The circular hole in an opaque screen is 6.00mm in diameter. It is perpendicularly illuminated by collimated light of wavelength 500nm. How many Fresnel zones will be "seen" from a point- P on the central axis 6.00m from the screen? Will that point be bright or dark? Roughly, what will the diffraction pattern look like on a vertical plane containing P?

Answer:

Mean = $70.8

Median = $70

Mode = $60

Step-by-step explanation:

From the line plot attached,

Prices of the sunglasses are,

$20, $20, $50, $50, $50, $60, $60, $60, $60, $60, $60, $70, $70, $70, $80, $80, $80, $80, $90, $90, $90, $90, $100, $100, $130

Since mean of the data = Average of the terms

                                       \(=\frac{\text{Sum of the terms in the data set}}{\text{Number of terms}}\)

                                       = \(\frac{2(20)+3(50)+6(60)+3(70)+4(80)+4(90)+2(100)+130}{(2+3+6+3+4+2+1)}\)

                                       = \(\frac{40+150+360+210+320+360+200+130}{25}\)

                                       = \(\frac{1770}{25}\)

                                       = $70.8

Median = Middle term of the data set

Since number of terms of the data set are odd (25)

Therefore, median = \((\frac{n+1}{2})\text{th term}\) [where n = number of terms in the data set]

                               = \(\frac{25+1}{2}\)

                               = 13th term

13th term of the data set is $70.

Therefore, Median = $70

Mode = Term repeated the most

In the data set $60 is the term which is repeated the most (6 times).

Therefore, Mode = $60

Answer:

44h

Step-by-step explanation:

money earned per extra hour worked=100+25/100×10.80=13.50

amount earned if working for 38 hours=10.80×38=410.40

remaining money=491.40-410.40=81

number of extra hours worked=81÷13.50=6

total hours worked=38+6=44h

There are 126 whole numbers less than 127.

To find the number of whole numbers that are less than 127, we need to count all the integers from 1 to 126 inclusive.

Since 1 is the smallest positive whole number, and 126 is the largest whole number less than 127, there are 126 whole numbers less than 127.

So, there are 126 whole numbers less than 127.

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In order to find how many minutes Leann swan this week, we just need to sum the time from each day:

Monday: 24 minutes

Tuesday: 18 minutes

Wednesday: 30 minutes

Thursday: 30 minutes

Friday: 30 minutes

So in total Leann swan 132 minutes this week.

Answer:

Step-by-step explanation:

x+y=10

1.50x+2.50y=22

Then use the the elimination method. The final answer is x=3, y=7.

If Ridgewood Savings Bank charges a $27 per check overdraft protection fee. The amount she will owe the bank after July 12 is: $1,071.42.

Total obligation can be defined as the amount a person owe another person or the debt amount a borrower  is expected to payback to a lender.

Balance $1,400

July 9 check ($1,380.15)

Balance $19.85

July 10 check ($765.67)

($670 + $95.67)

Balance -$745.82 (Overdraft)

Now let find the amount she owe

Balance -$745.82

July 11 check $130

Balance -$875.82

July 12 check $87.60

Ending balance -$963.42

Overdraft fee $108

($27 ×4)

Total obligation -$1,071.42

Therefore her total obligation is $1,071.42.

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The solution to the inequality -2x + 4 < 16 is x > -6.

To solve the inequality -2x + 4 < 16, you can follow these steps:

Start by isolating the variable term. In this case, the variable term is -2x. Move the constant term, which is +4, to the other side of the inequality by subtracting 4 from both sides:

-2x + 4 - 4 < 16 - 4

-2x < 12

Next, divide both sides of the inequality by the coefficient of x, which is -2. It's important to note that when you divide or multiply an inequality by a negative number, you need to reverse the direction of the inequality sign:

(-2x) / -2 > 12 / -2

x > -6

The solution to the inequality is x > -6. This means that any value of x greater than -6 would satisfy the original inequality. Graphically, this represents all the numbers to the right of -6 on the number line.

So, the solution to the inequality -2x + 4 < 16 is x > -6.

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Answer:

I would use associative property and the awnser should be -29+-18= -47

Step-by-step explanation:

i hope that helps im very sorry if thats not right

The bounds for a 95% confidence interval could be option (B) 72 and 79

We know that the 98% confidence interval has bounds of 73 and 80. This means that if we were to repeat the same experiment many times, we would expect that 98% of the time, the true population mean would fall within this range.

To find the bounds for a 95% confidence interval, we can use the fact that a higher confidence level corresponds to a wider interval, and a lower confidence level corresponds to a narrower interval.

Since we want a narrower interval for a 95% confidence level, we can expect the bounds to be closer to the sample mean. We can calculate the sample mean as the midpoint of the 98% confidence interval

(sample mean) = (lower bound + upper bound) / 2 = (73 + 80) / 2 = 76.5

Next, we can use the formula for a confidence interval:

(sample mean) ± (z-score) × (standard error)

where the z-score depends on the desired confidence level, and the standard error depends on the sample size and sample standard deviation. Since we don't have this information, we can assume that the sample size is large enough (i.e., greater than 30) for the central limit theorem to apply, and we can use the formula

standard error = (width of 98% CI) / (2 × z-score)

For a 98% confidence interval, the z-score is 2.33 (found using a standard normal distribution table or calculator). Plugging in the values, we get

standard error = (80 - 73) / (2 × 2.33) = 1.70

Now, we can use this standard error to calculate the bounds for a 95% confidence interval

(sample mean) ± (z-score) × (standard error) = 76.5 ± 1.96 × 1.70

Simplifying, we get

(lower bound) = 76.5 - 3.33 = 73.17

(upper bound) = 76.5 + 3.33 = 79.83

Therefore, the correct option is (B) 72 and 79

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The probability of choosing a 5 and then a 6 is 1/49

From the question, we have the following parameters that can be used in our computation:

The tiles

Where we have

Total = 7

The probability of choosing a 5 and then a 6 is

P = P(5) * P(6)

So, we have

P = 1/7 * 1/7

Evaluate

P = 1/49

Hence, the probability of choosing a 5 and then a 6 is 1/49

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Question

You randomly choose one of the tiles. Without replacing the first tile, you choose a second tile. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest tenth. The probability of choosing a 5 and then a 6

Answer:8

Step-by-step explanation:

12+12=24

40-24=16

8+8=16

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{8 \: feet}}}}}\)

Step-by-step explanation:

Given,

Perimeter of a rectangular rug ( P ) = 40 feet

Length of a rectangular rug ( l ) = 12 feet

Width of a rectangular rug ( w ) = ?

Finding the width

\( \boxed{ \sf{perimeter \: of \: rectangle = 2(l + w)}}\)

\( \longrightarrow{ \sf{40 = 2(12 + w)}}\)

\( \longrightarrow{ \sf{40 = 24 + 2w}}\)

\( \longrightarrow{ \sf{24 + 2w = 40}}\)

\( \longrightarrow{ \sf{2w = 40 - 24}}\)

\( \longrightarrow{ \sf{2w = 16}}\)

\( \longrightarrow{ \sf{ \frac{2w}{2} = \frac{16}{2} }}\)

\( \longrightarrow{ \sf{w = 8 \: ft}}\)

Width of a rectangular rug = 8 feet

Hope I helped!

Best regards! :D

To rotate a coordinate system onto another coordinate system using matrices, you can follow these steps:

1. Determine the angle of rotation: First, determine the angle by which you want to rotate the coordinate system. This angle will be used to create a rotation matrix.

2. Create a rotation matrix: The rotation matrix is a 2x2 or 3x3 matrix that represents the transformation of points in the original coordinate system to points in the rotated coordinate system. The elements of the rotation matrix can be determined based on the angle of rotation.

For a 2D rotation, the rotation matrix is:

 \(\[ \begin{matrix} cos\theta & -sin\theta \\ sin\theta & cos\theta \end{matrix} \]\)

For a 3D rotation around the x-axis, y-axis, and z-axis, the rotation matrices are:

\(Rx = \left[\begin{array}{ccc}1&0&0\\0&cos\theta&-sin\theta\\0&sin\theta&cos\theta\end{array}\right]\)

\(Ry = \left[\begin{array}{ccc}cos\theta&0&sin\theta\\0&1&0\\-sin\theta&0&cos\theta\end{array}\right]\)

\(Rz = \left[\begin{array}{ccc}cos\theta&-sin\theta&0\\sin\theta&cos\theta&0\\0&0&1\end{array}\right]\)

Note that θ represents the angle of rotation.

3. Apply the rotation matrix: To rotate a point or a set of points, multiply the coordinates of each point by the rotation matrix. This will yield the coordinates of the points in the rotated coordinate system.

For example, if you have a 2D point P(x, y), and you want to rotate it by angle θ, the rotated point P' can be obtained by multiplying the column vector [x, y] by the rotation matrix:

  [ x' ]  =  [ cosθ  -sinθ ]   [ x ]

  [ y' ] =   [ sinθ   cosθ  ] * [ y ]

Similarly, for 3D rotations, you would multiply the column vector [x, y, z] by the appropriate rotation matrix.

Rotating a coordinate system onto another coordinate system using matrices involves the use of rotation matrices. These matrices define how points in the original coordinate system are transformed to points in the rotated coordinate system.

The rotation matrices are constructed based on the desired angle of rotation. The elements of the matrix are determined using trigonometric functions such as cosine and sine. The size of the rotation matrix depends on the dimensionality of the coordinate system (2D or 3D).

To apply the rotation, the coordinates of each point in the original coordinate system are multiplied by the rotation matrix. This matrix multiplication yields the coordinates of the points in the rotated coordinate system.

By performing this transformation, you can effectively rotate the entire coordinate system, including all points and vectors within it, onto the desired orientation defined by the angle of rotation.

Matrix transformations provide a mathematical and systematic approach to rotating coordinate systems, allowing for precise control over the rotation angle and consistent results across different coordinate systems. They are widely used in computer graphics, robotics, and various scientific and engineering fields.

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Answer: I think the mean would be 7 but I’m not entirely sure

Hi, your midpoint is (-2, 1). Hope this helps, have a great day and please mark me brainliest:)

To produce g, function was reflected over the x-axis and | shifted up 3 units . Function g can be defined as g(x)=f(x-1)+4.

What is axis ?

An axis is a straight line around which an object or a geometric shape can rotate or be symmetrical. In a coordinate system, an axis is a line that serves as a reference for the location of points in space.

When a function f(x) is reflected over the x-axis, it changes the sign of the y-coordinate values. By reflecting the graph of f(x) over the x-axis, the new function g(x) will have the same shape as f(x) but with all y-coordinate values inverted.

Additionally, by shifting the function up 3 units, it means that the y-coordinate values of the new function g(x) will be 3 units greater than the y-coordinate values of the original function f(x).

So the transformation can be represented as:

g(x) = f(x-1) + 4

It is the horizontal shift of 1 unit to the right, and a vertical shift of 3 units up

To produce g, function was reflected over the x-axis and | shifted up 3 units . Function g can be defined as g(x)=f(x-1)+4.

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Answer:

Step-by-step explanation:

17

Answer:

Step-by-step explanation:

Given function is,

f(x) = 5x - 3

Where f(x) represents the output values and 'x' is the variable representing the input values.

For x = -2,

f(-2) = 5(-2) - 3

     = -13

For x = -1,

f(-1) = 5(-1) - 3

     = -8

For x = 0,

f(0) = 5(0) - 3

     = -3

For x = 1,

f(1) = 5(1) - 3

    = 2

For x = 2,

f(2) = 5(2) - 3

     = 7

For x = 3,

f(3) = 5(3) - 3

     = 12

Table for the input-output values will be,

x          -2           -1           0           1             2          3

f(x)      -13          -8         -3           2            7          12

Since the values of f(x) has a common difference of [-13 - (-8) = -5] negative five, given function will be a linear function.

After reducing all the book prices by 50%, the new median price is determined to be $7.70 (B)

To find the new median price after reducing all the book prices by 50%, we first need to calculate the reduced prices. By reducing each given price by 50%, we get $6.375, $7.40, $9.995, $4.975, $8.00, and $8.975 respectively.

Next, we arrange these reduced prices in ascending order: $4.975, $6.375, $7.40, $8.00, $8.975, and $9.995. The median is the middle value in this ordered list. Since there are six prices, the middle two values are $7.40 and $8.00.

To find the median, we take the average of these two values, which gives us ($7.40 + $8.00) / 2 = $7.70.

Therefore, the new median price, after reducing all the book prices by 50%, is $7.70 (B). This means that the median price of the books, after the reduction, is $7.70.

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Using matrix inversion method and perimeter of rectangle, the dimension of the rectangle are 16cm and 7cm

Let the length of the rectangle be l and the width be w. We know that l - w = 3.5 and 2l + 2w = 67. We can rewrite these equations as a system of linear equations in matrix form:

\($$\begin{bmatrix}1 & -1 \ 2 & 2\end{bmatrix} \begin{bmatrix}l \ w\end{bmatrix} = \begin{bmatrix}3.5 \ 67/2\end{bmatrix}$$\)

We can solve for \($\begin{bmatrix}l \ w\end{bmatrix}$\) by multiplying both sides of the equation by the inverse of the coefficient matrix:

\($$\begin{bmatrix}l \ w\end{bmatrix} = \begin{bmatrix}1 & -1 \ 2 & 2\end{bmatrix}^{-1} \begin{bmatrix}3.5 \ 67/2\end{bmatrix}$$\)

To find the inverse of the coefficient matrix, we can use the following formula:

\($$\begin{bmatrix}a & b \ c & d\end{bmatrix}^{-1} = \frac{1}{ad-bc} \begin{bmatrix}d & -b \ -c & a\end{bmatrix}$$\)

Plugging in the values for our matrix, we get:

\($$\begin{bmatrix}1 & -1 \ 2 & 2\end{bmatrix}^{-1} = \frac{1}{1 \cdot 2 - (-1) \cdot 2} \begin{bmatrix}2 & 1 \ -2 & 1\end{bmatrix} = \begin{bmatrix}1/2 & 1/4 \ -1/2 & 1/4\end{bmatrix}$$\)

Now we can substitute this matrix and the vector on the right-hand side of the equation into our formula to obtain the solution:

\($$\begin{bmatrix}l \ w\end{bmatrix} = \begin{bmatrix}1/2 & 1/4 \ -1/2 & 1/4\end{bmatrix} \begin{bmatrix}3.5 \ 67/2\end{bmatrix} = \begin{bmatrix}16 \ 7\end{bmatrix}$$\)

Therefore, the dimensions of the rectangle are 16 cm by 7 cm.

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Solution

(a)

(b)

(c)

The discount rate raised to nth power.

NPV is defined as Net Present Value. It is mainly used in capital budgeting and investment planning for the purpose of analyzing the project profit. NPV is the difference between  the present value of cash inflows and the present value of cash outflows in a period of time. The occurrence of cashflows in a series at different times is termed as NPV. NPV is a measure widely used in finance and commercial real estate. It is used to help taking decisions in accounting calculation. The cashflow that is discounted can be termed as NPV.

A simple example for NPV is, If a security offers a series of cashflows with an NPV of $30,000 and an investor pays exactly $30,000 for it, then the  investor's, NPV is $0.

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The open sentence involving the absolute value for the problem is |x - 105| ≤ 10.

From the question, we have the following parameters that can be used in our computation:

Mary's bowling score was within 10 pins of her average score of 105.

Let x represents the bowling score

So, the absolute difference can be represented as

|x - 105|

This value is within 10 pins of the average score of 105.

So, we have

|x - 105| ≤ 10.

Hence, the open sentence is |x - 105| ≤ 10.

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Answer:

Step-by-step explanation:

its 2,3.455

Answer:

13

Step-by-step explanation:

To find the unit pay

you first had to do 39/3 (39 divided by 3) and then that answer you get is payment she receives in an hour

hour: 1  |   3

Pays: 13|  39

HOPE IT HELPS:)

The real zeros of\(f(x)\) are:

\(x = -1/2, 2/3, 8/3\) Therefore, \(x = -1/2, 2/3, 8/3\) is the solution for the problem.

(a) The given factors of\(f(x)\)

are\((2x + 1)and (3x - 2)\).

In order to verify the given factors of\(f(x)\)

we use synthetic division. \(2x + 1: -1/2 |6 17 -5 -6 6 6 -14 12\)  

6 14 3 9 15 -3 -6 -3 The factor \((2x + 1)\) is verified.

(3x - 2): 2/3 |6 17 -5 -6 6 6 -14 12

6 23 0 -6 0 -6 -2 2

The factor \((3x - 2)\) is verified.

(b) We have to find the remaining factors of \(f(x)\) using the factors \((2x + 1)\)and `(3x - 2)`.

So, by factor theorem, the remaining factor of `f(x)` can be written as `ax + b`.

Therefore, \(f(x) = (2x + 1)(3x - 2)(ax + b)\)

By multiplying \((2x + 1)` and `(3x - 2)\) we get

\((2x + 1)(3x - 2) = 6x^2 - x - 2\)

We can now write,

\(f(x) = (2x + 1)(3x - 2)(ax + b)\)

\(f(x) = (6x^2 - x - 2)(ax + b)\)

We can now equate the given coefficients to find the values of `a` and `b`.

\(f(x) = (6x^2 - x - 2)(ax + b)\)

\(f(x) = 6ax^3 + (6b - a)x^2 + (-2b - 2a)x - 2b\)

Comparing the coefficients on both sides,

we have: Coefficient of

\(x^3: 6a = -6 = > a = -1\)

Coefficient of\(x^2: 6b - a = 17 = > 6b - (-1) = 17 = > 6b + 1 = 17 = > 6b = 16 = > b = 8/3\)

Therefore, the remaining factor of

\(f(x)\) is\(-x + 8/3\)

Thus,\(f(x) = (2x + 1)(3x - 2)(-x + 8/3)\)

(c) The complete factorization of \(f(x)\) is:

\(f(x) = (2x + 1)(3x - 2)(-x + 8/3)\)

(d) To find the real zeros of \(f(x)\)

we equate\(f(x)\) to zero and solve for\(x\)

\(f(x) = (2x + 1)(3x - 2)(-x + 8/3) = 0\)

So, the real zeros of \(f(x)\) are:\(x = -1/2, 2/3, 8/3\).

Therefore,

\(x = -1/2, 2/3, 8/3\) is the solution for the problem.

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The most appropriate choice for matrix will be given by-

The position number of all the matrix entries are

\(a_{11} = 0\\a_{12} = -1\\a_{13} = 3\\a_{14} = 5\\a_{15} = -2\\a_{21} = 7\\a_{22} = -8\\a_{23} = 6\\a_{24} = -4\\a_{25} = -9\\a_{31} = 1\\a_{32} = 2\\a_{33} = -3\\a_{34} = -5\\a_{35} = 8\)

What is a matrix?

Any arrangement of numbers in the form of rows and columns are called matrix. The numbers inside a matrix is known as elements of the matrix.

The position number of a matrix entry is denoted by \(a_{mn}\) where m denotes the row position and n denotes the column position.

We can do addition, subtraction, multiplication on matrix but two matrices cannot be divided.

Here,

The position number of a matrix entry is denoted by \(a_{mn}\) where m denotes the row position and n denotes the column position.

The given matrix is

\(\left[\begin{array}{ccccc}0 & -1 & 3 & 5 & -2\\7&-8&6&-4&9\\1&2&-3&-5&8\end{array}\right]\)

The position numbers of all the matrix entries are given below

\(a_{11} = 0\\a_{12} = -1\\a_{13} = 3\\a_{14} = 5\\a_{15} = -2\\a_{21} = 7\\a_{22} = -8\\a_{23} = 6\\a_{24} = -4\\a_{25} = -9\\a_{31} = 1\\a_{32} = 2\\a_{33} = -3\\a_{34} = -5\\a_{35} = 8\)

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Based on the limited information, it can be deduced that 1/5 of the ribbon is not in view.

In order to show the complete ribbon, we need to understand that in mathematical terms:

Since 4/5 of the ribbon is showing

This means that about 1- 4/5

= 1/5 of the ribbon is not in view.

With this knowledge, you can go ahead to complete your drawing, knowing that a full ribbon has a rectangular shape.

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Answer:

d

Step-by-step explanation:

its inverse so it will be the oppisite of 2/5

J in 55min

J in 45min ( bigger hose)

Alternative method

The trick is to convert the numbers you are given to numbers that you can add together.

You have minutes per pool. You can’t work with that. But if you take the reciprocal of each you get pools per minute.

So if the first hose fills 1/55 = 0.01818 pools per minute and the second one fills 1/45 = 0.0222 pools per minute, then both of them will fill 0.1818 + 0.0222 = 0.04040 pools per minute. If we take the reciprocal of that we end up with 1/0.04040 = 24.75 minutes per pool.

Answer:

64 ounces

Step-by-step explanation:

Since 1 lb = 16 oz, just do 4 × 16 = 64

If puppy weighs 4 pounds then the weigh in ounces is 64 ounces.

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

There are 16 ounces in a pound.

1 pound= 16 ounces.

Given that puppy weighs 4 pounds.

We have to find the wight in ounces.

To convert pounds to ounces, we need to multiply the weight in pounds by 16.

The puppy weighs 4 pounds x 16 ounces/pound

= 64 ounces

Hence, if puppy weighs 4 pounds then the weigh in ounces is 64 ounces.

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