Explain whether or not a continuous function can be considered a sequence.

Answers

Answer 1

Answer:

A function is considered continuous when it has no drastic changes in the sequence  known as discontinuities. If not continuous, a function is said to be discontinuous.


Related Questions

D²y(t) + 12 Dy(t) + 36y(t) = 2 e-5t y(0) = 1, Dy(0)=0 Solve the differemtial equation using Classical Method (30pts) and Laplace Transform Method(30pts)

Answers

The solution to the differential equation D²y(t) + 12 Dy(t) + 36y(t) = 2 \(e^{(-5t)}\), with initial conditions y(0) = 1 and Dy(0) = 0, is \(y(t) = (1 + 6t) e^{(-6t)}\).

To solve the given differential equation using the classical method, we can assume a solution of the form \(y(t) = e^{(rt)}\) and find the values of r that satisfy the equation. We then use these values of r to construct the general solution.

Using the classical method:

Substitute the assumed solution \(y(t) = e^{(rt)}\) into the differential equation:

D²y(t) + 12 Dy(t) + 36y(t) = \(2 e^{(-5t)}\)

This gives the characteristic equation r² + 12r + 36 = 0.

Solve the characteristic equation for r by factoring or using the quadratic formula:

r² + 12r + 36 = (r + 6)(r + 6)

= 0

The repeated root is r = -6.

Since we have a repeated root, the general solution is y(t) = (c₁ + c₂t) \(e^{(-6t)}\)

Taking the first derivative, we get Dy(t) = c₂ \(e^{(-6t)}\)- 6(c₁ + c₂t) e^(-6t).\(e^{(-6t)}\)

Using the initial conditions y(0) = 1 and Dy(0) = 0, we can solve for c₁ and c₂:

y(0) = c₁ = 1

Dy(0) = c₂ - 6c₁ = 0

c₂ - 6(1) = 0

c₂ = 6

The particular solution is y(t) = (1 + 6t) e^(-6t).

Using the Laplace transform method:

Take the Laplace transform of both sides of the differential equation:

L{D²y(t)} + 12L{Dy(t)} + 36L{y(t)} = 2L{e^(-5t)}

s²Y(s) - sy(0) - Dy(0) + 12sY(s) - y(0) + 36Y(s) = 2/(s + 5)

Substitute the initial conditions y(0) = 1 and Dy(0) = 0:

s²Y(s) - s - 0 + 12sY(s) - 1 + 36Y(s) = 2/(s + 5)

Rearrange the equation and solve for Y(s):

(s² + 12s + 36)Y(s) = s + 1 + 2/(s + 5)

Y(s) = (s + 1 + 2/(s + 5))/(s² + 12s + 36)

Perform partial fraction decomposition on Y(s) and find the inverse Laplace transform to obtain y(t):

\(y(t) = L^{(-1)}{Y(s)}\)

Simplifying further, the solution is:

\(y(t) = (1 + 6t) e^{(-6t)\)

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a sheet of gold weighing 10.0 g and at a temperature of 18.0°c is placed fl at on a sheet of iron weighing 20.0 g and at a temperature of 55.6°c. what is the fi nal temperature of the combined metals?

Answers

When different metals with different temperatures are placed together, they tend to exchange heat until the temperature becomes equal. This phenomenon is known as Thermal Equilibrium.

The final temperature of the combined metals can be calculated using the following formula:

Q = m * c * ∆T

Where,Q = Heat exchanged by metals m = Mass of metals c = Specific Heat of metal∆T = Change in temperature

Assuming no heat is lost to the surroundings, we can say that the Heat lost by the hot iron is equal to the Heat gained by the cold gold.

Hence, m1 * c1 * ∆T1 = m2 * c2 * ∆T2.

Rearranging the equation,

we get ∆T = (m1 * c1 * ∆T1) / (m2 * c2).

Now substituting the values, we get;For gold, m = 10 g, c = 0.129 J/g°C, ∆T = (Tfinal - 18°C).

For iron, m = 20 g, c = 0.449 J/g°C, ∆T = (55.6 - Tfinal).

We get ∆T = (10 * 0.129 * (Tfinal - 18)) / (20 * 0.449) = (1.29 * (Tfinal - 18)) / 8.98.

Now equating the two, we get (Tfinal - 18) / 8.98 = (55.6 - Tfinal) / 20.

Solving the equation,

we get Tfinal = (55.6 * 8.98 + 18 * 20) / (8.98 + 20) = 30.18°C.

Hence the final temperature of the combined metals is 30.18°C.

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Historically, the members of the chess club have had an average height of 5′6 ′′ with a standard deviation of 2 ′′. What is the probability of a player being between 5′3 ′′ and 5' 10"? (Submit your answer as a whole number. For example if you calculate 0.653 (or 65.3% ), enter 65. )

Answers

The probability of a player being between 5′3 ′′ and 5' 10" is 77%.

To calculate the probability of a player being between 5′3 ′′ and 5' 10", we need to standardize the values using the formula:

z = (x - μ) / σ

where x is the height of the player, μ is the mean height of the chess club members, and σ is the standard deviation of the heights.

For x = 5′3 ′′, z = (63 - 66) / 2 = -1.5

For x = 5'10", z = (70 - 66) / 2 = 2

Using a standard normal distribution table or calculator, we can find the area under the curve between z = -1.5 and z = 2, which represents the probability of a player being between 5′3 ′′ and 5' 10".

This area is approximately 0.7745 or 77%.

Therefore, the value obtained is 77%.

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teo has a combination of quarters loonies and toonies in his pocket .He knows he has 9 coins in total and that he has atleastone of each type of coin.
a) what is the probability that teo has more than $8
b) How many different combinations of coins could teo useto pay for an item that costs between $10 and $12, if he uses fewer toonies than loonies

Answers

a)  The probability is 1 out of the total number of combinations.

b) Each case would involve finding the possible combinations of quarters that would result in a total value between $10 and $12.

a) To determine the probability that Teo has more than $8, we need to consider the possible combinations of quarters, loonies, and toonies that would result in a total value greater than $8. Since Teo has 9 coins in total, we can analyze the different scenarios:

Case 1: Teo has 1 toonie, 1 loonie, and 7 quarters. The total value would be $2 + $1 + (7 * $0.25) = $2 + $1 + $1.75 = $4.75, which is less than $8.

Case 2: Teo has 2 toonies, 1 loonie, and 6 quarters. The total value would be $4 + $1 + (6 * $0.25) = $4 + $1 + $1.50 = $6.50, which is less than $8.

Case 3: Teo has 3 toonies, 1 loonie, and 5 quarters. The total value would be $6 + $1 + (5 * $0.25) = $6 + $1 + $1.25 = $8.25, which is greater than $8.

Therefore, there is only one possible combination out of the total combinations where Teo has more than $8.

b) To determine the number of different combinations of coins that Teo could use to pay for an item between $10 and $12, considering fewer toonies than loonies, we can analyze the possible scenarios:

Case 1: Teo has 0 toonies, 1 loonie, and a combination of quarters. The value of 1 loonie is $1. Teo needs to have additional coins totaling between $9 and $11, which can be achieved using different combinations of quarters.

Case 2: Teo has 1 toonie, 1 loonie, and a combination of quarters. The value of 1 toonie and 1 loonie is $3. Teo needs to have additional coins totaling between $7 and $9, which can be achieved using different combinations of quarters.

We can continue analyzing different cases where Teo has more toonies and/or more loonies.

Determining the exact number of different combinations of coins would involve listing and calculating each scenario, which can be time-consuming. Therefore, it would be more practical to use a systematic approach, such as generating combinations using mathematical or programming methods, to calculate the total number of different combinations of coins that meet the given criteria.

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PLEASE ANSWER THE FOLLOWING QUESTION GIVEN THE CHOICES!!!

PLEASE ANSWER THE FOLLOWING QUESTION GIVEN THE CHOICES!!!

Answers

Answer: 3/52

Step-by-step explanation:

You want to pick a diamond jack, diamond queen or diamond king

There are only 3 of those so

P(DJ or DQ or DK) = 3/52        There are 3 of those out of 52 total

Foster picked 50 figs and divided them into 5 baskets. If each fig was $3, how much is one basket?

Answers

Answer:

$30

Step-by-step explanation:

50÷5=10x3=30

Consider simple planer . 4-reguler graph with 6 verticles 4-regular means chat all verticles have degree 4. How many edges? how many regions ? Draw all verticies have degree Such a gr

Answers

A simple planar graph, 4-regular with 6 vertices will have 12 edges and 8 regions. Each vertex has a degree of 4, meaning it is connected to exactly 4 edges

To draw such a graph, we can start by placing the 6 vertices in a circular arrangement.

Each vertex will be connected to the 4 adjacent vertices, ensuring that the graph is 4-regular. By connecting the vertices accordingly, we will obtain a graph with 12 edges and 8 regions.

The regions are the bounded areas created by the edges of the graph when drawn on a plane.

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One-third of the students in Mrs. Hayko's class walk to school. Of the students who do not walk to school, four-fifths take the bus.

a.) What fraction of the students in Mrs. Hayko's class take the bus to school?

b.) How many students might be there in her class?​

Answers

Answer:

The possible number of students in Mrs. Hayko's class is limited to 15 or 30, as higher multiples of 15 would exceed the desired class size.

Step-by-step explanation:

a)

Let 'x' be the total number of students in Mrs. Hayko's class.

One-third of the students walk to school: (1/3)x.

The remaining students who do not walk to school: (2/3)x.

Four-fifths of the non-walking students take the bus: (4/5) * (2/3)x.

Simplify to find the fraction of students taking the bus: (8/15)x.

b)

Consider different values for 'x' to find a whole number of students taking the bus.

Start with a small number, such as x = 15.

Calculate the number of students taking the bus using (8/15)x.

If the result is a whole number, it's a possible class size.

Repeat with different values of 'x' until a whole number is obtained.

The possible number of students in Mrs. Hayko's class could be 15, 30, or any other multiple of 15.

Evaluate cos(780°) using the unit circle

Answers

The value of cos 780 using the unit circle is 0.5

Angle in a circle

Given the following angle

cos780

To get the equivalent angle, we will need to write the angle to fall between the angles in a circle

cos 780 = cos(780 - 720)

cos 780 = cos 60

cos 780 = 0.5

Hence the value of cos 780 using the unit circle is 0.5

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If vertical angles are congruent, then two lines cut by a transversal are parallel.
a. True
b. False

Answers

The answer is True. If two vertical angles are congruent, then two lines cut by a transversal will be parallel.

Vertical angles are angles that are opposite each other and share the same vertex. They are congruent angles, meaning that they have the same measure. When two angles are congruent, the sides of the angles are parallel. This means that the two lines cut by a transversal will also be parallel.

The formula for this is that if two angles are congruent, then the lines cut by a transversal are parallel. This is also known as the Angle-Angle-Angle (AAA) Postulate. This postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. This means that the lines cut by a transversal are parallel.

In other words, if two angles of a triangle are congruent, then the two sides of the triangle that make those angles are parallel. This is because the two angles are congruent, meaning that they have the same measure. Therefore, if two vertical angles are congruent, then two lines cut by a transversal will be parallel.

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The center of a normal curve is a. cannot be negative b. always equal to zero c. is the mean of the distribution d. is the standard deviation

Answers

The center of a normal curve is the mean of the distribution, making option C the right choice.

A normal distribution—also known as the bell curve or De Moivre distribution—occurs naturally in a variety of circumstances. Bell curve symmetry is present. The data will split in two, falling half to the left and half to the right of the mean.

The characteristics of a normal curve are as follows:

Bell-like symmetrical form.The distribution's mean and median, both of which are situated in their center, are equal. ≈ 68% of the data is within one standard deviation of the mean. ≈ 95% of the data is within two standard deviations of the mean. ≈ 99.7% of the data is within three standard deviations of the mean.

Thus, the center of a normal curve is the mean of the distribution, making option C the right choice.

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please help ! ASAP step by step explanation please ​

please help ! ASAP step by step explanation please

Answers

Answer:

0

Step-by-step explanation:

→ First find inverse cosine 1/2

60°

→ Now multiply this answer by 3 because then if you substitute it in you get 0.5

∝ = 180°

→ Now find sine of 180°

0

A bag of popcorn is placed in a microwave. After the first kernel pops, the number of kernels popped doubles every 30 seconds. If it takes exactly two minutes for every kernel in the bag to have popped, what would the time be on the microwave when 25% of the kernels have popped?

Answers

Let there be N number of kernels in the bag.

Given that the number o

The outside temperature is -13 degrees. The temperature drops by 9 degrees, but then increases by 16 degrees. What is the final temperature outside? *

Answers

Answer:

The final outside temperature = -6°

Step-by-step explanation:

GIven that :

the outside temperature = -13°

The temperature drops by 9°

But then increases by 16°.

The final temperature can be expressed as:

the outside temperature - temperature drop

= -( 13° - 9°)

= - 22°

it is said that the temperature later increase by 16°

∴  - 22° + 16°

= -6°

The final outside temperature = -6°

You have a deck of cards. You pull 2 cards. What is the probability of pulling a red
card or a king with replacement.

a. 15/26
b. 0
c. 7/13

Answers

Answer:

7/13

Step-by-step explanation:

i just took the quiz

A shoemaker sold a pair of for $245.99 if the buyer a $300.00 bill, how much will the buyer receive in change?

*two decimal places don't forget your $ sign. Example: $50.00 NOT 50*

Answers

Answer:

$54.01

Step-by-step explanation:

All you have to do is $300.00-$245.99 .

Find the area of the shape below

Find the area of the shape below

Answers

Answer:

32 units^2

Step-by-step explanation:

This is a trapezoid

The area of a trapezoid is found by

A = 1/2 (b1+b2) h

A = 1/2 ( 4+12) *4

A = 1/2 (16) *4

A =32

Answer:

I think the answer is 32.!

Step-by-step explanation:

Anyone please correct me if I'm wrong.

I would divide the 12 into 3 to get 4 for the 3 parts.

I will start with the triangle on the left 4 times 4=16. Divide it 1/2, which you get 8.

On the triangle on the right is the same, so 8.

The middle is 4 times 4=16.

Last 8+8+16=32.

I think the answer is 32 units.!

The length of a rectangle is 1 7/9 in and its width is 3/4 of its length. Find the area of this rectangle.

Answers

Answer:

The answer is 4/3 or 1.33 square units.

Step-by-step explanation:

Length = 1 + 7/9 = 16/9 units.

Width = 3/4 units.

Since area of rectangle = Length * Width

Area = 16/9 * 3/4 = 4/3 square units.

What percent of 70 is 84?
% of 70 is 84.

Answers

Answer:

120

Step-by-step explanation:

Just did this

Answer:

ig 174

Step-by-step explanation:

To rent a van, a moving company charges $30.00 plus $2.50 per mile. The table shows the total cost for the number of miles driven. Enter an equation in slope-intercept form to represent this situation. PLS HELP MEHHHHHH PLS IT'S 100 POINTS

Answers

Answer:

$30.00 to rent the van

.50 per mile x 150 miles

.50*150 = $75.00

30.00 + 75.00 = $105.00

you budgeted 100.00 you do not have enough money

Step-by-step explanation:

I hope that helps i already did this assignment and it was right :)

determine the surface area of a box whose length l is 21 feet, width w is 6 feet, and height h is 8.5 feet.

Answers

To determine the surface area of the box, we need to find the area of each of its six sides and add them together. Let's start with the top and bottom of the box, which are both rectangles with length l and width w. The area of one of these rectangles is: l x w = 21 ft x 6 ft = 126 sq ft

Since there are two of these rectangles (top and bottom), we need to multiply this by 2 to get the total area of both:
2 x 126 sq ft = 252 sq ft

Next, let's look at the four vertical sides of the box, which are also rectangles. Each one has a height of h and a width of either l or w. The area of one of these rectangles is:
h x l = 8.5 ft x 21 ft = 178.5 sq ft

Again, there are two of these rectangles (front and back) with area 178.5 sq ft each, and two more (left and right) with area w x h = 6 ft x 8.5 ft = 51 sq ft each. So the total area of all four vertical sides is:
2 x 178.5 sq ft + 2 x 51 sq ft = 409 sq ft

Finally, we can add up the areas of all six sides to get the total surface area of the box:
252 sq ft + 409 sq ft = 661 sq ft

Therefore, the surface area of the box is 661 square feet.

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Solve for m
-8m-=7-9m
M=?

Answers

Answer:

\(\boxed{m = 7}\)

Step-by-step explanation:

Hey there!

Well to solve for m in the given equation,

-8m = -7 - 9m

Single out m

+ 9 to both sides

m = 7

Hope this helps :)

Answer:

m = 7

Step-by-step explanation:

-8m+9m=7-9m

Add 9m to each side

-8m+9m=7-9m

m = 7

answerrrr plzzzzzzzzzzzzz

answerrrr plzzzzzzzzzzzzz

Answers

Answer:

33 big man

Step-by-step explanation:

i need brainliest plzz

Answer: 33

Explanation:

1) Subtract 5 from both sides of the equation

4+5=137

4x+5=137

4x+5=137

4+5−5=137−5

2)Simply

Subtract the numbers

Divide by 4

4=132

Cancel terms that are in both the numerator and denominator

Divide the numbers

=33

Solution

=33

need help asap ill give 100 points simplify the radicals

need help asap ill give 100 points simplify the radicals

Answers

Answer:

8d\(\sqrt{e}\)

Step-by-step explanation:

using the rule of radicals

\(\sqrt{ab}\)  = \(\sqrt{a}\) × \(\sqrt{b}\)

given

\(\sqrt{25d^2e}\) - \(\sqrt{d^2e}\) + 2\(\sqrt{4d^2e}\)

evaluating each term separately

\(\sqrt{25d^2e}\)

= \(\sqrt{25}\) × \(\sqrt{d^2}\) × \(\sqrt{e}\)

= 5 × d × \(\sqrt{e}\)

= 5d\(\sqrt{e}\)

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

\(\sqrt{d^2e}\)

= \(\sqrt{d^2}\) × \(\sqrt{e}\)

= d × \(\sqrt{e}\)

= d\(\sqrt{e}\)

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

\(\sqrt{4d^2e}\)

= \(\sqrt{4}\) × \(\sqrt{d^2}\) × \(\sqrt{e}\)

= 2 × d × \(\sqrt{e}\)

= 2d\(\sqrt{e}\)

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

then combining them gives

5d\(\sqrt{e}\) - d\(\sqrt{e}\) + 2(2d\(\sqrt{e}\))

= 4d\(\sqrt{e}\) + 4d\(\sqrt{e}\)

= 8d\(\sqrt{e}\)

If the diameter of the ball is 11 cm, what is the distance from the center of the ball to where the board meets the floor to the nearest tenth of a centimeter

Answers

The distance from the centre of the ball to where the ball meets the floor is 5.5 cm.

How to find the diameter of the ball?

The diameter of the ball is 11 centimetres, Therefore, the distance from the centre of the ball to where the ball meets the floor to the nearest tenth of a centimetres can be calculated as follows:

Therefore, the distance form the centre of the ball to the floor is the radius of the floor.

Hence,

distance from the centre of the ball to where the ball meets the floor = 11 / 2

distance from the centre of the ball to where the ball meets the floor = 5.5 cm

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What’s the mean,median,mode, and range of 5,28,16,32,5,16,48,29,5,35

Answers

Answer:

Step-by-step explanation:

5, 5, 5, 16, 16, 28, 29, 32, 35, 48

Mode: 5, 16

Median: 44/2 = 22

range: 48 - 5 = 43

mean: (5 + 5 + 5 + 16 + 16 + 28 + 29 +32 + 35 + 48)/10 = 219/10 = 21.9

natasha is in a class of 30 students that selects 4 leaders. how many ways are there to select the 4 leaders so that natasha is one of the leaders? a. (30 4 ) b. (29 4 ) c. (30 3 ) d. (29 3 )

Answers

the correct answer is b. (29 4), which represents the number of ways to select 4 leaders from the remaining 29 students after Natasha is already chosen as one of the leaders.

In this scenario, Natasha is already one of the leaders, so we need to select the remaining 3 leaders from the remaining 29 students. We can use the combination formula (n-1)C(r-1) to calculate the number of ways to choose the leaders.

Using the given options, we can determine the correct choice:

a. (30 4): This option represents selecting 4 leaders from the entire class of 30 students, not accounting for Natasha being one of the leaders.

b. (29 4): This option represents selecting 4 leaders from the remaining 29 students after Natasha is already chosen. This is the correct choice.

c. (30 3): This option represents selecting 3 leaders from the entire class of 30 students, not accounting for Natasha being one of the leaders.

d. (29 3): This option represents selecting 3 leaders from the remaining 29 students after Natasha is already chosen.

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For a family with 3 children, what is the probability that they have exactly 2 boys and 1 girl?

Answers

Answer:

\(\frac{3}{8}\)

Step-by-step explanation:

Possibilities (G for girls and B for boys):

GGG

GGB

GBG

GBB

BGG

BGB

BBG

BBB

Answer:

1/4

Step-by-step explanation:

There are a total of four possibilities,

- Three girls

- Three boys

- Two girls and One boy

- Two boys and One girl

and only one of those options are 2 boys and 1 girl

Please helppppppppppppppppppppppppppppppppppppppp

Please helppppppppppppppppppppppppppppppppppppppp

Answers

Answer:

Step-by-step explanation:

find the horizontal and vertical asymptotes of the curve. y = 3ex ex − 5

Answers

The graph of y = 3ex ex − 5 has a horizontal asymptote of y = 3 and a vertical asymptote of x = -3/5.

The equation y = 3ex ex − 5 can be rewritten as y = 3x2ex − 5. In order to find the horizontal and vertical asymptotes of this function, we must first find its degree of the numerator and denominator. The numerator is a second degree polynomial while the denominator is a first degree polynomial.

The horizontal asymptote will be the line y = b/a, where b and a are the coefficients of the highest degree terms in the numerator and denominator, respectively. In this case, b = 3 and a = 1, so the horizontal asymptote is y = 3.

The vertical asymptote of a function is the line x = a/b, where a and b are the coefficients of the highest degree terms in the numerator and denominator, respectively. In this case, a = 3 and b = -5, so the vertical asymptote is x = -3/5.

Therefore, the graph of y = 3ex ex − 5 has a horizontal asymptote of y = 3 and a vertical asymptote of x = -3/5.

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A randomized trial comparing the efficacy of two drugs showed a difference between the two (with a P value < 0.05). Assume that in reality, however, the two drugs do not differ. This is therefore an example of: calculate the percent difference between the voltage and current for the two circuits (i.e., original circuit vs equivalent circuit). explain the difference. How was Lena Horne affected by racism? Construct a polynomial function with the following properties: third degree, only real coefficients, 1 and 4+i are two of the zeros, y-intercept is 17 . Assignment 12 is Chapter 16 in your book. Indicate bow the following events will shift the fim's demand curve for labor increase it (T); decrease it (D); keep it the same (S). In your answer, you can simply answer as follows: a) D b) S c) I And so forth...you do not have to type out the word completely ot retype the events. (a) T Tochnological advances increase labor's productivity. (b) The wage rate increases. (c) The demand for the product that laboe produces decreases. (d) The wage rate decreases. (c) Absenaeeiem roduces labot's productivity; (f) The price of laborsaving machinery is reduced and the subutitution effect is greater than the output effect. An African elephant weighs 6.3 tons. Convert the weight to pounds. Factor. x28x+16 (x+8)2(x4)2 (x+4)2 (x8)2 Henry has p colored pencils. katie has 7 times as many pencils as henry. ben has 8 fewer pencils then Katie. How many pencils do they have in all? A runner A takes 4 minutes to travel 1 mile (1.6 km) and a marathon runner B takes 2.25 hours to travel 42 km. (a) Determine the average speeds. (b) How long would the marathon take if it were traveled at the speed of runner A. nicholas hart, cfa, is a portfolio manager for individuals. last year, hart's wife was hospitalized for several months. despite his best efforts to pay her bills, hart was forced to declare personal bankruptcy but did not disclose this to his clients. according to the cfa institute standards of professional conduct, hart: Ravine Corporation purchased 40 percent ownership of Valley Industries for $119,200 on January 1, 20X6 when Valley had capital stock of $252,000 and retained earnings of $46,000. The following data were reported by the companies for the years 20X6 through 20X9 Dividends Declared Operating Income Net Income Valley Year Ravine Corporation Valley Industries Ravine 20X6 20X7 20X8 20X9 $143,000 93,000 233,000 163,000 $44,000 64,000 10,000 54,000 $ 72,000 $34,000 72,000 54,000 40,000 102,000 34,000 92,000 Required a. What net income would Ravine Corporation have reported for each of the years, assuming Ravine accounts for the intercorporate investment using the cost method and the equity method? Net Income Year Cost Method Equity Method 20X6 20X7 20X8 20X9 Why did britain and france adopt a policy of appeasement?. The table below shows the age of atree along with its height. Use the tableto answer questions 13-14.Age(years)Height(feet)00247109152413What is the rate of change from year 2 toyear 72 Direct quotes should always be used as opposed to paraphrasing in speeches.Group of answer choicesTrueFalse I was at my wit's end as I could not find my hotel. I had never been to Patna before and I knew that I had to find help soon.What does my wits end mean find the unit tangent vector to the curve at the specified value of the parameter. r(t) = t3i 8t2j, t = 5 Which of the following theory is not considered one of the three mainstream theories of criminology?1) Differential association theory2) Anomie-strain theory3) Labeling theory4) Control theory Name the slope and y-intercept in the inequality y 5x - 20a. slope = -20 ; y intercept = 5b. slope = 5x ; y intercept = -20c. slope = 5 ; y intercept = -20d. slope = -20 ; y intercept = 5x HELPPPPPP MATHHHH pleaseee a race car driving around the road is unbalanced or balanced?