A 2-column table with 4 rows. Column 1 is labeled statement with entries tangent (2 x), = tangent (x + x), = startfraction tangent (x) + tangent (x) over 1 minus tangent (x) tangent (x) endfraction, = startfraction 2 tangent (x) over 1 minus tangent squared (x) endfraction. Column 2 is labeled reason with entries given, 1, 2, 3. The table shows the derivation of tan(2x). Select the correct reason for each step. Reason 1 is. Reason 2 is. Reason 3 is.

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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As the equation of tangent line is y = -3x, the value of slope, m is -3 and value of b is 0.

To find the equation of the tangent line at the point (π, -3π), we need to find the derivative of the function y = 3xcos(x), which is

y' = 3cos(x) - 3xsin(x)

and then evaluate the derivative at x = π to find the slope of the tangent line.

The slope at x = π is

m = 3cos(π) - 3πsin(π) = -3

So, the equation of the tangent line is y = -3x + b.

To find the value of b, we use the point (π, -3π) and the slope -3:

-3π = -3 * π + b

b = 0

So, the equation of the line tangent to the curve y = 3xcos(x) at the point (π, -3π) is y = -3x + 0 or simply y = -3x.

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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

Rectangles that represent the Riemann sum for the kth subinterval are displayed on the graph of f(x) on the interval [a,b]. The value of f(x) at the subinterval's right endpoint determines the height of each rectangle.

The function across the specified interval is represented graphically by the graph of f(x) over the interval [a,b]. The graph will display a line with the value of f(x) plotted on the y-axis and the values of the interval on the x-axis. Rectangles indicating the Riemann sum for the kth subinterval will also be displayed on the graph. The value of f(x) at the subinterval's right endpoint determines the height of each rectangle. This produces a graphic depiction of the function's area under the curve, which is equal to the total of the subintervals. Additionally, the graph will display the total number of rectangles, which represents the Riemann sum of the function on the specified interval.

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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 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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The length of the ladder is 12.9 feet

Assuming the height of the boat house is 12.6 feet

The problem is solved using the Pythagoras theorem is applicable to right angle triangle.  the formula of the theorem is

hypotenuse² = opposite² + adjacent²

The length of the ladder is the hypotenuse

plugging the values as in the problem

let x be the required distance

x² = 3.2² +12.6²

x² = 166.49

x = √166.49

x = 12.9 feet

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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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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:

This is what I found, but not sure if it's right.

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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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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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.

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 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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The solution to the equations are

The number of adults for 12 students is 3 adults

The number of adults for 24 students is 6 adults

The number of adults for 40 students is 10 adults

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

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

Given data ,

Let the number of students for 1 adult be 4 students

So , the proportion of students to adults is 1 : 4

Now , the equation will be

The number of adults for 12 students = 12 / 4

The number of adults for 12 students = 3 adults

The number of adults for 24 students = 24 / 4

The number of adults for 24 students = 6 adults

The number of adults for 40 students = 40 / 4

The number of adults for 40 students = 10 adults

Now , when the number of students is 33 students

The number of adults = 33 / 4 = 8.25 adults ≈ 8 adults

Hence , the proportion is 1 : 4

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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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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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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 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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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 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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Answer:

1st box = 200

2nd box = 7

3rd box = 237

4th box = 270

5th box = 333

Step-by-step explanation:

1st box:

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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Best investigator are to check the licked part of the envelope for a saliva sample.The correct option is B

An investigator is someone who carries out investigations especially as part of their job.

Therefore, An Investigators work with law enforcement agencies, individuals, and businesses to investigate and solve crimes to secure a successful conviction. They conduct detailed investigations of complex criminal activities and other violations of local, federal or state law.

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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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Independent of the input, the transfer function. In cases when the input is not a complex exponential, you are probably interested in the result. The answer is that the output can be computed via convolution as long as the input satisfies certain constraints .

How does transfer function work?

A mathematical function called a transfer function of a system, sub-system, or component theoretically simulates the output of the system for each potential input.

                             Transfer functions are also known as system functions or network functions. They are frequently employed in electronic and control systems.

Why is the transfer function only specified for LTI systems?

The ratio between the Laplace transforms of the input and output signals under initial circumstances of zero can be used to define the transfer function of the LTI system.

                              Alternately, when the beginning circumstances are disregarded, the transfer function is described as the output to input ratio in the sdomain.

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