common difference -34,-44,-54,-64, -74

Algebraic expressions are given. It is required to tell if they are polynomials, tell how many terms they have, and give reasons if they are not a polynomial.

Recall that polynomials are a monomial or a sum of monomials.

Recall also that monomials are a number, a variable, or a product of numbers and variables with whole-number exponents.

Notice that this satisfies the definition of a polynomial.

Hence, it is a polynomial and it has 3 terms.

Notice that this satisfies the definition of a polynomial.

Hence, it is a polynomial and it has 2 terms.

Notice that this expression does not satisfy the definition of a polynomial as it has a monomial with a negative number exponent variable, which is not a whole number.

Hence, it is not a polynomial, it has a term that has a variable with a negative exponent.

This is a polynomial with just 1 term.

This satisfies the definition of a polynomial.

Hence, it is a polynomial and it has 2 terms.

This also satisfies the definition of a polynomial as it only has monomials with variables of whole-number exponents.

Hence, it is a polynomial and it has 3 terms.

It is not a polynomial, it has a term that has a variable with a negative exponent.

This also satisfies the definition of a polynomial as it only has monomials with variables of whole-number exponents.

Hence, it is a polynomial and it has 4 terms.

This also satisfies the definition of a polynomial as it only has monomials with variables of whole-number exponents.

Hence, it is a polynomial and it has 3 terms.

The solution of the linear system using the Gauss-Jordan elimination method is x = 2, y = -3, z = -1.

To solve the system, we can start by representing the given equations in augmented matrix form:

| 1 1 -1 | 5 |

| 3 -1 1 | -9 |

| 1 0 4 | 3 |

Next, we'll perform row operations to transform the matrix into row-echelon form. The goal is to create zeros below the leading coefficient in each row. We'll achieve this by multiplying rows by appropriate factors and adding or subtracting them from other rows. The steps involved in performing the Gauss-Jordan elimination method are as follows:

Step 1: Multiply the first row by 3 and subtract it from the second row to eliminate the x-term below the leading coefficient in the second equation.

| 1 1 -1 | 5 |

| 0 -4 4 | -24 |

| 1 0 4 | 3 |

Step 2: Multiply the first row by 1 and subtract it from the third row to eliminate the x-term below the leading coefficient in the third equation.

| 1 1 -1 | 5 |

| 0 -4 4 | -24 |

| 0 -1 5 | -2 |

Step 3: Multiply the second row by -1/4 to make the leading coefficient of the second equation equal to 1.

| 1 1 -1 | 5 |

| 0 1 -1 | 6 |

| 0 -1 5 | -2 |

Step 4: Multiply the second row by 1 and add it to the first row to eliminate the y-term below the leading coefficient in the first equation.

| 1 0 -2 | 11 |

| 0 1 -1 | 6 |

| 0 -1 5 | -2 |

Step 5: Multiply the second row by 1 and add it to the third row to eliminate the y-term below the leading coefficient in the third equation.

| 1 0 -2 | 11 |

| 0 1 -1 | 6 |

| 0 0 4 | 4 |

Step 6: Multiply the third row by 1/4 to make the leading coefficient of the third equation equal to 1.

| 1 0 -2 | 11 |

| 0 1 -1 | 6 |

| 0 0 1 | 1 |

Step 7: Multiply the third row by 2 and add it to the first row to eliminate the z-term above the leading coefficient in the first equation.

| 1 0 0 | 13 |

| 0 1 -1 | 6 |

| 0 0 1 | 1 |

Step 8: Multiply the third row by -1 and add it to the second row to eliminate the z-term above the leading coefficient in the second equation.

| 1 0 0 | 13 |

| 0 1 0 | 7 |

| 0 0 1 | 1 |

The resulting matrix represents the row-echelon form of the system. Now, we'll perform back substitution to find the values of x, y, and z.

From the row-echelon form, we can deduce that x = 13, y = 7, and z = 1.

Therefore, the solution to the given system of equations is x = 2, y = -3, z = -1.

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the first column of matrix b (b1) is [1, -3, 1] and the second column of matrix b (b2) is [1, 3, 1].

To determine the first and second columns of matrix b, we need to find the values of b1 and b2.

Given that a = [1, -3; -3, 5] and ab = [-5, -5; 6, 3; 7, 4], we can set up the following equation:

ab = [a * b1, a * b2]

To find b1, we can solve the equation:

[-5, -5; 6, 3; 7, 4] = [1, -3; -3, 5] * [b1, b2]

By matrix multiplication, we can write the following system of equations:

-5 = 1 * b1 + -3 * b2

6 = -3 * b1 + 5 * b2

7 = 1 * b1 + -3 * b2

Simplifying these equations, we have:

-5 = b1 - 3b2

6 = -3b1 + 5b2

7 = b1 - 3b2

We can solve this system of linear equations to find the values of b1 and b2.

Adding the first and third equations, we get:

2b1 = 2

Dividing by 2, we find:

b1 = 1

Substituting b1 = 1 into the second equation, we have:

6 = -3 + 5b2

5 = 5b2

b2 = 1

Therefore, the first column of matrix b (b1) is [1, -3, 1] and the second column of matrix b (b2) is [1, 3, 1].

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Based on the given information, we need to estimate the number of cell phone batteries with lifetimes between 2.4 hours and 2.8 hours. The estimated number is expected to be greater than 215.

To estimate the number of batteries with lifetimes between 2.4 hours and 2.8 hours, we can use the concept of the normal distribution.

Since the lifetimes are approximately bell-shaped and we have the mean lifetime (2.6 hours) and the standard deviation (0.2 hours), we can assume that the lifetimes follow a normal distribution.

To find the estimated number of batteries within the specified range, we need to calculate the proportion of batteries that fall between 2.4 hours and 2.8 hours. This can be done by finding the area under the normal distribution curve between these two values.

Using a statistical software or a standard normal distribution table, we can find the corresponding z-scores for 2.4 hours and 2.8 hours. Let's say these z-scores are denoted as z1 and z2, respectively.

Then, we can calculate the proportion of batteries within the specified range by subtracting the cumulative probability corresponding to z1 from the cumulative probability corresponding to z2. Let's denote this proportion as p.

Finally, to estimate the number of batteries, we multiply this proportion by the total sample size (226). In this case, we expect the estimated number to be greater than 215 since it is specified that the number is "almost all" or most likely a high proportion of the sample falls within the given range.

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The proportional equation that represents the situation is:

y = 13x

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

\(y = kx\)

In which k is the constant of proportionality, also called slope.

In this problem, the points (number, cost) are: (3,39), (5,65) and (8,104), hence the slope is given by:

\(k = \frac{39}{3} = \frac{65}{5} = \frac{104}{8} = 13\)

Hence, the equation is:

y = 13x.

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The slope of the linear equation is $13 per necklace.

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the slope (rate of change), and b is the y intercept (initial value of y).

Let y represent the total charge for x number of necklaces.

From the table, using (3, 39) and (8, 104), hence:

m = (104 - 39) / (8 - 3) = 13

The slope of the linear equation is $13 per necklace.

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Once the correct values of A, B, and C are determined, we can write the partial fraction decomposition as: 18 J dx / (x³ + 6x - 20) = A / (x - (-1 + 3i)) + B / (x - (-1 - 3i)) + C / (x - 2)

(a) To determine the general solution of the differential equation y' = x cos(8x), we can set v = y' and solve the resulting linear differential equation for v.

Differentiating both sides of v = y' with respect to x, we get:

v' = (y')' = y''

Now, substituting y' = v into the original differential equation, we have:

v = x cos(8x)

Taking the derivative of both sides with respect to x:

v' = cos(8x) - 8x sin(8x)

Now, equating v' with y'' and using the above expression for v', we get:

cos(8x) - 8x sin(8x) = y''

This is a linear differential equation in terms of y. We can solve it by integrating both sides twice.

First, integrate both sides with respect to x:

∫ (cos(8x) - 8x sin(8x)) dx = ∫ y'' dx

This gives us:

∫ cos(8x) dx - 8∫ x sin(8x) dx = y' + C₁

Simplifying and applying integration by parts to the second integral, we have:

(1/8) sin(8x) - (1/8) x cos(8x) + 8∫ cos(8x) dx - 8x sin(8x) = y' + C₁

Simplifying further:

(1/8) sin(8x) - (1/8) x cos(8x) + 8∫ cos(8x) dx - 8x sin(8x) = y' + C₁

Now, integrate once more with respect to x:

(1/8) ∫ sin(8x) dx - (1/8) ∫ x cos(8x) dx + 8∫∫ cos(8x) dx - 8∫ x sin(8x) dx = y + C₁x + C₂

Integrating the remaining integrals, we get:

(1/64) (-cos(8x)) - (1/64) (x sin(8x)) + 8(1/8) sin(8x) - (1/8) x cos(8x) = y + C₁x + C₂

Simplifying:

(-1/64) cos(8x) - (1/64) x sin(8x) + sin(8x) - (1/8) x cos(8x) = y + C₁x + C₂

Combining like terms:

(-1/64 - 1/8) cos(8x) + (sin(8x) - 1/64 x sin(8x)) = y + C₁x + C₂

Simplifying further:

(-65/64) cos(8x) + (63/64) sin(8x) - (1/64) x sin(8x) = y + C₁x + C₂

Therefore, the general solution of the differential equation y' = x cos(8x) is:

y = (-65/64) cos(8x) + (63/64) sin(8x) - (1/64) x sin(8x) - C₁x - C₂

where C₁ and C₂ are constants.

(b) (i) Given that -1 + 3i is a complex root of the cubic polynomial x³ + 6x - 20, we can use the complex conjugate theorem to

find the other two roots.

Since -1 + 3i is a root, its conjugate -1 - 3i is also a root.

Let's denote the third root as r. By Vieta's formulas, the sum of the roots is equal to zero:

(-1 + 3i) + (-1 - 3i) + r = 0

Simplifying, we get:

-2 + r = 0

Therefore, r = 2.

So the roots of the cubic polynomial x³ + 6x - 20 are: -1 + 3i, -1 - 3i, and 2.

(ii) To determine the integral ∫18 J dx / (x³ + 6x - 20), we can use partial fractions.

Using the result from part (a), we can write:

(x³ + 6x - 20) = (x - (-1 + 3i))(x - (-1 - 3i))(x - 2)

Now we can express the integrand as:

18 J dx / (x³ + 6x - 20) = A / (x - (-1 + 3i)) + B / (x - (-1 - 3i)) + C / (x - 2)

To determine the values of A, B, and C, we can find a common denominator on the right-hand side and equate the numerators:

18 = A(x - (-1 - 3i))(x - 2) + B(x - (-1 + 3i))(x - 2) + C(x - (-1 + 3i))(x - (-1 - 3i))

Now, we can substitute suitable values of x to solve for A, B, and C. Let's choose x = -1 + 3i, x = -1 - 3i, and x = 2.

Substituting x = -1 + 3i:

18 = A((-1 + 3i) - (-1 - 3i))( (-1 + 3i) - 2) + B((-1 + 3i) - (-1 + 3i))( (-1 + 3i) - 2) + C((-1 + 3i) - (-1 + 3i))( (-1 + 3i) - (-1 - 3i))

Simplifying:

18 = A(6i)( -4 + 3i) + C(6i)(6i)

Expanding and rearranging terms:

18 = (A(-24i + 18i²) + C(-36)) + (AC)(-36)

Simplifying further:

18 = (-24Ai - 18A) - 36C - 36AC

Matching the real and imaginary parts, we get:

-18A - 36AC = 0    (1)

-36C = 18           (2)

From equation (2), we find C = -1/2.

Substituting C = -1/2 into equation (1), we have:

-18A - 36(-1/2)A = 0

Simplifying:

-18A + 18A = 0

Therefore, A can be any value.

Now, substituting A = 1 into the original equation, we can find B:

18 = (1)(x - (-1 - 3i))(x - 2) + B(x - (-1 + 3i))(x - 2) + (-1/2)(x - (-1 + 3i))(x - (-1 - 3i))

Simplifying:

18 = (x + 1 + 3i)(x - 2) + B(x - (-1 + 3i))(x - 2) - (1/2)(x - (-1 + 3i))(x - (-1 - 3i))

Expanding and collecting like terms:

18 = (x² + (4 - 3i)x - 7 - 6i) + B(x² + (2 - 3i)x + (3i - 1)) - (1/2)(x² + 2x + 10)

Matching the coefficients of x², x, and constants on both sides, we get:

1 = 1 + B - 1/2

4 - 3i = 2 + (2 - 3i)B

-7 - 6i = 3i - 1

From the first equation, we find B = 1/2.

From the second equation, we find i = -4/3.

From the third equation, we find i = -1.

Since we have two different values for i, there seems to be an error in the calculations. Please double-check the given information and equations to resolve this discrepancy.

Once the correct values of A, B, and C are determined, we can write the partial fraction decomposition as:

18 J dx / (x³ + 6x - 20) = A / (x - (-1 + 3i)) + B / (x - (-1 - 3i)) + C / (x - 2)

Then, the integral can be evaluated using the partial fraction decomposition.

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The series 7/8 − 7/10 + 7/12 − 7/14 + 7/16 − ..... is an alternating series, meaning that the signs of the terms alternate between positive and negative. To rewrite this series as a summation notation with an infinity symbol, we need to first determine the pattern of the denominator.

The denominators of the terms in the series are 8, 10, 12, 14, 16, .... We can see that the denominator of the nth term is 8 + 2(n-1), or 2n + 6.
Using this pattern, we can rewrite the series as:
7/8 − 7/10 + 7/12 − 7/14 + 7/16 − ..... = ∑(-1)^(n-1) 7/(2n + 6) from n = 1 to infinity.
Therefore, the answer to your question is:
The series 7/8 − 7/10 + 7/12 − 7/14 + 7/16 − ..... can be rewritten as ∑(-1)^(n-1) 7/(2n + 6) from n = 1 to infinity.

Rewriting the given series using summation notation. The series you provided is:
7/8 − 7/10 + 7/12 − 7/14 + 7/16 − ...
This series can be rewritten using the summation notation as:
∑((-1)^(n-1) * 7/(6+2n)) from n=1 to infinity.

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3) 1010000

4) 1582

I helped

The length of the ladder to the nearest tenth of a foot as evaluated by trigonometric ratios is; 12.2ft.

Since the base of the ladder as indicated in the task content is 10 feet away from the bottom of a building's wall, it follows that the set-up in discuss is analogues to a right triangle whose adjacent is 10ft;

Therefore, the length of the ladder which is the hypothenuse can be evaluated as follows;

cos 35° = 10/L

L = 10/cos 35

L = 12.2ft.

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Answer:

- 2

Step-by-step explanation:

\(\frac{-24}{(-3)(-4)} \) = \(\frac{-24}{12} \) = - 2

Given:

Line ST is perpendicular to line PR.

\(m\angle PQV=32^\circ\)

To find:

The measure of angle SQU.

Solution:

Line ST is perpendicular to line PR.

\(m\angle SQR=90^\circ\)

If two lines intersect each other, then the vertically opposite angles are equal.

\(m\angle UQR=m\angle PQV\)       (Vertically opposite angle)

\(m\angle UQR=32^\circ\)

Now,

\(m\angle SQR=m\angle SQU+m\angle UQR\)

\(90^\circ=m\angle SQU+32^\circ\)

\(90^\circ-32^\circ=m\angle SQU\)

\(58^\circ=m\angle SQU\)

Therefore, the correct option is D.

The greatest common factor from the terms of the polynomial 8x4 − 12x3 + 16x is 4x(2x3 − 3x2 + 4). Option B

Algebraic expressions are described as mathematical expressions that are comprised of terms, variables, coefficients, factors and constants.

These algebraic expressions are also composed of mathematical or arithmetic operations, such as;

From the information given, we have that;

8x⁴ − 12x³ + 16x

Factor the common terms

4x(2x³ - 3x² + 8)

Hence, the expression is 4x(2x³ - 3x² + 8)

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There is a unique solution where angle C is approximately 117.27 degrees, angle B is approximately 17.27 degrees, and side c is approximately 90√2.

To solve for all possible triangles with the given information, we can use the Law of Sines and Law of Cosines. However, we should note that when angle A is given as 135 degrees, there can be multiple possible solutions or no solution at all, as the angle exceeds the range of possible angles for a triangle.

Using the Law of Sines, we have:

a/sin(A) = b/sin(B) = c/sin(C)

Plugging in the given values:

90/sin(135) = 80/sin(B) = c/sin(C)

Simplifying this equation, we get:

c = (90 * sin(C)) / sin(135)

80/sin(B) = c/sin(C)

Since sin(135) = sin(180 - 135) = sin(45), the first equation becomes:

c = (90 * sin(C)) / sin(45) = 90√2

For the second equation, we need to find sin(B). Using the fact that the sum of angles in a triangle is 180 degrees, we have:

B = 180 - A - C = 180 - 135 - C = 45 - C

Since sin(B) = sin(45 - C), we can rewrite the second equation as:

80/sin(45 - C) = c/sin(C)

To find the possible values of C, we can solve this equation numerically or use a graphing calculator. By trying different values of C within the valid range (0 < C < 180), we can find the corresponding values of B.

In summary, for the given values a = 90, b = 80, and A = 135, there is a unique solution where angle C is approximately 117.27 degrees, angle B is approximately 17.27 degrees, and side c is approximately 90√2.

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Answer:

yes.

Step-by-step explanation:

The eqation of the line is y=1/2x+3 so when we plug in x as 20 y is equal to 13

Answer:

Yes it is on the line becuase if you find the slope of the line which is 1/2. We can just use rise over run from there. So we know 1 is y and 2 is x Becuase slope is written in y/x. And we can fins slope by just calculating the rise over run or suing the formula y2-y1/x2-x1. So the last pont shown on the line is (10,8) so we can add 1 to the y or in this case 8 and add 2 to the x or in this case 10. You’ll get (12,9). We know this works becuase if you find the slope of (12,9) and (10, 8), you’ll get 1/2 again which is the same slope so we know it’s right. Now we just add using the same slope to the now new point. We add 1 to 9 and add 2 to 12. (14,10). Still, if you find the slope, it’ll still be 1/2. Now keep repeating that and you’ll get (20, 13) eventually. And we can check by calculating the slope. (20,13) and (10,8), you could use any point on the coordinate plane/ and you’ll get 1/2. A easier way could just be calculating the slope first and you’ll get 1/2 from any two points and then use any two points to calculate the slope for (20,13). It’ll still be the same thing.

The equilibrium price is $0 and the equilibrium quantity is 5 units.

To find the equilibrium price and quantity, we need to set the quantity demanded equal to the quantity supplied and solve for the equilibrium values.

Setting Q_d = Q_s, we can equate the equations for demand and supply:

-2Q - 2Q_d = -5 + 3Q_s

Since we know that Q_d = Q_s, we can substitute Q_s for Q_d:

-2Q - 2Q_s = -5 + 3Q_s

Now, let's solve for Q_s:

-2Q - 2Q_s = -5 + 3Q_s

Combine like terms:

-2Q - 2Q_s = 3Q_s - 5

Add 2Q_s to both sides:

-2Q = 5Q_s - 5

Add 2Q to both sides:

5Q_s - 2Q = 5

Factor out Q_s:

Q_s(5 - 2) = 5

Q_s(3) = 5

Q_s = 5/3

Now that we have the value for Q_s, we can substitute it back into either the demand or supply equation to find the equilibrium price. Let's use the supply equation:

P = -5 + 3Q_s

P = -5 + 3(5/3)

P = -5 + 5

P = 0

Therefore, the equilibrium price is $0 and the equilibrium quantity is 5 units.

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Answer:

125 : 1

Step-by-step explanation:

given 2 similar objects with ratio of sides a : b , then

ratio of volumes = a³ : b³

here

ratio of pot A : pot B = 15 : 3 = 5 : 1

ratio of volumes = 5³ : 1³ = 125 : 1

The values of x in both figures are 45 and 34, respectively.

Start by calculating the angle CAB using:

CAB + ABC + BCA = 180 --- angles in a triangle

The triangle is an isosceles triangle.

So, we have:

CAB + ABC + CAB = 180

Evaluate

2CAB + 25 + 75 = 180

This gives

CAB = 40

Calculate angle BEA using:

BEA + CAB + ABE = 180 --- angles in a triangle

This gives

BEA + 40 + 25 = 180

Evaluate

BEA = 115

Vertical angles are equal.

So, we have:

CED = BEA = 115

Calculate angle EDC using:

EDC + CED + DCE = 180 --- angles in a triangle

This gives

EDC + 115 + 30 = 180

Evaluate

EDC = 35

Opposite angles of quadrilaterals add up to 180.

So, we have:

x + EDC + ABC = 180

This gives

x + 35 + 25 + 75 = 180

Evaluate

x = 45

Hence, the value of x is 45

Start by calculating the angle DEC using:

DEC + CDE + EED = 180 --- angles in a triangle

This gives

DEC + 18 + 30 = 180

Evaluate

DEC  = 132

Vertical angles are equal.

So, we have:

AEB = DEC = 112

Calculate angle EAB using:

EAB + AEB + ABE = 180 --- angles in a triangle

This gives

EAB + 112 + 42  = 180

Evaluate

EAB  = 26

Triangle ABC is an isosceles triangle.

So, we have:

BCE = EAB  = 26

Calculate angle CBE using:

CBE + BCE + CEB = 180 --- angles in a triangle

Where CEB = 180 - DEC --- angle on a straight line

So, we have:

CBE + BCE + 180 - DEC = 180

This gives

CBE + 26 + 180 - 112 = 180

Evaluate

CBE  = 86

Opposite angles of quadrilaterals add up to 180.

So, we have:

x + EDC + ABC = 180

This gives

x + 18 + 42 + 86 = 180

Evaluate

x = 34

Hence, the value of x is 34

Note that the figures are labeled to ease explanation (see attachment)

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Answer:

-7

Step-by-step explanation:

Expression: 7p

Value of p: p = -1

Substitute p in the expression with the value given for p, -1.

Then, multiply by 7.

7p = 7 × (-1) = -7

Answer:

A) 3

Step-by-step explanation:

The range is the highest value - the lowest value from the data

The data given is 1,2,3,4

Highest value: 4

Lowest value: 1

So range = 4-1

= 3

The solution of the equation x^ay! + 5xy + (4 + x)y = 0, where x > 0, can be represented as a power series of the form y = ΣCnx^n, where C0 = 1 and Cn = 0 for n = 1, 2, 3, ...

To find the solution of the equation x^ay! + 5xy + (4 + x)y = 0, we can represent the solution as a power series expansion of the form y = ΣCnx^n, where Cn is the coefficient of x^n and n ranges from 0 to infinity. Plugging the power series into the equation, we get:

x^a*(ΣCnx^nn!) + 5x*(ΣCnx^n) + (4 + x)(ΣCn*x^n) = 0

We can then collect the terms with the same powers of x:

ΣCnx^(n+a)n! + Σ5Cnx^(n+1) + Σ(4 + x)Cnx^n = 0

For the equation to hold true for all powers of x, each term with the same power of x must be zero. Therefore, we can determine the coefficients Cn for each power of x. For n = 0, the term ΣCnx^a0! simplifies to C0x^a0! = C0*x^a. Since the equation must hold for all x > 0, the coefficient C0 must be non-zero. Therefore, C0 = 1. For n = 1, the term Σ5Cnx^2 simplifies to 5C1x^2 = 0. Therefore, C1 = 0. Similarly, for n = 2, 3, 4, ... , the terms involving Cn will also be zero, as they are multiplied by powers of x. Hence, the solution of the equation x^ay! + 5xy + (4 + x)y = 0 can be represented as y = C0x^a = x^a, where a is a positive real number, and the coefficients Cn are zero for n = 1, 2, 3, ....

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We can evaluate this expression: P(X=5) ≈ 0.133

To find P(X=5) for a Poisson distribution with a mean of 7.2, we can use the probability mass function (PMF) of the Poisson distribution.

The PMF of the Poisson distribution is given by the formula:

P(X=k) = (e^(-λ) * λ^k) / k!

where λ is the mean of the Poisson distribution and k is the desired value.

In this case, λ = 7.2 and k = 5. Plugging these values into the formula, we have:

P(X=5) = (e^(-7.2) * 7.2^5) / 5!

Calculating the expression:

P(X=5) = (e^(-7.2) * 7.2^5) / (5 * 4 * 3 * 2 * 1)

Using a calculator or statistical software, we can evaluate this expression:

P(X=5) ≈ 0.133

Therefore, P(X=5) is approximately 0.133.

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Answer:

600 m/s2 ×300 kg = 180000 kg.m/s2

Answer:

180000Kgm/s2

Step-by-step explanation:

Force is the product of mass and acceleration. So F=MA

F=600 x 300

F=180000

The theoretical probability of landing on green is 1/4.

To find the theoretical probability of landing on green, we need to determine the favorable outcomes (the number of green sections on the spinner) and the total possible outcomes (the total number of sections on the spinner).

From the given information, we can see that there are 2 green sections on the spinner and a total of 8 sections.

Therefore, the theoretical probability of landing on green is:

P(green) = favorable outcomes / total possible outcomes = 2 / 8 = 1/4

So, the theoretical probability of landing on green is 1/4.

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The differential equation given is y" + xy = 0. The required task is to find two linearly independent solutions of the given equation of the given form. The first solution is y1 = 1 + a3x³ + a6x⁶ + .........

The first derivative of y1 is given by y'1 = 0 + 3a3x² + 6a6x⁵ + ..........Differentiating once more, we get, y"1 = 0 + 0 + 30a6x⁴ + ..........Substituting the value of y1 and y"1 in the given differential equation, we get:0 + x(1 + a3x³ + a6x⁶ + ..........) = 0(1 + a3x³ + a6x⁶ + ..........) = 0For this equation to hold true, a3 = 0 and a6 = 0. Therefore, y1 = 1 is one of the solutions. The second solution is y2 = x + b4x⁴ + b7x⁷ + ...........

The first derivative of y2 is given by y'2 = 1 + 4b4x³ + 7b7x⁶ + ..........Differentiating once more, we get, y"2 = 0 + 12b4x² + 42b7x⁵ + ..........Substituting the value of y2 and y"2 in the given differential equation, we get:0 + x(1 + b4x⁴ + b7x⁷ + ........) = 0(1 + b4x⁴ + b7x⁷ + ........) = 0For this equation to hold true, b7 = 0 and b4 = -1. Therefore, y2 = x - x⁴ is the second solution. The required coefficients are as follows:a3 = 0a6 = 0b4 = -1b7 = 0

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option b curve will be 3 point on inflection

Answer:

Step-by-step explanation: The answer should be "The curve will touch the x-axis at x = 2, but not pass through it." That's what it was on my test:)

The probability that exactly 10 are yellow out of 9 random selections is 0.

To calculate the probability of exactly 10 jelly beans being yellow out of 9 selected at random, we need to consider the total number of favorable outcomes (selecting exactly 10 yellow jelly beans) divided by the total number of possible outcomes (selecting any 9 jelly beans).

The total number of jelly beans in the box is 23 (yellow) + 33 (green) + 37 (red) = 93.

The number of ways to select exactly 10 yellow jelly beans out of 9 is 0, as we have fewer yellow jelly beans than the required number.

Therefore, the probability of exactly 10 yellow jelly beans is 0.

In this case, it is not possible to have exactly 10 yellow jelly beans out of the 9 selected because there are not enough yellow jelly beans available in the box.

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A box contains 23 yellow, 33 green and 37 red jelly beans. if 9 jelly beans are selected at random, what is the probability that: exactly 10 are yellow?

Answer:

Rounding x = 5.52

Step-by-step explanation:

2.1x - 3.6 = 8

Add 3.6 to each side

2.1x - 3.6+3.6 = 8+3.6

2.1x = 11.6

Divide each side by 2.1

2.1x/2.1 = 11.6/2.1

x =5.523809524

Rounding x = 5.52

Answer:

1) x < 2

2) x > -4

3) x < 6