how tofind probabilities, expected values and net expected values for a decision tree

The number of items that should be tested so that the probability that one or more items are found defective is at least 99% is:

234 items.

To determine the number of items that need to be tested to have a 99% probability that one or more items are found defective, we need to use the binomial distribution and its cumulative distribution function (CDF).

The binomial distribution is used to model the number of successful outcomes in a fixed number of independent trials, where each trial has a probability of success p.

Let's assume that the probability of finding a defective item is p.

To find the minimum number of items that need to be tested, we need to solve the equation:

Where n is the number of items tested and (1 - p)^n is the probability that none of the items are defective.

To solve this equation, we can use a numerical method or a spreadsheet software, or we can use an approximate formula:

For a typical value of p = 0.01 (1% defect rate), the minimum number of items that need to be tested is approximately:

So, in this case, it would be advisable to test at least 234 items to have a 99% probability that one or more items are found defective.

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By evaluatin a proportional relationship we will find the complete table:

grams:       11.4  |  22.8  | 68.4 | 114

packages:   1     |    2     |   6    |  10

We assume there is a proportional relation between the number of grams y and the number of packages x.

y = k*x

Using the second pair of the table (22.8, 2) we will get:

22.8 = k*2

22.8/2 = k

11.4 = k

So the proportional relation is:

y = 11.4*x

Now let's complete the table, when x = 1

y = 11.4*1 = 11.4

When x = 6

y = 11.4*6 = 68.4

when y = 114

114 = 11.4*x

114/11.4 = x

10 = x

Then the complete table is:

grams:       11.4  |  22.8  | 68.4 | 114

packages:   1     |    2     |   6    |  10

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The value of (x - y)(x - y), if xy = 3 and x² + y² = 25, is 19.

A binomial is an expression represented by the sum or a difference of two algebraic terms. Generally, we can express it as a+b. If we square this binomial, (a + b)², it can be expanded into a² + 2ab + b².

xy = 3

x² + y² = 25

Now,  (x - y)(x - y) = x² + y² -xy -xy

(x - y)(x - y) = x² + y² -2xy

Now put the values of x² + y² and xy

(x - y)(x - y) = 25 - 2 × 3

(x - y)(x - y) = 25 - 6

(x - y)(x - y) = 19

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The identity of the unknown is hexane, the second unknown is isopropyl alcohol, and the edge length of the jade cube is approximately 1.87 cm.

a. To determine the identity of the first unknown, we can compare the calculated density with the known densities of the liquids. The calculated density can be found by dividing the mass of the sample (3.310 g) by its volume (5.00 mL), giving us a density of 0.6620 g/mL.

Since the calculated density (0.6620 g/mL) is closest to the density of hexane (0.7851 g/mL), it is likely that the first unknown is hexane.

b. To determine the identity of the second unknown, we can use the same approach as in part a. By dividing the mass of the sample (4.061 g) by its volume (5.00 mL), we find the calculated density to be 0.8122 g/mL.

This density is closest to the density of isopropyl alcohol (0.7851 g/mL), so it is likely that the second unknown is isopropyl alcohol.

c. To find the edge length of the jade cube, we can use the formula for the volume of a cube: V = l^3. We know the mass of the cube (15.00 g) and its density (3.25 g/mL), so we can find its volume by dividing the mass by the density:

V = m/d = 15.00 g / 3.25 g/mL = 4.62 mL = 4.62 cm^3

Since the volume is equal to the edge length cubed, we can find the edge length by taking the cube root of the volume:

l = cuberoot(V) = cuberoot(4.62 cm^3) = approximately 1.87 cm.

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After solving the equation we know that the resultant value of a is 14.

A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation.

As in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about math equations.

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

So, we have the equation:

5a + 3-3a = 31

No, solve the equation as follows for 'a:

5a + 3-3a = 31

5a - 3a = 31 - 3

2a = 28

a = 28/2

a = 14

Therefore, after solving the equation we know that the resultant value of a is 14.

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Answer:

Please type or attach a question that you need help with. Currently, all you have is the statement "I still don`t get it."

To minimize our double integral, we want to find the region over which the function we are integrating has negative values

x^2 +y^2 − 9</= 0

Solving the inequality

x^2 +y^2 </= 9

We can verify this solution by graphing. f(x,y) = x^2 +y^2 − 9

Our function is a paraboloid. Only the negative values of f(x, y) are graphed here.

We can see that f(x, y) is negative below the circle in the x-y plane given by the formula x^2 + y^2 <= 9. If we were to include any points outside of this region in our integral, we would add positive values of f(x, y) to our double integral and the integral wouldn't be minimized

therefore, R : x^2 +y^2 </= 9

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Answer:

Step-by-step explanation:

THE ANSWEAR IS 58.5 OR 117/2

Answer:

4357

Step-by-step explanation:

Answer:

it's significant figure it have 4 significant figure

it have other value also percentage, rational and whole number

a. z= 0.80, b. z= -0.60, c. z= 1.40, The z-value is calculated by subtracting the population mean (μ) from the given x-value, and then dividing the result by the population standard deviation (σ).

The standardized z-value is used to measure the number of standard deviations away from the mean a given value lies. To calculate the z-value, we subtract the mean (μ) from the given x-value, and divide the result by the standard deviation (σ) of the population. For example, to calculate the z-value for x=325:

z= (325 - 300)/25 = 0.80

Similarly, for x=295:

z= (295 - 300)/25 = -0.60

And for x=350:

z= (350 - 300)/25 = 1.40

Therefore, the z-value for each of the x-values given is 0.80, -0.60 and 1.40 respectively.

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The required measure of the segment CF in the given triangle is 7.5 units.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°.

Here,

The median of the triangle is the line joining the midpoint of the side to the opposite vertex, so if f is the midpoint then,
CF = EC/2
CF = 15 / 2
CF  = 7.5 units

Thus, the required measure of the segment CF in the given triangle is 7.5 units.

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Answer:

y = 4

x= -6

Step-by-step explanation:

Substitution; so pretty much finding one equation and substituting it into the second

Let's find the equation of the top one... we'll find X (you can find either x or y though)

2x - 3y = -24

We'll add 3y to both sides

2x = 3y - 24

Dividing by 2 on both sides

x = (3y-24)/2... Simplifying it to x = 1.5y - 12

Let's put it into x + 6y = 18. Since we found X

1.5y - 12 + 6y = 18

Let's add 12

1.5y + 6y = 30

Combining like terms

7.5y = 30

Lastly, we'll divide by 7.5

y = 4

So now that we finally found Y, we can use either equation to solve for X. I'll do both to show both equations end up with the same X

2x-3y =-24

2x-3(4)=-24

2x-12=-24

2x=-12

x=-6

---------

x+6y=18

x+6(4)=18

x+24=18

x=-6

The standard deviation of ages in the room increases, while the median of ages stays approximately the same.

Standard deviation is a measure of the variability of a set of data points. The addition of a 30-year-old mother and an infant to the group of ten five- and six-year-olds increases the spread of the ages, thus increasing the standard deviation.

The median, on the other hand, is the middle value in a set of data points. Since the median only depends on the order of the values, not their magnitude, adding a mother and an infant to the group of children does not significantly affect the median age in the room, which would still be close to 5 or 6 years old.

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Answer:

The answer is the east region

Answer:

dteps

Step-by-step explanation:

answer

The length of the side AC of the right-angle triangle will be 117 units.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The tangent and radius of the circle intersect at the right angle. Then the value of 'x' is given as,

AC² = AB² + B²

x² = 45² + 108²

x² = 2025 + 11664

x² = 13689

x = 117 units

The length of the side AC of the right-angle triangle will be 117 units.

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Answer: 25.13cm

Step-by-step explanation:

Answer:

31.4 cm

Step-by-step explanation:

C=2πr

Plug in numbers: C= 2 * 3.14 * 5

Answer:

yes. see below

Step-by-step explanation:

area of a cylinder = top circle + bottom circle + lateral

lateral = perimeter of the circle * height = 2π*4 * 10 =80π

area of a circle = πr² = 9π

top & bottom =18π

total = 80π+18π =98π

Φ(x) = x^m is a solution for the equation a , when m = -9 or m = 1

for function

Φ(x) = x^m

then

dΦ/dx (x) = m*x^(m-1)

d²Φ/dx² (x) = m*(m-1)*x^(m-2)

then

for a expression

3x^2 (d^2y/dx^2) + 11x(dy/dx) - 3y = 0

3x^2*m*(m-1)*x^(m-2) + 11*x* m*x^(m-1) - 3*x^m = 0

3*m*(m-1)*x^m + 11*m*x^m- 3*x^m = 0

dividing by x^m

3*m*(m-1) + 11*m - 3 =0

3*m² + 8 m - 3 =0

m= [-8 ± √(64 + 4*3*3)]/2 = (-8±10)/2  

m₁ = -9 , m₂= 1

then Φ(x) = x^m is a solution for the equation a , when m = -9 or m = 1

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From these data, it is difficult to draw any meaningful conclusions about which waiters and waitresses earn larger tips.

The data only measure the percentage of the total bill left as a tip for one randomly selected waiter and one randomly selected waitress from each of the 50 restaurants during a 1-week period, which does not provide a large enough sample size to draw any meaningful conclusions. In order to draw more reliable conclusions, a larger, more comprehensive study should be conducted that measures the tips for multiple waiters and waitresses from each restaurant over a longer period of time.

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Answer:

Step-by-step explanation:

The diagonals of a quadrilateral divide it into two congruent triangles. In this case, the diagonals of quadrilateral ABCD with vertices A (-4,9), B (3,9), C(2,3), D(-5,3) are AC and BD.

To find the intersection point of the two diagonals, we can use the equations of the two lines.

The equation of line AC can be represented as y = mx + b, where m is the slope of the line and b is the y-intercept.

m = (y2-y1)/(x2-x1)

m = (3-9)/(2-(-4)) = -6/6 = -1

b = y1 - mx1

b = 9 - (-1)(-4) = 9+4 = 13

The equation of the line is y = -x + 13

Similarly, the equation of line BD can be represented as y = nx + c, where n is the slope of the line and c is the y-intercept.

n = (y4-y3)/(x4-x3) = (3-9)/(-5-3) = -6/8 = -3/4

c = y3 - nx3

c = 3 - (-3/4)(-5) = 3 + 15/4 = 27/4

The equation of the line is y = -3/4 x + 27/4

Now we can find the point of intersection (x,y) by solving the following system of equations

-x + 13 = -3/4 x + 27/4

Multiply the equation 1 by 4

-4x + 52 = -3x + 27

Add 3x to both sides

-x + 52 = 27

Subtract 27 from both sides

-x = -25

x = 25

Now we can substitute this value of x in any of the equation to find the value of y

y = -x + 13

y = -25 + 13

y = -12

So, the coordinates of the intersection of the diagonals of quadrilateral ABCD are (25,-12).

a) Not possible to determine the percentage of the length of seashells collected by Jaya that were between 3.5 and 7 inches.

b) 25% of the length of seashells collected by Jaya were between 2 and 3.5 inches.

c) It is not possible to determine the percentage of the length of seashells collected by Jaya that were more than 5 inches based on the information provided.

d) The range of lengths of seashells collected by Jaya was = 4.2 inches.

In statistics, the range is the difference between the highest and lowest values for a particular data collection.

For instance, if the provided data set is 2,5,8,10,3, the range is 10 - 2 = 8.

As a result, the range may alternatively be defined as the difference between the highest and lowest observations.

a) It is not possible to determine the percentage of the length of seashells collected by Jaya that were between 3.5 and 7 inches based on the information provided.

b) 25% of the length of seashells collected by Jaya were between 2 and 3.5 inches.

c) It is not possible to determine the percentage of the length of seashells collected by Jaya that were more than 5 inches based on the information provided.

d) The range of lengths of seashells collected by Jaya was 6.2 - 2 = 4.2 inches.

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The value of the given integration is =25, where the function is defined.

Integrals are the values of the function that are discovered through the integration process. Integration is the process of obtaining f(x) from f'(x). When all the little data are combined, problems with displacement and motion, area and volume, and other issues develop. Integrals assign numbers to functions in a way that describes these issues. We can determine the function f given the derivative f' of the function f. Here, the function f is referred to as integral of f' or antiderivative of f.

if the function f(x) defined as

[tex]f(x)=\left \{ {2 \ if \ {x < 2} \atop {x\ if\ x\geq 2}} \right.[/tex]

then find out the-

   [tex]\int_{-1}^{6}f(x) dx[/tex]

To find out the integral break it -1 to 2 and 2 to 6, where our function is defined as-

[tex]let\ I=\int_{-1}^{2}f(x)dx +\int_{2}^{6}f(x)dx\\\\I=\int_{-1}^{2}2dx+\int_{2}^{6}xdx\\\\=[2x]_{-1}^{2}+[x^2/2]_{2}^{6}\\\\= [4+1]+[18+2]=5+20\\=25 .[/tex]

Hence, the value of the given integration is =25, where the function is defined.

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56 feet is the total distance your cousin swings. This can be solved by using the concept of explicit formula.

From the term of the series, it is simple to get the explicit formula for the arithmetic sequence. For the mathematical series a, a + d, a + 2d, a + 3d,.......a + (n - 1)d, and the nth component in the sequence provides the explicit formula. Consequently, a = a + (n - 1)d serves as the explicit formula for the arithmetic series.

Given that,

You push your younger cousin on a tire swing one time and then allow your cousin to swing freely. On the first swing, your cousin travels a distance of 14 feet.

So, a₁ = 14 feet

the second swing the person travels a distance that is 75% of the first, hence, a₂ = 0.75 a₁

On the third swing it is a₃ = 0.75 a₂

since, a₂ = 0.75 a₁ and a₃ = 0.75 a₂

Now, using explicit formula we find that,

a₂ = 0.75 a₁ = 14 × 0.75

a₃ = 0.75 a₂ = 0.75 × (14 × 0.75) = 14 × (0.75)²

a₄ = 0.75 a₃ = 0.75 × 14 × (0.75)³

Thus, the general formula becomes: a(n) = 14 × (0.75)ⁿ

Now use formula for the Sum of infinite geometric series to calculate the total distance: S = a₁ / (1 - r)

S = 14 / ( 1 - 0.75)

S = 14 / 0.25

S = 56 feet

56 feet is the total distance your cousin swings.

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A straight duct extends in the z direction for a length L and has a square cross section, bordered by the lines x = plus minus B and y = plus minus B

z direction

f(x,y) = x² - y²         subject to   x² + y² = 1      g(x,y) = x² + y²- 1

δf(x,y)/ δx  = 2*x                                                 δg(x,y)/ δx  =    2*x                      

δf(x,y)/ δy  = - 2*y                                                 δg(x,y)/ δy  =    2*y

δf(x,y)/ δx  = λ* δg(x,y)/ δx

2*x = λ*2*x

δf(x,y)/ δy  = λ* δg(x,y)/ δy

- 2*y = λ*2*y

Then, solving

2*x = λ*2*x           x = λ*x      λ = 1

- 2*y = λ*2*y         y = - 1

x² + y²- 1 = 0         x²  + ( -1)² - 1 = 0      x = 0    

Point  P ( 0 ; -1 )  ; then at that point

f(x,y) = x² - y²             f(x,y) = 0 - ( -1)²     f(x,y) = - 1    minimum

b)  f( x, y ) =  3*x  + y            g ( x , y )  = x² +  y²  = 10

 δf(x,y)/ δx  = 3                   δg(x,y)/ δx  =  2*x

δf(x,y)/ δy   = 1                   δg(x,y)/ δy  =   2*y

δf(x,y)/ δx  =   λ * δg(x,y)/ δx      ⇒   3 = 2* λ *x    (1)

δf(x,y)/ δy   =  λ *  δg(x,y)/ δy     ⇒    1 = 2*λ * y    (2)

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The system will have solution when an arbitrary constant have infinitely many solutions when a-2b+c =0

What is Linera Alegebra?

The study of the planes and lines, vector spaces, and mappings needed for linear transforms is known as linear algebra. It was first defined in the 1800s to help solve systems of linear equations and is a relatively new subject of research.

Given,

x + y - z = 2x + 2y + z = 3x + y + (k^2-5)z

[tex]\left[\begin{array}{ccc}1&1&-1\\1&2&1\\1&1&R^{2}-5 \end{array}\right] \left[\begin{array}{ccc}2\\3\\R\end{array}\right] = (A:B)[/tex]

Apply [tex]R_{2}[/tex] ⇒ R2 -R1, R3⇒R3-R1

[tex]\left[\begin{array}{ccc}1&1&-1\\0&1&2\\0&0&R^{2}-4 \end{array}\right]\left[\begin{array}{ccc}2\\1\\R-2\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}1&1&-1\\0&1&2\\0&0&(K-2)(R+2)\end{array}\right] \left[\begin{array}{ccc}2\\1\\R-2\end{array}\right][/tex]

(1) For K = -2 the system has no solution as we get

[tex]\left[\begin{array}{ccc}1&1&-1\\0&1&2\\0&0&0\end{array}\right] \left[\begin{array}{ccc}2\\1\\-4\end{array}\right][/tex]

(2)For k =2 the system has infinite solution as we get

[tex]\left[\begin{array}{ccc}1&1&-1\\0&1&2\\-0&0&0\end{array}\right] \left[\begin{array}{ccc}2\\1\\0\end{array}\right][/tex]

(3) for K ∈ R, R∉ (-2,2) Here the system will have unique solution as doe above here we have

[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}A\\B\\C\end{array}\right][/tex]

Apply R2 = R2- 4R1

R3 = R3 -7R1

R1 To get

[tex]\left[\begin{array}{ccc}1&2&3\\0&-3&-6\\0&-6&-12\end{array}\right] \left[\begin{array}{ccc}A\\B-4A\\C-7A\end{array}\right][/tex]

Apply R2= R2 /3 To get

[tex]\left[\begin{array}{ccc}1&2&3\\0&1&2\\0&-6&-12\end{array}\right] \left[\begin{array}{ccc}A\\4A-B/3\\C-7A\end{array}\right][/tex]

Apply R1 = R1 - 2(R2)

[tex]\left[\begin{array}{ccc}1&0&-1\\0&1&2\\0&0&0\end{array}\right] \left[\begin{array}{ccc}-5A+2B/3\\4A-B/3\\A-2B+C\end{array}\right][/tex]

The system will have solution when an arbitrary constant have infinitely many solutions when a-2b+c =0

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