Problem 3
A bottle filling machine fills an average of 20,000 bottles
a day with a standard deviation of 2000. Assuming that
production is normally distributed and the year
comprises 260 working days, calculate the approximate
number of working days on which:
a) Under 18,000 bottles are filled
b) Over 16,000 bottles are filled
c) Between 18,000 and 24,000 bottles are filled.

The probability that the sample proportion is between 0.55 and 0.62 is 0.7962.

Probability is the measure of how likely an event is to occur out of the total number of possible outcomes. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. Probability is used to describe random events, such as the toss of a coin or the role of a die, as well as more complex events, such as the weather, stock market performance, and the success of a political candidate. A probability of 0.5, for example, means that there is a 50% chance that the event will occur.

This is calculated using the binomial probability formula, which is the probability of a certain outcome of a series of independent binary events. According to the formula, the probability of the sample proportion being between 0.55 and 0.62 is the sum of the individual binomial probabilities for each outcome within the range of 0.55 and 0.62. This is calculated as the sum of the binomial probabilities for each outcome (where p = 0.60): P(x=55) + P(x=56) + P(x=57) + P(x=58) + P(x=59) + P(x=60) + P(x=61) + P(x=62). The result is 0.7962.

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Answer:

Step-by-step explanation:

2+2 is 4

We knοw that diagοnal bisects each οther sο AE = CE

Since AE = CE, we have:

In mathematics, a rectangle is a fοur-sided plane figure with οppοsite sides parallel and equal in length, and fοur right angles. It is a type οf parallelοgram, where all angles are right angles, and οppοsite sides are cοngruent.

The length οf the rectangle is the distance between the twο lοnger sides, and the width οf the rectangle is the distance between the twο shοrter sides. The area οf a rectangle is given by the prοduct οf its length and width, while its perimeter is the sum οf the lengths οf all its sides.

4x + 7 = 5x + 2

Subtracting 4x frοm bοth sides, we get:

x + 7 = 2

Subtracting 7 frοm bοth sides, we get:

x = -5

Since x = -5, we can find AE and CE as fοllοws:

AE = 4x + 7 = 4(-5) + 7 = -13

CE = 5x + 2 = 5(-5) + 2 = -23

Nοw, we can find BD using the Pythagοrean theοrem:

[tex]BD^2 = AE^2 + BE^2[/tex]

BE = AB = AE tan(31°) ≈ -7.695 (using the given angle and AE)

[tex]BD^2 = (-13)^2 + (-7.695)^2[/tex]

BD ≈ 15.03

Therefοre, BD ≈ 15.03.

Tο find angle ECB, we can use the fact that angle EAB = angle ECD  

angle ECB = 90 - angle ECD

angle ECB = 90-31 = 59

Therefοre, angle ECB is apprοximately 59 degrees.

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This graph shows the national debt of some countries during a certain time period.

Graph is a data structure consisting of nodes connected by edges. It is used to represent a network of relationships between objects, such as in a computer network, social network, or other type of network. Graphs can be used to represent many types of data, such as distance, connectivity, and directions. Graphs can also be used to model real-world events, such as travel routes and social connections.

The national debt is the total amount of money that the government of a country owes to the public, businesses, and other countries. It is the sum of all past borrowing and represents the country's obligation to pay back the money that they have borrowed.

The graph clearly shows that the national debts of some countries have increased significantly during this time period. This trend is likely due to a combination of factors, including a higher demand for government spending, an increase in public borrowing, and economic stagnation, among others.

The increasing national debt can cause a number of problems for a country, such as an increase in the cost of borrowing for the government, a decrease in the availability and affordability of credit for citizens, and an increase in the country's overall debt burden. This can lead to slower economic growth, increased inequality, and a decrease in public services.

In order to reduce the national debt, governments must focus on increasing their revenues through taxation and controlling their spending. In addition, they must work to reduce the budget deficit by cutting costs, increasing efficiency, and investing in productive sectors of the economy. Furthermore, governments must strive to encourage economic growth through policies that promote job creation and investment.

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The national debt of during a certain time period was $9,000,000,000, which can be written in scientific notation as 9 x 109.

Graph is a data structure that is used to represent a collection of items connected by relationships. It consists of vertices or nodes that are connected by edges or arcs. Graphs are used to represent networks of communication, data organization, computational devices, the flow of computation and many other related concepts. They are widely used in computer science and other fields to represent the relationship between objects and data. Graphs are an essential tool for data visualization and analysis.

Scientific notation is a way of writing very large or very small numbers, typically numbers that have either a lot of zeroes or a decimal point. Scientific notation is written in the form of a number multiplied by a power of ten. The number 9 in this case is the coefficient, and the power of ten is 10 raised to the power of 9, or 109.

The graph shows the national debt of various countries over a certain period of time. The vertical axis of the graph represents the amount of national debt in billions of dollars. The horizontal axis of the graph represents the countries included in the data. The graph shows that most countries had an increase in their national debt from the beginning to the end of the period.

This increase in national debt can be attributed to a variety of factors. One factor is the increasing cost of public services, such as healthcare and education, as a result of population growth and rising demand for these services. Another factor is the increasing cost of debt servicing, which is the cost of paying interest on existing debt. Finally, countries may also be borrowing more to finance large infrastructure projects or to fund government spending. All of these factors contribute to an increase in national debt over time.

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1. The surface area of the pyramid is 115 cm²

(a) The area of the four triangles is 90 cm²

(b) The area of the square is 25 cm²

(c) The total surface area of the pyramid is 115 cm².

To calculate the surface area of the pyramid, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

(a) To find the area of the 4 triangles, we use the formula below

Where:

From the diagram,

Given:

Substitute these values into equation 2

(b) To find the area of the square, we use the formula below

Where:

Substitute these values into equation

(c) To find the total surface area of the pyramid, we use the formula

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B.20

18 x 17.5 equals 315.

315 divided by 15.75 equala 20.

The value of the length of the segment TM when JM is parallel to ST is 5 cm. Option B is the correct answer.

When two lines in a plane do not cross at any point, they are said to be parallel. Lines that never cross paths with one another and do not have a common junction point are said to be parallel. Lines can either be parallel or intersecting. Two lines are said to intersect when they cross at a certain location in a plane. A line is referred to as a transversal line if it crosses two or more other lines at different locations.

Given that, JM is parallel to ST.

We know that a parallel line inside the triangle divides the corresponding sides in equal ratio.

Thus,

JR/SJ = MR/TM

Substituting the values we have:

12/3 = 20/TM

TM = 20/4

TM = 5 cm

Hence, the value of the length of the segment TM when JM is parallel to ST is 5 cm. Option B is the correct answer.

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Hence, in response to the provided question, we can say that Hence, the solutions to the equation [tex]Ax^2 - 3x = 0 are x = 0 and x = 3/A.[/tex]

An algebraic equation is a method of connecting two quotes by using the equals symbol (=) to express equality. In algebra, an explanation is a definitive expression that verifies the equivalency of two formula. For example, the identical character divides the numbers 3x + 5 and 14. A linear equation might be used to recognize the connection that existing between the texts written on separate sides of a letter. The product and application both frequently the same. 2x - 4 equals 2, for example.

We can factor out x to get the answer to the equation Ax2 - 3x = 0.

x(Ax - 3) = 0

We can set each factor to zero and solve for x because the product of two factors is zero if and only if one or both of the factors are zero.

x = 0 or Ax - 3 = 0

If A is greater than zero, we can solve the second equation for x by adding 3 to both sides and dividing by A:

[tex]Ax-3 = 0 Ax-3 = 3 x = 3/A[/tex]

Hence, the solutions to the equation[tex]Ax^2 - 3x = 0 are x = 0 and x = 3/A.[/tex]

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The solution for the equation ax² - 3x = 0 are x = 0 and x = 3/a.

The equals sign (=), which expresses equality, is a way to join two quotes in an algebraic equation. An explanation in algebra is a conclusive phrase that confirms the similarity of two formulas. The same letter, for instance, divides the integers 3x + 5 and 14.

The relationship between the texts written on the different sides of a letter can be determined using a linear equation. Products and applications are usually interchangeable. In this case, 2x - 4 equals 2.

From the question,

We can factor out x to get the answer to the equation ax² - 3x = 0.

x (ax - 3) = 0

The product of two factors is zero if and only if one or both of the factors are zero, thus we can set each element to zero and find x.

x = 0 or ax - 3 = 0

By adding 3 to both sides and dividing by a, we may solve the second equation for x if a is greater zero:

ax = 3

⇒ x = 3/a

Therefore, the solutions of the equation are x = 0 and x = 3/a.

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Answer:

Step-by-step explanation:

[tex]i=2: \frac{3}{2} \times\frac{1}{3^2}=\frac{1}{6}[/tex]

[tex]i=3: \frac{3}{2} \times\frac{1}{3^3}=\frac{1}{18}[/tex]

[tex]i=4: \frac{3}{2} \times\frac{1}{3^4}=\frac{1}{54}[/tex]

[tex]i=5: \frac{3}{2} \times\frac{1}{3^5}=\frac{1}{162}[/tex]

[tex]i=6: \frac{3}{2} \times\frac{1}{3^6}=\frac{1}{486}[/tex]

[tex]sum=\frac{121}{486}[/tex]

Answer: (-3, 4)

Step-by-step explanation:

To find the coordinates of A’, simply subtract 3 from X (0) to represent a translation to the left, and add 4 to Y (0) to represent a translation upwards. Following this, we get (-3, 4).

Answer:

B) (-3,4)

Step-by-step explanation:

In the graph, you can see that if we move point A (0,0) three spaces to the left and 4 spaces up, it is now at the point (-3,4)

Helping in the name of Jesus.

Answer: $980

$25480

Step-by-step explanation:

Lambert will have R22 500 left over after paying tax.

How to solve and what is tax?

If Lambert earns R30 000 every month and 1/4 of that amount is paid as tax, then the amount of tax he pays every month can be calculated as:

Tax = (1/4) x R30 000

= R7 500

Therefore, after paying tax, Lambert will have the remaining amount left over, which can be calculated as:

Remaining amount = R30 000 - R7 500

= R22 500

So, Lambert will have R22 500 left over after paying tax.

Tax is a compulsory financial charge or levy imposed by a government or other authority on income, goods, services, or transactions. Taxes are typically levied as a percentage of income or the value of goods and services, and they are collected to fund public services and infrastructure, such as schools, hospitals, roads, and public utilities.

The tax system is an important source of revenue for governments around the world, and it is used to finance various public goods and services that are essential for the functioning of society.

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Answer:

a. 13n

Step-by-step explanation:

product signifies multiplication and 13n=13xn

a. 13

Answer:

[tex]\huge\boxed{\sf x = 5}[/tex]

Step-by-step explanation:

Each of two equal sides = 2x + 3

Third side = 2x

Perimeter = 36

We know that,

So,

36 = 2x + 3 + 2x + 3 + 2x

36 = 2x + 2x + 2x + 3 + 3

36 - 6 = 6x

30 = 6x

30/6 = x

5 = x

OR

Now,

The length of all three sides:

= 2x + 3

= 2(5) + 3

= 10 + 3

= 13

= 2x

= 2(5)

= 10

[tex]\rule[225]{225}{2}[/tex]

The graph of y=2ˣ-4 is as shown.

To graph the function y=2ˣ-4 and plot some points with integer coordinates, we can use a graphing calculator or an online graphing tool. Here are the steps:

Open a graphing tool, such as Desmos or GeoGebra.

Enter the function y=2ˣ-4 in the equation editor or function input box.

Adjust the x-axis and y-axis to fit the desired range. For example, we can set the x-axis from -5 to 5 and the y-axis from -5 to 10.

Plot some points with integer coordinates that fit the axes. Here are four possible points:

When x=0, y=2⁰-4= -2, so the point (0,-2) is on the graph.

When x=1, y=2¹-4= -2, so the point (1,-2) is on the graph.

When x=-1, y=2⁻¹-4= -4.5, so the point (-1,-4) is on the graph.

When x=2, y=2²-4= 0, so the point (2,0) is on the graph.

Plot these points on the graph by clicking or tapping on the corresponding locations. The graphing tool will connect the points and draw the graph of the function.

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Answer:

  ∠3 = 100°

  ∠2 = ∠4 = 80°

Step-by-step explanation:

You want the measures of the four angles where lines m and n cross, given that obtuse angle 1 is 100°.

Vertical angles 1 and 3 are congruent.

  ∠3 = 100°

Adjacent angles of a linear pair are supplementary:

  ∠2 = ∠4 = 180° -100°

  ∠2 = ∠4 = 80°

__

Additional comment

Angles 2 and 4 are also vertical angles, congruent to each other.

Answer:

698

Step-by-step explanation:

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1)d

n is the term that I want.  

[tex]a_{1}[/tex] is the first term.

d is the common difference.  In this case 7.  Seven is the number that the series is increasing every term

[tex]a_{100}[/tex] = 5 + (100-1)7

[tex]a_{100}[/tex] = 5 + (99)7

[tex]a_{100}[/tex] = 5 + 693

[tex]a_{100}[/tex] = 698

Helping in the name of Jesus.

The proof that the segments AA1 and BB1 are congruent using two columns is shown below

The two column proof to prove that the segments AA1 and BB1 are congruent is as follows:

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After answering the presented question, we can conclude that  then used expression the fact that translations retain angle measure to conclude that the measure of angle is preserved by translations [tex]$x$ is $60^\circ$.[/tex]

In mathematics, you can multiply, divide, add, or subtract. An expression is formed as follows: Expression, number, and math operator Numbers, parameters, and functions make up a mathematical expression. It is possible to contrast phrases and expressions.

Alfred's solution appears to be partial, as some gaps remain to be filled. Here's Alfred's solution in its entirety:

"If we translate along the directed line segment[tex]$\overrightarrow{IF}$, the following will happen: Line $\overleftrightarrow{HI}$ maps onto line $\overleftrightarrow{IJ}$ and line $\overrightarrow{IF}$ maps onto line $\overrightarrow{FI}$. Therefore, the image of angle $x$ will be exactly where the pre-image of angle $GFI$ was. Since translations preserve angle measure, the measure of angle $x$ must be $\boxed{60^\circ}$."[/tex]

In summary, Alfred utilised the translation property to map the given lines and angles onto their pictures, and then used the fact that translations retain angle measure to conclude that the measure of angle is preserved by translations [tex]$x$ is $60^\circ$.[/tex]

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Answer:

Step-by-step explanation:

Fill in the blanks in Alfred's solution.

If we perform a translation along the directed line segment IF, the following will happen:

- Line HI maps onto line FG.

- Line IF maps onto itself.

Therefore, the image of angle x will be exactly where the pre-image of angle IFG was. Since translation preserve angle measure, the measure of angle x must be 60º.

By taking these actions, Carmen may properly plan the rail lines for the unitary method  new train station and make sure they satisfy the requirements of travellers and the local community.

The unit technique is a method of problem-solving where you first calculate the value of a single unit, then multiply that value to get the answer. Simply expressed, a single unit value is extracted from a specified multiple using the unit method. For instance, 40 pens will set you back 400 rupees, or $1.01. The method used to accomplish this might be standardised. a solitary nation. anything has a distinctive component. Mathematics of matrices or operators, linear algebra, mathematical analysis, and its adjoint and reciprocal are all equivalent.

Carmen will need to think about a number of things while planning rail lines for a new train station, including the anticipated passenger volume, the population and demography of the neighbourhood, and the available financing for development.

Last but not least, Carmen should plan the rail lines to take into account any potential for future growth in the neighbourhood. This will make it more likely that the new railway station will be able to meet the needs of passengers in the future and won't need to undergo major renovations or expansions soon after it is built.

By taking these actions, Carmen may properly plan the rail lines for the new train station and make sure they satisfy the requirements of travellers and the local community.

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The measure of missing angles are ∠3 = 25°, ∠4 = 25°, ∠1 = 133°, ∠2 = 94°, ∠5 = 43° and ∠6 = 43°

A pοint where twο lines meet prοduces an angle.

The breadth οf the "οpening" between these twο rays is referred tο as a "angle". It is depicted by the figure.

Radians, a unit οf circularity οr rοtatiοn, and degrees are twο cοmmοn units used tο describe angles.

By cοnnecting twο rays at their ends, οne can make an angle in geοmetry. The sides οr limbs οf the angle are what are meant by these rays.

The limbs and the vertex are the twο main parts οf an angle.

We can see that

∠3 = ∠4                               ⇒ CPCT, As ΔDBA ≅ ΔDBC, SAS theorem

∠5 = ∠6                              ⇒ Isosceles triangle, thus two angles are equal

∠1 + ∠2 + 133 = 360°          ⇒ angle sum theorem

Now,

∠3 = 180 - 133 + 22

∠3 = 25°

also,

∠4 = 25°

Now,

∠1 = 133°     ⇒  CPCT

∠2 = 360 - (133 + 133)

∠2 = 94°

Now, ∠5  =  ∠6

As 180 - ∠2 = ∠5 + ∠6

180 - 94 = ∠5 + ∠6

180 - 94 = ∠5 + ∠6

86 = ∠5 + ∠6

2∠5 = 86

∠5 = 86/2

∠5 = 86/2

∠5 = 43°

∠6 = 43°

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Answer:

11.2896π square units

Step-by-step explanation:

A rhombus is a quadrilateral (a four-sided polygon) with sides of equal length. The diagonals of a rhombus bisect each other at right angles.

Let the vertices of the rhombus be A, B, C and D.

As the diagonals of rhombus ABCD are 3.5 and 12 units, then AC = 3.5 and BD = 12.

Place a circle centered at vertex C and tangent to sides AD and AB (refer to attachment 1).

The diagonals divide the rhombus into 4 congruent right triangles with legs measuring 1.75 units and 6 units.

Let the point of intersection of the two diagonals be M.

Use the tangent trigonometric ratio to find the measure of angle MAB in triangle AMB (refer to attachment 2).

[tex]\begin{aligned} \tan (\theta)&=\dfrac{\sf opposite \;side}{\sf adjacent\;side}\\\\ \implies \tan (MAB)& =\dfrac{6}{1.75}\\\\&=\dfrac{24}{7}\\\\\angle MAB&=\arctan\left(\dfrac{24}{7}\right)\end{aligned}[/tex]

The tangent of a circle is perpendicular to its radius.

Therefore, the radius of the circle with center C is a straight line from point C perpendicular to line segment AB (labelled in green in attachment 3). The point of intersection of the radius and side AB is E.

By drawing the radius (CE), we have created another right triangle, AEC, where its hypotenuse is the shortest diagonal of the rhombus (AC), its longest leg is the radius (CE), and the angle opposite the radius is angle MAB.

Using this information and the sine trigonometric ratio, we can calculate length of the radius of circle C:

[tex]\begin{aligned}\sin(\theta)&=\sf \dfrac{opposite\;side}{hypotenuse}\\\\\implies \sin\left(MAB\right)&=\dfrac{CE}{AC}\\\\\implies \sin\left(\arctan\left(\dfrac{24}{7}\right)\right)&=\dfrac{r}{3.5}\\\\0.96&=\dfrac{r}{3.5}\\\\r&=3.36\; \sf units\end{aigned}[/tex]

Now we have calculated the exact radius of the circle, we can find its area by substituting the value of r into the area of a circle formula:

[tex]\begin{aligned}\textsf{Area of a circle}&=\pi r^2\\&=\pi (3.36)^2\\&=11.2896 \pi\; \sf square \;units\end{aligned}[/tex]

Therefore, the exact value of the circle area is 11.2896π square units.

Note: Attachment 4 is the circle centered at the other 3 vertices of the rhombus. All circles are congruent and therefore have the same area.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-annually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &25 \end{cases} \\\\\\ A = 2000\left(1+\frac{0.07}{2}\right)^{2\cdot 25}\implies A=2000(1.035)^{50} \implies A \approx 11169.85[/tex]

Answer:

The sample size of an experiment can have a significant impact on the probabilities in a probability model. A larger sample size generally produces more accurate estimates of the probabilities of an event. This is because a larger sample size provides more data points that can be used to calculate the probabilities, which reduces the likelihood of random variation skewing the results.

For example, if you are conducting a coin toss experiment and flip a coin 10 times, the probability of getting heads may not be exactly 50%. However, if you flip the coin 1,000 times, the probability of getting heads will be much closer to 50% because the larger sample size reduces the impact of random variation.

Therefore, a larger sample size can lead to more realistic estimates of the probability of an event because it reduces the impact of random variation and provides more data points for analysis. However, it is also important to note that sample size alone does not guarantee accurate estimates of probability, and other factors such as selection bias and the quality of the experimental design can also affect the accuracy of the results.

Step-by-step explanation:

Answer: B, a counterclockwise rotation of 270 degrees about the origin.

Answer:

17

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

4 - (-5)

negative x negative = positive

- x (-5)= 5

4x5= 20

The equation of the model given written in point slope form is :

Final elevation = 50 m

From given information given :

9 meter = 14.5 seconds - - - - (1)

20 meter = 42 seconds - - - - (2)

(20 - 9)meters = (42 - 14.5) seconds

11 meters = 27.5 seconds

The formula for speed is: Distance / time = 11 / 27.5 = 0.4 meters per second

The equation in point slope form can be represented thus:

The initial velocity :

At y = 9 meters ; x = 14.5 seconds ; c = initial elevation

y = 0.4x + c

9 = 0.4(14.5) + c

9 = 5.8 + c

c = 9 - 5.8

c = 3.2 m

So, the in point - slope form, the equation can be written as :Y - 9 = 0.4(x - 14.5) while the initial elevation is 3.2 m.

Full question "A railway system on a hillside moves passengers at a constant rate to an elevation of 50 m. The elevations of a train are given for 2 different locations. Write an equation in point-slope form to represent the elevation of the train in terms of time. How can the equation be used to find the rate of increase in elevation of the train in meters per second?

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Answer:

  2831

Step-by-step explanation:

You want the index of the pixel at (x, y) = (15, 22) in a 128×128 array, if the pixel at (0, 0) has index 0, and the pixel at (0, 1) has index 128.

The index increase by 128 for each additional row (y-value), so the index of pixel (x, y) is ...

  i = x +128y

The index for pixel (15, 22) is ...

  i = 15 +128·22 = 15 +2816

  i = 2831 . . . . . index of pixel (15, 22)