the coefficient of x in the expansion of (a x)5 (1-2x)6, where a is positive, is 90. find the value of a.

Answers

Answer 1

In the given expansion ,the value of a = -4/3 .

Binomial Distribution:

The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments. Each asks a yes-no question and each has its own Boolean outcome: success (probability p) or failure (probability p) (probability q = 1-p.  A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a series of results is called a Bernoulli process. For one trial, n = 1, binomial distribution is Bernoulli distribution. The binomial distribution is the basis for the common binomial test of statistical significance.

In general, (A + B)⁵ = A⁵ + 5A⁴ᵇ + 10A²ᵇ*³ + 10A³ᵇ*² + 5AB⁴ + B⁵

So,

(3–2x)⁵= 3⁵ + 5*3⁴*(-2x) + 10* 3^3 *(-2x)^2 + 10*3^2*(-2x)^3 + 5*3*(-2x)^4 + (-2x)^5.

Multiplying that by (1 + ax) gives:

3^5 + 5*3^4*(-2x) + 10* 3^3 *(-2x)^2 + 10*3^2*(-2x)^3 + 5*3*(-2x)^4 + (-2x)^5 + ax(3^5 + 5*3^4*(-2x) + 10* 3^3 *(-2x)^2 + 10*3^2*(-2x)^3 + 5*3*(-2x)^4 + (-2x)^5).

In bold, we find the terms of x^2, so the coefficient of x^2 is 10*3^3*(-2)^2+a*5*3^4*(-2) = 360 - 810a

We know that this must equal 1440, so 360–810a = 1440.

Therefore a= -4/3.

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Related Questions

Help needed was not thought this

Answers

Answer:

Yes what is the question

Answer:

what is the question

Step-by-step explanation:

How do you solve an equation with 2 answers?

Answers

The quadratic formula x = [-b (b2 - 4ac)] / 2a] provides the solutions to the quadratic equation ax2 + bx + c = 0. (2a).

Given,

Equation with two answers are quadratic equations.

Quadratic equation;

The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x).

The solution for quadratic equation;

The quadratic formula x = [-b (b2 - 4ac)] / 2a]gives the solutions to the quadratic equation ax2 + bx + c = 0. (2a). Get the problem into standard form, ax2 + bx + c = 0, and then use the quadratic formula to solve the quadratic equation.

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I need help pleaseee

Answers

Answer: 1/10th

Step-by-step explanation:

20 different lengths, 2 are 21.5 = 2/20 reduce to 1/10 so 10%

30.9 divided by 100

PLEASE I NEED HELP ASAP

Answers

Answer:

0.309

Step-by-step explanation:

There are about 2.54 centimeters in 1 inch. if a segment is 2.7 centimeters long, how many inches is it, rounded to the nearest hundredth?

Answers

The number of inches made by a segment of 2.7 centimeters long, where 1 inch is 2.54 centimeters is 236 inches.

What is the symbol for an inch?

Please also notice that the sign for inches is the double prime ("), not the double quotation mark, the straight quotation mark, or even (gasp!) the two consecutive single quotation marks (").

What exactly is 1 inch?

The inch was defined as "three dry, spherical grains of barley set end to end lengthwise" during the early 14th century under King Edward II. The lengths of 12 poppy seeds together have also been used at various periods to define one inch. Since 1959, 2.54 cm has been the official definition of an inch.

From the above definition, we get that

The number of inches made by a segment of 2.7 centimeters long, where 1 inch is 2.54 centimeters is 236 inches.

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What is the measure of one of the central angles in the regular Pentagon What is the measure of one of the congruent base angles in triangle ABC?

Answers

The measure of one of the central angles of a regular pentagon is 72° .

In the question ,

a regular pentagon is given ,

we have to find the measure of one of central angle ,

we know that a pentagon has 5 equal sides .

and the sum of the central angles is 360° .

it is given that the pentagon is regular , So , all the central angles are equal in measure .

The central angle can be calculated using the formula ,

central angle = 360°/n , where n is number of sides .

substituting the value of number of sides as = 5 ,

we get ,

central angle = 360°/5 = 72° .

Therefore , the central angle is = 72°  .

The given question is incomplete , the complete question is

What is the measure of one of the central angles in the regular Pentagon ?

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a school show had ticket sales of $1345 the first night and $935 the second night. 180 student tickets were sold and 110 adult tickets were sold on the first night. 100 student tickets were sold and 90 adult tickets were sold. find the price of a student ticket.: * a) $5.75 b) $8.75 c) $6.50 d) $3.50 e) $7.50

Answers

A school show had sold the ticket sales of first and second nights. The price of a student ticket is $3.54, a So, the correct answer is option (d).

Total sale on tickets at the first night = $1345

Total sale on tickets at the second night = $935

Let the price of student ticket and adult ticket in school show be "$x" and "$y" respectively. According to problem,

On first night total sale,

180x + 110y = $1345 --(1)

On Second night total sale,

100x + 90y = $935 --(2)

we have to determine the price of student ticket i.e x and price of adult ticket i.e y .. We have a system of linear equation which consists two equations (1) and (2) . Now, we solve these equations using Substitution method,

From equation (2), 100x = 935 - 90y

=> x = (935 - 90y )/100 --(*)

Substitute the value of x in equation (1) 180x + 110y = $1345

=> 180(935 - 90y )/100 + 110y = 1345

Simplify ..

=> 168120 - 16200y + 11000y = 134500

=> 168120 - 134500 = 16200y - 11000y

=> 33620 = 5200y

=> y = 33620/5200

=> y = 6.46

put the value of y in equation (*) we get,

x = (935 - 90× 6.46)/100 = 3.536

Hence, the value of x is $3.536 and value of y is $6.46..

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How do you dilate an image with a scale factor?

Answers

To dilate an image with a scale factor, multiply the scale factor with the dimensions of the image

The dilation is the process of changing the size of the given shape or figure ,the shape of the figure will be always same. Therefore dilation is one form transformation of shapes

The scale factor is the ratio of the measurement of the new shape to the measurement of the original shape.

We can use the scale factor for the dilation

To get the dilate and image with scale factor, we have to multiply the scale factor with the measurement of the original shape

The equation will be

The dimension after dilation = scale factor × original dimensions

Therefore, to dilate an image, multiply the scale factor and the original dimensions

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Help with question 3

Answers

Answer:

3.75

Step-by-step explanation:

I BELIVE YOUR ANSWER IS 3.75

Answer:

3.75

Step-by-step explanation:

Pedro has a balance of $5810 on a credit card with an APR of 16.2%. Paying
off his balance in which of these lengths of time will result in him paying the
least amount of interest?
O 1 Month
2 Months
3 Months
4 Months

Answers

The least amount of interest, if Pedro has a balance of $5810 on a credit card with an APR of 16.2%, is $78.345 for one month, so option A is correct.

What is interest?

When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.

Given:

Pedro has a balance of $5810 on a credit card with an APR of 16.2%,

Calculate the simple interest for one month as shown below,

[tex]SI = P \times r \times t / 100[/tex]

SI = 5810 × 16. 2 × 1 / (12 ×100)   [time in year = 1 / 12]

SI = $78.345

SI =  5810 × 16. 2 × 2 / (12 ×100)   [For 2 months]

SI = $156.87

Therefore, the least amount of interest, if Pedro has a balance of $5810 on a credit card with an APR of 16.2%, is $78.345 for one month.

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9(-2)


Help I don't get it :'(

Answers

So, let's think about what it's asking

it next to the parentheses means to distribute, or multiply into.

Multiply 9 * -2

A negative times a positive is a negative.

9 * 2 = 9 + 9 = 18

Make the final answer negative because its a positive and a negative multiplied.  A positive and a positive multiplied gives you a positive.  A negative and a negative multiplied gives you a positive too.

-18

Write an equation in​ slope-intercept form of the line.
(Use integers or fractions for any numbers in the​ equation.)

Answers

Answer:

[tex]y=-\frac{1}{2} x+5[/tex]

Solve for ttt:
-18 = -3t−18=−3t

Answers

Answer: 4z

Step-by-step explanation:

Consider the following table. Is the relationship proportional? Explain your answer.
y
-27
12
57
147
-2
1
4
10

Answers

Answer:

The relationship shown in the table is not proportional. A proportional relationship is one in which the ratio of two quantities is always constant. In the table, we can see that the ratio of the values in the y column to the corresponding values in the x column is not constant. For example, the first two values in the y column are -27 and 12, which have a ratio of -27/1 and 12/2, respectively. These ratios are not equal, which indicates that the relationship is not proportional.

Furthermore, if the relationship were proportional, we would expect the values in the y column to increase at a consistent rate as the values in the x column increase. However, this is not the case in the table. For example, the first two values in the x column are 1 and 2, and the corresponding values in the y column are -27 and 12. The difference between these values is -27 - 12 = -39, which is a large negative value. However, the difference between the next two values in the y column is 57 - 147 = -90, which is a much larger negative value. This indicates that the relationship is not proportional, because the differences between the y values do not increase at a consistent rate as the x values increase.

Step-by-step explanation:

PLEASE HELP MEEEEEEE, GIVING 30 POINTS IF YOU SOLVE (MY THRID TIME REPOSTING THIS)


A rental car company charges $40.50 per day to rent a car and $0.15 for every mile driven. Elizabeth wants to rent a car, knowing that:

She plans to drive 125 miles.

She has at most $210 to spend.


Write and solve an inequality which can be used to determine x, the number of days Elizabeth can afford to rent while staying within her budget.

Answers

Answer: 4 days, more below

Step-by-step explanation:

40.50x + 0.15y < 210

(0.15)(125)=18.75

40.50x + 18.75 < 210

40.50x < 191.25

x < 4.7222222...

She can afford to rent the car for 4 days if she drives 125 miles and has 210$ to spend.

What is the slope of the line that passes through the points (2, -4) and (5, 2)? Write
your answer in simplest form.

Answers

Answer:

used formula

Step-by-step explanation:

y-y1=m(x-x1)

Which function is used to calculate maximum value?

Answers

Derivatives is used to calculate the maximum value of a function.

We will set the first derivative of the function to zero and solve for x to get the critical point. If we take the second derivative or f''(x), then we can find out whether this point will be a maximum or minimum. If the second derivative is positive, it will be a minimum value.

Derivatives

The rate of change of a function with respect to a variable. Derivatives are fundamental to the solution of problems in calculus and differential equations.

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c(1) = -20

c(n) = c(n − 1) + 10
Find the 2nd term in the sequence.

Answers

Answer:

-10

Step-by-step explanation:

So we are going to find c(2)

c(2)=c(1)+10

c(2)=-20+10

c(2)=-10

1. In the figure below, segments LJ and A F are perpendicular. What is the value of x+y?

2. In the figure below, LJ is perpendicular-bisector of A F. What is the value of m + n?

Answers

1) The value of the expression x + y is; 30

2) The value of the expression m + n is; 16

How to solve Algebraic Expressions?

1) We are told that segments LJ and A F are perpendicular. This means that; 4x + 50 = 90 and 7y - 50 = 90

Let us solve for x and y;

4x + 50 = 90

4x = 90 - 50

4x = 40

x = 10

Similarly;

7y - 50 = 90

7y = 90 + 50

7y = 140

y = 140/7

y = 20

Thus;

x + y = 10 + 20

x + y = 30

2) We are told that LJ is a perpendicular-bisector of A F. Thus;

AJ = FJ and AL = FL

Thus;

FL = AL gives;

3m = 42

m = 42/3

m = 14

Similarly;

2m + 3n = 34

2(14) + 3n = 34

28 + 3n = 34

3n = 6

n = 2

m + n = 14 + 2 = 16

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How do you split a sentence into two simple sentences?

Answers

To split a sentence into two simple sentences, first, highlight the clauses while dividing sentences. When necessary, add subjects or other words in place of subordinating liners to make sub-clauses autonomous.

In the given question we have to explain how we split a sentence into two simple sentences.

As we know that;

A basic sentence typically consists of a subject, a verb, and maybe an object and modifiers. It only has one independent clause, though. Here are a few illustrations: She composed.

First, highlight the clauses while dividing sentences. When necessary, add subjects or other words in place of subordinating liners to make sub-clauses autonomous.

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Why is area in square units?

Answers

The number of unit squares needed to completely cover a shape is its area. As a result, it is expressed and measured in square units.

The word "area" refers to a free space. The area of a thing is the amount of space it occupies in two dimensions. A closed figure's surface area is calculated by counting how many unit squares completely encircle the surface. The square unit is frequently expressed as square inches, square feet, etc., and is the accepted unit of area.

Consider, there are several squares with sides that are 1 unit by 1 unit wide in the grid. The surface area of each square is one square unit. Each square is a unit square. As a result, the area is stated and measured in square units.

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1) x-2y=15
2) x-3=4y
A) rearrange equation (2) to make x the ubject
B) uing your anwer to part a) olve the imultaneou equation uing ubtitution

Answers

x= -9 and y= -3

What is equation?

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about math equations.

A)  rearranging equation (2) to make x the subject

[tex]x-3=4y\\x-4y=3[/tex]

Also,

[tex]4y=x-3\\y=(x-3)/4[/tex]

by subtitution method

putting this value of y in equation 1)

[tex]x-2((x-3)/4)=15\\\\x-2x+6=15\\x=-9\\y=(-9-3)/4\\y=-3[/tex]

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I need help with question number 10 the question says Ash has 61 toothpicks but do I keep increasing by 1 until I get 61?

Answers

The largest figure that Ash can built with 61 toothpicks is of:

A composition of 12 hexagons.

How to obtain the largest figure?

The number of toothpicks needed is modeled with a linear function, defined as follows:

y = mx + b.

The coefficients of the function are given as follows:

m is the slope, representing the number of toothpicks per new figure.b is the y-intercept, representing the number of toothpicks of the first figure.

The number of toothpicks in each figure is represented by the following sequence:

(6, 11, 16, ...).

Hence the parameters are given as follows:

m = 5, b = 6.

Thus the definition of the function is of:

T(n) = 5(n - 1) + 6. (as the first figure is with n = 1).

T(n) = 5n + 1.

Then the number of hexagons with 61 toothpicks is obtained as follows:

5n + 1 = 61

5n = 60

n = 60/5

n = 12 hexagons.

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H(t)= 50- t/5

H(35)=
Please explain it

Answers

The value of the function H(t) = 50 - t / 5 at t = 35 will be 43.

What is a function?

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

H(t) = 50 - t / 5

At t = 35, the value of the function will be given as,

H(35) = 50 - 35 / 5

H(35) = 50 - 7

H(35) = 43

The value of the function H(t) = 50 - t / 5 at t = 35 will be 43.

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a certain star is 3.6 x 10^2 light years from the earth. one light year is about 5.9 x 10^12 miles how far from the earth in miles is the star

Answers

The earth is 21.24 x 10¹⁴ miles far from the star.

What are the light years?

A light-year is a significant length measure that is used to express astronomical distances. It is around 9.46 trillion kilometers, or 5.88 trillion miles, in length.

We have given,

1 light year = 5.9 x 10¹² miles

Distance of the star =  3.6 x 10² light years

To get this we just convert the distance of the star in light years into miles.

3.6 x 10² light years x( 5.9 x 10¹² miles/1 light years)

We cancel out the lightyears and then we are left with:

3.6 x 10² light years x 5.9 x 10¹² miles

In dealing with scientific notation, when we multiply them we can treat the coefficients and exponents of 10 separately.

Coefficients:

3.6 x 5.9 = 21.24

Exponents of 10:

10² x 10¹² = 10⁽²⁺¹²⁾ = 10¹⁴

Then we combine them again to form:

21.24 x 10¹⁴ miles

Hence, the earth is 21.24 x 10¹⁴ miles far from the star.

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Which graph represents y=^3square root x

Answers

Answer is shown down below please rate it if it’s right. Thanks

to calculate the expected risk premium on a stock, one must subtract the ________ from the stock’s expected return.

Answers

To calculate the expected risk premium on a stock, one must subtract the Inflation rate from the stock’s expected return.

How to complete the blank in the statement?

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

Expected risk premiumStock's expected return

Mathematically, the relationship between the expected risk premium and the stock's expected return is represented as follows

Expected risk premium = Stock's expected return - Inflation rate

This means that the Inflation rate must be subtracted from the stock’s expected return to calculate the expected risk premium

Hence, the statement that completes the blank is Inflation rate.

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You plug your phone in to charge. After 10 mins your phone is at 30%. If your phone is charging at a rate of 5% every 2 minutes, write an equation in point slope form representing the battery percent,y, after x minutes.

Answers

y-5=3(x-2) is the equation in point slope form representing the battery percent, y, after x minutes.

What is Slope of Line?

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

After 10 mins your phone is at 30%.

If your phone is charging at a rate of 5% every 2 minutes,

4 minutes=10%

6 minutes=15%

8 minutes=20%

10 minutes=25 %

The equation of point slope form.

y-5=3(x-2)

Hence, y-5=3(x-2) is the equation in point slope form representing the battery percent, y, after x minutes.

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Which equation repreent the line that pae through the point (2, -8) and (-3, 2)?

Answers

The Equation represent the line that passes through the points  (2, -8) and (-3, 2) is 2x + y + 4 = 0

Two point form is one of the important forms used to represent a straight line algebraically. The equation of a line represents each and every point on the line, i.e., it is satisfied by each point on the line.

The two point formula is used to represent a line algebraically using the coordinates of two points that lie on that line. The formula for two point form can be given as:

(y - y1) = m(x-x1) -----------(1)

where , m is slope of line given by => y2-y1/ x2 - x1

(x, y) is an arbitrary point on the line.

(x1, y1) and (x2 , y2) are coordinates of points lying on the line.

According to the question,

The required line passes through (2,-8) and (-3,2)

Slope : m = 2 - (-8) / -3 -2

=> m = 2+8/-5

=> m = 10/-5

=> m = -2

Substituting the values in equation (1)

(y - (-8)) = -2(x-2)

Solving,

=> y + 8 = -2x + 4

=> 2x + y + 4 = 0 is required equation of line

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Which president proposed the creation of the Environmental Protection Agency ?

Answers

President Richard Nixon proposed the creation of The Environmental Protection Agency (EPA).

What is the Environmental Protection Agency?

The Environmental Protection Agency is an independent government agency of the United States, which was considered mandatory by the government for environmental issues.

The Agency followed a series of measures to improve air quality, decrease greenhouse gas emissions, forbid water pollution, and invest in oil spill control measures.

The EPA had many obligations in the United States, two of which were to set industry standards to reduce their impact on the environment and investigate air pollution.

How did the EPA launch?

The operation of the agency began on December 2, 1970, after President Nixon had signed an executive order. The order established by the EPA was made official by signing by the committee hearings in the House and Senate.

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