Calculate the length w in the shape below.
Give your answer in centimetres to 2 d.p.

PROBABLITY

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

A library manager is interested in the number of people using the library. She decides to perform a count every 28th day for one year, starting next Monday. The systematic sampling method is this.

Hence, option (a) is the correct choice.

The library manager employs systematic sampling as a sample approach.

Systematic sampling is a form of probability sampling approach in which sample members are drawn from a larger population at random but with a set, periodic interval.

The sampling interval is determined by dividing the population size by the desired sample size.

Systematic sampling is a technique for picking a sample from a larger population at regular intervals. In this scenario, the library manager selects a sample of library users by tallying the number of persons every 28th day.

It is a systematic sampling approach since the intervals (28th day) are fixed and systematic.

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The function for distance jogged is d(t) = 3.3t and the inverse of the function is d(t)⁻¹ = 3.3/t.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Let, 'd' be the distance covered in miles, and 't' is the time in hours.

Therefore, From the given information d(t) = 3.3t.

Let, d(t) = y.

So, y = 3.3t.

t = 3.3/y.

d(t)⁻¹ = 3.3/t.

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Answer:

g(x) = -√3 (x/3 + 2) + 4.

Step-by-step explanation:

The expression that represents the sum of a number, half the number and 5 times the number is given as follows:

6.5x.

In which x is the number.

The number in this problem is unknown, hence the variable that represents the number is given as follows:

x.

Half the number is given as follows:

x/2 = 0.5x.

Five times the number is given as follows:

5x.

Then the sum of all these amounts is given as follows:

x + 0.5x + 5x = 6.5x.

We just combine the like terms, as they all have the same letter and exponent, hence we just add the coefficients.

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the answer for this question is  i don't know

So , bye

(a) This differential equation can be written in the form (*) with P(x) = 1, Q(x) = 2x, and n = 2.

(b) The substitution u = 1/y will transform it into the linear equation Du/dx +  0u = -2x

(c)Using the substitution in part (b), we rewrite the initial condition in part  u(1) = 1/y(1) = 1/4.

(d) the linear equation in part (b) is y = 1/(C - x) and  the solution that satisfies the initial condition in part (c) U(x) = -y⁻¹ = -x + C,

(e) Finally, solve for y(x) = 1/(1/4 + 1 - x) = 4/(5 - x).

What is  Bernoulli differential equation?

A Bernoulli differential equation is a type of non-linear ordinary differential equation of the form:

dy/dx + P(x)y = Q(x)yⁿ

where P(x) and Q(x) are functions of x and n is a constant. The equation is named after the Swiss mathematician Jakob Bernoulli.

These types of differential equations are important in various fields of science, such as physics, engineering, and economics. They are non-linear, meaning that the dependent variable y appears in both linear and non-linear terms, making them difficult to solve in general.

a) This differential equation can be written in the form (*) with P(x) = x, Q(x) = 2x, and n = 2.

b) The substitution u = y⁻¹ will transform it into the linear equation du/dx - xu = -2x.

c) Using the substitution in part (b), we rewrite the initial condition as u(1) = 1/4.

d) Now we solve the linear equation in part (b). The characteristic equation is given by d/dx(e[tex]\mathrm{(\int -xdx))}[/tex] = -xe[tex]\mathrm{(\int -xdx))}[/tex] which has the general solution u(x) = Ce[tex](-x^2/2)[/tex].

Using the initial condition, we find C = 1/4, so u(x) = 1/4e[tex](-x^2/2)[/tex].

e) Finally, we solve for y. From u = y⁻¹, we have y = 1/u = 4e[tex](-x^2/2)[/tex].

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Answer:

52-green

15-orange

Step-by-step explanation:

g + o = 67  

g = green, o = orange, x = total = 3o + 7

use substitution: (3o + 7) + o = 67

solve for o:4o + 7 = 67

4o = 60o

= 60/4 = 15

solve for g:

g + 15 = 67

g = 52

If a single marble is picked at random from the jar then the probability of it begin a blue marble is 9/32.

A glass jar containing five red 7 green 9 blue an 11 yellow marbles.

If a single marble is picked at random from the jar then we have to determine the probability of it begin a blue marble.

Red Marble = 5

Green Marble = 7

Blue Marble = 9

Yellow Marble = 11

Total Marble = Red Marble + Green Marble + Blue Marble + Yellow Marble

Total Marble = 5 + 7 + 9 + 11

Total Marble = 32

The probability of it begin a blue marble = Blue Marble/Total Marble

The probability of it begin a blue marble = 9/32

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Answer:No solution because 0≠12, so it like a trick question.



Step-by-step explanation: There is no solution because if you multiply the bottom equation by -2 everything will cancel making 0≠12.

The value of r is equal to the cube root of (V * (3π/4)).

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Let x be the cost of the small bag.

The large bag costs x + 30 more than the small bag.

So the cost of the large bag is x + (x + 30) = 2x + 30

The two-piece set of luggage cost is the sum of the cost of the small and large bag, so

122 = x + (2x + 30)

Solving this equation for x, we get:

x = 42

Therefore, the small bag costs 42 dollars and the large bag costs 2*42 +30 = 114 dollars.

Therefore , the solution of the given problem of coordinate plane comes out to be Y coordinates comes out to be -3 , -2, -1 , 0, 1,2,3

By portraying the inputs and outputs as a horizontal number line (the x axis) and a vertical number line (the y axis), respectively, the Cartesian coordinate plane enables us to perceive ordered pairs. The quantity in the x component is moved horizontally. Move to the right if x is positive. Move to the left if x is negative.

Here,

Given :

=> -30 , -20 ,-10 ,0 ,10, 20 , 30

=> So ,

Y coordinates comes out to be :

=> -3 , -2, -1 , 0, 1,2,3

An ordered pair of numbers, or x-coordinate and y-coordinate on the x-axis respectively, can be used to represent each point.

Written in parenthesis are ordered pairings (x-coordinate, y-coordinate). The source is situated at (0,0).

Check your coordinates, which are two numbers enclosed in parenthesis and separated by a comma, to see how to graph a point on the coordinate plane.

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The perimeter of the polygon is 169 inches.

The perimeter of a polygon is the total length of its sides. The tangents from a given circle are used to create the polygon in this problem.

We will apply the idea that if two tangents are drawn from the same point outside of a given circle, their lengths will always be identical.

This polygon has eight sides, which indicates that there are four pairs because their lengths are equal.

Therefore, the perimeter is equal to double the total of the four sides that were supplied to us.

Radius = 2(22+27+22+98)

perimeter is two (169)

Diameter: 338 inches

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Complete question -

The simplified form of the expression (2x+8)^6 is[tex]64x^6 + 1536x^5 + 15360x^4 + 819204x^3 + 245760x^2 + 393216x + 262144.[/tex]

To simplify the expression (2x + 8)^6, we need to raise the binomial (2x + 8) to the power of 6. This can be done using the binomial theorem.

The Binomial Theorem states that for any positive integer n and real numbers a and b, the expansion of the expression (a + b)^n is a sum of terms of the form (a^(n-k) * b^k * C(n,k)), where C(n,k) represents the binomial coefficient, which is equal to n!/(k!(n-k)!).

[tex](a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^(n-1) b^1 + ... + C(n, n-1)a^1 b^(n-1) + C(n, n)a^0 b^n[/tex]

Where C(n, k) is the binomial coefficient, given by C(n, k) = n! / (k! (n - k)!).

In this case, a = 2x and b = 8. So, substituting these values into the binomial theorem:

[tex](2x + 8)^6 = C(6, 0)(2x)^6 8^0 + C(6, 1)(2x)^5 8^1 + ... + C(6, 5)(2x)^1 8^5 + C(6, 6)(2x)^0 8^6[/tex]

Expanding each term, and combining like terms, we get:

[tex](2x + 8)^6 = 64x^6 + 1536x^5 + 15360x^4 + 819204x^3 + 245760x^2 + 393216x + 262144[/tex]

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The estimated mean of the distribution for the given question will be 10.

Mean = 13 + 52 + 48 + 28 + 28 + 23 + 14 + 13 + 10 + 4 + 2 + 4 + 2 + 1 + 1 + 0 + 2 + 0 + 0 + 0 + 1 + 1 + 1 + 1 + 1

Total number =25

Now, divided the sum by 25

We get, the mean is equal to 10.

In mathematics, particularly in statistics, there are various types of means. Every mean serves to condense a specific set of data, frequently to help understand the overall significance of a particular data set. Only numerical variables, whether continuous or discrete, can be used to calculate the mean. Simply dividing the total number of values in a data set by the sum of all of the values yields it. The calculation can be performed on unprocessed data or data that has been combined into a frequency table.

Note that the illustration for graph is: (check the attached image)

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The stability limit depends on the specific form of the equation, so you may need to adjust this value based on the specific equation you are working with.

The stability condition for the Euler's method applied to the equation

y' = f(x,y) is given by the following inequality:

|hf(x,y)| <= 1,

where h is the step size. To determine the largest step size for which Euler's method is stable, we need to find the maximum value of |hf(x,y)|. This maximum value is often referred to as the stability limit.

In your case, the equation is close to the simpler equation y' = a, which has the solution y = a*x + b. The stability limit for the Euler's method applied to this equation is 1, so we can take h <= 1 as the largest step size for which the method is stable. However, the stability limit depends on the specific form of the equation, so you may need to adjust this value based on the specific equation you are working with.

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Answer:

-3y

Step-by-step explanation:

-√(9y²) = -√((3y)²)

= -3y

Answer:

Where is the equation?

Step-by-step explanation:

I need it to solve this problem

Answer:

A

Step-by-step explanation:

Because (--3) is equal to 3 becuas ethe negative is not oustide the value and -(-4) is euqal to =4

So therefore, A is correct.

The false statement regarding Legendre polynomials is given as follows:

E) [tex]P_{2k}(0) = (-1)^k\frac{(2k)!}{2^{2k}k!}, k \in N[/tex]

The Legendre function of order v is the function that is a solution to the differential equation presented as follows:

(1 - x²)y'' - 2xy' + v(v + 1)y = 0.

Examples of Legendre polynomials are given as follows:

From the polynomial of order 2, with k = 2, we have that:

[tex]P_4(0) = 0.375[/tex]

While:

[tex](-1)^2 \times \frac{4!}{16 \times 2!} = \frac{24}{32} = 0.75[/tex]

Different result, hence statement D is false.

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Answer:

aₙ = aₙ₋₁ - 3, a₀ = 8

Step-by-step explanation:

Minus three every time thus the recursive equation would be aₙ = aₙ₋₁ - 3, a₀ = 8

Put n = 10

t(10) = 3(10) - 5 = 30 - 5 = 25

The domain of [tex]f^{-1}[/tex] is the set of all the y-values of the ordered pairs, which are {11, -2, -12, -9, 1}.

A domain is an area of administrative autonomy, authority, or control within the Internet. Domains are defined by the organization or entity that owns them, and are made up of a series of letters and/or numbers that follow the “dot” or period. For example, a domain name may be “example.com” or “example.org”. Domain names are used to identify and locate computers on the Internet and to route email.

The domain of f is the set of all the x-values of the ordered pairs, which are {-6, -13, -2, 11, 8}.

The range of f is the set of all the y-values of the ordered pairs, which are {11, -2, -12, -9, 1}.

The domain of f-1 is the set of all the y-values of the ordered pairs, which are {11, -2, -12, -9, 1}.

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Answer:

14 is a polynomial.

x+1 is a polynomial.

14vx is not a polynomial.

x-2 -2x+4 is a polynomial.

14 is a polynomial, x+1 is a polynomial, 14vx is not a polynomial, x-2 -2x+4 is a polynomial.

A polynomial is an equation made up of indeterminates and coefficients that only uses addition, subtraction, multiplication, and positive-integer powers of variables.

Polynomials are algebraic expressions with indeterminates and constants in them. Polynomials can be thought of as a mathematical dialect. They are used to express numbers in practically every subject of mathematics and are quite significant in others, such as calculus.

Polynomials cannot include the following:

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The LCM of 1-x^2 and (x-1)^3 is (x-1)^3.

To find the LCM, we take the polynomial with the highest degree (which determines the degree of the LCM) and then make sure that it contains all the terms from the other polynomials.

The degree of (x-1)^3 is 3 and the degree of 1-x^2 is 2.

So, we take (x-1)^3 as the starting point for the LCM and then add any missing terms from 1-x^2.

In this case, (x-1)^3 already contains all the terms from 1-x^2, so the LCM is (x-1)^3.

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1) "The analysis of past demand helps predict future demand" is true about Time series forecasting.

2) A researcher wants to test if elementary school children spend less than 30 minutes per day on homework. The alternative hypothesis for this example will be that the population mean is: less than 30 minutes.

Hence, option (A) is the correct choice.

3) Normal probability distribution is applied to: a continuous random variable

Hence, option (d) is the correct choice.

A time series is a sequence of data points indexed in time order in mathematics. A time series is most frequently defined as a succession of photos taken at evenly spaced moments in time. As a result, it is a series of discrete-time data.

Time series forecasting is the process of making scientific forecasts based on time stamped data from the past. It entails developing models based on previous data and utilizing them to make observations and drive future strategic decisions.

The straight-line approach, moving averages, simple linear regression, and multiple linear regression are the four basic forecast methodologies. The straight-line and moving average techniques both presume that the company's past results will be broadly consistent with future results.

We are provided the following details:

- Average mu in the population: 30

The following is an alternate theory.

[tex]$$H_1: \mu < 30 \text { ( Claim ) }$$[/tex]

For this case, the alternative hypothesis is that the population mean is less than 30 minutes.

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Answer:

Vertical Line Test

Step-by-step explanation:

If a vertical line is drawn on a graph of a relation and only intersects the graph at one point, then that graph represents a function. If there is no vertical line intersecting the graph at two or more points, then the graph does not represent a function.

The truth table for the above requirements is shown as the relationship between the coins inserted (N/D/Q) and the candies dispensed (Gummies/Licorice/Lollipops/Caramels/Chocolate).

A truth table is a mathematical table used in logic that spells forth the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables.

The truth table for the vending machine scenario is represented in following figure.

The table shows the relationship between the coins inserted (N/D/Q) and the candies dispensed (Gummies/Licorice/Lollipops/Caramels/Chocolate). A 1 in the table indicates that the candy is dispensed, while a 0 indicates that it is not.

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The total amount of the debit column in the adjusted trial balance is $5,400.

To find the total amount of the debit column in the adjusted trial balance, we need to sum up all the debit amounts listed in the accounts of teh given question.

Debits represent money being paid out of a particular account;

Looking at the trial balance provided, we can identify the following accounts with debit balances:

1. Cash: $500

2. Equipment: $2,000

3. Accounts Payable: $1,000

4. Common Stock: $700

5. Retained Earnings: $600

6. Service Revenue: $900

7. Operating Expenses: $600

8. Dividends: $100

In order to find the total amount of the debit column, we add up all these amounts,

Which gives us:

$500 + $2,000 + $1,000 + $700 + $600 + $900 + $600 + $100 = $5,400

Therefore, the total amount of the debit column in the adjusted trial balance is $5,400

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The required incorrect step is step 1, circle B should have been translated 7 units right and 9 units up. Option A is correct.

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r²

where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.

Here,
Circle A with a center at (3, 4) and a radius of 2 is similar to circle B with a center at (−4, −5) and a radius of 3.
To translate the circle B over circle A is given as 7 units right and 9 units up.

Thus, the required incorrect step is step 1, circle B should have been translated 7 units right and 9 units up. Option A is correct.

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