What is the value of the next term in the following sequence

1, 5, 25, 125, 625 . . .

The matrix A  eigenvalues and eigenvectors are as follows:

Eigenvalue λ1 = 1 with eigenvector v1 = [1, -1]

Eigenvalue λ2 = 6 with eigenvector v2 = [4, 1]

Using the equation  (A - λI)v = 0, where is an eigenvalue of A, I am the 2x2 identity matrix, and v is the associated eigenvector, we can determine the eigenvalues and eigenvectors of the matrix A = [[5, 4], [1, 2]].

First, we calculate the (A - λI) matrix's determinant:

det(A - λI) = |5-λ 4| = (5-λ)(2-λ) - 4 = λ^2 - 7λ + 6

|1 2-λ|

We obtain the characteristic equation by setting the determinant to zero:

λ^2 - 7λ + 6 = 0

We obtain two eigenvalues after solving for  λ :

λ = 1 and λ = 6

Next, For each eigenvalue, we identify the appropriate eigenvectors:

For λ = 1, We solve the system of linear equations represented by the equation(A - λI)v = 0:

4v1 + 4v2 = 0

v1 + v2 = 0

The second equation is evidently as straightforward as v1 = -v2. When we enter this into the initial equation, we get:

4v2 - 4v2 = 0

Thus, the eigenvector for λ = 1 is v = [1, -1].

For λ = 6, We solve the system of linear equations represented by the equation(A - λI)v = 0:

-v1 + 4v2 = 0

-v1 + 4v2 = 0

v1 - 4v2 = 0

It is evident that the first equation is just v1 = 4v2. When we enter this into the second equation, we get:

4v2 - 4v2 = 0

Thus, the eigenvector for λ = 6 is v = [4, 1].

Therefore, The matrix A  eigenvalues and eigenvectors are as follows:

Eigenvalue λ1 = 1 with eigenvector v1 = [1, -1]

Eigenvalue λ2 = 6 with eigenvector v2 = [4, 1]

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The probability of obtaining 3 heads in four flips of a fair coin is 1/4.

The probability of obtaining 3 heads in four flips of a fair coin can be calculated using the binomial probability formula. The formula is:

[tex]P(X = k) = (n choose k) * p^k * (1 - p)^{(n - k)}[/tex]

where P(X = k) is the probability of obtaining k successes (in this case, 3 heads), and n is the total number of trials (in this case, 4 flips).

p is the probability of success on a single trial (in this case, 0.5 since the coin is fair), and (n choose k) is the binomial coefficient, which represents the number of ways to choose k successes from n trials.

Plugging in the values, we get:

[tex]P(X = 3) = (4 choose 3) * 0.5^3 * (1 - 0.5)^{(4 - 3)}[/tex]

= 4 * 0.125 * 0.5

= 0.25

Therefore, the probability of obtaining 3 heads in four flips of a fair coin is 1/4 or 0.25

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Calculating antiderivatives, definite line integrals, double and triple integrals, and improper integrals is made easy using Wolfram | Alpha.

Wolfram| | Alpha does integral computations differently than people. It uses the Integrate function in Mathematica, which is the result of much mathematical and computational study. Integrate does integrals differently than individuals do. Instead, it makes use of robust, broad algorithms, which frequently need quite complex arithmetic. One includes determining an integral's general form, differentiating this form, and then resolving equations to match ambiguous symbolic parameters. The equations produced in this technique can be quite complicated, even for relatively basic integrands, and are best solved using Mathematica's robust algebraic computation capabilities. Converting integrals to generalized hypergeometric functions and then using collections of relations about these extremely complex mathematical functions is another method Mathematica utilizes to calculate integrals.

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Answer:

(-1, -5)

Equation form:

x=-1, y=-5

Step-by-step explanation:

Basically, all you have to do is solve for the first variable in one of the equations, then substitute the result into the other one. It's as simple as that.

Hope this helps

The error is in the second part of the solution.

The definition of an expression in math is a statement composed of terms and operations. The terms may be constant (numbers), or variables with coefficients. The operations may be addition, subtraction, multiplication, or division.

Given that the difference of two expressions, (x²+x) - (2x²-3x), we need to find the error in the solution given,

= (x²+x) - (2x²-3x)

= (x²+x) + (-2²-3x) [Error here]

= (x² - 2x²) + (x²-3x)

= -2²-2x

The error is in the second step,

(x²+x) + (-2²-3x)

When we multiply - sigh with a - sign, we will get a positive sign,

So, the correct step is =

(x²+x) + (-2²+3x)

The correct solution is =

= (x²+x) - (2x²-3x)

= x²+x-2x²+3x

= -2x²+4x

= 2x(2-x)

Hence, the error is in the second part of the solution.

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Answer:

1/15 chance

Step-by-step explanation:

BASKETBALL = 10 letters

taking out a B = 2/10 or 1/5

Then picking a vowel = 3/9 or 1/3

1/5 x 1/3 = 1/15 chance

Answer:

To answer this question, we first need to determine the perimeter of Shawn's garden. If we let x represent the side length of Shawn's garden, then the perimeter of Shawn's garden would be 4x.

Now, the perimeter of Charlie's garden is 12x + 20, which is 8x + 20 larger than the perimeter of Shawn's garden (4x). Therefore, the perimeter of Charlie's garden is 8x + 20 larger than the perimeter of Shawn's garden.

In calculus, 0^0 is an indeterminate form. It is not equal to infinity. But 0x0 is equal to zero.

Some of the indeterminate forms 0/0, 0×∞,∞/∞, ∞ −∞, ∞/0, [tex]0^{0}[/tex].

An unknown value is referred to as being "indeterminate." Even after inserting the limits, we are still unable to determine the original value, according to the indeterminate form of mathematics. When two functions are considered as a ratio, the indeterminate form frequently appears when both functions go closer to 0 in the limit. The term "indeterminate form 0/0" refers to these circumstances. The indeterminate form can also be created, much as addition, subtraction, multiplication, and exponential operations. If the limiting behavioral of separate components of the provided expression cannot identify the overall limit, a limit is said to be indeterminate.

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Answer:

most likely next spring

Step-by-step explanation:

Step-by-step explanation:

From the given information, by doing unit conversion 20 ounces is equal to approximately 1.25 pounds.

Unit conversion is the process of converting a given quantity from one unit of measurement to another. It involves using conversion factors or conversion equations to change the numerical value of the quantity while keeping the physical quantity constant. Common units of measurement include length, mass, volume, time, temperature, and many others.

To convert ounces to pounds, you can use the following conversion formula:

1 lb = 16 oz

So, to convert 20 ounces to pounds, you can divide 20 by 16:

20 oz ÷ 16 oz/lb = 1.25 lb (rounded to two decimal places)

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to tiny submit closer picture

Since Xavier states that the decay rate of the value of the car is 40%, an answer option that accurately describes Xavier's statement is: A) Xavier correctly determined the decay rate of the value of the car.

In Mathematics, an exponential function can be modeled by using this mathematical expression:

f(x) = a(b)^x

Where:

In this scenario, we can logically deduce that values of a certain type of car x years after it is purchased can be modeled by the following exponential function:

f(2) = 19,400(0.40)^2

By comparison, we have:

Decay rate (r) = 0.40, which simply means Xavier correctly determined it.

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The ages of the five family members as required are; 3, 10, 13, 42 and 42.

As evident, in the task content, let a, b , c , d , e represents the ages of the family members in ascending order.

Since the median of the ages is; 13, it follows that the the third term, c = 13.

Also, since the mode is 42, it follows that; d = e = 42.

Also, since the range of the ages is 39, it follows that; 42 - a = 39 and consequently a = 3.

Finally, since the mean age is 22; it follows from the mean formula that;

22 = ( 3 + b + 13 + 42 + 42 ) / 5

110 = b + 100

b = 10.

Ultimately, the ages of the five family members as required are; 3, 10, 13, 42 and 42.

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Answer:

4

Step-by-step explanation:

2x4=8, 8+11=19

128 pounds is equal to 58.059 kilograms.

To convert pounds (lbs) to kilograms (kg), you can use the conversion factor that 1 pound is equal to 0.45359237 kilograms.

To convert 128 pounds to kilograms, you can multiply 128 by the conversion factor:

= 128 lbs x 0.45359237 kg/lb

≈ 58.059 kilograms

Therefore, 128 pounds is equal to 58.059 kilograms.

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The probability a that a randomly selected student plays a sport, given that the student is a senior is 0.32

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

Using the above as a guide, we have the following:

P(Sport Given Senior) = 0.08/0.25

Evaluate

P(Sport Given Senior) = 0.32

Hence, the probability is 0.32

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0900 military time is 9:00 AM in the 24-hour time format used by the military, also known as the 24-hour clock.

The 24-hour clock is a timekeeping system that uses a continuous count of 24 hours, instead of two sets of 12 hours for AM and PM. In this system, each hour of the day is numbered from 0 to 23, and is referred to as "military time" or "24-hour time". So, 0900 military time is equivalent to 9:00 AM, with the "0" indicating the first hour of the day. This system is commonly used in the military, as well as in other fields where precise and standardized timekeeping is important, such as aviation and public transportation.

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The spring compressed in stopping the ore car is  4.4719 m.

For answer this we will apply the rule of the conservation of energy,

The conservation of energy principle states that in a closed system, the energy of interacting objects or particles remains constant. Kinetic energy, sometimes known as the energy of motion, was the first type of energy to be identified. The total of the kinetic energy of the particles before collision and the sum of the kinetic energy of the particles after collision are identical in some particle collisions, known as elastic collisions.

where:

[tex]E_i=E_f[/tex]

First, we will call:

[tex]E_i[/tex]:the automobile is parked

[tex]E_f[/tex]:when the spring is shortened

so:

[tex]E_i=E_f[/tex]

[tex]mgh=\frac{1}{2}kx^2[/tex]

where M is the vehicle's mass, g is gravity, h is height, K is the spring's constant, and X is the compressed spring used to halt the ore car. By substituting values, we obtain:

4800×9.8×13.8=[tex]\frac{1}{2}\times 410000\times x^2[/tex]

calculating x:

x = 4.4719 m

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The number of passes that John has attempted this year will be 500.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

John is a quarterback. This year, he completed 350 passes, which is 70% of all the passes he's attempted this year.

Let 'y' be the total passes that John attempted. Then the equation is given as,

0.70 = (350 / y)

y = 350 / 0.70

y = 500

The number of passes that John has attempted this year will be 500.

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Answer: its A

Step-by-step explanation: you welcome

The five number summary is 77.5.

First Quartile: 7.5

Median: 15.5

Third Quartile: 23.5

Maximum: 30

1, 2, 3, 4, 5, 6, 7, 8,9,10,11, 12, 13,14, 15, 16,17, 18, 19, 20 21, 22, 23, 24, 25, 26, 27, 28, 29, 30.

Minimum = 1

First Quartile = 7 + 8

                           2

                   = 15/2

                    = 7.5

Median = 15+ 16

                    2    

                =31/2

                =15.5

Third Quartile = 15 + 16

                              2

                        =  31/2

                         =   15.5

Maximum = 30

five - number summary = Minimum number +  Lower quartile (Q₁)  + median (Q₂) + Upper quartile  (Q₃) + maximum number

five - number summary = 1 + 7.5 + 15.5 + 23.5 + 30 = 77.5

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The relation 'x' and 'y' vary inversely, when x = 4, y = 5/2.

In its most basic form, a ratio is a comparison between two comparable quantities.

There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.

If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.

Given, The variables x and y vary inversely.

Let, y ∝ 1/x.

y = k/x.

2 = k/5.

k = 10.

Now, x = 4.

y = k/x.

y = 10/4.

y = 5/2.

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The tax money given by Andy is equivalent to $151.83.

Tax is a type of financial charge imposed by governmental organization on the individual to fund government spending and various public expenditures.

Given is that a bike shop in Belleville bought a mountain bike for $723 and marked it up 50% from the original cost.

Total cost of bike after marking it up -

{x} = $723 + ${50% of 723}

{x} = $723 + ${50/100 x 723)

{x} = $723 + $361.5

{x} = $1084.5

Money given by Andy as tax -

{t} = 14% of 1084.5

{t} = 14/100 x 1084.5

{t} = $151.83

Therefore, the tax money given by Andy is equivalent to $151.83.

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Answer:

7/10

Step-by-step explanation:

all number converted to decimals are X/1. X is any number.

0.7 is equal to 0.7/1

now fractions cannot contain a decimal number so we can times is by 10 to get 7/10.

Answer: 0.7, I think you multiply, algebraic answer ig

Step-by-step explanation:

Answer:

the answer is c 95

Step-by-step explanation:

180-41-44=95

a  triangle has 180 degrees

Answer: I think A. 75

Step-by-step explanation: why not pick A……

Hope this helps^^

Answer:

We can use Heron's Formula to calculate the area of a triangle given its three side lengths. The formula is:

A = √(s*(s-a)*(s-b)*(s-c)),

where s = (a + b + c)/2, a, b and c are the three sides of the triangle.

In this case, a = 15, b = y and c = (y-2). Therefore, we can plug these numbers in to get:

80 > √[(y + 7.5) * (y - 7.5) * (y - 2) * (y - 15)]

We can simplify this equation to get:

y^2 - 5y - 80 > 0

This equation can be solved using the quadratic formula, where the solution for y is:

y < 14.09 or y > 10.91

Therefore, the possible values for y are any number between 10.91 and 14.09.

The height of the cylinder is 7 inches and the the new volume of the package is 175.84 cubic inches

1. The formula for the volume of a cylinder is V = Bh, where B is the base area and h is the height. The base of the cylinder is a circle, and the formula for the area of a circle is A = πr^2.

Substituting the given values into the formula for the volume of a cylinder, we get:

87.92 = πr^2h

87.92 = 3.14(2^2)h

87.92 = 12.56h

h = 87.92/12.56

h ≈ 7

Rounding to the nearest inch, the height of the cylindrical package is 7 inches.

Part B:

If the company doubles the height while keeping the radius the same, the new height will be 2h. Therefore, the new volume will be:

V = πr^2(2h) = 2πr^2h

Substituting the given values into this formula, we get:

V = 2(3.14)(2^2)(2h)

V = 25.12h

To find the new volume, we need to substitute the value of h from Part A into this formula:

V = 25.12(7)

V ≈ 175.84

Rounding to the nearest hundredth, the new volume of the package is 175.84 cubic inches.

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The complete table is,

⇒ B = 41°

⇒ a = 9.525

⇒ b = 8.25

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The triangle is shown in figure.

Now, We have;

Two angles of triangle are,

⇒ A = 49°

⇒ C = 90°

Hence, We can formulate;

⇒ B = 180 - (49 + 90)

⇒ B = 180 - 139

⇒ B = 41°

And, By using Sine rule as;

⇒ sin A / a = sin B / b = sin C / c

Takin two identity as;

⇒ sin A / a = sin C / c

⇒ sin 49° / a = sin 90° / 12.7

⇒ 0.75 / a = 1/12.7

⇒ 0.75 × 12.7 = a

⇒ a = 9.525

⇒ sin B / b = sin C / c

⇒ sin 41° / b = sin 90 / 12.7

⇒ 0.65/b = 1/12.7

⇒ 0.65 × 12.7 = b

⇒ b = 8.25

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Answer:1/12

Step-by-step explanation:

Answer: 1/12

just a find a common denominator, and subtract, hope this helped =)