In the past, Alpha Corporation has not performed incoming quality control inspections but has taken the word of its vendors. However, Alpha has been having some unsatisfactory experience recently with the quality of purchased items and wants to set up sampling plans for the receiving department to use. For a particular component, X, Alpha has a lot tolerance percentage defective of 52 percent. Zenon Corporation, from which Alpha purchases this component, has an acceptable quality level in its production facility of 20 percent for component X. Alpha has a consumer's risk of 10 percent and Zenon has a producer's risk of 5 percent. a. When a shipment of Product X is received from Zenon Corporation, what sample size should the receiving department test

Answer:

Step-by-step explanation:

Answer:

y=-1/7x + 12/7

Step-by-step explanation:

Start by finding the slope

m=(1-0)/(-5-2)

m=-1/7

next plug the slope and the point (-5,1) into point slope formula

y-y1=m(x-x1)

y1=1

x1= -5

m=-1/7

y- 1 = -1/7(x - -5)

y-1=-1/7(x+5)

Distribute -1/7 first

y- 1=-1/7x + 5/7

Add 1 on both sides, but since its a fraction add 7/7

y=-1/7x + (5/7+7/7)

y=-1/7x+12/7

Answer:

Step-by-step explanation:

(-5,1) (2,0)

m=(y-y)/(x-x)

m = (0-1)/2- -5)

m = -1/7

(2,0)

y-0= -1/7 (x-2)

y = -1/7x + 2/7

Answer:

68.3 degrees

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan I = opp side / adj side

tan I = sqrt(82) / sqrt(13)

tan I = sqrt(82/13)

Taking the inverse tan of each side

tan ^-1 ( tan I) = tan ^-1( sqrt(82/13))

I = 68.2892

Rounding to the nearest tenth

I = 68.3 degrees

Answer:

[tex]56[/tex] choices

Step-by-step explanation:

We know that we'll have to solve this problem with a permutation or a combination, but which one do we use? The answer is a combination because the order in which the child picks the candy does not matter.

To further demonstrate this, imagine I have 4 pieces of candy labeled A, B, C, and D. I could choose A, then C, then B or I could choose C, then B, then A, but in the end, I still have the same pieces, regardless of what order I pick them in. I hope that helps to understand why this problem will be solved with a combination.

Anyways, back to the solving! Remember that the combination formula is

[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex], where n is the number of objects in the sample (the number of objects you choose from) and r is the number of objects that are to be chosen.

In this case, [tex]n=8[/tex] and [tex]r=3[/tex]. Substituting these values into the formula gives us:

[tex]_8C_3=\frac{8!}{3!5!}[/tex]

[tex]= \frac{8*7*6*5*4*3*2*1}{3*2*1*5*4*3*2*1}[/tex] (Expand the factorials)

[tex]=\frac{8*7*6}{3*2*1}[/tex] (Cancel out [tex]5*4*3*2*1[/tex])

[tex]=\frac{8*7*6}{6}[/tex] (Evaluate denominator)

[tex]=8*7[/tex] (Cancel out [tex]6[/tex])

[tex]=56[/tex]

Therefore, the child has [tex]\bf56[/tex] different ways to pick the candies. Hope this helps!

Answer:(

fx).(gx)=D. -40x^3+25x^2+45

Step-by-step explanation:

Answer:

distributive

Step-by-step explanation:

a(b + c)=ab + ac

it's distributive one

Answer:

I hope it help and I guess it is correct

Base case (n = 1):

• left side = 1×2² = 4

• right side = 1×(1 + 1)×(3×1² + 11×1 + 10)/12 = 4

Induction hypothesis: Assume equality holds for n = k, so that

1×2² + 2×3² + 3×4² + … + k × (k + 1)² = k × (k + 1) × (3k ² + 11k + 10)/12

Induction step (n = k + 1):

1×2² + 2×3² + 3×4² + … + k × (k + 1)² + (k + 1) × (k + 2)²

= k × (k + 1) × (3k ² + 11k + 10)/12 + (k + 1) × (k + 2)²

= (k + 1)/12 × (k × (3k ² + 11k + 10) + 12 × (k + 2)²)

= (k + 1)/12 × ((3k ³ + 11k ² + 10k) + 12 × (k ² + 4k + 4))

= (k + 1)/12 × (3k ³ + 23k ² + 58k + 48)

= (k + 1)/12 × (3k ³ + 23k ² + 58k + 48)

On the right side, we want to end up with

(k + 1) × (k + 2) × (3 (k + 1) ² + 11 (k + 1) + 10)/12

which suggests that k + 2 should be factor of the cubic. Indeed, we have

3k ³ + 23k ² + 58k + 48 = (k + 2) (3k ² + 17k + 24)

and we can rewrite the remaining quadratic as

3k ² + 17k + 24 = 3 (k + 1)² + 11 (k + 1) + 10

so we would arrive at the desired conclusion.

To see how the above rewriting is possible, we want to find coefficients a, b, and c such that

3k ² + 17k + 24 = a (k + 1)² + b (k + 1) + c

Expand the right side and collect like powers of k :

3k ² + 17k + 24 = ak ² + (2a + b) k + a + b + c

==>   a = 3   and   2a + b = 17   and   a + b + c = 24

==>   a = 3, b = 11, c = 10

Answer:

x is 5

Step-by-step explanation:

[tex] \frac{4x - 5}{9x - 5} = \frac{3}{8} \\ \\ 8(4x - 5) = 3(9x - 5) \\ 32x - 40 = 27x - 15 \\ 5x = 25 \\ x = \frac{25}{5} \\ \\ x = 5[/tex]

Step-by-step explanation:

as you can see as i solved above. all you need to do was to rationalize the both equations

Answer:

B. ∆LMN ≅ ∆OPQ because of ASA

Step-by-step explanation:

Two triangles are congruent if two angles and an included side of one triangle are congruent to two corresponding angles and a corresponding included side of the other.

From the information given, we have:

Two angles (<L and <M) in ∆LMN that are congruent to two corresponding angles (<O and <P) in ∆OPQ.

Also, included side in both triangles are congruent (ML ≅ PO).

Therefore, ∆LMN ≅ ∆OPQ by the ASA Theorem.

Answer:

W=7 and L=11

Step-by-step explanation:

We have two unknowns so we must create two equations.

First the problem states that  length of a rectangle is 10 yd less than three times the width so: L= 3w-10

Next we are given the area so: L X W = 77

Then solve for the variable algebraically. It is just a system of equations.

3W^2 - 10W - 77 = 0

(3W + 11)(W - 7) = 0

W = -11/3 and/or W=7

Discard the negative solution as the width of the rectangle cannot be less then 0.

So W=7

Plug that into the first equation.

3(7)-10= 11 so L=11

Answer:40, 80 and 62

Step-by-step explanation:

182-22= 160

160/4 = 40 so,

Shortest side is 40

Longest is 80

Third side is 62

Answer:

50%

Step-by-step explanation:

35 is halve of 70 therefore it is 50%

hope it helps u...........

Answer:

a) Everyone on the team talks until the entire team agrees on one decision.

Step-by-step explanation:

Option B consists of voting and not everyone would like the outcome. Option C is making an outsider the decision maker, which can't be helpful since he / she won't have as strong opinions as the team itself. Option D is just plain wrong as it defeats the purpose of team work and deciding as one team. So, I believe option A makes the most sense

Answer:

Not a function

Domain: {3,4}

Range: {4,5}

Step-by-step explanation:

A function is a relation where each input has its own output. In other words if the x value has multiple corresponding y values then the relation is not a function

For the relation given {(3, 4), (3, 5), (4, 4), (4, 5)} the x value 3 and 4 have more than one corresponding y value therefore the relation shown is not a function

Now let's find the domain and range.

Domain is the set of x values in a relation.

The x values of the given relation are 3 and 4 so the domain is {3,4}

The range is the set of y values in a relation

The y value of the given relation include 4 and 5

So the range would be {4,5}

Notes:

The values of x and y should be written from least to greatest when writing them out as domain and range.

They should be written inside of brackets

Do not repeat numbers when writing the domain and range

Answer:

b. The solution is a non empty set.

Step-by-step explanation:

There are no common elements.

Hey there!

First,  divide 5,000 by 10. You will get 500.

Now, 500 ÷ 10, and you will get your answer, 50.

Hope this helps! Have a great day!

Answer:

f(1) = -2

f(x) =1 when x=0 or x=-2

Step-by-step explanation:

f(1) is the y value when x=1

f(1) = -2

f(x) = 1 means find the x value when y=1

when y =1, x =0 and -2

Answer:

the answer is 4

Step-by-step explanation:

the answer will be positive

Answer:

B. 1 + ln 2 - ln x

General Formulas and Concepts:

Algebra II

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle ln(\frac{2e}{x})[/tex]

Step 2: Simplify

Answer:

y = 25x + 40

Step-by-step explanation:

The electrician charges $25 per hour.

The number of hours is x.

Therefore after x hours the electrician will charge $25x. (multiply the charge by the number of hours $25 * x)

Therefore fee(y) charged by the electrician = $40 + $25x

Hence y = 25x + 40

Answer:

0.0022 = 0.22% probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question, the elements are arranged, so we have to use the arrangements formula.

Arrangements formula:

The number of possible arrangements of n elements is:

[tex]A_{n} = n![/tex]

Desired outcomes:

Pine trees(6!) then the willows(6!) or

Willows(6!) then the pine trees(6!). So

[tex]D = 2*6!*6! = 1036800 [/tex]

Total outcomes:

12 trees, so:

[tex]T = 12! = 479001600 [/tex]

What is the probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other?

[tex]p = \frac{D}{T} = \frac{1036800 }{479001600 } = 0.0022[/tex]

0.0022 = 0.22% probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other.

Given:

The given expression is:

[tex]6x^2y-3xy-24xy^2+12y^2[/tex]

To find:

Part A: The expression by factoring out the greatest common factor.

Part B: Factor the entire expression completely.

Solution:

Part A:

We have,

[tex]6x^2y-3xy-24xy^2+12y^2[/tex]

Taking out the highest common factor 3y, we get

[tex]=3y(2x^2-x-8xy+4y)[/tex]

Therefore, the required expression is [tex]3y(2x^2-x-8xy+4y)[/tex].

Part B:

From part A, we have,

[tex]3y(2x^2-x-8xy+4y)[/tex]

By grouping method, we get

[tex]=3y(x(2x-1)-4y(2x-1))[/tex]

[tex]=3y(x-4y)(2x-1)[/tex]

Therefore, the required factored form of the given expression is [tex]3y(x-4y)(2x-1)[/tex].

Answer:

BC^2=10^2+30^2

Step-by-step explanation:

Using pythagorean theorem

[tex]\\ \sf\longmapsto BC^2=10^2+30^2[/tex]

[tex]\\ \sf\longmapsto BC^2=100+300[/tex]

[tex]\\ \sf\longmapsto BC^2=400[/tex]

[tex]\\ \sf\longmapsto BC=\sqrt{400}[/tex]

[tex]\\ \sf\longmapsto BC=20[/tex]

Answer:

The answer is "0.07404893".

Step-by-step explanation:

Applying the binomial distribution:

[tex]n = 22\\\\p= 82\%=0.82\\\\q = 1-0.82 = 0.18\\\\[/tex]

Calculating the probability for not enough seats:

[tex]=P(X>20)\\\\= P(21) + P(22)\\\\[/tex]

[tex]= \binom{22}{21} (0.82)^{21}(0.18)^1+ \binom{22}{22} (0.82)^{22}(0.18)[/tex]

[tex]=0 .06134598+ 0.01270295\\\\=0.07404893[/tex]

9514 1404 393

Answer:

  A. False

  B. False

  C. True

  D. True

  E. False

Step-by-step explanation:

A. False -- any triangle has at least two acute angles, whether it is acute, right, or obtuse.

B. False -- by definition, any polygon that is not convex is concave.

C. True -- the angle sum is the same regardless of whether the pentagon is convex or concave. (Provided it is a "simple" polygon, with no crossing sides.)

D. True -- the measure of the interior angle of a regular polygon increases as the number of sides increases. (see E)

E. False -- the exterior angles of a regular polygon are 360° divided by the number of sides. As the number of sides increases, the measure of each exterior angle decreases. (Interior angles are the supplement of exterior angles, so they increase as the number of sides increases.)

Answer:

a. 16 slug b. 3.2 ft

Step-by-step explanation:

a. Total mass of the rod

Since the linear density at a point of the rod,λ varies directly as the third power of the measure of the distance of the point form the end, x

So, λ ∝ x³

λ = kx³

Since the linear density λ = 2 slug/ft at then center when x = L/2 where L is the length of the rod,

k = λ/x³ = λ/(L/2)³ = 8λ/L³

substituting the values of the variables into the equation, we have

k = 8λ/L³

k = 8 × 2/4³

k = 16/64

k = 1/4

So, λ = kx³ = x³/4

The mass of a small length element of the rod dx is dm = λdx

So, to find the total mass of the rod M = ∫dm = ∫λdx we integrate from x = 0 to x = L = 4 ft

M = ∫₀⁴dm

= ∫₀⁴λdx

= ∫₀⁴(x³/4)dx

= (1/4)∫₀⁴x³dx

= (1/4)[x⁴/4]₀⁴

= (1/16)[4⁴ - 0⁴]

= (256 - 0)/16

= 256/16

= 16 slug

b. The center of mass of the rod

Let x be the distance of the small mass element dm = λdx from the end of the rod. The moment of this mass element about the end of the rod is xdm =  λxdx = (x³/4)xdx = (x⁴/4)dx.

We integrate this through the length of the rod. That is from x = 0 to x = L = 4 ft

The center of mass of the rod x' = ∫₀⁴(x⁴/4)dx/M where M = mass of rod

= (1/4)∫₀⁴x⁴dx/M

= (1/4)[x⁵/5]₀⁴/M

= (1/20)[x⁵]₀⁴/M

= (1/20)[4⁵ - 0⁵]/M

= (1/20)[1024 - 0]/M

= (1/20)[1024]/M

Since M = 16, we have

x' =  (1/20)[1024]/16

x' = 64/20

x' = 3.2 ft

9514 1404 393

Answer:

  3×10^8 m/s

Step-by-step explanation:

The desired speed is ...

  [tex]\dfrac{\dfrac{9.45\times10^{15}\text{ m}}{\text{yr}}}{\dfrac{3.15\times10^7\text{ s}}{\text{yr}}}=\dfrac{9.45}{3.15}\times10^{15-7}\text{ m/s}=\boxed{3.00\times10^8\text{ m/s}}[/tex]

__

Your calculator can help you figure this out.

9514 1404 393

Answer:

  67.0 square units

Step-by-step explanation:

The formula for the area is ...

  Area = 1/2ab·sin(C)

  Area = (1/2)(14)(28)sin(20°) ≈ 67.036 . . . . square units

The area of the triangle is about 67.0 square units.