Q2. (15 points) Find the following probabilities: a. p(X= 2) when X~ Bin(4, 0.6) b. p(X> 2) when X~ Bin(8, 0.2) c. p(3 ≤X ≤5) when X ~ Bin(6, 0.7)

(a) The Newton-Raphson method is an iterative technique for solving non-linear equations.

It involves updating initial estimates of the variables based on the function's derivative. In this case, we have a system of three non-linear equations with three variables (x₁, x₂, x₃). By applying the Newton-Raphson method, we can iteratively refine the initial values until the desired tolerance is achieved.

(b) The Gauss-Jacobi method is an iterative technique for solving systems of linear equations. It can be extended to solve non-linear systems by linearizing the equations using Taylor series expansion. In this method, we update each variable's value based on the previous iteration's values until convergence is reached.

(c) The Gauss-Seidel method is similar to the Gauss-Jacobi method, but it updates the variables' values in a different order. Instead of using the values from the previous iteration, it uses the updated values as soon as they are available. This method typically converges faster than Gauss-Jacobi but may not converge for all systems.

To solve the given system of equations using these methods, we start with initial values of 1 for all variables and iterate until the error is below the tolerable limit of 0.001. The specific iterative formulas for each method and the step-by-step calculations are necessary to provide a complete solution, but due to the word limit, they cannot be included here.

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(a) The Newton-Raphson method is an iterative technique for solving non-linear equations.

It involves updating initial estimates of the variables based on the function's derivative. In this case, we have a system of three non-linear equations with three variables (x₁, x₂, x₃). By applying the Newton-Raphson method, we can iteratively refine the initial values until the desired tolerance is achieved.

(b) The Gauss-Jacobi method is an iterative technique for solving systems of linear equations. It can be extended to solve non-linear systems by linearizing the equations using Taylor series expansion. In this method, we update each variable's value based on the previous iteration's values until convergence is reached.

(c) The Gauss-Seidel method is similar to the Gauss-Jacobi method, but it updates the variables' values in a different order. Instead of using the values from the previous iteration, it uses the updated values as soon as they are available. This method typically converges faster than Gauss-Jacobi but may not converge for all systems.

To solve the given system of equations using these methods, we start with initial values of 1 for all variables and iterate until the error is below the tolerable limit of 0.001. The specific iterative formulas for each method and the step-by-step calculations are necessary to provide a complete solution, but due to the word limit, they cannot be included here.

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A cable management panel is a simple device consisting of multiple connector blocks and ports used for cable management.

Cable management panels are essential components in organizing and maintaining the cables in a network or server environment. These panels typically feature multiple connector blocks and ports, allowing for the efficient routing and organization of cables. They provide a centralized location to neatly bundle and secure cables, reducing the risk of tangles, damage, or accidental disconnections. By using a cable management panel, organizations can improve the overall appearance and accessibility of their cabling infrastructure.

These panels are available in various sizes and configurations to accommodate different cable types and densities. They are commonly used in data centers, server rooms, network closets, and other IT environments where cable management is crucial. The connector blocks and ports in the panel may include options such as RJ45 jacks for Ethernet cables, fiber optic connectors, or other specific connectors depending on the requirements of the network.

The primary purpose of a cable management panel is to provide a structured and organized approach to cable management, ensuring better airflow, easier troubleshooting, and enhanced overall system performance. By keeping cables neatly organized and properly labeled, it becomes easier to identify and trace specific connections when needed. Additionally, **proper cable management** also helps to minimize signal interference and signal loss, ensuring reliable and efficient data transmission.

In summary, a **cable management panel** is a valuable device that facilitates the organization and management of cables in a network or server environment. It streamlines cable routing, reduces clutter, and improves overall system performance and maintenance.

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ANSWER

The light intensity is 7.0

STEP-BY-STEP EXPLANATION:

What to find? The value of the proportionality constant.

Given parameters

• Light intensity = 569 lumens

• Distance = 9

According to the question, Light intensity (I) is proportional to the inverse square of the distance.

This can be expressed mathematically as

Let the intensity of light be represented as I

Let the distance be represented as d

The next thing is to introduce a constant k

Recall that,

I = 569 lumens

d = 9

The next thing is to substitute the parameters into the above formula

Answer:

3

Step-by-step explanation:

7+4 is 11

11,22,33 is the maximum which is 3

Rational numbers can be written as decimals by dividing the numerator by the denominator. The result can be a terminating decimal (ends) or a repeating decimal (pattern repeats indefinitely).

Rational numbers can be written as decimals by dividing the numerator (the top number) by the denominator (the bottom number) of the fraction.

For example, let's consider the rational number 3/4. To write it as a decimal, we divide 3 by 4:

3 ÷ 4 = 0.75

So, 3/4 as a decimal is 0.75.

Similarly, for a rational number like 1/2:

1 ÷ 2 = 0.5

Hence, 1/2 as a decimal is 0.5.

In general, when dividing a numerator by a denominator, the result can be a terminating decimal (where the division ends) or a repeating decimal (where the division repeats a pattern indefinitely). For example, 1/3 as a decimal is 0.3333..., with the digit 3 repeating.

It's important to note that not all rational numbers can be expressed as terminating or repeating decimals. For instance, the square root of 2 (√2) is a rational number, but it cannot be precisely expressed as a decimal and is known as an irrational number.

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The length of the microorganism that measure 5μm is equivalent to 0.005 mm

It is the transformation of a value expressed in one unit of measurement into an equivalent value expressed in another unit of measurement of the same nature.

To solve this problem the we have to convert the units with the given information.

1mm is equal to 1000 μm

5μm * (1 mm/1000μm) = (5*1) / 1000 = 5/1000 = 0.005 mm = 5x10^-3 mm

The length of the microorganism that measure 5μm is equivalent to 0.005 mm

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Answer:

$56.

$83.99.

Step-by-step explanation:

She will save  40% of $139.99

= 0.40 * 139.99

= $56.

With the discount membership costs:

139.99 - 56

= $83.99.

Answer:

\(\frac{56}{25}\)

Step-by-step explanation:

Exact Form:

\(\frac{56}{25}\)

Decimal Form:

2.24

Mixed Number Form:

\(2\frac{6}{25}\)

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30 and 16 are the mean and standard deviation of Y.

X is a random variable with mean μ = 55 cm and a standard deviation σ = 8 cm. If Y = -2X + 140, let's find the mean and the standard deviation of Y.

If Y = -2X + 140, then E(Y) = E(-2X + 140) = -2E(X) + 140 = -2 × 55 + 140 = 30

So, the mean of Y is 30.

If Y = -2X + 140, then Var(Y) = Var(-2X + 140) = (-2)²Var(X) = 4Var(X)

If X is a random variable with mean μ = 55 cm and a standard deviation σ = 8 cm, then its variance is Var(X) = σ² = (8)² = 64

Thus, Var(Y) = 4Var(X) = 4(64) = 256

Taking the square root of the variance, we get the standard deviation of Y as follows:

SD(Y) = √Var(Y) = √256 = 16

Therefore, the mean of Y is 30, and the standard deviation of Y is 16.

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Answer:

(a) 1, 2, 3, 4, 6, 8, 12, 24

(b) 1, 2, 3, 4, 6, 9, 12, 18, 36

(c) 1, 5, 7, 35

(d) 1, 2, 4, 8, 16, 32

The possible outcomes of the game, in terms of first place, second place, and third place, are:

Mohsin, Yusuf, Luke

Mohsin, Luke, Yusuf

Yusuf, Mohsin, Luke

Yusuf, Luke, Mohsin

Luke, Mohsin, Yusuf

Luke, Yusuf, Mohsin

To list all the possible outcomes of the game, we need to consider the different permutations of the three players: Mohsin, Yusuf, and Luke. Since there are three players, there are a total of 3! (3 factorial) possible outcomes, which is equal to 3 x 2 x 1 = 6.

Using the table format, we can list the possible outcomes as follows:

Outcome 1: Mohsin, Yusuf, Luke

Outcome 2: Mohsin, Luke, Yusuf

Outcome 3: Yusuf, Mohsin, Luke

Outcome 4: Yusuf, Luke, Mohsin

Outcome 5: Luke, Mohsin, Yusuf

Outcome 6: Luke, Yusuf, Mohsin

Each outcome represents a different arrangement of the players in the first, second, and third places.

As a result, the following players might finish first, second, and third in the game: Mohsin, Yusuf, and Luke

Luke, Mohsin, and Yusuf

Luke, Yusuf, and Mohsin

Mohsin, Luke, and Yusuf

Yusuf, Mohsin, and Luke

Mohsin, Yusuf, and Luke

These outcomes represent all the different ways in which the players can finish the game.

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Answer:

456748

Step-by-step explanation:

you 463uy2iuswhk then 13456

Answer:

We know that A receives R500 less than C, so we can write:

4x = 9x - 500

Solving for x, we get:

5x = 500

x = 100

Now we can calculate the amounts received by each person:

A = 4x = 4(100) = R400

B = 7x = 7(100) = R700

C = 9x = 9(100) = R900

To check our answer, we can verify that the ratios of the amounts received by A, B, and C are indeed 4:7:9:

A:B = 400:700 = 4:7

B:C = 700:900 = 7:9

Therefore, the total amount divided is:

400 + 700 + 900 = R2000

So the amount that is divided is R2000.

Step-by-step explanation:

The total amount of money divided is R2000.

Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We are given that;

The ratio of A, B and C= 4:7:9

Now,

Let's start by assigning variables to the unknowns in the problem. Let's call the total amount of money "T". Then, if A receives 4x, B receives 7x, and C receives 9x, where "x" is some constant, we can write:

4x + 500 = C's share

We can also write an equation to represent the fact that the three shares add up to the total amount:

4x + 7x + 9x = T

Simplifying this equation, we get:

20x = T

Now we can substitute the first equation into the second equation and solve for x:

4x + 7x + (4x + 500) = 20x

15x + 500 = 20x

500 = 5x

x = 100

Now we can find the individual shares by multiplying x by the appropriate ratio factor:

A's share = 4x = 400

B's share = 7x = 700

C's share = 9x = 900

Finally, we can check that these add up to the total amount:

400 + 700 + 900 = 2000

Therefore, by the given ratio the answer will be R2000.

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Answer:

$50

Step-by-step explanation:

Price of the cell phone bought p = $40

% of markup in price = 25%

Selling price of the cell phone = p + (%)p

Selling price of the cell phone = P + (0.25)p

Selling price of the cell phone = p + 0.25p

Selling price of the cell phone = 1.25p

Selling price of the cell phone = 1.25 * $40

Selling price of the cell phone = $50

Answer:

(x-4)^2 -9

x^2+8x+7

x(x+8)+7

Step-by-step explanation:

(x+7) (x+1)

distributive property

x^2+ x+7x+7

combine like terms

x^2 +8x+ 7

Then solve each expression to find the one equivalent to x^2 + 8x+ 7

x=-7 and x+-1

Answer:

26.25 bottles

Step-by-step explanation:

A flower garden in the form of trapezoid is shown. The length of longer base is labeled 18 feet, shorter base is 15 feet, height is 4 feet, and one leg is 5 feet.

Formula for perimeter of a trapezoid = Side a + side b + length a + length b

For the trapezium shown, its perimeter step 1,

we have to find the missing length

Length a

We are given height = 4 feet

Length of the longer base = 18 feet

Length of the shorter base = 15 feet

Different would give us the base of the right angle triangle

= 18 - 15 = 3 feet

Using Pythagoras Theorem we can find the side a = c

a² + b² = c²

3² + 4² = c²

9 + 16 = c²

c = √25

c = 5 feet

Hence side a = 5 feet

Perimeter of the Trapezoid shown =

18 feet + 15 feet + 5 feet + 5 feet

= 38 feet.

From the question,

You need two bottles of fertilizer to treat the flower garden shown. How many bottles do you need to treat a similar garden with a perimeter of 105 feet

Hence:

38 feet = 2 bottles

105 feet = x bottles

Cross y

= 38 × x = 105 × 2

= 38x = 105 × 2

x = 105 × 2/38

x = 26.25 bottles

26.25 bottles of fertilizer is needed to treat the garden with a perimeter of 105

Note: Consider the solid object is a cylinder because the radius of base and height of the solid is given.

Given:

Radius of base = 7 cm

Height = 12 cm

To find:

The volume of the given solid.

Solution:

The volume of a cylinder is:

\(V=\pi r^2h\)

Where, r is the radius of the base and h is the height of the cylinder.

Putting \(r=7,h=12,\pi=\dfrac{22}{7}\) in the above formula, we get

\(V=\dfrac{22}{7}\times(7)^2\times (12)\)

\(V=22\times 7\times 12\)

\(V=1848\)

Therefore, the volume of the given solid is 1848 sq. cm.

The solution to the system is x1 = 8, x2 = 1, and x3 = -1.

To solve the systems, we will use the method of elimination. This method involves multiplying one or both equations by a constant in order to eliminate one of the variables.

First, we will eliminate x1 from the first and second equations by multiplying the first equation by -1 and then adding the two equations together:
-1(x1 - 3x2) = -1(5)
-x1 + 3x2 = -5

-x1 + x2 + 5x3 = 2
2x2 + 5x3 = -3
Next, we will eliminate x2 from the second and third equations by multiplying the second equation by -1 and then adding the two equations together:
-1(-x1 + x2 + 5x3) = -1(2)

x1 - x2 - 5x3 = -2
x2 + x3 = 0
x1 - 6x3 = -2

Finally, we will eliminate x3 from the second and third equations by multiplying the third equation by -5 and then adding the two equations together:

-5(x2 + x3) = -5(0)
-5x2 - 5x3 = 0

2x2 + 5x3 = -3
-3x2 = -3
x2 = 1

Now that we know the value of x2, we can substitute it back into the third equation to find the value of x3:
x2 + x3 = 0
1 + x3 = 0
x3 = -1
And finally, we can substitute the values of x2 and x3 back into the first equation to find the value of x1:
x1 - 3x2 = 5
x1 - 3(1) = 5
x1 = 8
So the solution to the system is x1 = 8, x2 = 1, and x3 = -1.

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ffggddaafvvcgghv de ryhvg

\(7 \tan^3 x - 21\tan x =0\\\\\implies 7\tan x(7 \tan^2 x -21) = 0\\\\\implies 7 \tan x = 0 ~~\text{or}~~ 7\tan^2 x -21 =0\\\\\implies \tan x = 0 ~~\text{or}~~ \tan x = \pm\sqrt{\dfrac{21}7} = \pm \sqrt 3\\\\\text{Now,}\\\\\tan x = 0\\\\\implies x = n \pi \\\\\implies x = 0, \pi ~~~~~~~~~~~~~;[\text{For n=0,1 and}~ [0, 2 \pi)}]\\\\\\\tan x = \sqrt 3 \\\\\implies x = n \pi + \dfrac{\pi}3\\\\\implies x = \dfrac{\pi}3, ~~\dfrac{4 \pi}{3} ~~~~~~~~;[\text{For n = 0,1 and }~ [0, 2\pi)]\\\\\\\)

\(\tan x = -\sqrt 3\\\\\implies x= n\pi - \dfrac{\pi}3\\\\\implies x = \dfrac{2\pi}{3},~~ \dfrac{5\pi}3 ~~~~~~~ ;[\text{For n=1,2 and}~ [0,2\pi)]\)'

\(\text{Combine all solutions,}\\\\x= 0, ~\pi, ~\dfrac{\pi}3,~ \dfrac{4 \pi}3 ,~ \dfrac{2 \pi}3 , ~\dfrac{5\pi}3\)

Answer:

Yea she drove

Step-by-step explanation:

Answer:

40 mph

Step-by-step explanation:

s=vt

v = s/t

putt values

Answer:

1.   70

Step-by-step explanation:

2.  105

Answer:

A: 70.311 repeat

B: 105.53

Step-by-step explanation:

im not sure if im correct but hope this helps

The correct option id D. There is a 9.52% chance that a random sample of 100 Cal State East Bay students would have more than our sample's 36 working full-time

A study was conducted to determine if more than 30% of Cal State East Bay students work full-time.

The sample of Cal State East Bay students selected was random.

Out of 100 students, 36 were found to be working full-time.

The p-value was calculated to be 0.0952.

The probability of having more than 36 Cal State East Bay students working full-time out of a random sample of 100 students is 9.52% if exactly 30% of Cal State East Bay students work full-time.

Therefore, it is concluded that the null hypothesis cannot be rejected.

The p-value is greater than 0.05 which shows the significance level.

Hence, we accept the null hypothesis.

The null hypothesis states that the proportion of Cal State East Bay students who work full-time is not greater than 30%.

The alternate hypothesis states that the proportion of Cal State East Bay students who work full-time is greater than 30%.

The test is a right-tailed test.

The sample proportion is p = 0.36. The test statistic is given as Z = (p - P0) / √ [P0 (1 - P0) / n]Z = (0.36 - 0.30) / √ [(0.30) (0.70) / 100] = 1.76The p-value is given as 0.0392.

Since the p-value is less than 0.05, we can reject the null hypothesis.

Thus, we can conclude that more than 30% of Cal State East Bay students work full-time.

Hence, option D is the correct answer.

There is a 9.52% chance that a random sample of 100 Cal State East Bay students would have more than 30% working full-time.

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Answer:

The slope is 7 and the relationship is increasing

Step-by-step explanation:

y=mx+b is slope intercept form.

m=slope

7 is in place of m is y=7x+30

7 is positive so the relationship is increasing.

Answer:

55

Step-by-step explanation:

You multiply 5 on both sides of the ratio, and you get 40 children : 15 adults. Adding that up, you would get 55 people.

Answer:

Step-by-step explanation:

Write and solve an equation of ratios.  The given ratio is 8:3.  The number of children is 40 and that of adults is 40 - c.  Note that c + (40 - c) = 40.

Solve the following equation of ratios for c:         8        40

                                                                               ---- = ----------

                                                                                3          a

Cross multiplying, we get 8a = 120, of 15.  Then a = number of adults = 24.

Here a = 15 and c = 40.  Check the ratio 40/15; does it equal 8/3?  YES

The total number of people at the pool is 40 + 24, or 64

Answer:

Step-by-step explanation:

y is always (1/3) of x.

Thus, if x = 0, y = 0; if x = 1, y = (1/3)(1) = 1/3, and so on.  The corresponding ordered pairs are (0, 0), (1, 1/3), (-2, -2/3)