An optical inspection system is used to distinguish among different part types. The probability of correct classification of any part is 0. 98. Suppose that three parts are inspected and that the classifications are independent. Let the random variable x denote the number of parts that are correctly classified. Determine the probability mass function and cumulative mass function of x.

Answer:

Numbers 15, 3, 1, and 21 are all in common with C & D. This is totaled up to 4 people.

Step-by-step explanation:

Answer:

Initial Value: 4

ROC: - 4/5

Step-by-step explanation:

I know you're short on time, if you want an explanation, let me know!

Answer:

Step-by-step explanation:

they amount of money are not the same

reason why;

the reason why its not the same is because 2x8x9=144 and 3x9x12=324 and the amount of money spent is different

The difference in price per cubic inch between the two sizes of cereal boxes is $0.0128.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The volume of the family-sized box of cereal is:

= 3 x 9 x 12

= 324 cubic inches

The volume of the regular-sized box of cereal is:

= 2 x 8 x 9

= 144 cubic inches

The price per cubic inch of the family-sized box is:

= 6 / 324

= 0.0185 dollars per cubic inch

The price per cubic inch of the regular-sized box is:

= 4.50 / 144

= 0.0313 dollars per cubic inch

The difference in price per cubic inch is:

= 0.0313 - 0.0185

= 0.0128 dollars per cubic inch

Therefore,

The difference in price per cubic inch between the two sizes of cereal boxes is $0.0128.

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a(n) = a(n-1) - 6.
The (n) and (n-1) is a subscript I just don't know to write it here.

Given:

A line passes through the points (-6, 8) and (-16, 33).

To find:

The slope of the line.

Solution:

If a line passes through two points, then the slope of the line is

\(m=\dfrac{y_2-y_1}{x_2-x_1}\)

The line passes through the points (-6, 8) and (-16, 33). Using the above formula, the slope of the line is

\(m=\dfrac{33-8}{-16-(-6)}\)

\(m=\dfrac{25}{-16+6}\)

\(m=\dfrac{25}{-10}\)

\(m=-2.5\)

Therefore, the slope of the line is -2.5.

Slope of the line passing through the points ( -6,8)  and (-16,33) will be -2.5.

Given information:

The line passes through the points ( -6,8)  and (-16,33).

It is required to find the slope of the line.

Slope of the line passing from two points  \((x_1,y_1) \; and\; (x_2, y_2)\) can be written as

\(m= \dfrac{y_2-y_1}{x_2- x_1}\)

So, the slope of the given line can be calculated as,

\(m= \dfrac{33-8}{-16- (-6)}\\m = \dfrac{25 }{-10} \\m = -2.5\)

Therefore the slope of given line will be -2.5.

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Answer:

500

Step-by-step explanation:

Let's say x represents the number of children's tickets sold, y represents the number of college tickets sold, and z represents the number of adult tickets sold.

For each child ticket sold, we add x to the total. Similarly, for college tickets, we add y and for adult tickets, we add z.

The total revenue can therefore be represented as

(child ticket revenue) + (college ticket revenue) + (adult ticket revenue) =

(price * quantity of children's tickets) + (price * quantity of college tickets) + (price * quantity of adult tickets) =

(1.5 * x) + (3 * y) + (5 * z) = 4950

The total amount of tickets is x+y+z = 1500

The number of college student tickets (y) is 100 less than the number of children's tickets (x), so y = x - 100.

Put these three equations together to get

(1.5 * x) + (3 * y) + (5 * z) = 4950

x+y+z = 1500

y = x-100

Substitute x-100 for y in the second equation

x+(x-100) + z = 1500

add 100 to both sides to isolate the variables

2x + z = 1600

subtract 2x from both sides to isolate the z

1600 - 2x = z

Substitute 1600-2x for z and x-100 for y in the first equation

(1.5 * x) + (3 * y) + (5 * z) = 4950

1.5x + 3*(x-100) + 5 * (1600-2x) = 4950

= 1.5x + 3x - 300 + 8000 - 10x

= 7700 - 5.5x

subtract 7700 from both sides to isolate the x and its coefficient

-2750 = -5.5x

divide both sides by -5.5 to isolate the x

x = 500

In this exercise we have to use the knowledge of finance to calculate the amount of tickets sold to children based on the profit made, in this way we can say that this value corresponds to:

500  children's tickets.

Let's say x represents the number of children's tickets sold, y represents the number of college tickets sold, and z represents the number of adult tickets sold.

For each child ticket sold, we add x to the total. Similarly, for college tickets, we add y and for adult tickets, we add z.

The total revenue can therefore be represented as:

\((child \ ticket\ revenue) + (college\ ticket\ revenue) + (adult\ ticket \ revenue) = \\=(price * children's \ tickets) + (price * college \ tickets) + (price * adults\ tickets)\)

Replacing the values ​​already known in the text in the formula given above, we have:

\((1.5 * x) + (3 * y) + (5 * z) = 4950\\\\\left \{ {{x+y+z = 1500} \atop {y = x-100} \right.\)

Substitute x-100 for y in the second equation

\(x+(x-100) + z = 1500\\2x + z = 1600\\1600 - 2x = z\\(1.5 * x) + (3 * y) + (5 * z) = 4950\\1.5x + 3*(x-100) + 5 * (1600-2x) = 4950\\= 1.5x + 3x - 300 + 8000 - 10x\\= 7700 - 5.5x\)

subtract 7700 from both sides to isolate the x and its coefficient

\(-2750 = -5.5x\\x = 500\)

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If the Blender originally cost $350, the discount percentage given on the damaged blender is 25%

To find the discount percentage, we need to calculate the difference between the original price and the discounted price, which is $350 - $262.50 = $87.50. This represents the amount of discount given on the blender.

To express this discount as a percentage of the original price, we divide the discount amount by the original price and then multiply by 100.

($87.50 / $350) * 100 = 0.25 * 100 = 25%

Therefore, the discount percentage given on the damaged blender is 25%.

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Let d equal the final amount it depreciates.

Let m equal the number of months.

Since d is the final amount, we put this at the very end of the equation.

Since it depreciates $25 every month, this number is going to be subtracted from the total price of the tablet ($650).

The final equation comes out too: d = 650 - 25m

Best of Luck!

The recursive sequence are: 17, 13, 9, 5, 1.

The recursive rule for the sequence  \(a_{n}\) = 17 - 4n is

\(a_{1\) = 17

\(a_{n}\) = \(a_{n-1}\) - 4 for n ≥ 2

Using this rule, we can find the first few terms of the sequence

\(a_{1\) = 17

\(a_{2}\) = \(a_{1\)  - 4 = 17 - 4 = 13

\(a_{3}\) = \(a_{2}\) - 4 = 13 - 4 = 9

\(a_{4}\) = \(a_{3}\) - 4 = 9 - 4 = 5

\(a_{5}\) = \(a_{4}\)  - 4 = 5 - 4 = 1

and so on.

Therefore, the recursive sequence are: 17, 13, 9, 5, 1.

The question is incorrect and correct question is '' Write a recursive sequence that represents the sequence defined by the following explicit formula  \(a_{n}\) = 17 - 4n and find \(a_{1\) and   \(a_{n}\) ''.

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Step-by-step explanation

The orange machine, the very end of the shovel part. That line is a slope. The middle part of the scooper could also be a slope. The very beginng part of the scooper is also a slope.  The bottom part of the scooper is also a slope. The bottom part at the end of the scooper could also be slope.

Answer:

x ≤ 7

Step-by-step explanation:

$56 (her budget) divided by $8 (which is the cost per pound) will equal x.  Since we do not know the actual answer of the number of pounds she will buy due to the fact she will spend less than $56, which is also making her open to buying a total of $56.   Since the question is asking for the possible numbers of pounds she will buy, we will use the identity for pounds to be x.  We don't know the actual amount she will buy so the answer is x ≤ 7.  She will buy either less than or exactly 7 pounds of candy.

A truth table is a table that describes the values of an input signal and the resulting output signal. The truth table can be used to determine the values of Boolean expressions by matching the input signal with the output signal.

The Boolean expressions can be derived from the truth table.In order to draw Truth Table for the given expressions and get their SOP and POS Boolean expression, we have to follow the below steps: Step 1: Truth Table for the given expressions

Truth Table for a) Y = A BC + AC + BC:

Truth Table for b) Y = (AB) + C(A + B):

Truth Table for c) Y = (A BC) A+D):

Truth Table for d) Y = A BC + (A + B)D:

Step 2: SOP (Sum of Product) and POS (Product of Sum) Boolean expression From the Truth Tables above, we can create the SOP and POS Boolean expression.

Here are the SOP and POS expressions for each of the given expressions:

a) Y = A BC + AC + BC- SOP: A B C + A C + B C- POS: (A + B) (A + C) (B + C)

b) Y = (AB) + C(A + B)- SOP: AB + AC + BC- POS: (A + C) (B + C)

c) Y = (A BC) A+D)- SOP: A B C + A D- POS: (A + D) (B + C) (A + D)

d) Y = A BC + (A + B)D- SOP: A B C + A D + B D- POS: (A + D) (B + D) (A + B)

Thus, the Truth Table for the given expressions and their SOP and POS Boolean expression are as shown above.

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Answer:

Use the formula for the trapeze

Step-by-step explanation:

Answer:

∠ C = 88°

Step-by-step explanation:

The opposite angles in a cyclic quadrilateral sum to 180°, then

8x - 4 + 7x + 4 = 180 , that is

15x = 180 ( divide both sides by 15 )

x = 12

Then

∠ C = 7x + 4 = 7(12) + 4 = 84 + 4 = 88°

b=32

Step-by-step explanation:

\( \sin(c)= \frac{opposite}{hypotenuse} \)

\( \sin(60) = \frac{ 16\sqrt{3} }{b} \)

\((b) \sin(60) = \frac{16 \sqrt{3} }{b} (b)\)

\((b) \sin(60) = 16 \sqrt{3} \)

\( \frac{(b) \sin(60) }{ \sin(60) } = \frac{16 \sqrt{3} }{ \sin(60) } \)

\(b = \frac{16 \sqrt{3} }{ \sin(60) } \)

\(b = 32\)

Answer:

Therefore, the direction of the vector is 180° - 29.3° = 150.7° (measured counterclockwise from the positive x-axis).

Step-by-step explanation:

To find the direction of the vector, we need to calculate its angle with respect to the positive x-axis. We can use the inverse tangent function to do this. The formula for the angle θ is:

θ = tan⁻¹ (y/x)

where y is the vertical component and x is the horizontal component of the vector.

In this case, the x-component is -22.2 m and the y-component is 12.6 m. So, we have:

θ = tan⁻¹ (12.6 / (-22.2))

Using a calculator, we find:

θ ≈ -29.3°

Since the x-component is negative, the vector points towards the negative x-axis. Therefore, the direction of the vector is 180° - 29.3° = 150.7° (measured counterclockwise from the positive x-axis).

Answer:

The correct answer is x= - 3

Step-by-step explanation:

The system of equations that correctly represents the situation of Lina and Sarika's ages are:

A system of equations is two or more equations solved concurrently or at the same time.

A system of equations is called simultaneous equations.

The sum of Lina and Sarika's ages = 31

Lina's age > Sarika's by 5 years

Let Lina's age = L

Let Sarika's age = S

L + S = 31... Equation 1

L - S = 5... Equation 2

2L = 36

L = 18.

Substituting L = 18 into either Equation 1 or 2:

18 + S = 31

S = 31 - 18

S = 13

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Answer:

yes the corresponding sides are proportional

Answer:

∠ G = 85°

Step-by-step explanation:

∠ G is an inscribed angle whose measure is half the measure of its intercepted arc.

the sum of the arcs in a circle = 360° , then

arc DF = 360° - 120° - 70° = 360° - 190° = 170° , then

∠ G = \(\frac{1}{2}\) DF = \(\frac{1}{2}\) × 170° = 85°

Answer:

(-8,0) (-1,0) (4,0)

Step-by-step explanation:

Just look at where y=0

Answer:

-8, -1 and 4

Step-by-step explanation:

look at where the line meets the x-axis and at what point

Answer:

L = 12ft

W = 13ft

Step-by-step explanation:

Let's use the two pieces of information to make 2 equations (we need 2 eqns to solve for 2 variables: Length and Width).

The length and width are consecutive integers

L+1=W

The area of the rectangle is 156 square feet.

L*W=156

We know that W=L+1 from our first equation, so substituting that information into our second equation we get

L*(L+1)=156

Let's distribute that L

L^2 + L = 156

and subtract 156 from both sides

L^2 + L - 156 = 0

Now we can use the quadratic formula to find L. L cannot be negative, so

L = 12

using our very first equation we know L, so we can solve for W.

L+1=W

12+1=W

W = 13

Answer:

14

Step-by-step explanation:

just did it (don't search up mr hands)

There are 11,440 ways to distribute 7 identical flyers into 10 different mailboxes, where each mailbox receives at most one flyer.

If we are allowed to put at most one flyer per mailbox and the flyers are identical, this problem involves distributing identical objects into distinct containers. The solution can be obtained using the stars and bars method.

We can represent the distribution of flyers as 7 stars (representing the flyers) and 9 bars (representing the dividers between the mailboxes). The number of ways to distribute the flyers is equal to the number of ways to arrange the 7 stars and 9 bars, which is given by the binomial coefficient:

${{7 + 9}\choose{9}} = {{16}\choose{9}} = \frac{16!}{9!7!} = 11440$

Therefore, there are 11,440 ways to distribute 7 identical flyers into 10 different mailboxes, where each mailbox receives at most one flyer.

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The question is incomplete but probably the full question is:

We want to distribute 7 flyers to 10 different mailboxes. How many ways can we do that if (a) We put at most one flyer per mailbox and the flyers are identical?

There are a few different ways to approach this question, but one possible explanation is based on the fact that the sine function is periodic, meaning it repeats itself over certain intervals.

The sine function has a period of 2π, which means that sin(x + 2π) = sin(x) for any value of x.Now, let's consider the interval [-2, 2] and imagine that we want to evaluate sin(x) for some value of x outside of this interval. Without loss of generality, suppose that x > 2 (similar arguments can be made for x < -2). Then, we can write x as x = 2πn + y, where n is some integer and y is a number in the interval [0, 2π) that represents the "extra" amount beyond the interval of [-2, 2]. (Note that this decomposition is possible because the period of the sine function is 2π.)

Now, we can use the fact that sin(x + 2π) = sin(x) to rewrite sin(x) as sin(2πn + y) = sin(y). Since y is in the interval [0, 2π), we can evaluate sin(y) using any method that works for that interval (e.g., a lookup table, a series expansion, a graph, etc.). In other words, we can always "wrap" any value of x outside of [-2, 2] into the interval [0, 2π) using the periodicity of the sine function, and then evaluate sin(x) for that "wrapped" value.

Now, why did we choose the interval [-2, 2] in particular? One reason is that this interval is convenient for many practical purposes, such as approximating the sine function using polynomial or rational functions (e.g., Taylor series, Chebyshev polynomials, Padé approximants, etc.). These approximations often work best near the origin (i.e., when x is close to 0), and the interval [-2, 2] contains the origin while still being small enough to be computationally tractable.

Another reason is that many real-world applications that involve trigonometric functions (e.g., physics, engineering, statistics, etc.) often involve angles that are small enough to be within the interval [-2, 2] (e.g., angles in degrees or radians that are less than or equal to 180 degrees or π radians). In these cases, evaluating sin(x) within the interval [-2, 2] is often sufficient for practical purposes.

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