How can I find the perimeter of rectangle

The function that describes the sequence maps each index or position to its corresponding value.

A sequence space is a vector space that contains endless sequences of real or complex numbers. It is used in functional analysis and related mathematical fields. It is, in essence, a function space whose constituents are functions from the natural numbers to the field K of real or complex numbers.

The notation f(2) = 4 indicates that a term in a sequence defined by a function has a value of 4 when the term's index or position is 2.

Because sequences are a collection of ordered pairs with the first element being the index or position of the term and the second being the term's value, they can be characterised as functions. The function that represents the series maps each index or location to its associated value, and these ordered pairs can be seen as points on a coordinate plane.

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The probability that daily production is between 28 and 45.9 liters is 0.024.

Standard deviation is the positive square root of the variance. Standard deviation is one of the basic methods of statistical analysis. Standard deviation is commonly abbreviated as SD and denoted by 'σ’ and it tells about the value that how much it has deviated from the mean value.

Given that, x₁=28, x₂=45.9, μ=38 and σ =4.3

We know that, Z=(x-μ)/σ

Z=standard score, x=observed value, μ=mean of the sample and σ=standard deviation of the sample

z =(38-28)/4.3= 2.32 and probability on the z-table is 0.9896

z = (38-45.9)/4.3 = -1.83 and probability on the z-table is 0.9656,  

Now, P(2.32<z<-1.83) = 0.9896-0.9656

= 0.024

Therefore, the probability that daily production is between 28 and 45.9 liters is 0.024.

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(200 - 100√2) / 16 is the rectangular form of the product c1*c2 for an equilateral triangle's vertices.

A triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same.

Here,

An equilateral triangle is a triangle with three equal sides. If 3-2i, 6-i, and c form the vertices of an equilateral triangle, then the distance between 3-2i and 6-i is equal to the distance between 3-2i and c.

The distance between two complex numbers a + bi and c + di can be found using the formula:

√((c - a)² + (d - b)²)

So, the distance between 3-2i and 6-i is:

√((6 - 3)² + (-1 - (-2))²) = √((3)² + (1)²) = √(9 + 1) = √10

And the distance between 3-2i and c is:

√((c - 3)² + (c - (-2))²) = √((c - 3)² + (c + 2)²)

Since these distances must be equal, we have:

√((c - 3)² + (c + 2)²) = √10

Squaring both sides:

(c - 3)² + (c + 2)² = 10

Expanding both sides:

c² - 6c + 9 + c² + 4c + 4 = 10

Combining like terms:

2c² + 10c + 5 = 10

Subtracting 10 from both sides:

2c² + 10c - 5 = 0

This is a quadratic equation, which can be solved using the quadratic formula:

c = (-b ± √(b² - 4ac)) / 2a

Where a = 2, b = 10, and c = -5. Plugging these values into the formula:

c = (-10 ± √(10² - 4 * 2 * -5)) / 2 * 2

c = (-10 ± √(100 + 40)) / 4

c = (-10 ± √(140)) / 4

c = (-10 ± 10√2) / 4

So there are two complex solutions, c1 = (-10 + 10√2) / 4 and c2 = (-10 - 10√2) / 4.

The product of these two solutions is:

c1 * c2 = ((-10 + 10√2) / 4) * ((-10 - 10√2) / 4)

= (100 - 100√2 + 100) / 16

= (200 - 100√2) / 16

(200 - 100√2) / 16 is the answer in rectangular form for the product c1*c2 for the vertices of an equilateral triangle.

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Answer:

61

Step-by-step explanation:

√(2+3)^2+(2+4)^2

=√5^2+6^2

=√25+36

=√61

So the number is 61

Answer: 154.28 feet

Step-by-step explanation:

The probability of having a 4 in a 30 roll is 5 times

The expected value, μ, of rolling a 4 on a fair number cube (with faces numbered 1 to 6) can be found by using the formula μ = np, where n is the number of trials (30 in this case) and p is the probability of success for an individual trial (rolling a 4).

The probability of rolling a 4 on a fair number cube is 1/6. Therefore, the expected value of rolling a 4 30 times can be calculated as follows:

μ = 30 * (1/6) = 5

So, Mr. Jackson can expect to roll a 4 approximately 5 times in 30 rolls of his number cube.

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To find the instantaneous speed of an object, we must make the time interval very small, so that the speed does not change appreciably.

How to find the speed?

Speed is a scalar quantity which tells how fast an object is moving, regardless of its direction.

To find the instantaneous speed of an object, we must make the time interval very short, so that the speed does not change appreciably. The formula for the instantaneous speed of an object is given by the limit as time approaches zero of the change in distance divided by the time over which that change occurs. The formula for average speed is simply the total distance traveled divided by the total time elapsed.

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The angle that is adjacent to the angle CED is the angle DEA.

When two angles have a similar vertex and side, they are referred to as neighbouring angles. The vertex of an angle is the point at which the rays that make up its sides come to an end. When adjacent angles have a same vertex and side, they can be a complimentary angle or supplemental angle.

An adjacent angle is complementary to another if the total of its adjacent angles is 90 degrees.

When the total of two adjacent angles is 180 degrees, they are supplementary to one another.

Two angles are said to be adjacent angles when they share a common vertex.

In the given figure the angle that shares the common vertex to angle CED is angle DEA.

Hence, the angle that is adjacent to the angle CED is the angle DEA.

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The expectation values are <x> = 1.25 x 10⁻¹⁰ ,  <x²>  =  2.07 x 10⁻²⁰

What is average?

The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.

We need to find expectation value of <x> and < x²>

average value for <x>   is given by a/2   where a = length of box

hence <x> = ( (2.5 x 10⁻¹⁰) /2) = 1.25 x 10⁻¹⁰

hence <x²> = (1.25 x 10⁻¹⁰)²  = 1.56 x 10⁻²⁰

<x²> = ( a/2 x 3.14 x n)²   x ( 4 x 3.14² x n² /3  -2)

hence <x²>  = ( 2.5 x 10⁻¹⁰ / 2 x 3.14 x 5)²   x ( 4 x 3.14² x 5² /3  -2)

  <x²>  =  2.07 x 10⁻²⁰

<x²>  is not equal to <x>²

The expectation values are <x> = 1.25 x 10⁻¹⁰,  <x²>  =  2.07 x 10⁻²⁰

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A. The properties of parallelogram involving slope is the slope of opposite sides of parallelogram are equal as the lines are parallel. Hence, the vertices ABCD form a parallelogram.

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

A parallelepiped is a three-dimensional shape with parallelogram-shaped faces.

A. The properties of parallelogram involving slope is the slope of opposite sides of parallelogram are equal as the lines are parallel.

B. The opposite sides of the parallelogram are parallel and equal, and their slopes are equal.

C. The given vertices of a parallelogram are:

A(-2, 0), B(0, 9), C(2, 0) and D(0, -9).

Calculate the slope of segment AB and CD.

The slope is given as:

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

For AB:

m = (9 - 0) / (0 + 2) = 9/2

For CD:

m = (-9 - 0) / (0 - 2) = 9/2

Since the slopes of the segments AB and CD are equal the two lines are parallel to each other. Hence, the vertices ABCD form a parallelogram.

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17 students played cricket more than basketball.

A pie chart is a type of graph where a circle is divided into certain sectors where each sector shows a proportion of the whole.

Pie chart showing the preference of the students is given below.

Total number of students = 300

We know that total degree of the circle = 360°

Students who played cricket = 90°

Number of students who played cricket will be (90° / 360°)th of 300.

Number of students who played cricket = (90° / 360°) × 300

                                                                   = 75

Students who played basketball = 70°

Number of students who played basketball = (70° / 360°) × 300

                                                                         = 58.33 ≈ 58

Students played cricket - Students played basketball = 75 - 58 = 17

Hence there are 17 students more in cricket than that in basketball.

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The total production of both countries when they did not specialize was 91 million / day.

Given the information that when the two countries did not specialize, the total production of chinos was 23 million pairs per day, and the total production of pistachios was 68, we can calculate the total production of both countries with the following equation:

Total Production = Chinos (23 million pairs / day) + Pistachios (68 million / day)

Therefore, the total production of both countries when they did not specialize was 91 million / day. This can be calculated as:

Total Production = 23 million pairs + 68 million = 91 million / day

Hence, the total production of both countries when they did not specialize was 91 million / day. This calculation can be represented by the following formula:

Total Production = Chinos (x) + Pistachios (y)

Where x = 23 million pairs and y = 68 million.

Therefore, the total production of both countries when they did not specialize was 91 million / day.

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The total number of seeds Frank is going to plant is 6b + 6 seeds.

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

Graden 1 = b

Graden 2 = 5b + 6

Frank is going to plant b seeds in one garden and 5b + 6 seeds in another garden.

The total number of seeds Frank is going to plant is:

b + (5b + 6) = 6b + 6

So Frank is going to plant 6b + 6 seeds.

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The amount when compounded quaterly and compounded continuously will be $16,979.44 and $17,713.02. And the difference is $733.58

Theoretically, long-term average interest means that interest is continuously earned on a current account as well as reinvested into the balance to increase future interest earnings.

The equation is given as,

[tex]\rm P=P_o \times e^{rt}[/tex]

The initital amount is $15,000 and the interest rate is 4.75% annually.

A. If the interest is compounded quarterly. Then the amount is given as,

[tex]\rm A = \$15,000 \times \left (1 + \dfrac{0.0475}{4} \right)^{42/4}[/tex]

A = $15,000 x 1.1319

A = $16,979.44

B. if the interest is compounded continuously. Then the amount is given as,

[tex]\rm A = \$ 15,000 \times e^{0.0475 \times (42 / 12)}[/tex]

A = $15,000 x 1.1808

A = $17,713.02

C. The difference in the amount of interest earned is given as,

Differenece = $17,713.02 - $16,979.44

Differenece = $733.58

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(a) f(x) =  [tex]log_2(x)[/tex] is a logarithmic function

(b) g(x) = ∜x is a root function

(c) h(x) = [tex]2x^3/(1 - x^2)[/tex] is a rational function

(d) u(t) = 1 - 1.1t + [tex]2.54t^2[/tex] is a polynomial of degree 2

(e) v(t) = [tex]5^t[/tex]is an exponential function

(f) w(θ) = sin θ [tex]cos^{2}\theta[/tex] is a trigonometric function.

(a) f(x) = [tex]log_2(x)[/tex] is a logarithmic function. Logarithmic functions have the logarithm of the independent variable as the output. Here, the logarithm base is 2.

(b) g(x) = ∜x is a root function. Root functions have the square root or higher roots of the independent variable as the output. Here, the root is a cube root.

(c) h(x) = [tex]2x^3/(1 - x^2)[/tex] is a rational function. Rational functions are functions that are expressed as the quotient of two polynomials. Here, the numerator is a cubic polynomial and the denominator is a quadratic polynomial.

(d) u(t) = 1 - 1.1t + [tex]2.54t^2[/tex] is a polynomial of degree 2. Polynomials are functions that are expressed as a sum of powers of the independent variable, with coefficients. The degree of a polynomial is the highest power of the independent variable.

(e) v(t) = [tex]5^t[/tex] is an exponential function. Exponential functions have the independent variable as the exponent. Here, the base is 5.

(f) w(θ) = sin θ [tex]cos^{2}\theta[/tex] is an algebraic function and a trigonometric function. Algebraic functions are functions that can be expressed using arithmetic operations and algebraic expressions. Trigonometric functions are functions that involve the ratios of the sides of a right triangle. Here, the function is a combination of sine and cosine functions.

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The complete question is -

Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function.

(a) f(x) =  [tex]log_2(x)[/tex]    

(b) g(x) = ∜x    

(c) h(x) = [tex]2x^3/(1 - x^2)[/tex]    

(d) u(t) = 1 - 1.1t + [tex]2.54t^2[/tex]                    

(e) v(t) = [tex]5^t[/tex]    

(f) w(θ) = sin θ [tex]cos^{2}\theta[/tex]

1. The two equations have different slopes.

2. The two equations have different intercepts.

3. The system of equations has one solution.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The number of solutions for a system of two linear functions is defined as follows:

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Answer:

if marip has a piece of string. He cuts off six-eights of it's length. how much is left it's 2

Answer:

see explanation

Step-by-step explanation:

W(2) = 5 , means

a puppy of 2 months has a weight of 5 pounds.

W(6) > W(4) , means

a puppy at 6 months has a greater weight than a puppy of 4 months

W(12) = W(15) , means

a puppy at 12 months is the same weight as a puppy of 15 months

Answer:

Below

Step-by-step explanation:

Pick any two points on the graph   say  2,70   and  3 , 105

  rise is   70 to 105 = 35     run is   2 to3 = 1

     rise/run = 35/1 = 35

Answer:

35

Step-by-step explanation:

gradient= rise/run

= 70-35/2-1

= 35

The equation 15 - x = 7 models the scenario because it represents the decrease in the number of cats that the zoo now nurses. It can be read as "15 (the number of cats originally) minus x (the number of cats moved) equals 7 (the number of cats the zoo now nurses)".

Answer:

53/63

Step-by-step explanation:

It is already in simplest form

Answer:

100 liters is equal to 100,000 milliliters.

Step-by-step explanation:

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 2545.10\\ P=\textit{original amount deposited}\dotfill &\pounds 2000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{each year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]2545.10 = 2000\left(1+\frac{\frac{r}{100}}{1}\right)^{1\cdot 4} \implies \cfrac{2545.10}{2000}=\left( 1+\cfrac{r}{100} \right)^4 \\\\\\ \cfrac{2545.10}{2000}=\left( \cfrac{100+r}{100} \right)^4\implies \sqrt[4]{\cfrac{2545.10}{2000}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[4]{\cfrac{2545.10}{2000}}=100+r\implies 100\sqrt[4]{\cfrac{2545.10}{2000}}-100=r\implies \boxed{6.2\approx r}[/tex]

The equations Ax = b are not compatible.

It is represented by an equal sign (=) and is used to solve for unknown values or to describe relationships between variables. Equations can be simple or complex, involving basic arithmetic operations or advanced mathematical concepts like trigonometry and calculus.

An equation can be used to solve for a single unknown value, for example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving us 2x = 4 and then dividing both sides by 2, giving us x = 2. In this example, x = 2 is the solution to the equation.

To determine whether the equations Ax = b are compatible and to compute a solution x, you would first form the augmented matrix [A|b]. Then, you would perform row operations on [A|b] to reduce it to an upper triangular matrix [C|d]. Finally, you would use the software package to solve the square system of equations Cx = d.

If the software terminates with an error message, it means that C is singular, and the equations Ax = b are not compatible. If the software finds the unique solution of Cx = d, it means that the equations Ax = b are compatible and that the solution x is unique. However, it is important to note that the uniqueness of the solution depends on the rank of A being equal to n. If the rank of A is less than n, the equations are not compatible, and if the rank of A is greater than n, the equations have infinitely many solutions.

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x = (300 - p) / 20

According to the equation, the quantity of kilos (x) of snig that will be sold is equal to the difference between 300 and p, divided by 20.

The price-demand connection for roast snig at the harvest festival on the planet Bozone can be represented by the equation p=300 - 20x. The formula specifies that 300 minus 20 times the number of kilogrammes (x) of snig sold is the price per kilogramme of snig (p) in the local currency (Bozats).

Using this equation, one can determine how much of the price must be reduced in order to sell 1 extra kilogramme of snig. The equation can be rewritten to solve for x in terms of p in order to accomplish this. This can be done by taking 300 off of both sides of the equation, multiplying both sides by 20, and then solving for x = (300 - p) / 20. This rearrangement has the effect of dividing the number of kilogrammes of snig that will be sold in terms of price per kilogramme by the difference between 300 and p. This equation can be used to calculate the price reduction required to sell an extra kilogramme of snig.

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