Components used in a cellular telephone are manu- factured with nominal dimension of 0.3 mm and lower and upper specification limits of 0.295 mm and 0.305 mm respectively. The x and R control charts for this process are based on subgroups of size 3 and they exhibit statistical control, with the center line on the x chart at 0.3015 mm and the cen- ter line on the R chart at 0.00154 mm.

Required:
a. Estimate the mean and standard deviation of this process.
b. Suppose that parts below the lower specifica- tion limits can be reworked, but parts above the upper specification limit must be scrapped. Estimate the proportion of scrap and rework produced by this process.
c. Suppose that the mean of this process can be reset by fairly simple adjustments. What value of the process mean would you recommend

The inverse function of the given function is [tex]\mathbf{= \dfrac{28+7x}{x-1}}[/tex]

A function g is the inverse of a function f, if and only if the values of y= f(x), x = g(y).

From the formula given:

[tex]\mathbf{y=f(x) = \dfrac{x+28}{x-7}}[/tex]

Let's substitute x with y;

[tex]\mathbf{y= \dfrac{x+28}{x-7}}[/tex]

[tex]\mathbf{x=\dfrac{y+28}{y-7}}[/tex]

Solve for y;

[tex]\mathbf{= \dfrac{28+7x}{x-1}}[/tex]

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The equation of the inverse function of the function f(x) = 3(x + 5)^2 - 4 is f-1(x) = -5 + √[1/3(x + 4)]

Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x); it also represents the opposite function

The function f(x) is given as

f(x) = 3(x + 5)^2 - 4

Express f(x) as y

So, we have

y = 3(x + 5)^2 - 4

Swap the positions of x and y

So, we have

x = 3(y + 5)^2 - 4

Add 4 to both sides of the equation

So, we have

x + 4 = 3(y + 5)^2

Divide through by 3

So, we have

1/3(x + 4) = (y + 5)^2

Take the square root of both sides

So, we have

√[1/3(x + 4)] = y + 5

Subtract 5 from both sides of the equation

So, we have

y = -5 + √[1/3(x + 4)]

Rewrite as

f-1(x) = -5 + √[1/3(x + 4)]

Hence, the equation of the inverse function of the function f(x) = 3(x + 5)^2 - 4 is f-1(x) = -5 + √[1/3(x + 4)]

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Answer:

7

Step-by-step explanation:

haha

for

for

haha

but

birthday

can

7 answer

Answer:

the answer is -2/729

Step-by-step explanation:

When you're given the first term and the common ratio, you just need to multiply the first term by the common ratio and then raise to the power of the nth term minus 1.

In this case, 6(-1/3)^7

Answer: answer is B

Step-by-step explanation:

use Pythagorean theorem to find other side. And sine is opposite side over hypotenuse.

Answer:

Undefined (DNE)

Step-by-step explanation:

Any vertical line has an undefined slope.

Answer:

D.  I, II, and III

Step-by-step explanation:

A discontinuous function is a function which is not continuous.  

If f(x) is not continuous at x = a, then f(x) is said to be discontinuous at this point.

To prove whether a function is discontinuous, find where it is undefined.

A rational function is undefined when the denominator is equal to zero.

Therefore, to find the values that make a rational function undefined, set the denominator to zero and solve.

Function I

Denominator:  x - 2

Set to zero:  x - 2 = 0

Solve:  x = 2

Therefore, this function is undefined when x = 2 and so the function is discontinuous.

Function II

Denominator:  4x²

Set to zero:  4x² = 0

Solve:  x = 0

Therefore, this function is undefined when x = 0 and so the function is discontinuous.

Function III

Denominator:  x² + 3x + 2

Set to zero:  x² + 3x + 2 = 0

Solve:  

⇒ x² + 3x + 2 = 0

⇒ x² + x + 2x + 2 = 0

⇒ x(x + 1) + 2(x + 1) = 0

⇒ (x + 2)(x + 1) = 0

⇒ x = -2, x = -1

Therefore, this function is undefined when x = -2 and x = -1, and so the function is discontinuous.

Therefore, all three given functions are discontinuous.

hi

f°g  mean apply  g(x) and  then use result of  g(x) as  "x" in f(x)

so as  g(x) = x² +1   and  f(x) = 3x+2

so if we call  g(x)   X  we have  

f( X) =  3 X +2

now we replace  " X"  for it's value

f(X) =  3 ( x² +1) +2

f(X) =  3x² +3 +2

f(X) = 3x² +5

so  f°g = 3x² +5

The solution of the inequality by method of interval is x = [5,∝) and x = [-2,0]∪[8,-∝).

The first inequality is (x² - 25)/(x + 10) ≥ 0

⇒ x² - 25 ≥ 0

⇒ x² ≥ 25

∴ x ≥ 5

Thus the domain of the given inequality from method of interval is x = [5,∝).

The second inequality is (x + 2)(x² - 64)/(x² + 45) ≤ 0

⇒ (x + 2)(x² - 64)≤ 0

Either (x + 2)≤ 0 or (x² - 64)≤ 0

Either x ≤ -2 or x ≤ 8

Thus , the combined domain of the given inequality from method of interval is x = [-2,0]∪[8,-∝) .

Therefore, the solution of the inequality by method of interval is x = [5,∝) and x = [-2,0]∪[8,-∝).

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The perimeter of the decking area is 800cm.

It is important to note that the decking area takes the shape of a rectangle

The formula for determining the perimeter of the decking area is given as;

Perimeter = 2 multiplied by the sum of the length and width of the rectangle

It is mathematically written as;

Perimeter = 2 ( length + width)

Where;

Now, let's substitute the values into the formula

Perimeter = 2 ( 150 + 250)

Sum the bracket

Perimeter = 2 ( 400 )

Perimeter = 2 × 400

Perimeter = 800 cm

Thus, the perimeter of the decking area is 800cm

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The converse, inverse and contrapositive of each conditional statement include:

A conditional statement can be defined as a type of statement that can be written to have both a hypothesis and conclusion. Thus, it typically has the form "if P then Q."

Where:

P and Q represent sentences.

In this scenario, we would write the converse, inverse and contrapositive of each conditional statement as follows:

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The probability that at least 8 patients show improvement is; 0.94

The formula for Binomial Probability Distribution is;

P(X = r) = nCr * p^(r) * (1 - p)^(n - r)

where;

n = number of trials

r = number of specific events you wish to obtain

p is  probability of success

From the question, we have;

n = 12

r = 8

p = 81% = 0.81

The probability that at least 8 patients show improvement is expressed as;

P(X ≥ 8) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)

Using online binomial probability calculator gives us;

P(X ≥ 8) = 0.11954 + 0.22649 + 0.28967 + 0.22453 + 0.07977

P(X ≥ 8) = 0.94

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Answer:

Step-by-step explanation:

hello here is an solution

Step-by-step explanation:

++++5

+++++++_2

1=false

true

false

false

The weighing of the man on the earth given the ratio is 174 pounds

Equate the ratio

6 : 1 = x : 29

6/1 = x/29

6 × 29 = 1 × x

174 = x

x = 174 pounds

Complete question:

The ratio of the weight of an object on the earth to the moon is 6:1. If a man weighs 29 pounds on the moon, calculate his weighing on the earth.

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The value of angle 20 is as follows:

m∠20 = 50.9 degrees.

When parallel lines are cut by a transversal, angle relationships are formed. This include corresponding angles, alternate angles , vertical angles etc.

Therefore, line l and m are parallel lines cut by the two transversal.

Hence,

m∠6 ≅ m∠20 (alternate angles)

Therefore, alternate angles are congruent

m∠20 = 2x - 4

m∠19 + m∠20 = 180 (angles on a straight line)

5x - 8 + 2x - 4 = 180

7x - 12 = 180

7x = 180 + 12

7x = 192

x = 192 / 7

x = 27.4285714286

x = 27.43

Therefore,

m∠20 = 2(27.43) - 4

m∠20 = 50.8571428571

m∠20 = 50.9 degrees.

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Answer:

The Sequence

Step-by-step explanation:

the Sequence is a decrease by 2 and a increase of 4. So subtract 2 by 10 to get 8 then add 4 to get 12 and so on.

Answer:

max{x²-4x²+5} = 5 at x = 0

Step-by-step explanation:

1. Find the critical numbers by finding the first derivative of f(x), set it to 0 and solve for x.

[tex]f'(x)=0[/tex]

We get:

[tex]f(x) = -3x^2+5\\f'(x) = -6x\\-6x = 0\\x = 0[/tex]

So the critical number is x = 0.

2. Evaluate the first derivative by plugging in the critical number and see if the derivative is positive or negative on both sides:

[tex]f'(x)[/tex] is positive when the x < 0 (for example: -6*(-1)=+)

[tex]f'(x)[/tex] is negative when the x > 0 (for example: -6*(1)=-)

Therefore, you have a local maximum.

Now just get the Y value by plugging in the critical number in the original function. [tex]f(0)=5[/tex]

local maximum is (0,5)

Step-by-step explanation:

there are several formulas that could play a role.

but in our case, where we have velocities and the deceleration, we are going to use

fV = iV + at

fV = final velocity (0 on our case)

iV = initial velocity (40 m/s in our case)

a = acceleration (-15 m/s² in our case)

t is the time it takes to reach fV.

0 = 40 + (-15)t = 40 - 15t

15t = 40

3t = 8

t = 8/3 = 2.666666666... seconds

so, it takes 2.6666666... or 2 2/3 seconds to bring the vehicle to a standstill.

The value of n given the form of the function is (b) positive odd number

The form of the graph is given as:

f(x) = a(x + k)^1/n + c

For the given graph, we have the following features:

a > 0 --- a is positive

k > 0 --- k is positive

c < 0 --- c is negative

If n is an even number, the function would be undefined because the even root of a number is undefined

However, the function is defined if n is an odd number,

Hence, the value of n given the form of the function is a positive odd number

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The largest possible total area of the four pens is 285610 ft²

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the length of the pen and x represent the width of the pen.

Hence:

Perimeter = x + y + x + y + x + x + x = 2y + 5x

2y + 5x = 3380    

y = (3380 - 5x)/2      (2)

Area (A) = xy

A = x * (3380 - 5x)/2      

A = (3380x - 5x²)/2      

The maximum area is at A' = 0, hence:

A' = (1/2)(3380 - 10x)

0 = (1/2)(3380 - 10x)

10x = 3380

x = 338 ft.

2y + 5(338) = 3380    

y = 845 ft.

Largest possible total area = 338 * 845 = 285610 ft²

The largest possible total area of the four pens is 285610 ft²

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The quotient of the given expression is 1/3

Fractions are written as a ratio of two integers

Given the expression below'

-1/9 / (-1/3)

Change the division to multiplication

-1/9 * -3/1

1/9 * 3/1

1/3

Hence the quotient of the given expression is 1/3

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The answer is [tex]\boxed {\frac{dy}{dx} = \frac{y^{x}logy-yx^{y-1}}{x^{y}logx-xy^{x-1}}}[/tex].

Apply logarithmic differentiation on each side.

LHS

RHS

Equating both sides

Answer:

18.4 units

Step-by-step explanation:

We can use the distance formula, d = [tex]\sqrt{(x_{1}-x_{2}) ^{2} +(y_{1}-y_{2}) ^{2}}[/tex] to find the length of the line segment.

d = [tex]\sqrt{(x_{1}-x_{2}) ^{2} +(y_{1}-y_{2}) ^{2}}[/tex] = [tex]\sqrt{(5+12) ^{2} +(-10+3) ^{2}}[/tex] = [tex]\sqrt{(17) ^{2} +(7) ^{2}}[/tex]=[tex]\sqrt{338}[/tex]=18.38

Answer:

244 ft

Step-by-step explanation:

Scale: 1/2 in = 16 ft

Scale length = 7 5/8 inches

Real length = ?

We can use a proportion.

1/2 in : 16 ft = 7 5/8 in. : x

(1/2)/16 = (7 5/8)/x

(1/2)x = 16 × 7 5/8

(1/2)x = 122

x = 244

Answer: C. 244 ft  

Answer:

1.  x = -1  y= -2
2. infinitely many solutions

3. x = 6 y= -7

4.no solution

5. x = -3 y = -17

6. x= 3 y = 7

Step-by-step explanation:

1) y=x-1

7x+6y= -19

6y= -19 -7x

y= (-7x-19)/6

since x-1 and (-7x-19)/6 are both equal to y they are equal to each other

this is how to get x

x-1 = (-7x-19)/6

6x-6 = -7x-19

13x = -13

x = -1

now put back -1 in the equation to get y

y=x-1

y = -1 -1

y= -2

2)-10x+2y=-12

y=5x-6

2y= -12 + 10x

y= -6 + 5x

y = 5x - 6

5x-6 = 5x - 6

0 = 0

when something is

equal to itself its

infinitely many solutions

(when something is not equal to something its no solution)

((when something is equal to just one answer its one solution)

3) y= -4x+17

y=x-13

-4x+17 = x-13

30 = 5x

x = 6

y=x-13

y=6-13

y= -7

4) -3x-15y=8

x+5y=5

-3x-15y=8 -> y = -1/15(3x-8)

5y=5-x -> y= 1/5 (5-x)

-1/15(3x-8) = 1/5 (5-x)

-x-8/3 = 5-x

0 = 23/3

(when something is not equal to something its no solution)

5) -3x+6y=-3

3x-y=8

-3x+6y= -3 -> y = 1/6(3x-3)

3x-y=8 -> y = 3x-8

1/6(3x-3) = 3x-8

3x-3 = 18x-48

x-1 = 6x - 16

5x = -15

x = -3

3x-y=8

3(-3)-y=8

-9-8 = y

y = -17

6) -6x+6y=24

-3x-8y=1

-6x+6y=24 -> y = 1/6(6x+24) -> y = x+4

-3x-8y=1 -> -3x-1 = 8y -> y = 1/8 (-3x-1)

1/8 (-3x-1) = x+4

-3x-1 = 8x+32

11x = 33

x= 3

-6x+6y=24

-6(3)+6y=24

-18 + 6y = 24

6y = 24 + 18

6y = 42

y = 7

Parallelogram is the quadilateral  ABCD with vertices A(-1,0), B(4, 0),

C(5, 4), and D(0, 4)

A parallelogram is a quadrilateral whose opposite sides are parallel and equal.

first, find the length of the sides of the quadilateral.

AB = [tex]\sqrt{(4-(-1))^2+0-0^2} \\[/tex]= [tex]\sqrt{5^2+0}[/tex] = [tex]\sqrt{25}[/tex] = 5

BC = [tex]\sqrt{(5-4)^2+(4-0)^2}[/tex] = [tex]\sqrt{1^2+4^2}[/tex] = [tex]\sqrt{1+16} = \sqrt{17}[/tex]

CD = [tex]\sqrt{(0-5)^2+(4-4)^2} = \sqrt{(-5)^2+0} = \sqrt{25-0} = 5[/tex]

DA = [tex]\sqrt{(-1-0)^2+(0-4)^2} = \sqrt{(-1)^2+(-4)^2} = \sqrt{1+16} = \sqrt{17}[/tex]

opposite side length is equal.

so quadilateral is parallelogram.

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The most precise name for quadrilateral ABCD with vertices

A(-1,0), B(4, 0), C(5, 4), and D(0, 4) is parallelogram.

Hence, the most precise name for quadrilateral ABCD with vertices A(-1,0), B(4, 0), C(5, 4), and D(0, 4) is a parallelogram.

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The customer will to pay $2,970 in 12 days.

What does 3/10 mean?

3/10 is cash discount term which means that a discount of 3% would be given to the customer if payment for the goods purchased is made within 10 days of purchase.

In this  case, 3% is not applicable since the payment was made after 12 days.

What does 1/20 mean?

1/20 is cash discount term which means that a discount of 1% would be given to the customer if payment for the goods purchased is made within 20 days of purchase, the payment is within this range, hence, a 1% discount would be applied to invoice price so as to determine the cash payable

cash payable=$3,000*(1-1%)

cash payable=$3,000*0.99

cash payable=$2,970

What does n/30 mean?

It means a payment is expected latest after 30 days which does not entitle the customer no discount.

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