A manager wishes to build x-bar and range charts for a process. The sample size is five, the mean of sample means is 16.01, and the average range is 5.3. What are the upper and lower control limits for the x-bar chart and R-chart?

Answer:

  (0, -6)

Step-by-step explanation:

You can find an ordered pair by choosing a value for one of the variables and solving the resulting equation for the other variable.

It is often convenient to choose 0 as a value for one of the variables.

For x = 0

  0 -y = 6

  y = -6 . . . . multiply by -1

One ordered pair is (0, -6).

__

For y = 0

  3x -0 = 6

  x = 2 . . . . divide by 3

Another ordered pair is (2, 0).

Outcome 1 2 3 4 5 6 7 8

Probability 1/28 1/14 3/28 1/7 5/28 3/14 1/4 2/7

Since the die is weighted such that each number is k times more likely to land facing up than the previous number, we can set up the following probability distribution:

Outcome 1 2 3 4 5 6 7 8

Probability k 2k 3k 4k 5k 6k 7k 8k

To find the value of k, we know that the probabilities must add up to 1:

k + 2k + 3k + 4k + 5k + 6k + 7k + 8k = 1

28k = 1

k = 1/28

Thus, the probability distribution for the face landing up is:

Outcome 1 2 3 4 5 6 7 8

Probability 1/28 2/28 3/28 4/28 5/28 6/28 7/28 8/28

Simplifying, we get:

Outcome 1 2 3 4 5 6 7 8

Probability 1/28 1/14 3/28 1/7 5/28 3/14 1/4 2/7

Therefore, the probability of rolling each number on the octahedral die is as shown in the table above.

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Answer: \(V=216.64\ in.^3\)

Step-by-step explanation:

Given

Height of cup \(h=10.2\ inch.\)

radius of cup \(r=2.6\ inch.\)

assume the cup is in the shape of a cylinder

The volume of the cylinder is \(\pi r^2h\)

Put the values

\(\Rightarrow V=\pi \times 2.6^2\times 10.2\\\Rightarrow V=216.64\ in.^3\)

Answer:

y = 2x/3 +6

Step-by-step explanation:

using the formula y=mx+b .........where m is the slope, b is the is the point, where the line intersects the y axis

y = 2/3 x + 6

Solution:

Note that:

To find b, first, we need to identify the standard equation.

Now, let's compare the formula with the equation.

The value of b is 6.

Let x = percentage of carbon dioxide in the room as a function of time t (in minutes) is x(t) = 0.15% + (0.05% - 0.15%) * (1 - (2t/180)), where t is time in minutes.

This equation is derived by considering the balance of carbon dioxide in the room. The rate of change of the percentage of carbon dioxide in the room is equal to the difference between the rate of inflow of fresh air (with 0.05% carbon dioxide) and the rate of outflow of mixed air (with x% carbon dioxide). This equation can be used to calculate the percentage of carbon dioxide in the room as a function of time.  

As time increases, the percentage of carbon dioxide in the room decreases since the rate of inflow of fresh air is greater than the rate of outflow of mixed air. Initially, the percentage of carbon dioxide in the room is 0.15% and as time increases, it decreases to 0.05%. In other words, the percentage of carbon dioxide in the room approaches 0.05% asymptotically as t increases.

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Answer:

she cant

Step-by-step explanation:

Sarkis cannot draw a triangle with these side lengths. Therefore, option A is correct.

Given that, a triangle with sides measuring 4 ft, 10 ft, and 16 ft.

What are the conditions to construct a triangle?

In the triangle, the sum of any two sides is always greater than the third side. The difference between any two sides of the triangle is always less than the third side.

Sarkis cannot draw a triangle with these side lengths. Therefore, option A is correct.

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The sum of the polynomials x^2 + 9 and -3x^2 - 11x^4 - 4 is - 11x^4  -2x^2 + 5

The polynomials are given as:

x^2 + 9

-3x^2 - 11x^4 - 4

The sum is represented as:

x^2 + 9 -3x^2 - 11x^4 - 4

Collect like terms

- 11x^4  -3x^2 + x^2 + 9 - 4

Evaluate the sum

- 11x^4  -2x^2 + 5

Hence, the sum of the polynomials is - 11x^4  -2x^2 + 5

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Answer:

1

Step-by-step explanation:

The square mil area for a 2 inch wide by 1/4 inch thick copper busbar is 500 square mils.

To find the square mil area for a 2 inch wide by 1/4 inch thick copper busbar, we need to multiply the width and thickness of the busbar in mils.

1 inch = 1000 mils

So, the width of the busbar in mils = 2 inches x 1000 mils/inch = 2000 mils

And, the thickness of the busbar in mils = 1/4 inch x 1000 mils/inch = 250 mils

Therefore, the square mil area of the copper busbar = width x thickness = 2000 mils x 250 mils = 500,000 square mils.

Hence, the square mil area for a 2 inch wide by 1/4 inch thick copper busbar is 500,000 square mils.

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It is true, as The term "ecological correlation" refers to correlations based on rates or averages that frequently appear in political science or sociology and tend to exaggerate the significance of a link.

Correlations describe the connections between different variables. Strong, weak, positive, or negative expressions are all possible. 1 = Causation need not always follow from correlation. A statistical measure of the linear relationship between two variables is called correlation (that is, do they change at a constant rate). Without defining cause and effect, this is a common method for illustrating straightforward connections. To illustrate the connection between two quantitative variables, statistical language employs correlation. Additionally, we consider that this connection is linear. In other words, when one variable changes by a given amount, the other variable also changes by a fixed amount, but only by one unit.

The term "ecological correlation" refers to correlations based on rates or averages that frequently appear in political science or sociology and tend to exaggerate the significance of a link.

So, it is true.

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The value of a+b+c is 12, The area of a cyclic quadrilateral can be expressed as: Area = r * s * sqrt(3) / 4, where r is the radius of the circle and s is the semi-perimeter of the quadrilateral.

In this case, the semi-perimeter of the quadrilateral is s = a + b + c.

The area of the circle is pi * r^2.

The ratio of the area of the quadrilateral to the area of the circle is:

Area of quadrilateral / Area of circle = (r * s * sqrt(3) / 4) / (pi * r^2) = (s * sqrt(3)) / (4 * pi * r)

We are given that h = 2r / sqrt(3) and h = c.

Substituting these values into the equation, we get:

(s * sqrt(3)) / (4 * pi * r) = (a + b + c) * sqrt(3) / (4 * pi * r)

Simplifying the equation, we get:

a + b + c = 12

Therefore, the value of a+b+c is 12.

The area of a cyclic quadrilateral can be expressed as:

Area = r * s * sqrt(3) / 4, where r is the radius of the circle and s is the semi-perimeter of the quadrilateral.

In this case, the semi-perimeter of the quadrilateral is s = a + b + c.

The area of the circle is pi * r^2.

The ratio of the area of the quadrilateral to the area of the circle is:

Area of quadrilateral / Area of circle = (r * s * sqrt(3) / 4) / (pi * r^2) = (s * sqrt(3)) / (4 * pi * r)

We are given that h = 2r / sqrt(3) and h = c.

Substituting these values into the equation, we get:

(s * sqrt(3)) / (4 * pi * r) = (a + b + c) * sqrt(3) / (4 * pi * r)

Simplifying the equation, we get:

a + b + c = 12

Therefore, the value of a+b+c is 12.

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The variety of nonrandom sampling that takes proportions into consideration is: c) quota

Quota sampling is the variety of nonrandom sampling that takes proportions into consideration. In quota sampling, the researcher selects a specific number of participants from each subgroup of the population based on their proportion in the overall population. This ensures that the sample represents the different subgroups in the population proportionately.

In quota sampling, the researcher selects participants based on specific characteristics or proportions to ensure that the sample represents the target population accurately. The researcher sets quotas for different groups or segments based on known proportions or desired representation in the population.

For example, if a population consists of 60% males and 40% females, a quota sample might be designed to include the same proportions of males and females. The researcher would continue to select participants from each group until the quotas are met.

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Answer:

x=9.3

Step-by-step explanation:

use SohCahToa

in this case u use cos

cos(41°)=7/x

x=7/cos(41)

x=9.275090953

x=9.3

Using the given data on the number of live multiple-delivery births for women aged 15 to 54, we need to calculate probabilities related to the age groups of the mothers. The probability of a randomly selected multiple birth involving a mother aged 30 to 39 will be determined, as well as the probabilities of not being in the age range, being less than 45, and being at least 40. Finally, we need to interpret whether a multiple birth involving a mother aged at least 40 is unusual.

(a) To calculate the probability of a randomly selected multiple birth involving a mother aged 30 to 39, we sum the number of multiple births in that age group and divide it by the total number of multiple births for women aged 15 to 54.

P(30 to 39) = 2822 / (89 + 508 + 1631 + 2822 + 1855 + 374 + 119)

(b) To find the probability of a randomly selected multiple birth involving a mother who is not aged 30 to 39, we subtract the probability found in part (a) from 1.

P(not 30 to 39) = 1 - P(30 to 39)

(c) To determine the probability of a randomly selected multiple birth involving a mother aged less than 45, we sum the number of multiple births for age groups below 45 and divide it by the total number of multiple births for women aged 15 to 54.

P(less than 45) = (89 + 508 + 1631 + 2822 + 1855 + 374) / (89 + 508 + 1631 + 2822 + 1855 + 374 + 119)

(d) To find the probability of a randomly selected multiple birth involving a mother aged at least 40, we sum the number of multiple births for age groups 40-44 and 45-54, and divide it by the total number of multiple births for women aged 15 to 54.

P(at least 40) = (374 + 119) / (89 + 508 + 1631 + 2822 + 1855 + 374 + 119)

Interpretation: The answer to part (d) will determine whether a multiple birth involving a mother aged at least 40 is unusual. If the probability is less than 0.05, it can be considered unusual. Therefore, we need to compare the calculated probability to 0.05 and select the correct choice.

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Answer:

37 is the correct answer

The required probability of loosing both the contracts with 61% chances of winning first contract and 74% chances of second contract is equal to 0.1014.

Probability of winning the first contract 'P(A)' = 61%

                                                                  = 0.61

Probability of winning the second contract 'P(B)' = 74%

                                                                       = 0.74

Probability of loosing both the contracts is

=  [ 1 - P(A) ] × [ 1 - P(B) ]

= [ 1 - 0.61 ]  × [ 1 - 0.74 ]

= 0.39 × 0.26

= 0.1014

Therefore, the probability of loosing both the contracts as per given contracts winning possibility is equal to 0.1014.

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Answer: = −2/13

Step-by-step explanation:

1. Divide both sides of the equation by the same term

2. Simplify:

Cancel terms that are in both the numerator and denominator

Answer:

16.65 feet

Step-by-step explanation:

Okay, we have three boards that are each 6.85 feet long. If we cut 3.4 feet off one board, that board has:

6.85

−

3.4

=

3.45

feet left

If we cut off 0.5 feet off another board, that board has:

6.85

−

0.5

=

6.35

feet left

So, if we take our three new boards, the total length of plywood left is:

6.85

+

3.45

+

6.35

=

16.65

feet

Hope this helps!

The side EC is 6 units.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given that Point B lies on line AC, as shown on the coordinate grid below.

AD = 2 units,

DB = 3 units, and

BE = 4 units

We need to find EC.

As we observe the triangle ADB is similar to BEC.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

AD is corresponding side of BE and DB is corresponding side of EC.

As the sides are proportional

2/3=4/x

2x=12

x=6

Hence, the side EC is 6 units.

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The value of x would be 28 and the measure of angle M will be 90 degrees.

That parallelogram in which adjacent sides are perpendicular to each other is called a rectangle.

A rectangle is always a parallelogram and a quadrilateral but reverse statement may or may not be true.

WE have been given the Quadrilateral MNOP is a rectangle, and ∠M = 3x + 6.

WE know that interior angle of the rectangle are 90 degrees each.

Therefore,

∠M = 3x + 6 = 90

3x + 6 = 90

3x = 90 - 6

3x = 84

x = 84/3

x = 28

Hence, the value of x would be 28 and the measure of angle M will be 90 degrees.

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Answer:

I think its Fibonacci numbers.

Answer:

29

Step-by-step explanation:

1+3=4, 3+4=7, 7+11=18, so 18+11 = 29

Answer:

Because we actually divide by 10 when a number is multiplied by 0.1.

Step-by-step explanation:

Let \(a\) be a number.

When we multiply a number by 10:

\(a \times 10 = 10 a\) (One '0' is increased in the number)

For example:

\(23 \times 10 = 230\)

Considering a decimal number:

\(2.3 \times 10 = 23\)

Multiplying a number with 0.1 (which is actually \(\frac{1}{10}\)) means dividing the number by 10.

\(23\times 0.1 =23\times \frac{1}{10}=2.3\)

Considering a decimal number:

\(2.3 \times 0.1 = 2.3 \times \frac{1}{10} = 0.23\)

Therefore, When multiplying a number by 0.1, move the decimal to the left.

Answer:

Sample Response: You move the decimal to the right when multiplying a number by 10 because you are making the number bigger. You move the decimal to the left when multiplying a number by 0.1 because you are making the number smaller.

Step-by-step explanation:

hope this helps

Answer:

x<25

Step-by-step explanation:

Johnny cannot work more than 25 hours each week that implies that the inequality sign cannot be an equal to. I do not know if there is an option where x is less than 25, but if there is that would be the answer.

To determine the coordinates of vector AT in this base, we first need to find the coordinates of points B' and C.

Let's start by finding the coordinates of B'. Since B' divides side CA in the ratio 4:4 from C, we can use the following formula to find its coordinates:

B' = (4C + 4A)/8

Simplifying this expression, we get:

B' = (C + A)/2

Similarly, we can find the coordinates of C using the fact that it divides AB in the ratio 3:5 from A:

C = (3A + 5B)/8

Now, we can use these coordinates to find the equation of lines BB' and CC.

The equation of line BB' can be found using the point-slope form:

BB': y - yB = (yB' - yB)/(xB' - xB) * (x - xB)

Substituting the coordinates of B and B', we get:

BB': y - 0 = (yB'/2)/(xB'/2) * (x - 1)

Simplifying this expression, we get:

BB': y = (yB'/xB') * x - yB'/2

Similarly, we can find the equation of line CC:

CC: y = (yC'/xC') * x - yC'/2

Now, we can find the coordinates of point T by solving the system of equations formed by the equations of lines BB' and CC:

(yB'/xB') * x - yB'/2 = (yC'/xC') * x - yC'/2

Simplifying this expression, we get:

x = (yC' - yB') / ((yC'/xC') - (yB'/xB'))

Substituting this value of x into the equation of line BB', we get:

y = (yB'/xB') * ((yC' - yB') / ((yC'/xC') - (yB'/xB'))) - yB'/2

Simplifying this expression, we get:

y = ((yB' * xC') - (yC' * xB')) / (2 * (xC' - xB'))

Now, we can find the coordinates of point T:

T = (x, y)

Substituting the coordinates of B', C, and T into the expression for vector AT, we get:

AT = T - A

Simplifying this expression, we get:

AT = ((x - xA), (y - yA))
In triangle ABC, let B' and C' be points on sides CA and AB, respectively. B' divides CA in a 4:4 ratio from C, meaning CB':B'A = 4:4, and C' divides AB in a 3:5 ratio from A, meaning AC':C'B = 3:5.

Let A be the origin, and let AB = a and AC = b be the vectors forming a base in the plane. Since B' divides CA in half, the position vector of B' is the midpoint of CA, so B' = (1/2)b. Similarly, C' divides AB in a 3:5 ratio, so C' = (5/8)a.

Now, let's consider triangle B'C'T. Since T is the intersection of BB' and CC', we can write the vectors BT and CT in terms of B'T and C'T, respectively:

BT = B'T + TB
CT = C'T + TC

Since B'T and C'T are parallel to b and a, respectively, we can write:

BT = k1 * b
CT = k2 * a

Here, k1 and k2 are constants. Now, using the ratios CB':B'A and AC':C'B, we can write:

k1 * b = 4 * (TB - (1/2)b)
k2 * a = 5 * (TC - (5/8)a)

Finally, we want to find the vector AT. Since AT = TB + TC, we can substitute the expressions for TB and TC from the above equations and solve for AT:

AT = (k1 * b + (1/2)b) + (k2 * a + (5/8)a)

The coordinates of the vector AT are given in terms of the base vectors a and b, with the constants k1 and k2 accounting for the position of the point T in the triangle.

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Answer: Your answer would be C: 90 N: 36 B: 16

17.5 I solved it as a square then devided it

The vector x whose image under T is b is given by: x=[35] and the vector x is unique and the answer is NO.

Let A=⎡⎣⎢10−211−1−215⎤⎦⎥ and b=⎡⎣⎢3−1−7⎤⎦⎥.We are given that a linear transformation T:R2→R2 as T(x)=Ax and we need to find a vector x whose image under T is b. We have to solve the system Ax=b to find the vector x. Using elementary row operations, we have to bring the augmented matrix [A|b] into row echelon form and then solve the system as follows:1→2:R2R2−2R1→R2[10−211−1−215∣∣3−1−7]→[10−211−1−215∣∣3−1−7]→[10−211−1−215∣∣3−1−7]R3−3R1→R3[10−211−1−215∣∣3−1−7]→[10−211−1−215∣∣3−1−7]→[10−211−1−215∣∣3−1−7]R3−7R2→R3[10−211−1−215∣∣3−1−7]→[10−211−1−215∣∣3−1−7]→[10−211−1−215∣∣3−1−7]So the system of linear equations becomes :[10−211−1−215∣∣3−1−7][10−211−1−215∣∣3−1−7][10−211−1−215∣∣3−1−7][10−211−1−215∣∣3−1−7]The above system has row echelon form. By back substitution we have:z=−4y+3x−7y+5x=3Which gives the solution: x=[35]Therefore, the vector x whose image under T is b is given by: x=[35].Hence, the vector x is unique and the answer is NO.

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Answer: 45.84, or 46 miles rounded up

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