Find the nth term of this quadratic sequence 3, 11, 25, 45, ...​

The real numbers can be classified as either rational or irrational numbers.

1. Rational Numbers:
Rational numbers can be expressed as the ratio (or fraction) of two integers. They can be written in the form p/q, where p and q are integers and q is not equal to zero. Rational numbers can be positive, negative, or zero. Some examples of rational numbers include 1/2, -3/4, and 5.

2. Irrational Numbers:
Irrational numbers cannot be expressed as the ratio of two integers. They are non-repeating and non-terminating decimals. Irrational numbers can be positive or negative. Some examples of irrational numbers include √2, π (pi), and e (Euler's number).

It is important to note that the set of real numbers contains both rational and irrational numbers. Every rational number is a real number, but not every real number is a rational number. This means that there are real numbers that cannot be expressed as a fraction.

In summary, the classification of real numbers as rational or irrational depends on whether they can be expressed as a ratio of integers (rational) or not (irrational). The set of real numbers contains both rational and irrational numbers, providing a comprehensive representation of all possible values on the number line.

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Answer:

20 weeks

Step-by-step explanation:

This question, luckily, can be solved with a very simple algebraic expression.

Let w = the amount of weeks.

\(25w = 500\)

So from here, we need to divide both sides by 25 to get w by itself: \(w = 20\)

Therefore, it will take Aubree 20 weeks to have enough money to buy the computer.

Answer:

4 ( -x^3 + 2x - x)

Step-by-step explanation:

refer the attachment

Answer:

\(total \: number \: of \: rolls = 6 \\ number \: of \: rollsof \: \: green = x \\ number \: of \: rolls \: of \: yellow = 6 - x \\ then \: \\ x \times 9 + (6 - x) \times 1 = 22 \\ 9x + 6 - x = 22 \\ 8x + 6 = 22 \\ 8x = 22 - 6 \\ 8x = 16\\ x = \frac{16}{8} \\x = 2\\then \: number \: of \: green \: = x = 2 \\ number \: of \: yellow = 6 - x = 6 - 2 = 4 \\ thank \: you\)

Dana found 6 rolls of yellow ribbon and green ribbon. Each roll of yellow ribbon was 1 meter long and each roll of green ribbon was 9 meters long. If Dana found 22 meters of ribbon in total, Dana found 4 rolls of yellow ribbon and 2 rolls of green ribbon.

Let's assume the number of rolls of yellow ribbon is "x" and the number of rolls of green ribbon is "y".

Each roll of yellow ribbon is 1 meter long, so the total length of yellow ribbon would be "x" meters.

Each roll of green ribbon is 9 meters long, so the total length of green ribbon would be 9y meters.

The problem states that the total length of ribbon found is 22 meters, so we can set up the equation:

x + 9y = 22

We also know that Dana found 6 rolls of ribbon in total, so we can set up another equation:

x + y = 6

We now have a system of equations:

x + 9y = 22

x + y = 6

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

Let's use the elimination method to solve the system:

Multiply the second equation by 9 to make the coefficients of "x" the same:

9(x + y) = 9(6)

9x + 9y = 54

Now we can subtract the first equation from the modified second equation:

(9x + 9y) - (x + 9y) = 54 - 22

8x = 32

x = 32 / 8

x = 4

Substitute the value of x back into the second equation:

4 + y = 6

y = 6 - 4

y = 2

Therefore, Dana found 4 rolls of yellow ribbon and 2 rolls of green ribbon.

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A conversion of the equation \(f(t) = 259e^{-0.01t}\) to the form \(f(t) = ab^{t}\) is \(f(x) = 259(0.99)^t\).

a = 259

b = 0.990

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

\(f(x) = a(b)^x\)

Where:

By comparing the two the exponential functions, we can logically deduce the following initial value or y-intercept:

initial value or y-intercept, a = 259.

For the rate of change (b), we have:

\(e^{-0.01t} = b^t\\\\e^{(-0.01)t} = b^t\\\\b = e^{(-0.01)}\)

b = 0.990.

Therefore, the required exponential function is given by:

\(f(x) = 259(0.99)^t\)

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Complete Question:

Convert the equation \(f(t) = 259e^{-0.01t}\) to the form \(f(t) = ab^{t}\)

a =

b =

give answer accurate to three decimal places

John needs to make an annual beginning-of-the-year payment of approximately $369,238.68 to fund the estimated college costs of $196,000 in 10 years, given the after-tax rate of return of 8.65% compounded annually.

To compute the annual beginning-of-the-year payment necessary to fund the estimated college costs, we can use the present value of an annuity formula.

The present value of an annuity formula is given by:

P = A * [(1 - (1 + r)^(-n)) / r],

where P is the present value, A is the annual payment, r is the interest rate per period, and n is the number of periods.

In this case, John wants to accumulate $196,000 in 10 years, and the interest rate he can earn is 8.65% compounded annually. Therefore, we can substitute the given values into the formula and solve for A:

196,000 = A * [(1 - (1 + 0.0865)^(-10)) / 0.0865].

Simplifying the expression inside the brackets:

196,000 = A * (1 - 0.469091).

196,000 = A * 0.530909.

Dividing both sides by 0.530909:

A = 196,000 / 0.530909.

A ≈ 369,238.68.

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Answer:

5445

Step-by-step explanation:

We can use distributive property.  a*(b - c) = (a*b) - (a *c)

  99 = 100 - 1

55 * 99 = 55 * (100 - 1)

            = 55*100 - 55*1

            = 5500 - 55

            = 5445

Answer: 4-4z

Step-by-step explanation: Coming the like terms in order to simplify the equation. There are four z's and they combine as they are like terms. Since we don't know the value of z, thats the most simplified form.

The values are;

⇒ F ∩ H = Ф

⇒ F ∪ H = (- ∞, 7]

What is Coordinates?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

F and H are defined as;

F = {v | v < 4 }

H = {v | v ≥ 7 }

Now,

Since, F and H are defined as;

F = {v | v < 4 }

H = {v | v ≥ 7 }

Hence, The values are;

F ∩ H = {v | v < 4 } ∩  {v | v ≥ 7 }

         = Ф

And, F ∪ H = {v | v < 4 } ∪  {v | v ≥ 7 }

                 = (- ∞, 7]

Thus, The values are;

⇒ F ∩ H = Ф

⇒ F ∪ H = (- ∞, 7]

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The number of candy bar that she bought is 6

The total amount that she spend for soda and candy= $12

The cost of one soda = $3

The cost of one candy bar = $1.50

Number of soda that she bought = 1

Consider the number of candy bar that she bought as x

Then the equation will be

3×1 + 1.50 × x = 12
Multiply the terms

3 + 1.50x = 12

Move 3 to right hand side of the equation

1.50x = 12 - 3

1.50x = 9

Move 1.50 to the right hand side of the equation

x = 9 / 1.50

x = 6

Hence, the number of candy bar that she bought is 6

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3/4 is the answer.

Step-by-step explanation:

20-5=15

15/20=3/4

3/4

please

Answer:

I’m so sorry, I just had help on this problem earlier, I forgot how to do it, but the answer is 32

Step-by-step explanation:

(a) Two-hypothesis are used for each experiment,

(b) They go by the names of Null and Alternate Hypothesis.

(c) We actually test the Alternate hypothesis.

Part(a) : In most experimental designs, there are two hypotheses: the null hypothesis (H₀) and the alternative hypothesis (Hₐ).

Part(b) : The Hypotheses are generally classified as "Null-Hypotheses" or "Alternative-Hypotheses".

The "Null-Hypothesis" (H₀) is defined as a statement that assumes there is no significant difference or relationship between variables or that an intervention has no effect.

The "Alternative-Hypothesis" (Hₐ) is defined as a statement that assumes there is a significant difference or relationship between variables or that an intervention has an effect.

Part (c) : The hypothesis being-tested in an experiment is generally the "Alternative-Hypothesis" (Hₐ) because the "Null-Hypothesis" (H₀) is assumed to be true until evidence is found to reject it.

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The given question is incomplete, the complete question is

(a) How many hypothesis are used for each experiment?

(b) What name do they go by?

(c) Which one we actually test?

The number is 15.

Let's represent the unknown number by "x".

A number is a numerical unit of measurement and labelling in mathematics. The natural numbers 1, 2, 3, 4, and so on are the first examples. Number words are a linguistic way to express numbers.

Given that this number's "2 over 3" equals 10, the following equation can be used to represent it:

\(2/3 \times x = 10\)

To find the value of "x", we can solve for it by multiplying both sides of the equation by the reciprocal of 2/3, which is 3/2:

\((3/2) \times 2/3 \times x = (3/2) \times 10\\x = 15\)

Therefore, the number is 15.

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Let x be the cost of one rose bush and y be the cost of one carnation.

Then we have the system of equations:

x * 9 + y * 12 = 210

x * 3 + y * 1 = 40

To determine the method that is most efficient to solve this system, we can use the fact that one of the equations has already solved for one of the variables, y.

We can use substitution to solve for the other variable, x.

Substitute y = (40 - 3x) into the first equation:

x * 9 + (40 - 3x) * 12 = 210

Simplify:

x * 9 + 480 - 36x = 210

Solve for x:

9x - 36x = 210 - 480

-27x = -270

x = 10

Substitute x = 10 into the second equation:

10 * 3 + y = 40

Solve for y:

y = 10

Therefore, one rose bush costs $10 and one carnation costs $10.

The most efficient method to solve the system was substitution, since one of the equations already solved for one of the variables.

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The expression that represents the amount spent is  0.8x + 7.50

The given parameters are

Discount = 20%

Necklace = 7.50

Let the cost of the dress be x

So, the expression that represents the amount Sammie spent is

Expression = (1 - Discount) * x + Necklace

This gives

(1 - 20%) * x + 7.50

Evaluate

0.8x + 7.50

Hence, the expression that represents the amount spent is  0.8x + 7.50

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The computation (u x v) × w will result in a vector quantity.

Among the given computations, (u x v) × w will result in a vector quantity. Let's break down each computation to understand their outcomes.

(u x v) × w: The cross product of vectors u and v results in a new vector, and then this vector is crossed with vector w. Both cross-products yield vector quantities, so the final result will also be a vector.

(u x v) - (w x 2): The cross product of u and v is subtracted from the cross product of w and 2. Cross products yield vector quantities, but the subtraction operation will result in a vector if the magnitudes and directions are different. Otherwise, it will be a scalar.

Therefore, the computation (u x v) × w will definitely result in a vector quantity, while the computation (u x v) - (w x 2) may or may not result in a vector, depending on the specific vectors involved.

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Answer:

\(\begin{array}{|c|c|c|} \cline{1-3}\text{Time of day} & \text{Frequency} & \text{Angle size}\\\cline{1-3}\text{Morning} & 45 & 180\\\cline{1-3}\text{Afternoon} & 15 & \textbf{60}\\\cline{1-3}\text{Evening} & 30 & \textbf{120}\\\cline{1-3}\end{array}\)

========================================================

Explanation:

In the morning, Chris has 45 clients out of 90 total for the week. This represents the fraction 45/90.

Multiply top and bottom by 4 to get to 180/360. I chose 4 because 90*4 = 360.

So that's how your teacher got 180 degrees for the morning angle.

Or you could compute 45/90 = 0.5 and then say 0.5*360 = 180.

The morning clients make up 50% of all his clients.

-------------------------------

For the afternoon, he has 15 clients out of 90.

15/90 = (15/90)*(4/4) = 60/360

I multiplied top and bottom by 4 like last time.

However, this time I got 60 as the numerator.

So a 60 degree angle is used for the afternoon clients.

------------------------------

In the evening, he has 30 clients to give us the fraction 30/90.

Like before, multiply top and bottom by 4

30/90 = (30*4)/(90*4) =  120/360

We use a 120 degree angle here.

a.Stored attribute b.Minimum cardinality c. entity type- relationship type d. strong entity type weak entity type e. degree cardinality f. required attribute optional attribute g. composite attribute multivalued attribute h. ternary relationship has a strict contrast .

a. Stored attribute represents a characteristic or property of an entity that is directly stored in a database. It can be easily accessed and retrieved. On the other hand, a derived attribute is not directly stored but is calculated or derived from other attributes. It is derived using formulas, calculations, or rules based on the stored attributes.

b. Minimum cardinality specifies the minimum number of occurrences an entity can have in a relationship. For example, a minimum cardinality of 1 means that an entity must have at least one occurrence in the relationship. Maximum cardinality, on the other hand, defines the maximum number of occurrences an entity can have in a relationship. It sets an upper limit on the number of associations an entity can have.

c. An entity type represents a distinct object in the real world, such as a customer, employee, or product. It has its own attributes and may participate in relationships with other entity types. On the other hand, a relationship type represents an association or connection between two or more entity types. It describes how entities are related or connected to each other.

d. A strong entity type exists independently and has its own primary key. It can be uniquely identified on its own without depending on any other entity types. A weak entity type, however, depends on a strong entity type for its existence. It does not have its own primary key and relies on a foreign key relationship with a strong entity type.

e. Degree refers to the number of entity types participating in a relationship. It represents the number of entity types connected by the relationship. Cardinality, on the other hand, describes the number of occurrences or instances of one entity type that can be associated with another entity type in a relationship. It specifies how many entities can participate in the relationship.

f. Required attributes are attributes that must have a value and cannot be left empty or null. They are necessary for the completeness and integrity of the data. Optional attributes, on the other hand, are attributes that may or may not have a value. They are not mandatory and can be left empty.

g. A composite attribute is an attribute that can be further divided into sub-attributes. It is composed of multiple components or parts, representing a hierarchical structure. On the other hand, a multivalued attribute can have multiple values for a single occurrence of an entity. It allows an entity to have multiple instances or occurrences of the attribute.

h. A ternary relationship involves three

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To calculate the duration of the shift, you need to subtract the clock-in time from the clock-out time.

In this case, the shift worker clocked in at 1730 hours (5:30 PM) and clocked out at 0330 hours (3:30 AM). However, since the clock is based on a 24-hour format, it's necessary to consider that the clock-out time of 0330 hours actually refers to the next day.

To calculate the duration of the shift, you can perform the following steps:

1. Calculate the duration until midnight (0000 hours) on the same day:

  - The time between 1730 hours and 0000 hours is 6 hours and 30 minutes (1730 - 0000 = 6:30 PM to 12:00 AM).

2. Calculate the duration from midnight (0000 hours) to the clock-out time:

  - The time between 0000 hours and 0330 hours is 3 hours and 30 minutes (12:00 AM to 3:30 AM).

3. Add the durations from step 1 and step 2 to find the total duration of the shift:

  - 6 hours and 30 minutes + 3 hours and 30 minutes = 10 hours.

Therefore, the duration of the shift was 10 hours.

The earned amount by Dale in 3 years is: 15 dollars.

How to calculate the amount?

To calculate the annually amount based on the principal money is by using simple interest method. This interest was given by the bank. And it is calculated by multiplying the principal amount, rate and time and divided by 100.

According to the question, the given amount parameters for the simple interest calculation is as follows:

Principal amount: $100

Rate of interest: 5%

Time(years): 3 years

Using standard simple interest formula, we get:

S.I. = (P x R x T)/100

S.I. = (100 x 5 x 3)/100 = 15 dollars

Hence, the earned amount by Dale in 3 years is: 15 dollars

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We can plot the vector r(t) and the vector N(T) at the given value of t = T.

To find the principal unit normal for the vector-valued function r(t) = sin(t)i + tcos(t)j + tk, we need to compute the derivative of r(t) with respect to t and then normalize it to obtain a unit vector.

First, let's find the derivative of r(t):

r'(t) = cos(t)i + (cos(t) - tsin(t))j + k

Next, we'll normalize the vector r'(t) to obtain the unit vector:

||r'(t)|| = sqrt((cos(t))^2 + (cos(t) - tsin(t))^2 + 1^2)

Now, we can find the principal unit normal vector by dividing r'(t) by its magnitude:

N(t) = r'(t) / ||r'(t)||

Let's evaluate the principal unit normal at t = T:

N(T) = (cos(T)i + (cos(T) - Tsin(T))j + k) / ||r'(T)||

To sketch the situation, we can plot the vector r(t) and the vector N(T) at the given value of t = T.

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The original linear function is:

y = 2*x + 4   with the point (1, 6)

The translated function is:

y = 2x + 7

And the translated point is (-3, 1)

First, we want to write a random linear function, I will use:

y = 2*x + 4

To find a point on that line, we can just evaluate the function in x = 1, we will get:

y = 2*1 + 4

y = 2 + 4

y = 6

So we have the point (1, 6)

Now we want to translate it 4 units to the left and 5 units down.

To translate it 4 units to the left, we need to add 4 to the argument.

y = 2*(x + 4) + 4

And to translate it  5 units down, we just need to subtract 5, we will get:

y = 2*(x + 4) + 4 - 5

Now we can simplify this to get:

y = 2*x + 2*4 + 4 - 5

y = 2x + 8 + 4 - 5

y = 2x + 7

The new coordinates of the point are the same as the last ones, but we subtract 4 to the x-value and 5 to the y-value:

(1 - 4, 6 - 5) = (-3, 1)

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Notice that, since B is the center of dilation, B'=B. Furthermore, is a dilation all the distances are enlarged by a factor equal to the dilation factor; thus,

Calculate BC using the formula below,

Therefore,

Hence,

The answer is B'C'=31.32

The raccoon's kits, weighing 2(1)/(2) pounds each, have a total weight of 5 pounds combined.

To calculate the total weight of the kits, we need to multiply the weight of each kit by the number of kits.

Weight of each kit = 2(1)/(2) pounds

Number of kits = 2

Total weight of the kits = Weight of each kit × Number of kits

Total weight of the kits = 2(1)/(2) × 2

Total weight of the kits = 5 pounds

Therefore, the kits weigh a total of 5 pounds in all.

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Step-by-step explanation:

fog(x)=f(x-3)

=(x-3)²+2

=x²-6x+9+2

=x²-6x+11

½*b*h = area of ∆

½*2h*h = 256

h² = 256

therefore, h = √256

h = 16m.

Answer:

16km

Step-by-step explanation:

The area formula for a triangle is ...

A = (1/2)bh

We are told that b=2h, so this becomes ...

 A = (1/2)(2h)(h) = h²

Substituting the given area, we can find h:

 256 km² = h²

 (√169) km = h = 16 km

Answer:

The girl is 2.5 meters below sea level

Step-by-step explanation:

We are told in the question that:

A girl is snorkeling 1 meter below sea level

Hence, her elevation in meters below the sea level = -1m

We are told in the question that:

She then dives down another 1.5 meters

Once again: Her elevation in meters below the sea level = -1.5m

How far below sea level is the girl?

This is calculated as:

-1 m + -1.5m

= -1m - 1.5m

= -2.5m

Therefore, the girl is 2.5 meters below sea level

Stacey meets Andrew 1.5 hours after she starts travelling at 11:30 AM and Andrew meets Stacey 2 hours after he starts travelling at 11:30 AM.

How to solve this problem?
Stacey and Andrew in the mentioned problem will meet in a time frame only when the both have travelled equal distances in respect to another.

Given, speed at which Andrew was travelling = 12 mi/h
Speed at which Stacey was travelling = 16 mi/h
Let the time taken by Stacey be = t hours
Therefore, the time taken by Andrew = (t + 0.5) hours
When Stacey overtakes Andrew, they must have covered the same distance, therefore:
16t = 12×(t + 0.5) ⇒ 16t = 12t + 6 ⇒ 4t = 6 ⇒ t = 6/4 ⇒ t = 3/2 ⇒ t = 1.5
Therefore, Stacey meets Andrew 1.5 hours after she starts travelling at 11:30 AM and Andrew meets Stacey 2 hours after he starts travelling at 11:30 AM.

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The solution is, simplification of the expression 6(5+5i) / (-2i) (3i⁵) is:

-5 - 5i.

Here, we have,

given that,

the expression is:

6(5+5i) / (-2i) (3i⁵)

now, we have to simplify this expression.

we know that,

i² = 1

so, (i²)³ = 1²

or, i⁶ = 1

we have,

6(5+5i) / (-2i) (3i⁵)

=30 + 30i / (-6i⁶)

=6(5+5i) / -6 * 1

=(5+5i) / -1

= - (5+5i)

= -5 - 5i

Hence, The solution is, simplification of the expression 6(5+5i) / (-2i) (3i⁵) is: -5 - 5i.

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