Ten samples of size =8 have been collected from a production process manufacturing shafts for fuel pumps. The shaft diameter is critical and it has been measured for each shaft. The process is in statistical control. Table Q(d) (i) Analyse the values of the centre line, LCL and UCL for the x-bar and R charts using the constants given in Table Q(d). The calculated values of x-bar and R for each sample are shown below. (ii) Formulate the x-bar and R charts and plot the sample data on the charts. (iii) Appraise the information provided by the x-bar chart.

Answer:

1/4

Step-by-step explanation:

[tex] \frac{1}{2} - ( \frac{1}{8} + \frac{1}{8} )[/tex]

Add the value of the numbers in parentheses.

[tex] \frac{1}{2} - \frac{2}{8} [/tex]

Simplify 2/8 by dividing the numerator and denominator by 2.

[tex] \frac{1}{2} - \frac{1}{4} [/tex]

Multiply the numerator and denominator of 1/2 by 2 to have the same denominator as 1/4 in order to be able to subtract.

[tex] \frac{2}{4} - \frac{1}{4} [/tex]

[tex] \frac{1}{4} [/tex]

Answer:

14 minutes

Step-by-step explanation:

4 x every 100 bottles

100, 200, 300 = 3

4 x 3 = 12

if 4 minutes is for every 100 bottles, then 50 is half of 100. so 4 divided by 2 is 2

12 + 2 = 14

Answer:

where are the graphs? I have to see them to give a correct answer

Answer:

[tex] \huge{ \fbox{ \sf{10x - 17}}}[/tex]

Step-by-step explanation:

[tex] \sf{ \: 2(3x - 5) + 4x - 7}[/tex]

Distribute 2 through the parentheses

[tex] \mapsto{ \sf{6x - 10 + 4x - 7}}[/tex]

Add the like terms : 6x and 4x

Like terms are those which have the same base.

[tex] \mapsto{ \sf{10x - 10 - 7}}[/tex]

[tex] \underline{ \text{Remember!}} : [/tex] The negative integers are always but added but posses the negative ( - ) sign.

[tex] \mapsto{ \sf{10x - 17}}[/tex]

Hope I helped!

Best regards! :D

~[tex] \text{TheAnimeGirl}[/tex]

Answer:

Step-by-step explanation:

[tex]2(3x - 5) + 4x - 7\\\\\mathrm{Expand}\:2\left(3x-5\right):\quad 6x-10\\\\=6x-10+4x-7\\\\\mathrm{Simplify}\:6x-10+4x-7:\\\\\quad 10x-17[/tex]

Answer:

In 23 hours they make 80.5 bagels. The unit rate is 3.5 bagels per hour

Step-by-step explanation:

Divide 10 hours by 10 hours to get 1 hour.

Divide 350 bagels by 10 to get the unit rate (which is 3.5)

Multiply the unit rate by 23, and you get 80.5 hours.

Answer:

24

Step-by-step explanation:

this will probably help, Every complementary angle is equal to 90 so the other angle must be....24

The total dollar change in labor expense from this 15% increase in productivity is [calculated value]. The percent change in labor expense is [calculated value].

Part I: Effective cost per hour per employee

To calculate the effective cost per hour per employee, we need to consider various factors such as base wage, fringe benefits, paid time off, and the number of working hours per year.

Base hourly wage: $12.30 per hour

Number of working hours per day: 8 (1 shift)

Number of holidays: 5

Number of vacation days: 7

First, let's calculate the total fringe benefits per hour:

Fringe benefits = 37% of base wage = 0.37 * $12.30 = $4.551

Next, let's calculate the paid time off per hour:

Paid time off = (Number of holidays + Number of vacation days) * 8 hours = (5 + 7) * 8 = 96 hours

Now, let's calculate the effective cost per hour per employee:

Effective cost per hour = Base hourly wage + Fringe benefits + (Paid time off * Base hourly wage)

Effective cost per hour = $12.30 + $4.551 + (96 * $12.30)

Part II: Reduction in labor cost

To calculate the reduction in labor cost due to a 15% increase in productivity, we need to consider the total number of working hours needed and the change in productivity.

Number of working hours needed every year: 306,050

Productivity increase from 70% to 85%: 85% - 70% = 15%

First, let's calculate the initial number of workers needed:

Initial number of workers = Number of working hours needed / (Productivity rate / 100)

Initial number of workers = 306,050 / (70 / 100)

Next, let's calculate the new number of workers needed after the productivity increase:

New number of workers = Number of working hours needed / (New productivity rate / 100)

New number of workers = 306,050 / (85 / 100)

Finally, let's calculate the total dollar change in labor expense:

Total dollar change in labor expense = (Initial number of workers - New number of workers) * Effective cost per hour * Number of working hours per year

To calculate the percent change in labor expense, we can use the following formula:

Percent change in labor expense = (Total dollar change in labor expense / Initial labor expense) * 100

Please provide the values for Effective cost per hour and Initial labor expense to calculate the final answers in Part I and Part II.

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The table can be completed by filling in the columns corresponding to the properties of each quadrilateral. These properties include the number of congruent sides, the number of right angles, and the number of pairs of parallel sides.

Different types of quadrilaterals have distinct characteristics, and the table helps identify and compare these properties.

To complete the table, we need to consider the properties of each quadrilateral mentioned:

Kite: A kite has two pairs of congruent sides, no right angles, and no pairs of parallel sides.

Trapezoid: A trapezoid has no congruent sides, no right angles, and one pair of parallel sides.

Isosceles Trapezoid: An isosceles trapezoid has two congruent sides, no right angles, and one pair of parallel sides.

Parallelogram: A parallelogram has no congruent sides, no right angles, and two pairs of parallel sides.

Rectangle: A rectangle has two pairs of congruent sides, four right angles, and two pairs of parallel sides.

Rhombus: A rhombus has four congruent sides, no right angles, and no pairs of parallel sides.

Square: A square has four congruent sides, four right angles, and two pairs of parallel sides.

By filling in the corresponding columns for each property in the table, we can accurately describe the unique characteristics of each quadrilateral and compare their properties side by side.

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The Cpk (Process Capability Index) for this machine is 0.5 (rounded to 3 decimal places).

To calculate the Cpk (Process Capability Index), we need to consider the specification limits and the process variation.

The Cpk is given by the formula:

Cpk = min[(USL - μ) / (3σ), (μ - LSL) / (3σ)], Where:

USL = Upper Specification Limit

LSL = Lower Specification Limit

μ = Process mean

σ = Process standard deviation

In this case, the Upper Specification Limit (USL) is 2 + 0.004 = 2.004 inches, and the Lower Specification Limit (LSL) is 2 - 0.004 = 1.996 inches.

Given that the process mean (μ) is 2.001 inches and the process standard deviation (σ) is 0.002 inch, we can substitute these values into the formula:

Cpk = min[(2.004 - 2.001) / (3 * 0.002), (2.001 - 1.996) / (3 * 0.002)]

Cpk = min[0.003 / 0.006, 0.005 / 0.006]

Cpk = min[0.5, 0.833]

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Answer:

divide both sides by 4

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

divide 100 by 4 because 4 times x is 100.

Answer:

The square root of 37 is approximately 6.0827. To determine which two integers it lies between, we can find the integers that are closest to the square root of 37.

The integer that is smaller than 6.0827 is 6, and the integer that is larger than 6.0827 is 7.

Therefore, the square root of 37 is between the integers 6 and 7.

Answer:

Equations made up of multiple variables like formulas.

Step-by-step explanation:

Similar to how y = mx+b has many letters in it but we can input known values to solve for the values that we want.

Answer:

mixed number 9 49/100  improper 949/100

Step-by-step explanation:

9.49 = 9 49/100 and 949/100

The independent variable in an experiment is the variable that is deliberately manipulated or changed by the experimenter. It is the variable that is under the control of the researcher and is varied throughout the experiment to measure its effect on the dependent variable.

The dependent variable is the variable that is being measured in the experiment and is influenced by the independent variable.In the given experiment, Diana placed three tomato plants (A, B, C) under three different types of light and measured the height of each plant after 3 weeks. The independent variable in this experiment is the type of light because it is the variable that is being manipulated or changed by Diana.

She is varying the type of light to see its effect on the height of the tomato plants. The dependent variable in this experiment is the height of the tomato plants because it is the variable that is being measured and is influenced by the independent variable.

In the given experiment, Diana placed three tomato plants (A, B, C) under three different types of light and measured the height of each plant after 3 weeks. The aim of this experiment is to determine the effect of different types of light on the growth of tomato plants. To carry out this experiment, Diana manipulated the type of light and measured the height of the tomato plants. The independent variable in this experiment is the type of light because it is the variable that is being deliberately manipulated by Diana.

The three types of light are the independent variables that are being tested to see if they affect the growth of the tomato plants differently.

By exposing each tomato plant to a different type of light, Diana is testing the effect of light on plant growth. The dependent variable in this experiment is the height of the tomato plants because it is the variable that is being measured and is influenced by the independent variable. The height of the tomato plants will be different depending on the type of light they are exposed to.

The experiment will be based on the results obtained from measuring the height of the tomato plants. If the tomato plants exposed to one type of light grew taller than those exposed to other types of light, then it can be concluded that the type of light has an effect on the growth of tomato plants. However, if all the tomato plants grow to the same height, then it can be concluded that the type of light does not affect the growth of tomato plants. Therefore, the independent variable in this experiment is the type of light, while the dependent variable is the height of the tomato plants.

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Answer:

1) A

2) C

Step-by-step explanation:

Question 1)

We have the function:

[tex]y=2(x+2)^2-3[/tex]

Notice that this is a quadratic function in the vertex form:

[tex]y=a(x-h)^2+k[/tex]

Where (h, k) is the vertex point, a is the leading co-efficient, and h is also the axis of symmetry.

Let's identify these characteristics first. Our leading co-efficient a is 2.

And our vertex is (-2, -3). It is not (2, -3) because (x+2) is the same as (x-(-2)).

We want to find the minimum or maximum value of our function, as well as the domain and range.

First, by looking at our leading co-efficient, which is 2, we can see that it's positive. Therefore, our parabola curves upwards.

Therefore, we will have a minimum value. And this minimum value will be our vertex.

Our vertex is (-2, -3). Therefore, our minimum value is at y=-3.

The domain of all quadratics is always all real numbers.

For the range, we refer to our minimum/maximum value.

Our parabola curves upwards and our minimum value is at y=-3.

Therefore, our range is all numbers greater than or equal to -3.

The choice that represents all of these answers is A.

Question 2)

We have:

[tex]y=2(x+2)^2-4[/tex]

Again, this is in vertex form. Let's identify our characteristics.

Our leading co-efficient a is 2, so the graph curves upwards.

And our vertex is at (-2, -4).

The axis of symmetry is the same as the x-coordinate of our vertex. Therefore, our axis of symmetry is at x=-2.

So, this function has a vertex at (-2, -4) and an axis of symmetry at x=-2.

The choice that represents these characteristics is C.

So, our answer is C.

And we're done!

Answer:

1.6 pages

Step-by-step explanation:

Answer:

1.6

Step-by-step explanation:

Sorry, I can't really explain this, but I hope this helps!

The smallest positive integer greater than one that yields a remainder of one when divided by any single positive integer greater than 1 is 2.

An integer is a whole number that can be positive, negative, or zero and is not a fraction. It is either 0 (zero), a positive natural number (such as 1, 2, or 3), or a negative integer denoted by a minus sign (such as 1, 2, or 3).

Let's verify this by considering various divisors greater than 1:

When divided by 2: Remainder = 0 (not 1)

When divided by 3: Remainder = 2 (not 1)

When divided by 4: Remainder = 2 (not 1)

When divided by 5: Remainder = 2 (not 1)

...

As we can see, no positive integer greater than 1 other than 2 satisfies the condition of yielding a remainder of 1 when divided by any single positive integer greater than 1.

Therefore, 2 is the smallest positive integer that meets this criterion.

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Answer:

30

Step-by-step explanation:

0.6*50=30

Solution:

The dice have 6 faces, and it is possible to get a 2 only once, so the possibility of getting a 2 is 1/6.There are three possible outcomes of getting an odd number: 1, 3, or 5.

Therefore, the probability of getting an odd number is 3/6, which reduces to 1/2.

The possibility of getting a 2 or an odd number is the probability of getting a 2 plus the probability of getting an odd number minus the probability of getting a 2 and an odd number (since 2 is even).

P(2 or odd) = P(2) + P(odd) - P(2 and odd)

Since 2 is not an odd number, getting a 2 and an odd number simultaneously is not feasible.

Therefore, the equation is:P(2 or odd) = 1/6 + 1/2 - 0= 4/6= 2/3Answer: Therefore, the probability of getting a 2 or odd is 2/3.

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Answer:

7 x 10 ^ -6 power i believe is the right answer

Step-by-step explanation:

When putting a decimal such as 0.0000000009 in scientific notation the exponent will be negative. To figure out how to write scientific notation just find the number that you need to multiply by to get the number we have now. To get to 0.000007 we need to find 7 and multiply that by a negative exponent so that it turns into a decimal. We see that the decimal point from the number 7 moves over 6 times to the left to get 0.000007 meaning that our exponent is -6.

Answer:

I believe this is talking about the vertical, and horizontal lines that are drawn to connect the diagonal line(the line by itself); for the rise, and run; or change in y over change in x. This forms right(90 degree) triangles with the change in y being the vertical part, the change in x being the horizontal part, and the diagonal part being the slope to connect the start, and finishing point.

From observing the graph, you can tell that the x axis counts by 1/2 every unit, and that the y axis counts by 1 every unit.

Since the y goes down 1 every unit and to the right 1 every unit with an x axis that counts by 1/2, and a y axis that counts by 1:

slope = change in y / change in x = -1 × 1 / 1 × 1/2 = -1 / 1/2 = -2 [this is the slope]

down is negative, up is positive.

To sketch two indifference curves for Harry's indifference curve equation U = min([tex]X_1[/tex] , 3[tex]X_2[/tex] ), we need to plot the relationship between popcorn ([tex]X_1[/tex] ) and butter ([tex]X_2[/tex] ) while considering different levels of utility.

First, let's consider two specific utility levels and find the corresponding values of [tex]X_1[/tex] and [tex]X_2[/tex] .

Indifference Curve 1: U = min([tex]X_1[/tex] , 3[tex]X_2[/tex] ) = 2

To find the values of [tex]X_1[/tex]  and [tex]X_2[/tex]  that yield a utility level of 2, we can set [tex]X_1[/tex]  = 2 and 3[tex]X_2[/tex]  = 2, which gives [tex]X_2[/tex]  = 2/3.

So, one point on Indifference Curve 1 is ([tex]X_1[/tex]  = 2, [tex]X_2[/tex]  = 2/3).

Indifference Curve 2: U = min([tex]X_1[/tex] , 3[tex]X_2[/tex] ) = 4

Similarly, to find the values of [tex]X_1[/tex]  and [tex]X_2[/tex]  that yield a utility level of 4, we set [tex]X_1[/tex]  = 4 and 3[tex]X_2[/tex]  = 4, which gives [tex]X_2[/tex]  = 4/3.

So, one point on Indifference Curve 2 is ([tex]X_1[/tex]  = 4, [tex]X_2[/tex]  = 4/3).

Now, we can plot these two points on a graph with [tex]X_1[/tex] 1 on the x-axis and [tex]X_2[/tex]  on the y-axis. Here's a sketch of the indifference curves.

The first indifference curve (U = 2) is a straight line with a slope of 1, passing through the point (2, 2/3).

The second indifference curve (U = 4) is also a straight line with a slope of 1, passing through the point (4, 4/3).

Please note that these are just two points on the indifference curves, and the curves themselves continue beyond these points. The indifference curves represent different levels of utility, with higher curves indicating higher utility levels.

It's important to remember that these curves are based on the given utility function U = min([tex]X_1[/tex] , 3[tex]X_2[/tex] ), which implies that Harry's preference is to have at least as much popcorn as 3 times the amount of butter.

Correct Question :

Harry's indifference curve for popcorn ([tex]X_1[/tex] ) and butter ([tex]X_2[/tex] ) is U=min([tex]X_1[/tex] , 3[tex]X_2[/tex] ). Sketch two indifference curves. Make sure your axes and intercepts are labeled.

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Answer:

(-6, 3)

Step-by-step explanation:

A(-9, -1)

B(-3, 7)

Calculate midpoint:

(-9 + -3) / 2 = -6

(-1 + 7) / 2 = 3

M(-6, 3)

Answer:

38

Step-by-step explanation:

If you add 3 to the numbers, then you add 3 to the average, or mean.

Answer:

38

Step-by-step explanation:

24 * 35 = 840

24 * 3 = 72

840 + 72 = 912

912 / 24 = 38

Step-by-step explanation:

Slopes of the parallel lines are equal.

The products of the Slopes of the perpendicular lines are equal to - 1

Answer: Slopes of the parallel lines are equal.

The given matrix A = [[3, 1], [0, 0]] has a pseudoinverse A⁺. To verify that A and A⁺ satisfy the four Penrose conditions, we need to check the equations: 1. AA⁺A = A, 2. A⁺AA⁺ = A⁺, 3. (AA⁺)⁻¹ = AA⁺, and 4. (A⁺A)⁻¹ = A⁺A.

To find the pseudoinverse A⁺ of matrix A, we can use the formula: A⁺ = (AᵀA)⁻¹Aᵀ, where Aᵀ is the transpose of A.

First, we calculate AᵀA: AᵀA = [[3, 1], [1, 1]].

Then, we calculate (AᵀA)⁻¹: (AᵀA)⁻¹ = [[1/2, -1/2], [-1/2, 3/2]].

Finally, we calculate A⁺: A⁺ = (AᵀA)⁻¹Aᵀ = [[1/2, -1/2], [-1/2, 3/2]][[3, 1], [0, 0]] = [[1/2, 1/6], [-1/2, 1/6]].

Now, let's verify the Penrose conditions:

AA⁺A = [[3, 1], [0, 0]][[1/2, 1/6], [-1/2, 1/6]][[3, 1], [0, 0]] = [[3, 1], [0, 0]] = A.

A⁺AA⁺ = [[1/2, 1/6], [-1/2, 1/6]][[3, 1], [0, 0]][[1/2, 1/6], [-1/2, 1/6]] = [[1/2, 1/6], [-1/2, 1/6]] = A⁺.

(AA⁺)⁻¹ = [[3, 1], [0, 0]][[1/2, 1/6], [-1/2, 1/6]]⁻¹ = [[3, 1], [0, 0]][[2, 2], [-2, 6]] = [[1, 0], [0, 0]] = AA⁺.

(A⁺A)⁻¹ = [[1/2, 1/6], [-1/2, 1/6]][[3, 1], [0, 0]][[1/2, 1/6], [-1/2, 1/6]]⁻¹ = [[1/2, 1/6], [-1/2, 1/6]][[2, 2], [-2, 6]] = [[1, 0], [0, 0]] = A⁺A.

Therefore, A and A⁺ satisfies all four Penrose conditions.

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Answer:

23-22i

Step-by-step explanation:

The equivalent expression of (-45 - 22i) + 2(5 - 3i)(5 + 3i) is 23 - 22i

The complex expression is given as:

(-45 - 22i) + 2(5 - 3i)(5 + 3i)

Apply the difference of two squares on the expression

(-45 - 22i) + 2(5^2 - (3i)^2)

Evaluate the squares

(-45 - 22i) + 2(25 + 9)

Expand the bracket

-45 - 22i + 68

Evaluate the like terms

23 - 22i

Hence, the equivalent expression of (-45 - 22i) + 2(5 - 3i)(5 + 3i) is 23 - 22i

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Answer:

281

Step-by-step explanation:

plug y value into expression

86(32) + 25 - 78(32)

pemdas says we must multiply first

2752 + 25 - 2496

2777 - 2496

281

Answer:

86(32)+25-78(32)= 281  thats the answer THANK YOU

Step-by-step explanation: