How do you do 3 terms in binomial expansion?

Answer:

[tex]b=\dfrac{2V}{ah}-c[/tex]

Step-by-step explanation:

Given equation:

[tex]V=\dfrac{1}{2}a(b+c)h[/tex]

Multiply both sides of the equation by 2:

[tex]\implies 2 \cdot V=2 \cdot \dfrac{1}{2}a(b+c)h[/tex]

[tex]\implies 2V=a(b+c)h[/tex]

Divide both sides by ah:

[tex]\implies \dfrac{2V}{ah}=\dfrac{a(b+c)h}{ah}[/tex]

[tex]\implies \dfrac{2V}{ah}=b+c[/tex]

Subtract c from both sides:

[tex]\implies \dfrac{2V}{ah}-c=b+c-c[/tex]

[tex]\implies \dfrac{2V}{ah}-c=b[/tex]

Therefore:

[tex]\implies b=\dfrac{2V}{ah}-c[/tex]

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

A score that is 3 standard deviations above the mean is consider as a very high score relative to the rest of the scores in the population.

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

The sum of all values divided by the total number of values determines the mean  of a dataset.

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The given data is 24,26,23,26,22,25,26,28

There are the following values as shown in the given data.

To find the mode first we have to assign each value that how many times it appears.

1. 24-1 the number 24 appears only 1 time.

2. 26-3 the number 26 appears three times.

3. 23-1 the number 23 appears only one time.

4. 22-1 the number 22 appears only one time.

5. 25-1 the number 25 appears only one time.

6. 28-1 the number 28 appears only one time.

So, the mode of the given data is 26 as it appears the most number of times.

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The volume of a pyramid that has the same base and height if a prism has a volume of 45 m cube is 15 cu. m.

In this question we have been given the volume of a prism which is of 45 m cube.

we need to find the volume of a pyramid that has the same base and height.

We know that the formula of the volume of prism is:

V = base area * height of prism  

From given, V = 45 m^3

But as we know prism and pyramid have same base area and height.

We know that the formula for the volume of pyramid.

volume of pyramid = 1/3 * base area * height

volume of pyramid = 1/3 * V

volume of pyramid = 1/3 * 45

volume of pyramid = 15 cubic meter

Therefore, the volume of pyramid is 15 m^3

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Step-by-step explanation:

To find this algebraic phrase, we need to use the rules of algebra to express the given statement in mathematical notation. The given statement says that the sum of three times the opposite of a number and -7 is some unknown value.

We can start by expressing the opposite of a number in mathematical notation. The opposite of a number is equal to the number multiplied by -1. So, we can write the opposite of a number as -x.

Next, we can express the fact that the opposite of a number is being multiplied by 3. To do this, we can simply write 3(-x) to represent three times the opposite of a number.

Finally, we can express the fact that -7 is being added to the result. To do this, we can simply write 3(-x) - 7 to represent the sum of three times the opposite of a number and -7.

Therefore, the algebraic phrase for the sum of three times the opposite of a number and -7 is 3(-x) - 7.

The average savings per year in the last five years is 29,814.40 Option D

Generally, Average savings refers to the amount of money that a person or household has saved over a particular period of time, divided by the number of months or years in that period.

It is a measure of the average amount of money that is saved each month or year. The average savings rate can vary widely depending on a person's income, expenses, and financial goals. Some people may have very high average savings rates, while others may have very low average savings rates.

To estimate the average savings per year in the last five years, you need to add up the amounts saved in those years and divide by the number of years.

The amounts saved in the last five years are $70,453, $87,977, $54,718, $40,684, and $28,270, for a total of $291,182.

Dividing this by 5 gives an average of $58,236.40 per year, so the answer is 29,814.40 Option D

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Preview how to add two-digit numbers to refresh our memory before we look at how to add two numbers with four or more digits.

One result, known as the sum, is produced when two or more integers are added together. It is advisable to arrange two or more integers vertically while adding them, making sure that the digits with the same place value are in the same column. Every one of the ones should be in its own column, followed by every ten in its own column, and so on.

here ,

As you align the place value columns, write the numbers directly above one another.

From the right to the left, add the numbers in each column.

Fill in the space provided beneath each column of digits with the solution to each addition.

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It is formed by simply drawing lines connecting the data points. Also called linear chart.

A line chart is a graphical representation of changes that occur over a period of time. A line chart has a horizontal axis called the x-axis and a vertical axis called the y-axis. The x-axis usually has a period of time over which we want to measure the quantity of a particular thing or item on the y-axis. Line charts are useful for analyzing trends, whether the quantity on the y-axis is increasing or decreasing over time. A line chart clearly shows an uptrend or a downtrend.

The line chart above represents bike sales by bike company from January to June, with the x-axis representing the time interval and the y-axis representing the number of bikes sold per month. Black dots in the graph indicate data points. A data point in a line chart represents the magnitude or number corresponding to a specific time on the x-axis. In this example, 50 bikes were sold in January. 30 bikes were also sold in February. This data can be interpreted by month using data points. Line segments connecting these individual data points show whether bike sales are trending upwards or downwards.

The key points of line charts are:

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Answer:

Step-by-step explanation:(t-by)(4t+3by)

The first term in the first bracket is multiplied by the last bracket

t(4t+3by)=4t^2+3bty

The second term in the first bracket is multiplied by the last bracket

-by(4t+3by)=-4bty-3b^2y^2

Add the results together and simplify where possible

4t^2+3bty-4bty-3b^2y^2=4t^2-bty-3b^2y^2

In Euclidean geometry, parallel lines (lines that never intersect) are equidistant in the sense that the distance of any point on one line from the nearest point on the other line is the same for all points.

In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet. They can be both horizontal and vertical. We can see parallel lines examples in our daily life like a zebra crossing, the lines of notebooks, and on railway tracks around us.

There are 3 main rules:

Corresponding angles are equal. A line cutting across two parallel lines creates four pairs of equal corresponding angles, as in the diagram below.

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Answer:

d = 18

Step-by-step explanation:

d = square root (x2 -  x1)^2 + (y2 - y1)^2

Point A ( -1,2) Point B (1,-2)

Now let's put the number in

d = square root ( 1 -(-1)^2 + (-2 - 2)^2

Now let's get rid of the square root, and we have

(1-(-1) + (-2 -2)^2

2 + (-4)^2

2 + 16

18

So, the distance AB = 18

Answer:

[tex]AB = 4.5[/tex]

Step-by-step explanation:

⭐To find the distance between two points, you can use the distance formula: [tex]d = \sqrt{(x_2-x_1)^2 +(y_2 - y_1)^2}[/tex], where:

First, identify the coordinates you need to find the distance between, and label one coordinate as [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex].

Next, substitute [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] into the distance formula.

[tex]d = \sqrt{(1-(-1))^2+(-2-2)^2}[/tex]

[tex]d = \sqrt{(1+1)^2+(-4)^2}[/tex]

[tex]d = \sqrt{2^2+(-4)^2}[/tex]

[tex]d = \sqrt{4+16}[/tex]

[tex]d = \sqrt{20}[/tex]

∴ d ≈ 4.5

it is always important to carefully evaluate the assumptions of the model and confirm that it is an appropriate fit for the data.

What is Explanatory Variables?

A researcher-manipulated variable is an explanatory variable when it comes to an experiment. It serves as a measurement of the change brought about in the response variable. A predictor variable or an independent variable are terms that are frequently used to describe an explanatory variable.

It is not possible to determine whether a Poisson regression model would be a good choice for any of the explanatory variables without further information.

To determine whether a Poisson regression model is a good fit for the data, you will need to consider the following:

The relationship between the response variable (i.e., the observed species counts) and the explanatory variables should be modeled using a linear relationship. This can be visually assessed by creating scatterplots of the logged response variable against each of the explanatory variables and examining the pattern of the points. If the points form a roughly linear pattern, then a Poisson regression model may be appropriate.

The response variable should follow a Poisson distribution. This can be assessed by examining the distribution of the logged response variable using a histogram or a Q-Q plot. If the distribution is approximately symmetrical and has a single peak, then a Poisson regression model may be appropriate.

The residuals (i.e., the difference between the observed and predicted values) of the model should be approximately normally distributed with a mean of zero. This can be assessed by creating a plot of the residuals against the fitted values and examining the pattern of the points. If the points form a roughly random pattern centered around zero, then the model is likely to be a good fit.

If all of these conditions are met, then a Poisson regression model may be a good choice for modeling the relationship between the response variable and the explanatory variables.

However, it is always important to carefully evaluate the assumptions of the model and confirm that it is an appropriate fit for the data.

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  Answer: [tex]9x^{2} -6x^{2} y+y^{2}[/tex]

  Step-by-step explanation:

Applying the perfect square formula:[tex](a-b)^{2} = a^{2}- 2ab+ b^{2}[/tex]

[tex](3x^2- y)^2= (3x^2)^2- 2*3x^2*y+ y^2[/tex]

Simplifying this further, we get:

[tex]9x^2- 6x^2y+y^2[/tex]

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The unit conversion from celsius to fahrenheit is given by the formula

F = (9/5)C + 32.

The same attribute is expressed using a unit conversion but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometers, feet, or any other measurement unit instead of miles.

We know we can convert temperatures from celsius to fahrenheite or from fahrenheite to celsius.

The conversion of celsius to fahrenheit is given by the formula,

C = (5/9)(F - 32).

Now, we have to solve for F.

C = (5/9)F - (160/9).

Now to get rid of the fraction we'll multiply 9 to each term.

9C = 5F - 160.

5F = 9C + 160.

Solving for F we have,

F = (9/5)C + 32.

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The equation for adding "n" numbers in a row is [a + (a + 1) + (a + 2) +.... a + (n-1)]. As a result, (n/2) (first number + last number) is the sum of "n" consecutive numbers or "n" terms of AP (Arithmetic Progression). The formula for even consecutive numbers is 2n, 2n+2, 2n+4, 2n+6, and so on.

The next two odd consecutive integers are (2n + 3) and (2n + 5) if 2n + 1 is an odd number. For illustration, assume that 2n + 1 is the odd number 7. Its successive numbers are identified as (7 + 2) and (7 + 4), or 9 and 11. Consecutive odd numbers are odd integers that are separated by 2 and come after one another. If the number x is odd, then the numbers x + 2, x + 4, and x + 6 are also odd.

Any collection of consecutive odd numbers starting with 1 has a sum that is always equal to the square of the total number of digits. If the numbers 1, 3, 5, 7, 9, 11,..., and (2n-1) are odd, then the sum of the first odd number is 1. First two odd numbers added together equal 1 + 3 = 4 (4 = 2 x 2). Two successive odd numbers added together are always divisible by 4.

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As the data are given in the question [tex]x^{2}+7[/tex],

It is a quadratic equation because it has a degree of 2.

The standard form of a quadratic equation is expressed as, ax² + bx + c = 0, where

x represents an unknown (variable)

a, b, and c represent known numbers, where a ≠ 0

The values of x that satisfy the equation are called solutions of the equation, and roots or zeros of the expression on its left-hand side.

The given equation has a = 1, b = 0, and c = 7. Therefore, all the values are there in the form of the standard equation, so it is a quadratic equation.

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Question - How is [tex]x^2+7[/tex] a quadratic equation?

A. From the Limit Comparison Test, the series converges conditionally.

The Limit Comparison Test can be used to determine whether a given series converges or diverges. In this case, the given series is sigma^infinity_k = 0 9(-1)^k/k^4 + 2.

To use the Limit Comparison Test, we need to compare the given series to a known series. For example, we can compare it to the series sigma^infinity_k = 1/k^4.

We can then calculate the ratio of the two series:

sigma^infinity_k = 0 9(-1)^k/k^4 + 2

sigma^infinity_k = 1/k^4

Ratio: sigma^infinity_k = 0 9(-1)^k / (1/k^4)

Since the limit of the ratio of two series is a finite number, the given series converges. However, since the ratio is not 1, it converges conditionally, not absolutely.

Therefore, the answer is A - From the Limit Comparison Test, the series converges conditionally.

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(a) When r = 12, then the value of M would be M = 504.

(b) When M = 224, then the value of r would be r = 64.

What is a direct variation?

The relationship between two values where their ratio equals a constant number is known as a direct proportion or direct variation.

In the given question, M is directly proportional to r²

M ∝ r²

M = kr²

Now When r = 2, M = 14,

k = 14/(2)²

k = 7/2

(a) When r = 12,

   M = (7/2)(12)² = (7/2)*144 = 72 * 7

  M = 504

(b)When M = 224,

  224 = (7/2)r² = (224*2)/7 = 32 * 2

  M = 64

Hence,

(a) When r = 12, then the value of M would be M = 504.

(b) When M = 224, then the value of r would be r = 64.

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The probability that the ticket holds the winning numbers is given as follows:

1/29,322,216.

A probability is calculated by the division of the number of desired outcomes by the number of total outcomes.

For the Megaball, we have that you pick one from a set of 27, hence the probability is given as follows:

p = 1/27.

For the Winnerball, you must pick the correct combination of 5 numbers from a set of 44.

Applying the combination formula, the number of combinations of 5 numbers from a set of 44 is given as follows:

C(44,5) = 44!/(5! x 39!) = 1,086,008.

Then the probability of getting the correct combination is given as follows:

p = 1/1,086,008

The probability of a ticket holding the winning numbers is given as follows:

p = 1/27 x 1/1,086,008 = 1/29,322,216.

The complete problem is given as follows:

The lottery in our state consists of two drawings. First, a MegaBall is picked from among 27 numbered balls. Second, five WinnerBalls are picked from among 44 numbered balls. To win the lottery, you must pick the MegaBall number correctly and also pick the numbers on the five WinnerBalls (but you don't need to get the order right for the WinnerBalls). What is the probability that the ticket I hold has the winning numbers?

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Answer:

so to mu calculation I prideict your answer is 10

Answer:

1/3

Step-by-step explanation:

There are 12 students in total and 4 liked Midsummer Night's Dream

Therefore 4 out of the 12 students like the play the best which can be represented in a fraction

4/12 - When you represent this as a fraction, it is also the probality, when randomly selected, a Shakespeare student likes the play the best.

This probability can then be simplified by dividing the denominator and numerator by 4

4/4 = 1 and 12/4 = 3

So, the answer is 1/3

The polynomial p(x) must have at least two zeros.

A polynomial p(x) can have a maximum, minimum, or neither at any given point. The number of zeros of p(x) is equal to the number of positive and negative changes in the sign of the coefficients of the polynomial.

Since p(1) has a relative maximum at (-20), a relative minimum at (13) and a relative maximum at (57), there must be at least two changes in the sign of the coefficients. Therefore, the polynomial p(x) must have at least two zeros.

To determine how many zeros the polynomial has, we will need to calculate the sign of the coefficients at each point. For example, if the coefficient of x2 is positive at x = -20, but negative at x = 13, then we know that the polynomial has one zero between -20 and 13. We can use this method to determine the number of zeros of p(x).

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C. The amount he gained each month in order from least to greatest is One-eighth, 0. 75, two-fifth, tart fraction 5 over 6 end fraction.

Sam recorded how many pounds he gained each month for four months and recorded. First, we need to convert the fractions into decimals. One-eighth is equal to 0.125, two-fifth is equal to 0.4, and the tart fraction 5 over 6 end fraction is equal to 0.833.

Therefore, the amounts gained each month in order from least to greatest are 0.125, 0.75, 0.4, and 0.833.4. The correct answer is C. One-eighth, 0. 75, two-fifth, tart fraction 5 over 6 end fraction.

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The sum of the two linear expressions with only terms will be zero when the equations are x + y = a and x - y = -a.

A set of variables called an equation is one in which two mathematical expressions are equivalent to one another.

Let two linear equations are,

x + y = a

and x - y = b

The sum of the equations,

x + y + x - y = a + b

2x = a + b

x = (a + b)/2

The value of the x should be 0,

(a + b)/2 = 0

a + b = 0

a = - b

To get the sum of linear expressions with only x term, be zero, the coefficient of the linear equations should be equal and with negative sign.

The required linear equations are,

x + y = a

and x - y = -a

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From the conditions provided and solving the equation using the variables of the question, The number of chicken wings is 6 and mozzarella sticks is 8.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

The methods used for solving equations are:

x= number of chicken wings

x+2 = number of mozzarella sticks

60x+ 90(x+2) = 1080

150x+180=1080

150x=1080-180

x=900/150

x=6

x+2 = 8

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Answer:

x = 3 and JL = 18

Step-by-step explanation:

JN and NL are equal to each other so set both equations equal to each other
15 - 2x = 4x - 3

solve for x by moving terms to other side

x = 3

plug in 3 for x in JN's equation

JN = 15 - 2(3)

JN = 9

Since JN and NL are equal to each other, JL is just the sum of those two lengths combined

so all you have to do is double JN

9 x 2

is 18

so JL is 18

Answer:

10$

Step-by-step explanation:

Because if you divide you get 10$ per hour so if you divide 50 by 5 = 10 so your answer is 10$.

Hope this helps :D

The combinations of partial quotients that can be used to find the quotient of 84÷4 are given as follows:

What is the partial quotient method?

when a division is done applying the partial quotient method, consecutive subtractions are done with n groups of the divisor. Each partial quotient is the number of groups of each term and the final quotient is the sum of the partial quotients.

The final quotient of 84÷4 as follows:

84÷4 =21

hence the sum of quotients is 21.

The possible combinations are only two.

The other combinations are incorrect.