Question 2 (12 marks) A home-printer manufacturer would like to conduct a survey to study their customers' opinion about the photo printer. A new model of photo printer was launched 3 months ago, and 1000 customers have filled in the online warranty cards. Based on the list of these 1000 customers, 20 customers have been selected randomly for the survey. (a) The sample was selected by systematic sampling method. Unique identity numbers were assigned to the customers from0001−1000. Suppose it is known that customer with identity number 0131 was included in the sample. Write down the identity numbers of the next three selected customers after 0131. Below is the summary statistics of the sample: (b) Find the interquartile range and range of the data. (c) Comment on the skewness of the data. Explain your answer with detailed comparison. (d) Another sample of 10 customers have been collected. The sample mean of this sample is 70 and the minimum and maximum data are 50 and 110 respectively. Combine the two samples, find the mean and range for the combined sample with 30 data.

The LCM of A = a^3× b^2×c and B=a^5 ×b×c^4×d in exponential form is a^5 × b^2 × c^4 × d^1.

To find the LCM (Least Common Multiple) of two numbers, we need to find the greatest power of each prime factor that occurs in either number.

The prime factors in the given expressions are a, b, c, and d. For each prime factor, we need to find the greatest power that occurs in either A or B.

For a: The highest power of a that occurs in A is a^3, and the highest power that occurs in B is a^5. Therefore, the LCM must include a^5.

For b: The highest power of b that occurs in A is b^2, and the highest power that occurs in B is b^1. Therefore, the LCM must include b^2.

For c: The highest power of c that occurs in A is c^1, and the highest power that occurs in B is c^4. Therefore, the LCM must include c^4.

For d: The highest power of d that occurs in A is d^0, and the highest power that occurs in B is d^1. Therefore, the LCM must include d^1.

Putting all of this together, we have:

LCM(A,B) = a^5 × b^2 × c^4 × d^1

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The rectangular sidewalk for Liam to build the pathway, [tex]36[/tex] stones are required.

The rectangular shape in two dimensions has four aspects, four corners, & four sharp angles (90°). Equal and equal opposing sides make form a rectangle. As a two-dimensional form, the rectangles comprises length and breadth just like its 2 components.

Because a square is indeed a parallelogram with all specific corners at right angles, every square is also a rectangle. To be a square, a rectangle's sides must all have the same length, hence not all rectangles are squares.

Area of the walkway [tex]=length * width[/tex]

[tex]24*6=144[/tex] square feet

Area of each stone [tex]= length of each side * width of each side[/tex]

[tex]=2ft*2ft=4[/tex] square feet

Number of stones needed [tex]=\frac{Area of walkway }{Area of each stone}[/tex]

Number of stones needed [tex]=\frac{144}{4}=36[/tex] stones

Therefore, Liam will need [tex]36[/tex] stones to make the walkway.

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The percentage of college seniors' undergraduate major that is engineering is 36.25%.

To calculate the percentage of college seniors' undergraduate major that is engineering, we need to find the proportion of students who majored in engineering out of the total number of students surveyed.

We see that out of the 400 college seniors surveyed, 145 majored in engineering. Therefore, the proportion of students who majored in engineering is 145/400. To convert this proportion to a percentage, we multiply it by 100. So, (145/400) x 100 = 36.25%.

Therefore, 36.25% of the college seniors surveyed had an undergraduate major in engineering.

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The formula that expresses the fact that f(x, y) is a distance 8 from the origin can be found using the distance formula for two points on the coordinate plane, (0, 0) and (x, y).

The distance formula is given by d = √(x2−x1)2+(y2−y1)2where (x1, y1) = (0, 0) and d = 8. Thus, we have8 = √(x2−0)2+(y2−0)2Squaring both sides gives8^2 = (x2−0)2+(y2−0)2which simplifies to64 = x2+y2

Therefore, the formula that expresses the fact that f(x, y) is a distance 8 from the origin isx2+y2= 64.

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The factors of the expression are (2x + 3) (2x - 9). The solution has been obtained by using factorization.

What is factorization?

Writing a number or other mathematical object as the result of numerous factors, typically smaller or simpler terms of the same kind, is known as factorization or factoring in mathematics.

We are given an expression as 4[tex]x^{2}[/tex] - 12x -27.

On factoring it, we get

⇒ 4[tex]x^{2}[/tex] - 12x -27

⇒ 4[tex]x^{2}[/tex] + 6x - 18x -27

⇒ 2x (2x + 3) - 9 (2x + 3)

⇒ (2x + 3) (2x - 9)

Hence, the factors of the expression are (2x + 3) (2x - 9).

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Length οf the smaller οf the twο missing sides (the secοnd leg) is 80

In mathematics, the Pythagοrean theοrem οr Pythagοras' theοrem is a fundamental relatiοn in Euclidean geοmetry between the three sides οf a right triangle. It states that the area οf the square whοse side is the hypοtenuse (the side οppοsite the right angle) is equal tο the sum οf the areas οf the squares οn the οther twο sides.

Let x be the length οf the smaller οf the twο missing sides (the secοnd leg). Then the length οf the larger missing side (the hypοtenuse) is (x + 2), since the twο sides are cοnsecutive even integers.

By the Pythagοrean theοrem, we have:

[tex]18^2 + x^2 = (x + 2)^2[/tex]

Simplifying and expanding the right side, we get:

[tex]324 + x^2 = x^2 + 4x + 4[/tex]

Subtracting x^2 frοm bοth sides, we get:

324 = 4x + 4

Subtracting 4 frοm bοth sides, we get:

320 = 4x

Dividing bοth sides by 4, we get:

x = 80

Therefοre, the length οf the smaller οf the twο missing sides (the secοnd leg) is 80.

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The area under the curve of the given function from x=1 to x=5 is -64.17.

The area under a curve is the area between the curve and the x-axis in a certain range. To calculate the area under a curve, we will use the definite integral of the function. The definite integral of a function f(x) from x=a to x=b is defined as

[tex]∫baf(x)dx[/tex]

For the given function f(x) = x^3 - 5x^2 + 2x + 8, the definite integral from x=1 to x=5 is

[tex]∫51(x^3 - 5x^2 + 2x + 8)dx = [x^4/4 - 5x^3/3 + x^2 - 8x]5[/tex]

Substituting x=1 and x=5 gives

[54 - 5(125)/3 + 25 - 8(5)] = -64.17

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The bond would pay the bondholder the following sum of $1,000 annually.

The bond being offered by Company ABC has a par value of $1,000, a fixed coupon rate of 5% per year, and a maturity of 10 years.

The coupon rate of 5% per year means that for each $1,000 bond, the bondholder will receive an annual interest payment of $50 (5% of $1,000).

Therefore, out of the given options, the correct amount that the bondholder would receive each year is $50.

It's important to note that this interest payment is fixed and does not change over the 10-year term of the bond. At maturity, the bondholder would receive the par value of $1,000 back from the company.

So, over the course of 10 years, the bondholder would receive a total of $500 ($50 per year) in interest payments, in addition to the return of the $1,000 par value at maturity.

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A DVD club charges nonmembers $20. 50 to purchase a DVD. Members pay $18 per DVD for a one-time membership cost of $25. The cost is the same for members and nonmembers on the first purchase is 10.

Let's call the number of DVDs "d". For non-members, the cost of purchasing d DVDs is:

Cost for non-members = 20.50d

For members, the cost of purchasing d DVDs is:

Cost for members = 25 + 18d

We want to find the value of d for which the cost is the same for members and non-members. In other words, we want to find the value of d that satisfies the equation:

20.50d = 25 + 18d

To solve for d, we can start by subtracting 18d from both sides of the equation:

2.50d = 25

Then, we can divide both sides by 2.50:

d = 10

Therefore, the cost will be the same for members and non-members on the first purchase if the number of DVDs purchased is 10.

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The answer is not provided among the options given.

An equation known as proportion shows that the two ratios given are equal to one another. In other terms, the proportion declares that the two ratios or fractions are equal.

To solve for the value of b that makes the proportion true, we can use cross-multiplication:

12 = 21A

12b = 21A

b = 21A/12

To determine the specific value of b, we need to know the value of A. However, since A is not given in the question, we cannot determine the value of b. Therefore, the answer is not provided among the options given.

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Answer:

4 th option bcoz [tex]x^{y+2}=x^{y}x^{2[/tex]

Answer:

30. Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer:

210

Step-by-step explanation:

The measure of ik in the given equation can be calculated by subtracting the sum of IR (which is equal to jkh) and mjk from 180e degrees.

In order to calculate the measure of ik in the given equation, we must use the formula for interior angles of a triangle which is the sum of all angles in a triangle is 180 degrees. In this equation, we are given the measures of two of the angles, IR and mjk. Therefore, the measure of ik can be calculated by subtracting the sum of IR and mjk from 180 degrees.

Given that IR = jk, we can calculate the measure of ik by first calculating the measure of jk. We are given that mik = (11x + 2), so we can solve for x and use that value to calculate jk. If we solve for x, we find that x = (mik-2)/11. We can then use that value to calculate jk, which equals mik-mjk. In this equation, we are given that mjk = (12x - 7), so jk = (11x + 2) - (12x - 7). Simplifying, we find that jk = 9x + 9.

Now that we have the measure of jk, we can calculate the measure of ik by subtracting the sum of jk and IR from 180 degrees. Since IR = jk, we can substitute jk in for IR, so ik = 180

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the quotient of 125 ÷ 25.1 is approximately equal to 5/1.004 or 4.98 (rounded to two decimal places).

Why it is and what is quotient?

We can rewrite the division 125 ÷ 25.1 as multiplication by the reciprocal of 25.1:

125 ÷ 25.1 = 125 × 1/25.1

Now, we can simplify this expression by multiplying the numerators and denominators:

125 × 1/25.1 = (125/1) × (1/25.1) = 125/25.1

Finally, we can simplify this fraction by dividing both the numerator and denominator by their greatest common factor (GCF), which is 5:

125/25.1 = (25 × 5) / (5 × 5.02) = 5/1.004

Therefore, the quotient of 125 ÷ 25.1 is approximately equal to 5/1.004 or 4.98 (rounded to two decimal places).

In mathematics, the quotient refers to the result obtained from dividing one quantity by another. It is the answer to a division problem, and is typically expressed as a fraction or decimal. For example, the quotient of 10 divided by 2 is 5, written as 10 ÷ 2 = 5.

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Answer: the very top answer -> A

The point (3, -5π/3) can be represented by the formula x = 3, y = -5π/3.

The point (3, -5π/3) can be represented by the formula x = 3, y = -5π/3. To calculate this, we first find the x-coordinate, which is simply 3. To find the y-coordinate, we must first multiply 5 and π. 5π = 15.78. We then divide 15.78 by 3, which gives us 5.26. To make this a negative number, we add a negative sign, giving us -5.26. We can then convert this to fraction form by dividing the numerator and denominator by the greatest common factor, which is 1. This gives us -5π/3.

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Complete question:

What point represents (3, negative StartFraction 5 pi Over 3 EndFraction)?

Answer:

A

Step-by-step explanation:

The current yield of the bond is 11.76% and the yield to call is 19.51%.

The current yield of the bond can be calculated using the following formula:

Current Yield = (Annual Interest Payment/Bond Price) * 100

In this case, the annual interest payment is 10% of the face value of the bond (5 * $100 = $500). The bond price is $41, so the current yield is 11.76%:

Current Yield = ($500/$41)*100 = 11.76%.

The bond is callable at 103 as of 2032, so the call premium is 103 – 41 = 62. This means that if the bond is called, the investor will receive an additional payment of $62 per bond (5 * $62 = $310). The yield to call is the total annual return the investor will receive if the bond is called:

Yield to Call = (Annual Interest Payment + Call Premium)/Bond Price * 100

In this case, the yield to call is:

Yield to Call = ($500 + $310)/$41 * 100 = 19.51%.

This means that if the bond is called in 10 years, the investor will receive an annual return of 19.51%.

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If the force is 270 Newton and the area is 0.03 square meter, the pressure is equal to 9,000 N/m².

In Mathematics, pressure can be defined as a measure of the force exerted per unit area of an object or physical body. This ultimately implies that, it is usually measured in Newton per meter square.

Mathematically, the pressure of a physical object can be calculated by using this formula:

P = F/A

Where:

By substituting the given parameters, we have:

Pressure, P = 270/0.03

Pressure, P = 9,000 N/m².

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All four conditions have been met, the conditions for statistical inference for testing a difference in population proportions have been satisfied. The conditions for statistical inference for testing a difference in population proportions are:

Random samples: Both schools have selected simple random samples of their respective student populations, which satisfies this condition.

Large sample size: Both schools have over 2,000 students, which satisfies the large sample size condition.

Independent samples: The samples from schools A and B are independent, as the students from one school do not affect the students from the other school.

Success-failure condition: The sample sizes are large enough to satisfy the success-failure condition, which states that there should be at least 10 successes and 10 failures in each sample. Both schools have well over 10 successes and failures in their respective samples.

Since all four conditions have been met, the conditions for statistical inference for testing a difference in population proportions have been satisfied.

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hm, dunno.

2w^2(5w + 6)(-5w + 6)

Answer:

2w^2(6 + 5w)(6 - 5w)

Step-by-step explanation:

As per the given distance, the angle that is made by the ramp with the ground is 19.1 degrees

Let's call the angle we're trying to find theta (θ). We can use the tangent function to calculate θ, as follows:

tan(θ) = opposite / adjacent

We know the opposite side (height of the ramp) is 3.5ft, and the adjacent side (distance along the ground) is 10ft. Plugging these values into the tangent equation, we get:

tan(θ) = 3.5 / 10

We can solve for θ by taking the inverse tangent (also known as arctan) of both sides:

θ = arctan(3.5 / 10)

Using a calculator, we find that θ is approximately 19.1 degrees. Therefore, the ramp makes an angle of 19.1 degrees with the ground.

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The distance after 79 minutes is 11 miles.

We know that the distance can be modeled with a linear equation like:

y = ax + b

Where a is the slope and b is the y-intercept.

We know that if the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope can be written as:

a = (y₂ - y₁)/(x₂ - x₁)

Here we know the points (39, 45) and (61, 26.3)

Then we can write:

a = (26.3 - 45)/(61 - 39) = -0.85

So we can write:

y = -0.85*x + b

To find the value of b we can replace the values of one of the points, i will use (39, 45) to get.

45 = -0.85*39 + b

45 + 0.85*39 = b

78.15 = b

So the line is:

y =  -0.85*x + 78.15

The distance after 79 minutes is.

y =  -0.85*79 + 78.15

y = 11

The distance left is 11 miles.

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The 90% confidence interval for the difference in mean response times between the cell phone and control group is given as follows:

(12.6, 82.2).

The estimate of the differences is given as follows:

585.3 - 537.9 = 47.4.

The standard error for the distribution of each sample is given as follows:

Hence the standard error for the distribution of differences is given as follows:

sqrt(16.4² + 12.8²) = 20.8.

The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 27 + 27 - 2 = 52 df, is t = 1.6747.

The lower bound of the interval is given as follows:

47.4 - 1.6747 x 20.8 = 12.6.

The upper bound of the interval is of:

47.4 + 1.6747 x 20.8 = 82.2.

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Answer:

[tex]x=\frac{5}{2},\:x=3[/tex]

Step-by-step explanation:

[tex]\mathrm{Factor\:}2x^2-11x+15[/tex]

[tex]\mathrm{Break\:the\:expression\:into\:groups}[/tex]

[tex]\left(2x^2-5x\right)+\left(-6x+15\right)[/tex]

[tex]\mathrm{Factor\:out}\:x\:\mathrm{from}\:2x^2-5x:\quad \:x\left(2x-5\right)[/tex][tex]\mathrm{Factor\:out}\:-3\:\mathrm{from}\:-6x+15:\quad \:-3\left(2x-5\right)[/tex]

[tex]x\left(2x-5\right)-3\left(2x-5\right)[/tex]

[tex]\mathrm{Factor\:out\:common\:term\:}2x-5[/tex]

[tex]\left(2x-5\right)\left(x-3\right)[/tex]

[tex]\mathrm{Using\:the\:Zero\:Factor\:Principle:\quad \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0[/tex]

[tex]2x-5=0\quad \mathrm{or}\quad \:x-3=0[/tex]

[tex]\mathrm{Solve\:}\:2x-5=0:\quad x=\frac{5}{2}[/tex]

[tex]\mathrm{Solve\:}\:x-3=0:\quad x=3[/tex]

[tex]\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}[/tex]

[tex]x=\frac{5}{2},\:x=3[/tex]

Answer:

x = 4

Step-by-step explanation:

- 6 + [tex]\frac{x}{4}[/tex] = - 5 ( add 6 to both sides )

[tex]\frac{x}{4}[/tex] = 1 ( multiply both sides by 4 to clear the function )

x = 4

To reach the revenue needed to cover expenses and begin turning a profit, or 120x = 120(92) = $11,040, the business must sell at least 92 guitars.

To start making a profit, the music company needs to generate enough revenue to cover its costs. The revenue function is given by r(x) = 120x, where x is the number of guitars manufactured and sold.

The cost function is given by c(x) = 100x + 1840, where 1840 represents the fixed cost (such as rent, salaries, etc.) associated with setting up the manufacturing process.

To determine the total revenue required to start making a profit, we need to find the break-even point where the revenue generated is equal to the total cost incurred:

r(x) = c(x)

Substituting the given functions, we get:

120x = 100x + 1840

Solving for x, we get:

20x = 1840

x = 92

Therefore, the company needs to sell at least 92 guitars to generate a revenue of 120x = 120(92) = $11,040, which is the amount required to cover its costs and start making a profit. If the company sells fewer than 92 guitars, it will not be able to cover its costs and will incur a loss.

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Step-by-step explanation:

1. Calculate the mean for each sample.

Sample #

1

234

2

3

5

6

7

8

9

O ACCESS Virtual Learning 2022

Sample Items

(1, 1, 2, 0)

(2, 2, 0, 1)

(1, 1, 1, 2)

(2,0, 1, 0)

(2, 2, 0, 1)

(1, 1, 2, 3)

(3, 2, 0, 0)

(1, 1, 1, 1)

(3, 1, 1, 1)

x

Check the picture below.

[tex]\textit{Law of sines} \\\\ \cfrac{\sin(\measuredangle A)}{a}=\cfrac{\sin(\measuredangle B)}{b}=\cfrac{\sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{39}{\sin(53^o)}=\cfrac{JN}{\sin(65^o)}\implies \cfrac{39\sin(65^o)}{\sin(53^o)}=JN\implies 44.3\approx JN \\\\\\ \cfrac{39}{\sin(53^o)}=\cfrac{JS}{\sin(62^o)}\implies \cfrac{39\sin(62^o)}{\sin(53^o)}=JS\implies 43.1\approx JS[/tex]

Make sure your calculator is in Degree mode.