Give the equation for a circle with the given center and radius. center at (-1, 3), radius = 4

Answers

Answer 1

Answer:

(x + 1)² + (y - 3)² = 16

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (- 1, 3 ) and r = 4 , then

(x - (- 1) )² + (y - 3)² = 4² , that is

(x + 1)² + (y - 3)² = 16

Answer 2

Answer:

(x+1)^2 + (y-3)^2 = 16

Step-by-step explanation:

The standard form of an equation of a circle with center (h,k) and radius r is (x-h)^2 + (y-k)^2 = r^2.  Plugging in those values, we get (x-(-1))^2 + (y-3)^2= 4^2  = (x+1)^2 + (y-3)^2 = 16.


Related Questions

Is anyone really good at math?

Answers

Answer: 12 cm

Step-by-step explanation:

[tex]\mathtt{Using\ the \ pythagorean \ theorem: \\}[/tex]

[tex]a^2+b^2=c^2, \\\ we\ can\ plug\ in\ values\ for\ a,\ b,\ and\ c[/tex]

[tex]L=a\ and\ M=b\ and\ N=c[/tex]

Therefore,

[tex]L^2+35^2=37^2\\L^2+1225=1369\\L^2=144\\\sqrt{L^2} =\sqrt{144} \\L=\pm12\\Taking\ only\ the\ positive\ answer,\ we\ get:\\\large\boxed{L = 12cm}[/tex]

We have: L² + M² = N²

=> L² = N² - M² = 37² - 35² = 144 = 12²

=> L = 12

ANSWER: B.12

OK done. Thank to me :3

A central role of members at this time is to recognize and deal with the many forms of?

Answers

Answer:

Resistance

Step-by-step explanation:

On the interval [0, 2π), which points are intersections of r = 5 4 sin(θ) and r = −6 sin(θ)? check all that apply.

Answers

Correct option is D) and E)

(3,7π/6),(3,11π/6)

What is Point of intersection?

Point of intersection is the point where two lines or two curves meet each other.

The point of intersection of two lines of two curves is a point.

If two planes meet each other then the point of intersection is a line.

The term "point of intersection" refers to the intersection of two lines. The equations a1x+b1y+c1=0 and a2x+b2y+c2=0, respectively, are used to represent these two lines. The two lines' intersection point is shown in the following figure. The intersection of three or more lines can also be located.

According to the given information:

let

5 + 4 sin(θ) = −6 sin(θ)

Then get

θ= -1/2

Then you can make it

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I understand that the question you are looking for is:

On the interval [0, 2π), which points are intersections of r = 5 4 sin(θ) and r = −6 sin(θ)? check all that apply.

A) -3,7/6

B) (-3,11/6)

C) (3,7/6)

D) (3,11/6)

On a coordinate plane, a parabola opens to the left. It has a vertex at (0, 0), a focus at (negative 2, 0), and a directrix at x = 2.

Which equation represents the parabola shown on the graph?
y2 = –2x
y2 = –8x
x2 = –2y
x2 = –8y

Answers

The equation represents the parabola shown on the graph is  x^2 = - 8y . Option D

How to determine the equation

We were given the following parameters;

Vertex ( 0, 0 )Focus ( -2, 0)Directrix , at x = 2

The standard for a parabola is given as;

y² = 4ax

It can also be written as;

x² = 4ay

Given the focus as ( -2, 0), we have the value of 'a' to be -2

Now, let's substitute the value into the standard equation of a parabola

x^2 = 4ay

x^2= 4 × -2 × y

Multiply through

x^2 = - 8y

The equation of the parabola is x^2 = - 8y

Thus, the equation represents the parabola shown on the graph is  x^2 = - 8y . Option D

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Answer:

b

Step-by-step explanation:

trust

my car uses 8.5L of pertrol per 100km travelled. If I travel 400km, how many litres of petrol will my car use?

Answers

Answer:

34 L

Step-by-step explanation:

there are four 100 km(s) in 400 km

so

8.5 * 4 is what you need to do to find your answer

8.5 * 4 = 34

34 L is your answer

A graph of a line goes through the points (zero, four) and (negative six, zero).


Find the equation of the line using exact numbers.

Answers

The equation of the line is y = 2/3x + 4

How to find the equation of the line using exact numbers?

The points on the line are given as:

(zero, four) and (negative six, zero).

Rewrite the points properly as

(0, 4) and (-6, 0)

The slope of the line is calculated using:

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

Substitute the known values in the above equation

m = (0 - 4)/(-6 - 0)

Evaluate

m = 2/3

The equation of the line is then calculated as:

y = mx + b

This gives

y = 2/3x + b

So, we have:

4 = 2/3 * 0 + b

Evaluate

b = 4

Substitute b = 4 in y = 2/3x + b

y = 2/3x + 4

Hence, the equation of the line is y = 2/3x + 4

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Consider this quadratic equation.
2x²2²-1=3x+4
Which equation correctly applies the quadratic formula?
COA
OB.
OC.
OD.
2=
H=
H=
-(-3) ± √(-3)²-4(2)(-5)
-(-3);
2
-(-3) ± √(-3)²-4(-5)
(2)
-(-3) ± √(-3)²(2)(-5)
(2)
-(-3) ± √(-3)²-4(2)(-5)
2(2)

Answers

Answer:

-(-3) ± √(-3)^2 - 4(2)(-5) / 2(2)  (the last choice).

Step-by-step explanation:

Im ignoring the 2^2 in the equation

The equation transforms to

2x^2 - 3x - 5 = 0    (standard form)

So x = -(-3) ± √(-3)^2 - 4(2)(-5) / 2(2)

GEOMETRY STUFF!! PLSS HELPP, NEED ANSWERS AND SOLUTIONS RN!!

Answers

Applying the angle bisector and triangle proportionality theorem, the solutions are:

16. x = 1/2 or x = 4

17. x = 5

18. x = −1 or x = 6.

What is the Angle Bisector Theorem?

The angle bisector theorem states that when a line segment divides one of the angles of a triangle into two halves, it also divides the triangle to form segments that are proportional to each other.

16. 3x/(x - 1) = (x + 4)/(x - 2) [triangle proportionality theorem]

Cross multiply

(x - 1)(x + 4) = 3x(x - 2)

x² + 3x - 4 = 3x² - 6x

x² - 3x² + 3x - 4 + 6x = 0

-2x² + 9x - 4 = 0

Factorize -2x² + 9x - 4

(−2x + 1)(x − 4)

-2x = -1

x = 1/2

or

x = 4

17. (2x + 2)/(x + 3) = (4x - 2)/(2x + 2)

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

4x² + 8x + 4 = 4x² + 10x - 6

Combine like terms

4x² - 4x² + 8x - 10x = -4 - 6

-2x = -10

x = -10/-2

x = 5

18. (2x + 3)/(x + 4) = x/(x - 2) [angle bisector theorem]

Cross multiply

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

Expand

2x² - x - 6 = x² + 4x

2x² - x - 6 - x² - 4x = 0

x² - 5x - 6 = 0

Factorize x² - 5x - 6 = 0

(x+1)(x−6) = 0

x = −1 or x = 6

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which expression is equivalent to (60x^(20)y^(24))/(30x^(10)y^(12)

a. 2x^(2)y^(2)
b. 2x^(10)y^(12)
c. 30x^(2)y^(2)
d.30x^(10)y^(12)

Answers

Answer:

b.  2x^10y^12.

Step-by-step explanation:

(60x^(20)y^(24))/(30x^(10)y^(12)

60 / 30 = 2

x^20 / x^10 = x^(20-10) = x^10

y^(24) / y^(12) = y^(24-12) = y^12.

Thus, the answer is:

2x^10y^12.

Answer:

b. 2x^(10)y^(12)

Step-by-step explanation:

(60x^(20)y^(24))/(30x^(10)y^(12)

when there is division we simplify that by subtracting the power

by using rules of indices

[tex] \frac{x^a}{x^b}=x^{a-b}[/tex]

and number can be divided easily

[tex] \frac{60}{30}*\frac{x^{20}}{x^{10}}*\frac{y^{24}}{y^{12}}[/tex]

[tex] 2*x^{20-10}y^{24-12}[/tex]

[tex] 2x^{10}y^{12}[/tex]

so answer is b. 2x^(10)y^(12)

Choose the correct discount or markup. if an item has a retail price = $995 and a discount of 15%, how much is the discount? it is $ .

Answers

Answer:

$149.25

Step-by-step explanation:

The discount is 15% of $995

Find the Discount

[tex]15\%\times995[/tex]

Note that percentages can also be written as that number over 100.

[tex]\frac{15}{100}\times995[/tex]

Simplify the fraction

[tex]\frac{3}{20}\times995=\frac{2985}{20}=149.25[/tex]

Therefore the discount is $149.25.

Answer:

$149.25

Step-by-step explanation:

help with equation points included

Answers

The logarithmic equation f(x) = log₈(x + 1) + 4 is shifted left by 1 unit and up by 4 units

How to determine the transformation?

The logarithmic equation is given as:

f(x) = log₈(x + 1) + 4

The parent function of the logarithmic equation is

y = log₈(x)

When the logarithmic equation is translated 1 unit left, we have:

y = log₈(x + 1)

When the logarithmic equation is translated 4 units up, we have:

y = log₈(x + 1) + 4

This means that the logarithmic equation f(x) = log₈(x + 1) + 4 is shifted left by 1 unit and up by 4 units

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$10- (5.80+28 cents)

Answers

Answer is $3.92
Step by step
Using PEMDAS we perform the math inside the Parenthesis first. (5.80 + .28) = 6.08
Now we have $10 - 6.08 = $3.92
Problem solved
The answer is 3.92, in which pemdas can help u solve for it.

10. The product of -2 and a number n is increased by 15. The result is greater than 3. Choose the inequality that represents the solution set to the problem. A. n>6/ B. n-6 D. n​

Answers

Answer:

-2n+15>3

Step-by-step explanation:

1/2.x + 3 ( x-1 ) - 5 = 30

Answers

Answer:

1/2.x+3(x-1)-5=30

1/2.x+3x-3-5=30

(1/2+3)x-8=30

7/2.x-8=30

7/2.x=38

7x=76

x=76/7

CMIIW

What is the value of x that makes l1||l2?

A. 14
B. 11.6
C. 10
D. 26.7

Answers

Answer:

10

Step-by-step explanation:

By the alternate interior angles theorem,

[tex]4x=2x+20 \\ \\ 2x=20 \\ \\ x=10[/tex]

Quick algebra 1 assignment for some points and brainliest!

(EASIER THAN IT LOOKS)

Only help if you know the answer PLEASE HELP EXPERTS AND GENIUSES ITS DUE TOMMAROW

(ANSWER ALL 4 PARTS OF THE ASSIGNMENT PLEASE :p )

Answers

1. The 100 prisoner experiment: 100 prisoners are about to be executed (you can use paper stick figures to model 100 prisoners, or you can do about 10), but the warden has agreed to allow all prisoners to be commuted to a 6-month sentence if they can pass one game. The game states that 100 pieces of paper with each of the prisoner's numbers are to be randomly shuffled into boxes that have random prisoner's numbers (where the number on the paper does not match the number on the boxes.) Each prisoner is allowed to open 50 boxes to find their number such that they have a [tex]\frac{1}{2}[/tex] chance of finding their number. If you find your number, you are cleared to another room to wait. If you don't, then you've messed up huge. If even one prisoner does not find their number, all the prisoners die. If all of the prisoners find their numbers, they all get 6-month sentences instead. The chance of all the prisoners randomly finding their numbers is [tex](\frac{1}{2})^{100}[/tex], which is about a 0.0000000000000000000000000000008% chance. 30 zeros after the decimal placement. For reference, two people have a better chance of picking up the same grain of sand from any of the beaches in the world than finding their numbers randomly.

The Vickrey Auction can be modeled into an experiment by testing people's psychological thinking. You can do this with any of your friends. In a Vickrey auction, you put your bids into a closed letter. For an item, the highest bidder wins the auction, but does not pay what he or she put their bid under in the auction, but rather pays what the second bidder had bidded. It teaches people to be more honest, because if you bid the highest and win, you pay the second-highest bidder's payment, which could also be almost equally as high and could cost you a fortune for an undervalued item.

Another great experiment you can do is to measure the different unsynchronizations of analog clocks that are not close together. Scientists have measured atomic clocks that are just a millimeter apart that start ticking in different measures.

2. I select the 100-prisoner experiment.

3. A curved graph like -x^2 would fit perfectly.

4. A quadratic function would fit my experiment the best. The best graph to use would be [tex]y = -x^2[/tex]. An equation with a large curve would be the best for this type of experiment to graph success and failure. More than three quarters of my graph wouls be full of failure and maybe a little more than 10% would be full of success if repeated over 100,000 times. I am not too sure though.

pls helpp

1. There are 3 1/2 groups of students ready to load buses for a field trip. Each group will fill one bus 2/5 of the students on each bus are boys. How many buses would it take to carry only the boys.
2. Mark is going to a pool party. It is 2 3/4 miles from his house. Mark decides to ride his bicycle, but he has a flat tire 2/3 if the way there. How far is Mark from his house?

Answers

you will need 2 busses to only transport the boys.Mark is at (1 + 5/6) miles of his house.How many buses would it take to carry only the boys?

We know that there are (3 + 1/2) groups, such that each group fill one bus.

2/5 of the students are boys, then the number of groups that we can make only with boys is:

(2/5)*(3 + 1/2) = 6/5 + 1/5 = 7/5 = 5/5 + 2/5 = 1 + 2/5

Then you can make one and a little less than a half of a group, which means that you need 1 and 2/5 of a buss to transport the boys, rounding that to the a whole number, you will need 2 busses to only transport the boys.

How far is Mark from his house?

The original distance is:

D = (2 + 3/4) miles.

But Mark only covers 2/3 of that distance, then we have:

d = (2/3)*D = (2/3)*(2 + 3/4) miles = (4/3 + 2/4) miles

d = (4/3 + 1/2) miles = (8/6 + 3/6) miles = (1 + 5/6) miles

Mark is at (1 + 5/6) miles of his house.

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A plan for a baseball diamond is drawn in a coordinate plane. The baseball diamond is in the shape of a square with vertices at approximately (0, 64), (64, 0), (0, -64), and (-64, 0). One unit in the coordinate plane represents 1 ft. What is the approximate area of the baseball diamond?

Answers

The area of the baseball diamond is 8192 sq. units.

We assume the square-shaped, baseball diamond to be ABCD with A = (0, 64), B = (64, 0), C = (0, -64), and D = (-64, 0).

The side of the square can be computed using the distance formula,

D = √((x₂ - x₁)² + (y₂ - y₁)²), when the endpoints of a line are (x₁, y₁) and (x₂, y₂).

Thus, the side of the square,

a = √((x₂ - x₁)² + (y₂ - y₁)²),

or, a = √((64 - 0)² + (0 - 64)²) {Considering A(0,64) and B(64, 0) as the endpoints,

or, a = √(64² + (-64)²),

or, a = √(4096 + 4096),

or, a = 64√2 units.

Now, the area of the square can be calculated using the formula, A = a², where A is the area and a is the side of the square.

Thus, the area of the square = (64√2)² = 4096*2 = 8192 sq. units.

Thus, the area of the baseball diamond is 8192 sq. units.

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A regular pentagonal prism has a volume of 2,850 cubic millimeters. what is the height of the prism? a regular pentagonal prism with height labeled h. the pentagonal base has side edge labeled 12 millimeters. apothem from center to a base edge is labeled 5 millimeters. the height of the prism is millimeters.

Answers

Answer:

Height = 19mm.

Step-by-step explanation:

Area of a regular polygon =  (A * P) / 2 where A = side / (2 * Tan (π / N)) where, N = Number of sides, A = Apothem,  P = Perimeter.

Here A = 5, P = 5*12 = 60 so

Area  of the base  = (5 * 60) / 2 = 150 mm^2.

Volume = area base * height so

Height = volume / area of base

            = 2850 / 150

            = 19 mm.

The height of the prism is h = 19 mm

What is the volume of a prism?

A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.

The volume of a prism is the product of its base area and height

Volume of Prism = B x h

where B = base area of prism

h = height of prism

Given data ,

A regular pentagonal prism has a volume of 2,850 millimeters³

The pentagonal base has side edge labeled 12 millimeters.

And , Apothem from center to a base edge is labeled 5 millimeters

Area of a regular polygon =  (A x P) / 2

where A = side / (2 * Tan (π / N))

and , N = Number of sides, A = Apothem,  P = Perimeter

h = 2850 / 150

On simplifying , we get

h = 19 mm

Hence , the height is 19 mm

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Lee wants to fence off a rectangular area that is 36 feet squared in size for a vegetable garden. He is considering three garden lengths of 6 ft, 9 ft, and 12 ft. He wants to determine which garden would require the least amount of fencing.

Determine the dimensions of the garden that would require the least amount of fencing.

Answers

tried my best to show the steps!! all i did was isolate to find the missing widths attached to the respective lengths (divided surface area by width) and then multiply both sides by two and add them together to find the perimeter.

The dimensions of the garden that would require the least amount of fencing are 6 ft in length and 6 ft in width.

The dimensions are the sides of a geometric shape.

The lengths of the three gardens are given as 6 ft, 9 ft, and 12 ft respectively.

If the area of the garden is 36 feet squared, then the widths for the three lengths will be as follows:

The width of the garden with a length of 6 ft [tex]= \dfrac{36}{6} = 6\ ft[/tex]

The width of the garden with a length of 9 ft [tex]= \dfrac{36}{9} = 4\ ft[/tex]

The width of the garden with a length of 6 ft [tex]= \dfrac{36}{12} = 3\ ft[/tex]

The parameters are calculated as:

The parameter of the garden with dimensions (6 ft, 6 ft) = 2(6 + 6) = 24 ft

The parameter of the garden with dimensions (9 ft, 4 ft) = 2(9 + 4) = 26 ft

The parameter of the garden with dimensions (12 ft, 3 ft) = 2(12 + 3) = 30 ft

The least of the parameter is of the garden with dimensions (6 ft, 6 ft).

Thus, the garden with dimensions (6 ft, 6 ft) would require the least amount of fencing.

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The variables x and y vary directly. If one pair of the values is x = 3 and y = 12, write an equation that shows the relationship between x and y.

A. y = 4x
B. x/y = 4
C. y = x/4
D. x = 4y

Answers

y=4x seems the best answer

johns first three test scores out of 100 are 84,78,82. what did he score on his fourth test if the average for all four tests is 80 out of 100

Answers

Answer:

76

Step-by-step explanation:

In order for John's average to be 80, the sum of all of his test scores must be 4*80 = 320. We can add 84, 78, and 82 to get 244, and then we subtract 244 from 320 to obtain the answer 76.

Answer:

Step-by-step explanation:

80 * 4 = 320

84 + 78 + 82 + x = 244

244 + x = 320

x = 320 - 244

x = 76

How do i solve for the maximum and minimum of z?

Answers

Answer:

Step-by-step explanation:

[tex]We\ summarize\ (1) \ and\ (2),\ \ (2) \ and\ (3):\\\displaystyle\\\left \{ {{2x\geq -6\ |:2} \atop {-2x\geq -6\ |:(-2)}} \right. \ \ \ \ \ \left \{ {{x\geq -3} \atop {x\leq 3}} \right. \ \ \ \ \ \Rightarrow\ \ \ \ x\in[-3;3].\\[/tex]

[tex]2)\ We\ subtract\ equation\ (2) \ from \ equation (1),[/tex]

Find the cofactors of each entry in the first row of the matrix . ac11 = ac12 = ac13 =

Answers

The cofactors of each entry in the first row of the matrix exist

[tex]$$Ac_{11 }= -13[/tex]

[tex]Ac_{12} = 44[/tex]

[tex]Ac_{13} = 27[/tex]

We have to estimate the cofactors of each entry in the first row of the matrix.

What is the matrix?

A set of numbers exists arranged in rows and columns to create a rectangular array. The numbers exist named the elements, or entries, of the matrix.

Thus the cofactors of each entry in the first row of the matrix exist

[tex]$$Ac_{11 }= -13[/tex]

[tex]Ac_{12} = 44[/tex]

[tex]Ac_{13} = 27[/tex]

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A lawn-mowing company is trying to grow its business. it had 30 clients when they started its business and wants to increase by 6 new clients each week. use an arithmetic sequence to write a function to represent this real-world situation and determine the range of the function for the first four weeks of data. f(x) = 6x 30; 0 ≤ y ≤ 4 f(x) = 6x 24; 0 ≤ y ≤ 4 f(x) = 6x 30; 30 ≤ y ≤ 48 f(x) = 6x 24; 30 ≤ y ≤ 48

Answers

The function to represent the problem is f(x)=6x+24 and the range is 30[tex]\leq[/tex]y[tex]\leq[/tex]48.

What is arithmetic sequence formula?

If the terms of a sequence differ by a constant, we say the sequence is arithmetic. If the initial term ([tex]a_{0}[/tex]) of the sequence is a and the common difference is d, then we have,

[tex]a_{n}[/tex]=a+(n-1)d

Initial number of clients=30

Number increase per week= 6

So, we can make an arithmetic sequence fir six weeks

30,36,42,48

Here, first term, a=30

Common difference, d=6

Range is [30,48]

The explicit formula of an arithmetic sequence is

[tex]a_{n}[/tex]=a+(n-1)d

Put a=30, d=6, n=x

[tex]a_{x}[/tex]=30+(x-1)6

[tex]a_{x}[/tex]=30+6x-6

[tex]a_{x}[/tex]=6x+24

Therefore, The function to represent the problem is f(x)=6x+24 and the range is 30<=y<=48

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which graph below shows the solutions for the linear inequality y>- 1/3x + 1

Answers

The graph that shows the solutions for the inequality, y > -1/3x + 1 is: C. Graph A.

How to Find the Graph of a Linear Inequality?

The inequality sign, ">" means that the graph of the inequality has a dashed line where the shaded part is above the boundary line and the boundary line is dashed or dotted. If "≥" is used, the boundary line would not be dashed or dotted and the shaded area would be above it.

On the other hand, "<" is used when the shaded area is below the boundary line and the boundary line is a dashed line. If "≤" was used, the boundary line won't be dashed or dotted, while the shaded area would be below the boundary line that is not dotted.

Given y > -1/3x + 1, the slope (m) = change in y / change in x is -1/3.

Graph A has a slope of -1/3 and the shaded part is above the boundary line.

Therefore, the graph that shows the solutions for y > -1/3x + 1 is: C. Graph A.

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Find a power series for the function, centered at c. g(x) = 4x x2 2x − 3 , c = 0

Answers

The power series for given function [tex]g(x)=\frac{4x}{(x-1)(x+3)}[/tex] is [tex]g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)[/tex]

For given question,

We have been given a function g(x) = 4x / (x² + 2x - 3)

We need to find a power series for the function, centered at c, for c = 0.

First we factorize the denominator of function g(x), we have:

[tex]\Rightarrow g(x)=\frac{4x}{(x-1)(x+3)}[/tex]

We can write g(x) as,

[tex]\Rightarrow g(x)=\frac{1}{x-1}+\frac{3}{x+3}\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1+\frac{x}{3} }\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1-(-\frac{x}{3} )}\\[/tex]

We know that, [tex]\frac{1}{1-x}=\sum{_{n=0}^\infty}~{x^n}[/tex] if |x| < 1

and [tex]\frac{1}{1-(-\frac{x}{3} )}=\sum{_{n=0}^\infty}~x^n(-\frac{x}{3} )^n[/tex]  if [tex]|\frac{x}{6}| < 1[/tex]

[tex]\Rightarrow g(x)=-\sum{_{n=0}^\infty}~x^n+\sum{_{n=0}^\infty}~x^n(-\frac{x}{3} )^n\\[/tex]     if |x| < 1 and  if [tex]|\frac{x}{6}| < 1[/tex]

[tex]\Rightarrow g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)[/tex] if |x| < 1

Therefore, the power series for given function [tex]g(x)=\frac{4x}{(x-1)(x+3)}[/tex] is [tex]g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)[/tex]

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Please solve the attachment which is given, and give me the answer. Thank you for your lovely time! <3

Answers

Answer:

1. 36 liters

2. 3 kg

Step-by-step explanation:

because 12 liters is 4kg if you multiply both by 3 you’ll get that 12 kg is equal to 36 liters


also, if you divide both by 4, you’ll see that 1kg is equal to 3 liters. Then with this knowledge, yiucc be an see that if you multiply both by 3; 3 kg will be 9 liters! :)

Answer:

1.) 36 litres

2.) 3 kg

Step-by-step explanation:

In this case there is a ratio of 1:3 of mass to volume.  If we know the mass, the volume is 3 times that.  If we know the volume, the mass is that divided by 3.

If the population standard deviation σ=25. What is the required minimum sample size to construct a 95 confidence level for the population mean with an allowable error of ±3?

Answers

The required minimum sample size to construct a 95% confidence level for the population mean is 267.

In this question,

In the probability and statistics theory, the confidence interval of the population parameter is the estimated range of values we are sure with a certainty that our parameter will lie within, the range being calculated from the sample obtained. The smaller is the margin of error, the more confidence we have in our results.

The population standard deviation, σ = 25

Confidence level for the population mean = 95%

Margin of error = ±3

Let n be the sample size of the population

The z-score for the confidence level of 95% for the population mean is 1.96.

The formula of margin of error is

[tex]E=\frac{z \sigma}{\sqrt{n} }[/tex]

Now, the sample size of the population can be calculated as

[tex]n=(\frac{z\sigma}{E} )^{2}[/tex]

On substituting the above values,

⇒ [tex]n=(\frac{(1.96)(25)}{3} )^{2}[/tex]

⇒ [tex]n=(\frac{49}{3}) ^{2}[/tex]

⇒ [tex]n=(16.33)^{2}[/tex]

⇒ n = 266.77 ≈ 267

Hence we can conclude that the required minimum sample size to construct a 95% confidence level for the population mean is 267.

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The percentage of the battery's capacity that is charged as a function of time (in minutes) is graphed.
A first quadrant coordinate plane. The horizontal axis is from zero to thirty-two-point-five with a scale of two point five and is titled Time in minutes. The vertical axis is from zero to one hundred with a scale of five and is titled Capacity, percent charged. The graph of the line is y equals two x plus forty. The graph ends at thirty minutes.
A first quadrant coordinate plane. The horizontal axis is from zero to thirty-two-point-five with a scale of two point five and is titled Time in minutes. The vertical axis is from zero to one hundred with a scale of five and is titled Capacity, percent charged. The graph of the line is y equals two x plus forty. The graph ends at thirty minutes.
At what rate is the battery charged?
Choose 1 answer:
Choose 1 answer:

(Choice A)
A
111 percent per minute

(Choice B)
B
202020 percent per minute

(Choice C)
C
101010 percent per minute

(Choice D)
D
222 percent per minute

Answers

The rate at which battery charges is 10 percent per minute.

According to the statement

we have given that the charging capacity of battery in the graphical representation.

And we from this we have to find the percentage by which battery charges.

And the graphical representation given is :

The horizontal axis is from zero to thirty-two-point-five with a scale of two point five and is titled Time in minutes. The vertical axis is from zero to one hundred with a scale of five and is titled Capacity, percent charged. The graph of the line is y equals two x plus forty. The graph ends at thirty minutes.

A first quadrant coordinate plane. The horizontal axis is from zero to thirty-two-point-five with a scale of two point five and is titled Time in minutes.

And according to this representation it is clear that the percentage by which battery charges is 10 percentage per minute.

So, The rate at which battery charges is 10 percent per minute.

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