A sequence can be generated by using an=an−1+17, where a1=15 and n is a whole number greater than 1.

What are the first 5 terms in the sequence?

32, 49, 66, 83, 100
17, 32, 47, 62, 77
15, 32, 49, 66, 83
15, 30, 45, 60, 75

The volume of the frustum of a pyramid with square base of side "b", square top of side "a", and height "h" is (b² - a²) × h / 3 cubic units.

The two primary divisions of calculus, differential calculus and integral calculus, are concerned with rates of change and slopes of curves.

A pyramid's frustum can be thought of as two pyramids with the same height "h" and square bases on sides "a" and "b," as well as a square top on side "a" and that height.

The formulas below give the volume of a pyramid with a square base and sides "s" and height "h":

The volume of a pyramid with square base of side "s" and height "h" is given by:

V = (s² × h) / 3

The volume of the frustum can be found by subtracting the volume of the smaller pyramid from the volume of the larger pyramid:

V = [(b² × h) / 3] - [(a² × h) / 3] = (b² - a²) × h / 3

Hence, the volume of the frustum of a pyramid with square base of side "b", square top of side "a", and height "h" is (b² - a²) × h / 3 cubic units.

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The ratio of the volume of the triangular prism to the volume of the cuboid is 1:2.

The volume of a triangular prism is calculated by multiplying the area of the base by the height of the prism. The volume of a cuboid is calculated by multiplying the length, width, and height of the cuboid.

For a triangular prism with base area A and height h, the volume is A x h.

For a cuboid with length l, width w, and height h, the volume is l x w x h.

Therefore, the ratio of the volume of the triangular prism to the volume of the cuboid is A x h : l x w x h, which simplifies to 1:2.

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The ratio of Areas is 1:1.

A quadrilateral with one set of parallel opposite sides is a trapezium. The bases and legs of a trapezium are referred to as parallel and non-parallel, respectively. It also goes by the name trapezoid.

As, The diagonals of a trapezium divide each other proportionally.

AO / OC = OB/ OD

Also, OA= OB and OC= OD

So, OA/ OC = 1: 1

In Triangle DOC and BOA

<AOB = <COD (Vertical Opposite angle)

<BAO = <OCD ( Alternate Interior angle)

By AA similarity Criteria  Triangle DOC and BOA are similar.

So, ar (Δ DOC)/ ar (ΔBOA)

= DO / OB = OC / OA = DC / BA

As, the ratio of corresponding length is equal.

So, the ratio of Triangle is 1:1

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Line of fit go through (1, 10) and (10, 1) to best fit the data.

Scatterplots are the plotting of set of points on a vertical axis and an horizontal axis. The shows the correlation extent between the numbers of the observed quantities.

Line of best fit of the scatterplot should go through as many points as possible of the graph.

If we draw a line passing through the pair of points given in the options, the line passing through (1, 10) and (10, 1) passes through (9, 2), (7, 4) and (3, 8).

No other line drawn through points in the options passes through 5 points.

Hence the line of best fit is the line passing through (1, 10) and (10, 1).

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The probability of getting at least one tails on the last two flips is 8/25.

The probability of getting a tails on a single toss of the coin is 3/5. Therefore the probability of getting tails on the last two flips is (3/5)^2. This is because the coin tosses are independent of one another.

Therefore the probability of getting at least one tails on the last two flips is 1 - (3/5)^2 = 8/25.

This is because the probability of getting two tails is (3/5)^2, and the probability of getting at least one tails is the complement of that. Therefore the probability of getting at least one tails on the last two flips is 8/25.

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The limit does not exist if the graph features a vertical asymptote with one side going toward infinity and the other toward negative infinity.

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The limit of (x-3) / (x-9) as x approaches 9 does not exist due to the undefined value in the denominator.

The limit is an important concept in calculus that describes the behavior of a function as the independent variable approaches a specific value.

In this problem, we want to find the limit of the expression (x-3) / (x-9) as x approaches a specific value.

To find the limit, we must substitute values of x that are very close to the specific value and see what the expression approaches.

However, it is important to note that if the limit does not exist, then the function is undefined or has a vertical asymptote at the specific value.

In this case, it is easy to see that the limit does not exist as x approaches 9 because the denominator of the fraction is equal to 0, which is undefined.

The fraction becomes undefined at x = 9 and the limit does not exist.

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Answer:

C; both the relation and inverse are functions

Step-by-step explanation:

A function has no more than one output for a specific input, therefore, the original set of points is a function.

To find the inverse, you swap the x and y, so you would get:
(0, -5), (-2, -1), (1, -2), (4, 0), (2, 1), (-1, 2)

The inverse is also a function, because each input has only one output.

Based on the definition of congruent triangles, m<X = 45 degrees.

Congruent triangles are two triangles that have exactly the same size and shape, which connotes that every corresponding parts of the triangles are equal.

Given EFG = XYZ, therefore, the measure of angle E will be congruent to the measure of angle X.

m<E = m<X

m<E = 180 - 90 - 60

m<E = 30°

Therefore, m<X = 30°.

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Answer:

D.) the ovens temperature after 1 minute.

Step-by-step explanation:

if "x" is the number of minutes that have passed then the output is the temp after the oven was preheating for 'x" amount of minutes

The number of cards in the deck that are either a jack or a heart = 16

We know that a standard deck of cards has four suites.

These four suits are:

a) Hearts,

b) Clubs,

c) Spades,

d) Diamonds.

Each suite has thirteen cards.

These thirteen cards are:

Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen and king.

This means, the entire deck of cards has 52 cards total.

The number of Jack cards in a standard deck of cards = 4

The number of Hearts in a standard deck of cards = 13

This means, there are 13 + 3 = 16 cards in the deck are either a jack or a heart.

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The corresponding angles must be equal for the transversal to join two parallel lines.

In the intersection of two parallel lines and a transversal, corresponding angles are created. The opening and closing of a lunchbox, completing a Rubik's cube, and endless parallel railroad tracks are a few examples of matching angles in daily life.

The angles in the same corners of two lines, which are typically parallel, are referred to as corresponding angles when they cross each other across a plane (a transversal). In two separate shapes, corresponding sides and angles refer to a pair of matching sides or angles that are in the same location.

Every matching angle is not created equally. The transversal must connect two parallel lines in order for the corresponding angles to be equal. The equivalent angles that are created when a transversal encounters a line that is not parallel are not congruent and have no connection to one another.

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After integration, the expression will be[tex]S=8(sin^{3}(t+\frac{\pi}{3} )(-cos(t+\frac{\pi}{3}+t^{2}+\frac{\pi}{12t})-8tsin^{2}(t+\frac{\pi}{3})[/tex]

Integration is the process of calculating an integral. Integrals are used by mathematicians to compute a range of useful quantities, such as areas, volumes, displacement, etc. Usually, when we talk about integrals, we mean definite integrals. Indefinite integrals are used for antiderivatives. Integration is one of the two primary calculus topics in mathematics, along with differentiation (which measure the rate of change of any function with respect to its variables).

An integral that has both the upper and lower boundaries is said to be definite. Only a real line may be used for X to lay. A Riemann Integral is another name for the Definite Integral.

∫f(x)dx from a to b.

The definition of integrals without upper and lower bounds. It appears as follows:

A definite Integral is represented as:

∫f(x)dx = F(x) + C

Where C is any constant and the function f(x) is called the integrand.

Now,

Right expression is

[tex]\frac{dS}{dt} = 8sin^{2}(t+\frac{\pi}{12} )[/tex]

After integration

[tex]S = 8sin^{2} (t+\frac{\pi}{12} ).dt[/tex]

[tex]S=8(sin^{3}(t+\frac{\pi}{3} )(-cos(t+\frac{\pi}{3}+t^{2}+\frac{\pi}{12t})-8tsin^{2}(t+\frac{\pi}{3})[/tex]

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255.255.255.0 is written as /24 in slash notation (/n).

Slash notation is a compact way to show or write an IPv4 subnet mask. When you use slash notation, you write the IP address, a forward slash (/), and the subnet mask number.

1- To find the subnet mask number:

2- Convert the decimal representation of the subnet mask to a binary representation.

Count each “1” in the subnet mask. The total is the subnet mask number.

In IPv6, slash notation is used to represent the network identifier prefix for an IPv6 network. The prefix is expressed as a slash (/) followed by the prefix size, which is a decimal number between 1 and 128.

Thus, 255.255.255.0 is written as /24 in slash notation (/n).

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The points are reflections of each other across the y-axis is,

⇒ ( x, - y)

Reflection is a type of transformation that flip a shape in mirror line, so that each point is the same distance from the mirror line as its reflected point.

We have to given that;

One point is in quadrant lll.

And, The points are reflections of each other across the y-axis.

Now, Let a point is in quadrant III = (-x, - y)

Where, x > 0, y > 0

We know that;

The rule of the reflection across the y - axis is,

⇒ (x, y) → (- x, y)

Thus, We get;

The points are reflections of each other across the y-axis is,

⇒ (- x, - y) → (- (-x), - y)

               → (x, - y)

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Answer:

1st box = 200

2nd box = 7

3rd box = 237

4th box = 270

5th box = 333

Step-by-step explanation:

1st box:

If Bob wants to catch an elevator before the door closes. He is 42ft away when the door starts to close. How fast does he have to run in order to catch the elevator is: 12.50 ft/s.

Let's v represent Bob's speed in ft/s.

First, let's find the time it takes for the door to close from 4.1 ft to 0.7 ft:

t = (4.1 - 0.7) / 1.1 = 3.4 / 1.1

t = 3.09 s

Next, let's find the distance Bob has to cover in that time:

d = 42 - 3.4

d = 38.6 ft

Now we can find Bob's speed using the formula:

d = v * t

Solving for v:

v = d / t = 38.6 / 3.09

v= 12.50 ft/s (rounded to the nearest hundredth)

Therefore  Bob needs to run at a speed of 12.50 ft/s in order to catch the elevator.

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The basis for the nullspace is the set {(-3,1,0,1), (0,1,0,0)}.

The basis for the nullspace of the matrix can be found by reducing the augmented matrix to row echelon form and finding the free variables. The free variables correspond to the columns that have a leading entry of 0 and non-zero entries below it, which are the basis vectors for the nullspace.

Using row operations, the augmented matrix can be reduced to:

1  2 -4  5 | 0

0  1 -3  2 | 0

0  0  0  0 | 0

From this, we can see that the free variables are x2 and x4, so the basis for the nullspace is:

-3 x2 + x4

x2

So the basis for the nullspace is the set {(-3,1,0,1), (0,1,0,0)}.

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The length of AE is given as follows:

AE = 7 units.

The midsegment of a triangle states that the segment connecting the midpoints of two sides of a triangle is parallel to and half the length of the third side.

The midsegment of the triangle in this problem is given by the following segment:

BD.

The length of BD is given as follows:

BD = 2 - (-1.5)

BD = 3.5 units.

Hence the length of AE is obtained as follows:

AE = 2BD

AE = 2 x 3.5

AE = 7 units.

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The answer to all the following options is given below along with the suitable reasoning.

a. Incorrect. If a system of linear equations has more unknowns than equations and the reduced row echelon form of the augmented matrix has two nonzero rows, the system is inconsistent and has no solutions.

b. Incorrect. A system of linear equations with more unknowns than equations is underdetermined and can have either no solutions or an infinite number of solutions.

c. Correct. A matrix can be row-reduced to an echelon form, which is a simpler form that makes it easier to find the solution to the system of linear equations represented by the matrix.

d. Correct. Every matrix can be row-reduced to a unique reduced row echelon form by performing a sequence of elementary row operations, which are reversible and preserve the solutions of the system of linear equations.

e. Correct. Adding a multiple of one row to another row is one type of elementary row operation used in row-reducing a matrix to its reduced row echelon form.

f. Correct. If a system of linear equations has three unknowns and the reduced row echelon form of the augmented matrix has three nonzero rows, then the system is consistent and has a unique solution.

g. Correct. Adding a multiple of one row to another row is one type of elementary row operation used in row-reducing a matrix to its reduced row echelon form.

h. Incorrect. Some of the statements are correct.

Therefore, The answer to all the following options is given above along with the suitable reasoning.

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The answer to all the following options is given below along with the suitable reasoning.

a. Incorrect. If a system of linear equations has more unknowns than equations and the reduced row echelon form of the augmented matrix has two nonzero rows, the system is inconsistent and has no solutions.

b. Incorrect. A system of linear equations with more unknowns than equations is underdetermined and can have either no solutions or an infinite number of solutions.

c. Correct. A matrix can be row-reduced to an echelon form, which is a simpler form that makes it easier to find the solution to the system of linear equations represented by the matrix.

d. Correct. Every matrix can be row-reduced to a unique reduced row echelon form by performing a sequence of elementary row operations, which are reversible and preserve the solutions of the system of linear equations.

e. Correct. Adding a multiple of one row to another row is one type of elementary row operation used in row-reducing a matrix to its reduced row echelon form.

f. Correct. If a system of linear equations has three unknowns and the reduced row echelon form of the augmented matrix has three nonzero rows, then the system is consistent and has a unique solution.

g. Correct. Adding a multiple of one row to another row is one type of elementary row operation used in row-reducing a matrix to its reduced row echelon form.

h. Incorrect. Some of the statements are correct.

Therefore, The answer to all the following options is given above along with the suitable reasoning.

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Answer:

6 hours

Step-by-step explanation:

create a proportion:

54 km/4 hrs equals 81km/? hours

[tex]\frac{54}{4}[/tex] = [tex]\frac{81}{?}[/tex]

solve a proportion by cross-multiplying:

54? = 324

? = 324/54

? = 6

Answer:

6 hr

Step-by-step explanation:

If 54 km --> 4 hr then,

81 km  --> ? hr

You can make a rule of three:

? hr = (81*4)/54

? hr = 6

So 81 km in 6 hours

The value of r'(1) is 112.

To find the derivative of r(x) at x = 1, we'll use the chain rule. The chain rule states that if r(x) = f(g(h(x))), then the derivative of r(x) with respect to x is given by r'(x) = f'(g(h(x))) * g'(h(x)) * h'(x).

When r(x) = f(g(h(x))) by chain rule

r'(x) = f'(g(h(x))) * g'(h(x)) * h'(x)

So r'(1) =  f'(g(h(1))) * g'(h(1)) * h'(x)

As h(1) = 2 and h'(1) = 4

r'(1) = f'(g(2)) * g'(2) * 4

As g(2) = 4 and g'(2) = 4

r'(1) = f'(4) * 4 * 4

As f'(4) = 7

r'(1) = 7 * 4 * 4

r'(1) = 112

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Divide your interest rate by the number of payments you’ll make that year

How to calculate simple interest

By utilizing the following calculation, you may get your total interest:

Interest is calculated as follows: principal loan amount x interest rate x duration

The simple interest formula is $20,000 x.05 x 5 = $5,000 in interest, for instance, if you take out a $20,000 loan with a five-year term and a 5% interest rate.

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"Simple Interest is Principal x Interest Rate x Time" is the written formula.The simplest method for computing interest is using this equation.

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£479.42 is  the income tax Angela gets deducted each month.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, Angela earns £35 240 a year. She has to pay income tax. She is allowed to earn £6475 before paying tax. She pays 20% tax on the rest.

So,

taxable income = 35,240-6,475

taxable income = 28,765

Since She pays 20% tax

Thus,

The Total tax = 28,765 * 20%

the total tax = 5,753

Since Her employer deducts the income tax each month.

so,

Income tax deducted each month =  5,753/12

Income tax deducted each month =  479.417

Therefore, the income tax Angela gets deducted each month is £479.42.

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The percentage by which the number has to be decreased is 20%.

It represents a mathematical relationship or calculation. For example, the expression "2x + 3" is an algebraic expression that represents a linear equation with a variable x and constants 2 and 3. Algebraic expressions can be simplified, evaluated for specific values of the variables, and used to solve equations.

Given:

A number is increased by 25%

To find:

The percentage by which it has decreased

Solution:

The percentage by which the number has to be decreased is 20%.

We can find the percentage by following the given steps-

We know that a number increased by a percentage decreases by a different percentage.

Let us assume that the number is 100.

We know that this number has been increased by 25%.

So, the new number=100+25% of 100

=100+25/100×100

=100+25

=125

Now, the new number is 125.

Let us assume that this number has to be decreased by X% to obtain 100.

So, 125-X% of 125=100

125-X/100×125=100

125-1.25X=100

125-100=1.25X

25=1.25X

25×100/125=X

2500/125=X

X=20%

Therefore, the percentage by which the number has to be decreased is 20%.

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The neg-ations of the given statements are: a) John is not 200 pounds or he is less than 6 feet and b) Neither Tom's watch was slow nor was the bus late.

To answer this question first let's understand what negation is.

Neg-ation is a concept in mathematical reasoning which is represented by the symbol "∼" and represents the opposite of the given mathematical statement. For example negation of “A and B” is “not(A) or not(B).

a) The neg-ation of the statement "john is 200 pounds, and he is at least 6 feet" is "John is not 200 pounds or he is less than 6 feet"

b) The neg-ation of the statement "tom’s watch was slow or the bus was late" is "Neither Tom's watch was slow nor was the bus late."

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Answer:

$2280

Step-by-step explanation:

38000*6% =2280

The sequence aₙ = sin (4n)/2n + √n diverges because it does not have a limit that can be expressed in a finite manner.

A sequence is a set of numbers that follow a certain pattern. The behavior of the sequence as n approaches infinity determines whether the sequence converges or diverges.

In this case, the sequence

=> aₙ = sin (4n)/2n + √n.

To determine whether the sequence converges or diverges, we need to find the limit as n approaches infinity.

However, in this case, the limit as n approaches infinity is DNE, meaning it does not exist. This means that the sequence diverges, as it does not approach a limit as n approaches infinity.

In this case, the sequence

=> aₙ = sin (4n)/2n + √n

converges to DNE, meaning that it does not have a limit that can be expressed in a finite manner.

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