1. Find the 15th term in the sequence if a1= 3 and d= 4

2. Find Sn for the arithmetic series where a1= 5, an= 119, n= 20


3. Find Sn for the arithmetic series where a1= 12, d= 6, n= 15


4. Find the 6th term in the geometric sequence where a1= 2, a6= 64, r= 2


5. Find Sn for the geometric series where a1= 2 , r= 4, n= 6

Note that the measure of ∠AED is 123°. (Option D) This is arrived at using the properties of a 4 sided polygon and angles on a straight light postulate.

A polygon is a planar figure characterized by a limited number of straight line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both. A polygonal circuit's segments are known as its edges or sides.

We know that the sum of angles in a polygon is 360°

Since ∠ABD = 46°

That is Sum of Angles in ΔBDC Less (79+57) =

180 - (101)

= 46°

And ∠EDB = 180-79 (angles on a straight line)

⇒ ∠EDB = 101°

And ∠BAE = 90° (Given)

Thus,

∠AED = 360 - 90-46-101; Thus

∠AED = 123°

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Answer:

Below

Step-by-step explanation:

Line DE grows to 5 as you move to the midpoints of  BC  and AC....

   go the the other half of the way to the end AB and it grows another 5  for a total of 10

Answer:

50+50=100
50/2=25
125km in 2 and a half hours

Step-by-step explanation:

Umm I'm assuming this isn't a trick question and saying just add 50+50 for 2 hours and then divide 50 by 2 to get 25. so 125 I hope i'm right :')

Answer:

Step-by-step explanation:

The man would walk 125km.

Explanation: The man would walk 125km, because if every hour he is walking 50km then if he walks for 2.5 hours, then all you have to do is multiply 50km by 2.5 hours.

Answer: The slope of a line can be found using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line.

Plugging in the given points, we get:

m = (-1 - (-6)) / (5 - 8)

m = 5 / -3

m = -5/3

So the slope of the line that passes through the points (8, -6) and (5, -1) is -5/3.

Step-by-step explanation:

The values for the variables a and b in the parallelogram are 2 and 3 respectively.

The parallelogram STVW have two pairs of parallel sides hence VW = TS and TV = SW.

We shall evaluate for variables a and b as follows:

3a + 11 = a + 15

3a - a = 15 - 11 {collect like terms}

2a = 4

a = 4/2 {divide through by 2}

a = 2

3b + 5 = b + 11

3b - b = 11 - 5 {collect like terms}

2b = 6

b = 6/2 {divide through by 2}

b = 3

Therefore, the values for the variables a and b in the parallelogram are 2 and 3 respectively.

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The sets of numbers could not represent the three sides of a triangle is

{12, 17, 30}.

The triangle inequality theorem explains the connection between a triangle's three sides. This theorem states that for any triangle, the sum of the lengths of the first two sides is always greater than the length of the third side.

Given:

a)  {12, 17, 30}

Using Triangle Inequality

12 + 17 < 30 This, measurement cannot give Triangle.

b) {15, 21, 33}

Using Triangle Inequality

15+ 21 > 33

21+33>15

33+15>21

This measurement give Triangle.

c)  {4, 6, 7}

Using Triangle Inequality

4 + 6 > 7

6+7>4

7+4 > 6

This measurement give Triangle.

d) {12, 27, 37}

Using Triangle Inequality

12+ 27 > 37

27+ 37 > 12

12 + 37 > 27

This measurement give Triangle.

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Clinical Chemistry Principles, Techniques, and Correlations 7th ed. Bishop is False.

A typical analytical technique (the method used to determine a chemical or physical property of a chemical substance, chemical element, or mixture.) for dissolving a chemical combination into its constituent parts so that each part may be carefully examined is called "chromatography."

The liquid or gaseous medium that moves the items to be separated over the stationary phase of a chromatography device at varying speeds is called as mobile phase.

In chromatography, the stationary phase can be either a solid or a liquid matrix. The mobile phase, which moves through the stationary phase, typically occurs in a liquid or a gas.

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The graph of the function f(x) = 3√(3 - x) is at the end of the answer.

We want to graph the function f(x) = 3√(3 - x)

To do so, we need to find some points on that line, to find the points we need to evaluate the function in some values of x

if x = -1

f(-1) = 3√(3 + 1) = 3*2 = 6

if x = 3

f(3) = 3√(3 - 3) = 3*0 = 0

if x = -6

f(-6) = 3*√(3 + 6) = 3*3 = 9

if x = -13

f(-13) =  3*√(3 + 13) = 3*4 = 12

Then the points are (-1, 6), (3, 0), (-6, 9), (-13, 12)

Now we can just graph these 4 points and connect them with a curve, the graph of the function is below.

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The sum of the series

[tex]$b 2 b 4 b 6 b 8 b {10}$ is $b_2 \left (1-\dfrac{7^5}{4^5} \right ) \over 1-\dfrac{7}{4} = 180 \left (1-\dfrac{2401}{1024} \right ) \over \dfrac{3}{4} = 135.75$.[/tex]

The given series is a geometric series, which means that each successive term is multiplied by a common ratio to obtain the next term. The sum of the first 10 terms of this series is 180. Thus, the common ratio is [tex]$\dfrac{7}{4}.$[/tex]

Now to find the sum of the series [tex]$b 2 b 4 b 6 b 8 b {10}$[/tex], we apply the formula for the sum of the first n terms of a geometric series, which is [tex]$b_1 \left (1-r^n \right ) \over 1-r$[/tex], where [tex]$b_1$[/tex] is the first term, [tex]$r$[/tex] is the common ratio, and [tex]$n$[/tex] is the number of terms.

In our case, [tex]$b_1 = b_2$, $r = \dfrac{7}{4}$[/tex] and n = 5. Thus, the sum of the series [tex]$b 2 b 4 b 6 b 8 b {10}$ is $b_2 \left (1-\dfrac{7^5}{4^5} \right ) \over 1-\dfrac{7}{4} = 180 \left (1-\dfrac{2401}{1024} \right ) \over \dfrac{3}{4} = 135.75$.[/tex]

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The equation for line 1 is y = x+6 and equation for line 2 is y= -x-4. The domain and range is as follows,

y = x+6 {(x,y)| x≤ -5 , y≤ 1}

y= -x-4  {(x,y) x≥-5, y≤1}

The line 1 passes through points (-6,0) and (-5,1).

Equation for a line is  y= Ax+B

Using two points we can formulate the following equations

-6A+B =0

-5A+B =1

Subtracting the two equations,

-A = -1, so A= 1

-6A+B = 0

-6 ×1 + B = 0

B= 6

So the equation for the line by substituting values of A and B is

y= x+6

The domain is all values ≤-5 and range is all values ≤1

The line 2 passes through (0,-4) and ( -5,1)

Formulating equations using points

B= -4

-5A+B =1

A = -1

Substituting in equation for line 2

y = -x-4

The domain is all values ≥ 5 and range is all values ≤1.

So the equation, domain and range of line 1 is y = x+6 {(x,y)| x≤ -5 , y≤ 1} and for line 2 is y= -x-4  {(x,y) x≥-5, y≤1}

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The complete question is included as image

We can prove this statement by using the Pigeonhole Principle.

Let's say we have a collection of n integers and we want to demonstrate that at least one of them, or the sum of several of them, is a multiple of n.

Consider the 0, 1, 2,..., n-1 possible remainders when these integers are divided by n.

There must be at least one remainder that appears more than once since there are n numbers and only n potential remainders.

Case 1: Choose two integers from the set, say a and b, such that a b (mod n), that is, a and b have the same remainder when divided by n, if a remainder occurs more than once.

Since their remainders cancel out, their difference a - b is a multiple of n.

As a result, we have identified an integer that is a multiple of n in the set.

Case 2: The sum of any two integers in the set may be taken into consideration if there are no remainders that appear more than once.

Two integers a and b can be added together using the formula a + b = qn + r, where q is the quotient and r is the residual after a + b is divided by n.

The Pigeonhole Principle states that two pairs of integers must have the same remainder when combined modulo n since there are n potential remainders but only n-1 possible values for the remainder r (from 0 to n-1).

These pairings should be (a1, b1) and (a2, b2), where (a1 b1 (mod n) and (a2 b2) (mod n).

Then, there is:

(a1 + b1) + (a2 + b2) = (a1 + a2) + (b1 + b2) ≡ 0 (mod n)

thus the remainders of a1 + a2 and b1 + b2 are equal modulo n.

As a result, n is a multiple of the sum of these four numbers.

In either scenario, we have demonstrated that any collection of n integers contains either an individual integer that is a multiple of n or an aggregate of many numbers that is a multiple of n.

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Answer:

x = 24

Step-by-step explanation:

In a parallelogram, adjacent angles are supplementary.

             ∠B + ∠C = 180°

        5x + 2x + 12 = 180

                7x + 12 = 180

Subtract 12 from both sides,

                   7x = 180 - 12

                  7x  = 168

Divide both sides by 7,

                  x = 168 ÷7

                 [tex]\boxed{x = 24^\circ}[/tex]

The solution to the system of equations is x = -1 and y = -3

From the question, we have the following parameters that can be used in our computation:

-2x+2y=-4

3x + 3y = -18

Multiply (1) by 1.5

So, we have the following representation

-3x + 3y = -6

3x + 3y = -18

Add the equations

6y = -24

So, we have

y = -3

This means that

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

Evaluate

2x = -2

Divide

x = -1

Hence, the value of x is -1

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5) The equation of population after year 2000 is expressed as;

P = 65x + 622

6) Population in the year 2012 is; P = 1402 students

The parameters given are;

Population in 2003 = 817

Population in 2006 = 1012

Thus;

Average population growth per year = (1012 - 817)/3

Average population growth per year =  65 people

Now, we see that the population of people in the year 2000 was 622.

Thus;

5) Equation of population is;

P = 65x + 622

where x is number of years after year 2000

6) Population in the year 2012 which is 12 years after year 2000 is;

P = 65(12) + 622

P = 1402

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If two random variables are uncorrelated, they are independent and the covariance of X and Y is 0.

Probability is a measure of the likelihood of an event occurring.

In this case, we are given that P(X = -1) = 1/3, P(X = 0) = 1/3, and P(X = 1) = 1/3.

We are also given a second random variable Y, which is defined in terms of X. Y takes on the value of 1 when X = 0, and 0 otherwise. The probability distribution of Y is the set of probabilities associated with each possible value of Y. In this case, Y can only take on the values 0 or 1, so

=> P(Y = 0) = P(X = -1) + P(X = 1) = 2/3 and P(Y = 1) = P(X = 0) = 1/3.

The joint distribution of X and Y is the set of probabilities associated with each possible combination of X and Y. In this case, there are three possible combinations: (X = -1, Y = 0), (X = 0, Y = 1), and (X = 1, Y = 0). The joint probabilities are simply the products of the marginal probabilities of X and Y.

=> P(X = 0, Y = 1) = P(X = 0) * P(Y = 1) = (1/3) * (1/3) = 1/9.

Finally, we can calculate the covariance of X and Y, which is a measure of how much the two variables vary together. The formula for covariance is:

=> Cov(X,Y) = E[XY] - E[X]E[Y].

Using the joint distribution we calculated earlier, we can find

=> E[XY] = (-1)(2/9) + (0)(1/3) + (1)(2/9) = 0

and

=> E[X] = (-1)(1/3) + (0)(1/3) + (1)(1/3) = 0.

We can also find

=> E[Y] = (0)(2/3) + (1)(1/3) = 1/3.

Therefore,

=> Cov(X,Y) = 0 - (0)*(1/3) = 0.

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AB line segment correctly represents the perpendicular bisector of line segment XY.

Line segment is the part of line which have two endpoint and bounded by two distinct end points and it contain every point on the line which is between its endpoint.

Given that;

There are 4 doted lines are shown.

Now, From all dotted line;

Line segment AB divides the line segment XY into two equal parts.

Hence, AB line segment correctly represents the perpendicular bisector of line segment XY.

Thus, ''AB line segment'' correctly represents the perpendicular bisector of line segment XY.

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-13y + 7 - 11 - 4y can be written as -17y - 11.

Expression is a way of conveying emotions, thoughts, or ideas through verbal or nonverbal means. It is often used to communicate an individual's feelings, beliefs, or opinions, and can be expressed through language, art, music, dance, and other forms of communication. Expression can be used to convey a wide range of emotions, from joy and excitement to anger and sorrow. Expression is an essential part of communication, and without it, we would not be able to effectively convey our thoughts, feelings, and desires. The way we express ourselves can also be a reflection of our personality and can give people an insight into who we are. Expression is also important for self-expression, as it allows us to explore our own thoughts and emotions, and express them in a way that may be more comfortable for us.


This can further be written as -17y × (-1) - 11. Therefore, the expression can be written as a multiplication as -17y × (-1) - 11.

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Answer:

See below for answers

Step-by-step explanation:

Part A

[tex]\displaystyle V=\pi\int\limits^d_c {(R^2-r^2)} \, dy\\=\pi\int\limits^3_0 {\biggr(\biggr(\frac{y^2}{9}\biggr)^2-\biggr(\frac{y}{3}\biggr)^2\biggr)} \, dy\\=\pi\int\limits^b_a {\biggr(\frac{y^4}{81}-\frac{y^2}{9}\biggr)} \, dy[/tex]

Make sure to write the functions in terms of y since you rotate on a vertical axis.

Part B

[tex]\displaystyle V=\pi\int\limits^b_a {(R^2-r^2)} \, dx\\=\pi\int\limits^1_0 {((3-3\sqrt{x})^2-(3-3x)^2)} \, dx\\=\pi\int\limits^1_0 {((9-18\sqrt{x}+9x)-(9-18x+9x^2))} \, dx\\=\pi\int\limits^1_0 {(-18\sqrt{x}-9x-9x^2)} \, dx[/tex]

Make sure to fix the radii so they start at y=3.

Answer:1,283.803

Step-by-step explanation:

the question is mistake

Answer:

C

Step-by-step explanation:

In table C, each time x increases by one, y increases by 26 correspondingly. This suggests that y = 26x. The other 3 tables do not show a consistent pattern or relationship between x and y.

Table A can be disproved because, though it seems at first to be a multiple of -2 for every x value, the third data value (3, -16) disproves this. It would have to be (3, -6) for this relationship.

Table B has no clear pattern; the difference from the y values corresponding to x=1 and x=2 is 23, while the difference between x=2 and x=3 is also 23. However, there is no x & y relationship that can be defined to find x or y when given the other.

Table D has no clear pattern; the difference between x=1 and x=2 is 6, but the difference between x=2 and x=3 is 7.

Answer: The correct answer is A. If the graph of the system shows parallel lines, then there are infinite solutions.

When two linear equations in the system have the same slope and different y-intercepts, the lines will be parallel and will never intersect. This means that there is no solution to the system.

On the other hand, when two linear equations in the system have different slopes, the lines will intersect at exactly one point, which is the unique solution to the system.

So, in summary:

Parallel lines: no solution

Intersecting lines: one solution

Infinite solutions: lines are the same.

Step-by-step explanation:

RAID, which stands for Redundant Array of Inexpensive Disks, is a data storage technology that combines multiple physical disks into a single logical unit to provide data redundancy, improved performance, and increased storage capacity.

RAID accomplishes this by distributing data across multiple disks, so that if one disk fails, the data can be rebuilt from the remaining disks.

There are several different RAID levels to choose from, each with its own benefits and trade-offs. For a personal server with the goal of data backup and redundancy, RAID 1 would be a good choice.

Setting up RAID 1 is relatively straightforward. You'll need two identical hard drives of sufficient size, and a RAID controller (which may be built into the motherboard). You can then configure the RAID controller to mirror the data between the two drives, so that they appear as a single logical drive to the operating system.

It's worth noting that RAID is not a substitute for regular backups. While it can provide protection against disk failures, it won't protect against other types of data loss, such as accidental deletion or corruption. It's still important to have a regular backup schedule, and to store backups offsite or in the cloud to protect against physical damage or theft.

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The statement that is true when comparing the two accounts after 10 years is: A: "Hannah's account has more money than Frank's account".

To compare the amount of money in the two accounts after 10 years, we can use the formula for continuous compound interest:

A = Pe^(rt)

where A is the amount of money in the account after t years, P is the principal (initial amount), r is the annual interest rate (expressed as a decimal), and e is the mathematical constant approximately equal to 2.71828.

For Frank's account, we have:

A = 2500e^(0.05410) = 4244.96 dollars (rounded to the nearest cent)

For Hannah's account, we have to take into account the quarterly compounding. The formula for quarterly compound interest is:

A = P(1 + r/n)^(nt)

where n is the number of compounding periods per year (4 for quarterly compounding), and t is the time in years. Thus, we have:

A = 3000*(1 + 0.032/4)^(4*10) = 4412.09 dollars (rounded to the nearest cent)

Therefore, the amount of money in Hannah's account after 10 years is greater than the amount in Frank's account.

"

Complete question

frank invests $2,500 in an account that has an annual interest rate of 5.4% compounded continuously. hannah invests $3,000 in an account that has an annual interest rate of 3.2% compounded quarterly. which of the following statements is true when comparing the amount of money in the two accounts after 10 years?

A: Hannah's account has more money than Frank's account

B: : Frank's account has more money than Hannah's account

"

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To calculate the distance traveled by the satellite, we need to find the circumference of the circle it traces in the sky. The circumference can be found using the formula:

C = 2 * π * r

where r is the radius of the circle (i.e., the distance from the center of the earth to the satellite), and π is pi, approximately equal to 3.14.

r = 36,000 km

C = 2 * π * 36,000 km

C = 72,000 * π km

Next, we need to find what fraction of the circumference the satellite has traveled in one hour. This is given by the fraction of the total circle the satellite has traced, which is equal to the angle it has formed divided by 360°.

fraction = 32° / 360°

Finally, we can multiply the circumference by the fraction to find the distance traveled by the satellite:

distance = C * fraction

distance = 72,000 * π * 32° / 360° km

Rounding the result to the nearest kilometer, the satellite has traveled approximately:

distance = 73,382 km

So, the satellite traveled approximately 73,382 km in one hour.

C = 45 + 0.25t. The 45 represents the baseline amount that she is charged per month. The t represents each additional text, and the 0.25 represents how much she is charged for each additional text.

The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is a point on the line.

Substituting the given values, we get:

y - 11 = (3/2)(x - 12)

Expanding and simplifying, we get:

y - 11 = (3/2)x - 18

y = (3/2)x - 7

Therefore, the equation of the line that passes through the point (12, 11) with slope 3/2 is y = (3/2)x - 7 in slope-intercept form or y - 11 = (3/2)(x - 12) in point-slope form.

Answer:

[tex]59^{\circ}[/tex]

Step-by-step explanation:

Adjacent angles of a parallelogram are supplementary.

[tex]5x-11+11x-33=180 \\ \\ 16x-44=180 \\ \\ 16x=224 \\ \\ x=14[/tex]

Opposite angles of a parallelogram are congruent.

[tex]m\angle N =m\angle P \implies m\angle P=5(14)-11=59^{\circ}[/tex]

1) The center of mass of a right-circular cone with a base radius r, height h, and a non-uniform mass density varies as the square of the distance from apex (tip of the cone) is:

ρ(x, y, z) = k × ([tex]\sqrt{(x^2 + y^2 + z^2)}[/tex])²

where k is a constant of proportionality.

2) The center of gravity of a very thin right-circular conical shell of a base radius R, and height h is: 2h/3

1) Let us assume that m represents the total mass of the right-circular cone.

The center of mass for the x, y, and z-coordinates would be:

x-coordinate:

[tex]x_{cm}[/tex] = (1/m) × ∫∫∫_V x × ρ(x, y, z) × dV

y-coordinate:

[tex]y_{cm}[/tex] = (1/m) × ∫∫∫_V y × ρ(x, y, z) × dV

z-coordinate:

[tex]z_{cm}[/tex] = (1/m) × ∫∫∫_V z × ρ(x, y, z) * dV

where V - the volume of the cone,

ρ(x, y, z) - the mass density function,

Since the mass density varies as the square of the distance from the apex, we have:

ρ(x, y, z) = k × ([tex]\sqrt{(x^2 + y^2 + z^2)}[/tex])²

where k is a constant of proportionality.

Substituting this into the above equations, we find the center of mass of the cone.

2) Let us assume that x’ be the distance from the vertex of the cone to any point on the axis of the  right-circular conical shell.

Also R be the radius of the base of the  right-circular conical shell and ‘h’ is the height of the  right-circular conical shell.

Let r be the distance of any point on the cone from the axis of the  right-circular conical shell , the distance being measured perpendicular to this axis.

And l is the distance of any point on the  right-circular conical shell directly from the vertex.

r/R = z/h = l / L

Let us assume that σ be the surface density of mass of the cone.

The formule for center of mass of a system is given by,

x=∫z.σ dA / ∫σdA

but dA = 2πr.dl which is an infinitesimal area around the circle.

After solving this expression we get x = 2h/3

Therefore, the center of gravity of a very thin right-circular conical shell of a base radius R, and height h is given by 2h/3

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jump discontinuities x= DNE

removable discontinuities x= DNE

infinite discontinuities x= -2, 2

other discontinuities x= DNE

The function has an infinite discontinuity at x=-2 and x=2 because the denominator of the fraction, x^2 + 4, approaches 0 as x approaches -2 or 2.