account(account) -> None

account: Bank Account; remove  Account(account: None)

Bank Account: get  Account(Account number: string)

For the Bank Account class, the design by contract obligations would be:

Pre-conditions:

amount > 0

withdraw(amount): amount > 0 and balance >= amount

Check Balance(): None

Post-conditions:

deposit(amount): balance += amount

withdraw(amount): balance -= amount

Check Balance(): return balance

The design by contract responsibilities for the Customer class would be:

Pre-conditions:

Add account(account): account not in accounts

Post-conditions:

Add account(account): accounts. append(account)

remove (account): accounts.

get account (account number): return the Bank Account object with the given account Number.

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Answer:

  7²

Step-by-step explanation:

You want to know what 7×7 is when it is written using an exponent.

At its most basic, an exponent signifies repeated multiplication. It represents the number of times a value appears as a factor in the product.

The expression 7×7 has 7 as a factor 2 times. It can be written as 7 with an exponent of 2.

  7×7 = 7²

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The vector v+w has a magnitude of 2√2 and its direction is along the positive x-axis.

What is meant by vector?

A vector is a quantity that has both magnitude and direction. It is represented as an arrow with its length representing the magnitude and its direction representing the direction of the quantity.

What is meant by the x-axis?

The x-axis is the horizontal line on a coordinate plane that is used as a reference for plotting and describing the positions of points in two-dimensional space. It is often referred to as the "horizontal axis" or the "abscissa".

According to the given information

Here the vector v has a magnitude of 2 and a direction of 45° so the components of vector v are:

v_x = 2 cos 45° = √2

v_y = 2 sin 45° = √2

Vector w has a magnitude of 2 and a direction of 45° South of East. This means that the angle between vector w and the positive x-axis is 45°, and the angle between vector w and the negative y-axis is 45°. Therefore, the components of vector w are:

w_x = 2 cos 45° = √2

w_y = -2 sin 45° = -√2

Now we can add the components of vectors v and w to find the components of the vector v+w:

(v+w)_x = v_x + w_x = √2 + √2 = 2√2

(v+w)_y = v_y + w_y = √2 - √2 = 0

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Answer:

266

Step-by-step explanation:

36 hours x 7 people.

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Answer: 266 hours

Step-by-step explanation:

38 x 7 = 266 hours. Each worker worked 38 hours, and there are 7 people. So, multiply worker by time.

Answer:

5x - 9 and 3x + 9 are two mathematical expressions. The first expression, 5x - 9, represents a value obtained by multiplying 5 by x and then subtracting 9. The second expression, 3x + 9, represents a value obtained by multiplying 3 by x and then adding 9. Both expressions can be simplified further or used in various mathematical operations depending on the context of the problem or equation in which they are being used.

Answer:-45 and -3

Step-by-step explanation:

If Joan has a square flower bed with a side length of 4 meters filled with tulips, the density of tulips in the bed is 22.1 tulips per square meter.

To find the density of tulips for the area of the bed, we need to divide the total number of tulips by the area of the bed. The area of the square flower bed is the side length squared, so in this case, it is 4 meters x 4 meters = 16 square meters.

So, the density of tulips in the bed is 354/16 ≈ 22.1 tulips per square meter. This means that there are approximately 22.1 tulips growing in every square meter of the flower bed.

The density is a measure of the amount of something per unit of space, so in this case, it is the number of tulips per square meter. It is a useful metric for understanding how many of something is present in a given area, which can be important for planning and management purposes.

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The equivalenet expression is 54[tex]n^{-11}[/tex]

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

To simplify the given expression, we need to apply the power of a power rule, which states that to raise a power to another power, we need to multiply the exponents.

Starting with:

([tex]6n^-5[/tex])([tex]3n^-3[/tex])²

We can simplify as follows:

([tex]6n^-5[/tex])([tex]9n^-6[/tex])

Now, we can use the product of powers rule, which states that when multiplying two powers with the same base, we add their exponents.

Therefore:

6 x 9 = 54

[tex]n^-5 * n^-6 = n^-11[/tex]

So the simplified expression is:

[tex]54n^-11[/tex]

Therefore, the expression [tex](6n^-5)(3n^-3)^2[/tex] is equivalent to [tex]54n^-11.[/tex]

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The expression that is equal to (6n-5)(3n-3) option D, 54n11.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

We can use the distributive property of multiplication to expand the expression (6n - 5)(3n - 3) as follows:

(6n - 5)(3n - 3) = 6n(3n) - 6n(3) - 5(3n) + 5(3)

                 = 18n² - 18n - 15n + 15

                 = 18n² - 33n + 15

Therefore, the expression that is equivalent to (6n - 5)(3n - 3) is 18n² - 33n + 15, which is option D.

So, the answer is option D, 54n11.

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The length of the other side will be 3.

To obtain the length of the other side of the rectangle, given the approximation of 1.62, we will first divide 4.9, the known side by x, the unknown side, and equate this to 1.62.

If we are using the approximation of 1.62, then the length of the other side of the rectangle will be 4.9/x = 1.62

1.62x = 4.9

x = 3

So, the length of the other side, which in this case is shorter is 3.

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The missing step in the two column proof is

Statement              Reason

Δ DAC ≅ ΔBCA    ASA congruence theorem

The ASA theorem, also known as the angle side angle theorem, is a rule used in geometry to determine whether two triangles are congruent (meaning they have the same shape and size).

The angle side angle theorem states uses the side two parameters which includes:

The parameters are used for the theorem to say that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

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Answer: 480 in²

Step-by-step explanation:

    To calculate the surface area, we will find the area of each side and add it together.

Area of the rectangular sides can be found with A = LW:

    A = LW

    A = (12 in)(10 in)

    A = 120 in²

    A = LW

    A = (12 in)(10 in)

    A = 120 in²

    A = LW

    A = (12 in)(12 in)

    A = 144 in²

All the rectangular sides added together:

    120 in² + 120 in² + 144 in² = 384 in²

    Now, we will find the triangle sides. The formula for a triangle is [tex]A=\frac{BH}{2}[/tex], but since we have two congruent triangles I will not be dividing by 2.

    A = BH

    A = (12 in)(8 in)

    A = 96 in²

Lastly, I will add them both together:

384 in² + 96 in² = 480 in²

Answer:

x = 35

Step-by-step explanation:

since the figures are similar then the ratios of corresponding parts are in proportion, that is

[tex]\frac{x}{10}[/tex] = [tex]\frac{14}{4}[/tex] = [tex]\frac{7}{2}[/tex] ( cross- multiply )

2x = 7 × 10 = 70 ( divide both sides by 2 )

x = 35

The quantity of pounds of dog food that Mrs. Evans should buy that would be enough for her dog = 720 ounces.

The total number of days the food is required to last = 90 days.

The quantity of dog food in ounce the dog eat per day = 4 × 2 = 8 ounces.

Therefore the quantity of pounds that will be enough for the dog for the whole 90 days would be = ?

That is;

1 day = 8 ounces

90 days = X

Make X the subject of formula;

X = 90× 8

= 720 ounces

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U is located in the plane or vector that A's columns span.

A mathematical concept with both magnitude and direction is a vector. It is frequently used to symbolise forces like the gravitational pull of an object or the electrical forces that exist between charged particles. It can be expressed mathematically as a line segment with two ends, a direction, and a magnitude.

Part 1

To calculate the resulting vector, vector operations including addition, subtraction, multiplication, and division can be used. The individual x, y, and z components of a vector—which stand for its magnitude and direction—can also be determined.

Part 2

Why the answer in Part 1 is correct?

Part 1's answer I gave was A. Yes, writing u as a linear combination of the columns of A after multiplying A by the vector [4, 20, 8]. This is so because the vector [4, 20, 8] may be expressed as a linear combination of the columns of A since it is a solution to the system of linear equations generated by the augmented matrix [A|u]. U is thus in the plane that is covered by the columns of A.

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Matching each function with the transformation that took place gives:

g(x) = -(x - h)ⁿ: Reflection across the x-axis

j(x) = axⁿ + k: Translation of k units up

m(x) = (x + h)ⁿ - k: Translation of h units to the left

Vertical dilation: Functions of form f(x) = 2ⁿ are vertically dilated.

In mathematics, a transformation refers to a process of changing the size, position, or orientation of a geometric object or a function.

Transformations are usually expressed as a set of rules or equations that determine how each point or element in the original object or function maps to a corresponding point or element in the transformed object or function. Common types of transformations include translations, rotations, reflections, dilations, and combinations of these operations.

Transformations are widely used in many areas of mathematics, physics, engineering, and computer science to study and model complex systems and phenomena.

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We can expect 4 of the next 20 pastries served to be bran muffins based on the given data.

What is meant by the term data?

Data refers to a collection of facts, statistics, measurements, or observations that are gathered and analyzed to gain insights or information about a particular topic or subject. Data can be both quantitative (numerical) and qualitative (descriptive) in nature, and it can be obtained from various sources, such as surveys, experiments, sensors, or records. The processing and interpretation of data can lead to new discoveries, trends, or predictions in various fields, including science, business, and technology.

According to the given information

The proportion of bran muffins out of the total pastries served can be calculated by dividing the number of bran muffins by the total number of pastries:

The proportion of bran muffins = 2 / (1 + 3 + 2 + 2 + 2) = 2 / 10 = 0.2

This means that 20% of the pastries served are bran muffins. To find out how many of the next 20 pastries served should be expected to be bran muffins, we can multiply 20% by 20:

The number of expected bran muffins = 0.2 * 20 = 4

Therefore, we can expect 4 of the next 20 pastries served to be bran muffins based on the given data.

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On day zero, the number of students who know the rumor are 2 people who are Susanna and Liz.

On day 2, the number of students would be 12 students.

The number of days till 32 students know the rumor is 6 days.

2 students (Susanna and Liz) know the rumor on day 0.

On day 2, the number of students who know the rumor will be the initial number of students (2) plus 5 students for each day that has passed (5 * 2 = 10). So, on day 2, 2 + 10 = 12 students know the rumor.

To find the number of days it will take for 32 students to know the rumor, we can set up an equation using the given information:

2 (Susanna and Liz) + 5 x number of days = 32

Now, we can solve for the number of days:

5 x number of days = 32 - 2

5 x number of days = 30

number of days = 30 / 5

number of days = 6

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Step-by-step explanation:  

1. Quota Sampling: This method involves identifying specific subgroups of respondents that need to be included in the study in a specific proportion to the population.

2. Convenience Sampling: This sampling technique involves selecting the sample based on the availability of participants at the time of the study.

3. Stratified Sampling: This technique divides the population into subgroups or strata based on similarities, with the elements within each group being relatively homogeneous and heterogeneous among the other subgroups.

4. Purposive Sampling: This type of sampling is based on the intention or purpose of the study, and the sample is selected based on the researcher's judgment or knowledge of the population.

5. Judgment Sampling: This sampling technique depends on some pre-set standards, and the representative sample is selected based on the researcher's judgment or experience. 6. Simple Random Sampling: This technique involves using randomization to ensure that every element of the population has an equal chance of being selected for the sample. 7. Snowball Sampling: This sampling method is used in situations where the population is completely unknown or rare, and it relies on referrals from the initial participants to identify subsequent participants.

8. Hypothesis Sampling: This type of sampling is guided specifically by a hypothesis, and the sample is selected based on the research question being asked.

9. Qualitative Sampling: This technique is used in qualitative research and involves a systematic, subjective approach used to describe life experiences and give them meaning.

LO. Quantitative Sampling: This technique involves an objective, systematic, empirical investigation of observable phenomena through the use of computational techniques.

Based on the information provided, the polygon can be classified as a trapezoid.

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