An expression is shown. 590.92 - 219.38 What is the value of the expression?​

The formula tan(w) = (\(e^{iw}\) - \(e^{-iw}\)) / (i(\(e^{iw}\) + \(e^{-iw}\))) can be used to find the values of arctan(1 + i). By substituting z = 1 + i into the formula and simplifying, we can determine the corresponding values of arctan(1 + i).

To find the values of arctan(1 + i), we can use the formula tan(w) = \((e^{iw} - e^{-iw}) / (i(e^{iw} + e^{-iw}))\). Let's substitute z = 1 + i into this formula:

tan(w) = (\(e^{iw}\) - \(e^{-iw}\)) / (i(\(e^{iw}\) + \(e^{-iw}\)))

      = (\(e^{iw}\)\(- e^{-iw}) / (i( + e^{-iw})) * (e^{-iw} / e^{-iw})\)

      = (\(e^{iw}\) - \(e^{-iw}\)) / (i(\(e^{iw}\) + \(e^{-iw}\))) * \(e^{-2iw}\)

Now, let's simplify the expression:

tan(w) = (\(e^{iw}\) - \(e^{-iw}\)) / (i(\(e^{iw}\) + \(e^{-iw}\))) * \(e^{-2iw}\)

      = (\(e^{iw}\) - \(e^{-iw}\)) *\(e^{-2iw}\) / (i(\(e^{iw}\) + \(e^{-iw}\)))

      = (\(e^{3iw}\) - 1) / (\(e^{3iw}\) + 1)

To find the values of arctan(1 + i), we need to solve the equation (e^3iw - 1) / (e^3iw + 1) = 1 + i. By equating the real and imaginary parts on both sides of the equation, we can determine the values of w. Substituting these values back into arctan(z) = w, we can find all the values of arctan(1 + i).

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Answer:

One expression equivalent to y^1/5 using radicals is the fifth root of y, which can be written as √[5]{y}.

The he statement d(k) + (k + 1) = d(k+1) is true for all natural numbers, n, by mathematical induction.

To prove that the statement is true for all natural numbers, n, we can use mathematical induction.

The statement we want to prove is that d(k) + (k + 1) = d(k + 1), where d(n) represents the total number of dots in a pattern of n squares.

Base Case (n = 1):

First, let's prove the statement for the base case, n = 1.

For n = 1:

d(1) + (1 + 1) = d(1) + 2

Now, consider a single square with 1 dot.

In this case, d(1) = 1.

So, we have:

1 + 2 = 3

Now, let's consider a pattern of 2 squares (n = 2).

The first square has 1 dot, and the second square has 2 dots. So, d(2) = 1 + 2 = 3.

So, the statement is true for n = 1.

Inductive Hypothesis (Assume true for n = k):

Now, assume that the statement is true for some arbitrary natural number k.

That is, assume that: d(k) + (k + 1) = d(k + 1)

Inductive Step (Prove true for n = k + 1):

To prove that the statement is true for n = k + 1.

d(k + 1) + (k + 2) = d(k + 2)

Now, consider a pattern of (k + 1) squares.

By the inductive hypothesis, assume that the statement is true for k squares:

d(k) + (k + 1) = d(k + 1)

Now, let's add one more square to the pattern.

This square will have (k + 2) dots.

So, the total number of dots in the pattern of (k + 1) squares plus the (k + 2) dots in the additional square is:

d(k + 1) + (k + 2)

And by the inductive hypothesis, d(k) + (k + 1) = d(k + 1).

Therefore:

d(k + 1) + (k + 2) = (d(k) + (k + 1)) + (k + 2) = d(k) + (k + 1) + (k + 2)

Now, simplify:

d(k + 1) + (k + 2) = d(k + 1) + (k + 1 + 1)

So, it is shown that for n = k + 1, d(k + 1) + (k + 2) = d(k + 1) + (k + 1) + 1.

Since it is assumed the statement to be true for k and proved it for k + 1, it is shown that the statement is true for all natural numbers, n, by mathematical induction.

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The number of tablets that should be taken for inspection if the permissible relative standard deviation in the measurement is to be

(a) 20.% is 324 tablets

(b) 14% is 181 tablets

(c) 7% is 78 tablets

(d) 3% is 32 tablets.

To determine how many tablets should be taken for inspection to achieve a permissible relative standard deviation (RSD) of 20%, we can use the following formula:

n = (RSD * mean)^2 / (variance * (1 - mean))

where n is the number of tablets that need to be inspected, RSD is the permissible relative standard deviation, mean is the proportion of tablets that fail to meet the requirement (in this case, 5.5%), and variance is the variance of the proportion of tablets that fail to meet the requirement.

Plugging in the given values, we get:

n = (20% * 5.5%)^2 / (0.0055 * (1 - 5.5%))

Calculating this expression gives us n = 324 tablets.

To determine how many tablets should be taken for inspection to achieve a permissible relative standard deviation of 14%, we can use the same formula, with the value of RSD set to 14%. This gives us n = 181 tablets.

To determine how many tablets should be taken for inspection to achieve a permissible relative standard deviation of 7%, we can use the same formula, with the value of RSD set to 7%. This gives us n = 78 tablets.

To determine how many tablets should be taken for inspection to achieve a permissible relative standard deviation of 3%, we can use the same formula, with the value of RSD set to 3%. This gives us n = 32 tablets.

It's important to note that these calculations assume that the proportion of tablets that fail to meet the requirement is 5.5%. If the proportion of tablets that fail to meet the requirement has changed (e.g., due to changes in the coating method), then the number of tablets that need to be inspected will also change.

The number of tablets that should be taken for inspection if the permissible relative standard deviation in the measurement is to be

(a) 20.% is 324 tablets

(b) 14% is 181 tablets

(c) 7% is 78 tablets

(d) 3% is 32 tablets.

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The size of the given table is 4 x 6 . A table is a group of data arranged in rows and columns. It's a method of organizing and displaying data in a logical manner Therefore, the size of the table is 4 x 6. Answer: C) 4 x 6..

Tables can be used to compare, show relationships, and reveal patterns in data. They're widely used in statistical analyses and scientific reports .

The size of the table refers to the number of rows and columns in the table. The number of rows is referred to as the table's width, while the number of columns is referred to as the table's height. To determine the size of a table, count the number of rows and columns.  For instance, in the given table below,

Rows: C1Columns: Worksheet columns A B C D FAll0 hours1 4 10 5 5 25< 2 hours4 6 10 1 1 22>=2 hours7 5 5 0 0 17All12 15 25 6 6 64The table has 4 rows and 6 columns. Therefore, the size of the table is 4 x 6. Answer: C) 4 x 6.

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To find the value of the variable "a" and the values of Y and Z, we can use the given information. We are told that Y is between X and Z, which means that Y is greater than X and less than Z.

From the given information, we have:
X Y = 7a
YZ = 5a
XZ = 6a + 24

Since Y is between X and Z, Y should be greater than X and less than Z.

Let's set up an inequality to represent this:
X < Y < Z

Now, let's substitute the given expressions:
7a < Y < 5a

To simplify this inequality, we can divide all parts by "a":
7 < Y/a < 5

Since we want Y to be between X and Z, Y/a should be greater than the value of X/a and less than the value of Z/a.

So, we can write two separate inequalities:
7 < Y/a   ...(1)
Y/a < 5   ...(2)

Now, let's consider the equation XZ = 6a + 24.
We know that XZ = YZ + XY, so we can substitute the given values:
6a + 24 = 5a + 7a

Simplifying this equation:
6a + 24 = 12a

Subtracting 6a from both sides:
24 = 6a

Dividing both sides by 6:
4 = a

Now that we know the value of a, we can substitute it back into our inequalities (1) and (2) to find the values of Y and Z:

From (1):
7 < Y/4
Multiply both sides by 4:
28 < Y

From (2):
Y/4 < 5
Multiply both sides by 4:
Y < 20

Therefore, the value of the variable a is 4, and the values of Y and Z are such that Y is greater than 28 and less than 20.

The value of the variable "a" is 4, and there is no solution for the values of Y and Z, as the inequality contradicts the given statement that Y is between X and Z.

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Answer:

(2,-3)

Step-by-step explanation:

Answer:

y= \(\frac{3}{2}\)x -3

Step-by-step explanation:

Answer:

-2(x-1) - x + 3 = -1

First if all, we operate the parenthesis knowing that \(a(b+c) = ab + ac\):

-2(x-1) - x + 3 = -1 ---->.-2x -2*(-1) - x + 3 = -1

Now, we operate:

.-2x -2*(-1) - x + 3 = -1 ----> -2x + 2 - x + 3 = -1

Now we operate another time to put all the x together and the independent terms too:

-2x + 2 - x + 3 = -1 ----> -3x + 5 = -1

We substract 5 at both sides to have only the x at one side:

-3x + 5 = -1 ----> -3x + 5 - 5 = -1 - 5 ----> -3x = -6

As both sides have a minus (-) we can eliminate it:

-3x = -6 ----> 3x = 6

We divide both sides by 3 to have only a x:

3x = 6 ----> 3x/3 = 6/3 ----> x = 2

Now, we know that x=2. We can also verify it by replacing it on the first equation:

-2(x-1) - x + 3 = -1 ---> -2(2-1) - 3 + 3 = -1 ---> -2(1) - 2 + 3 = -1 ---> -2 - 2 + 3 = -1

Now we know it's true, as we have replaced it and we got he answer.

2 hours 30 minutes

Step-by-step explanation:

60/90=100/x

60x=9000

x=150 minutes or 2 hour 30 minutes

Answer:

2 hours 30 minutes

Step-by-step explanation:

Speed = Distance/Time

Time = Distance/Speed

The car covers 60Km in 1 hour 30 minutes i.e. 90 minutes:

Speed = 60Km*60/90 mins

= 40km/hr

To cover 100 km at the same speed, i.e.:

Time = 100Km/40km/hr

= 2.5 hrs

= 2 hours 30 minutes

The domain on which the graph described as in the image is increasing is to be determined; (-4, ∞).

It follows from the task content that the domain for which the function described by the graph is increasing is to be determined.

Since the graph is a quadratic function which opens upward and whose minimum point is at; x = -4.

Also, since a graph of a function, f(x) is increasing when f'(x) > 0.

Therefore, by observation the graph is increasing on the domain defined by; (-4, ∞).

Put simply, the function is increasing in the Domain; x > -4.

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Answer:

True?

Step-by-step explanation:

I think its true but I'm not 100% sure so I would go with true. Try thinking of your past problems that you used and think about that maybe? But in then mean time, I would go with True

I think its false. If am incorrect, you can report me :(

A bit is a unit of information in computing that can have two values, typically represented as 0 and 1. A bit string of length 9 is a sequence of 9 digits, each of which is either 0 or 1.

(a) How many bit strings of length 9 or less are there?

To find the number of bit strings of length 9 or less, we can sum the number of bit strings of each length from 0 to 9.

For a bit string of length 0, there is only one possible string - the empty string.

For a bit string of length 1, there are two possible strings - 0 or 1.

For a bit string of length 2, there are four possible strings - 00, 01, 10, or 11.

For a bit string of length 3, there are eight possible strings - 000, 001, 010, 011, 100, 101, 110, or 111.

And so on, up to length 9.

That is:

1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256= 511.

There are 511 bit strings of length 9 or less.

(b) How many bit strings of length 9 or less are there, including the empty string of length zero?

To find the number of bit strings of length 9 or less, we can use the same method as above, but exclude the strings of length 10:

1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256= 511

There are 511 bit strings of length 9 or less, including empty string.

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The area in square meters will the oil slick cover is 9.5×10⁶ m².

15 barrels of diesel spilt into the ocean, where each barrel contains 42 gallons. Thereby the total volume of the oil spilt by 15 barrels is calculated as follows:

The total volume of the oil spilt by 15 barrels = 15× 42 gallons.

=630 gallons

1 gallon = 3.78541 liters

Volume in L = 630 gallons × 3.78541 liters/ 1 gallon

= 2384.8083 L

1 L = 10⁻³ m³

2384.8083  L = 2384.8083 × 10⁻³ m³

= 2.3848083 m³

The area covered by the oil spill has to be determined, where the thickness of the oil spill is given to be 2.5×10² nm.

1 nm = 10⁻⁹ m

Thereby, 2.5×10² nm = 2.5×10²×10⁻⁹ m

= 2.5×10⁻⁷ m

Area (m²) = volume (m³)/thickness (m)

= 2.3848083 m³/ 2.5×10⁻⁷ m

= 0.95392×10⁷ m²

= 9.5×10⁶ m²

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Answer:29x+10y<60

Step-by-step explanation:

She has $60 to spend.

And no tax. it should be 29x+10y>(less than or equal to) $60.

Step-by-step explanation:

I suspect you mean

11³ × 11 = ?

11³ ÷ 11 = ?

11³ × 11 = 11⁴

11³ ÷ 11 = 11²

why ?

11³ = 11×11×11

11³ × 11 = 11×11×11 × 11 = 11×11×11×11 = 11⁴

11³ ÷ 11 = 11×11×11 / 11 = 11×11 × 1 = 11×11 = 11²

The dimensions of the container of least cost are 15 inches by 15 inches by 3 inches, and the least cost of the container is $990.

Let the side of the square base of the rectangular container be x, and the height be y. The volume of the container can be expressed as xy² = 2250. From this, we can solve for x in terms of y using x = (2250/y²) as shown in equation (1).

Next, let's consider the cost of the sides (C). The cost of the sides is directly proportional to the surface area of the sides of the container, which is given by 2xy + 4y². Therefore, we can express the cost of the sides as C = k(2xy + 4y²) in equation (2), where k is a constant.

Since we are looking for the dimensions of the container of least cost, we need to minimize the cost function. To do this, we can differentiate the cost function with respect to y and set it equal to zero. This will give us the critical point where the cost is minimized.

Differentiating C with respect to y, we get dC/dy = 2k(x + 4y). Setting this equal to zero, we have 0 = 2k(x + 4y). Simplifying this equation, we get y = x/4 as shown in equation (3).

From equations (1) and (3), we have x = 15 and y = 3 inches. Therefore, the dimensions of the container of least cost are 15 inches by 15 inches by 3 inches.

To find the total cost, we calculate the cost of the top and bottom of the container (2xy) which is $2(15²) = $450, and the cost of the sides (4y²) which is $3(4*15*3) = $540. The total cost is the sum of these costs, which is $450 + $540 = $990.

In conclusion, the dimensions of the container of least cost are 15 inches by 15 inches by 3 inches, and the least cost of the container is $990.

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Step-by-step explanation:

1. 42m below the sea level.

2. you withdrawn 42 dollars from 100.

3. -14°C or -14°F or -14K.

4. your height increased from 242inches to 245 inches. your height increased by 3 inches !

hope this helps you.

Answer:

its b

Step-by-step explanation:

got it right on edge

The volume of the metal in the cylinderical pipe given the dimensions of the larger and smaller cylinders is 271.30 mm³.

A cylinder is a three-dimensional object. It is a prism with a circular base.

Volume of a cylinder = nr^2h

Where:

The volume of the metal in the cylinderical pipe = 3.14 x 10 x [(8.4/2)² - 6/2)²] = 271.30 mm³

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Answer:

13

Step-by-step explanation:

radius of the circle​ (r) = √12²+5² = √169 = 13

The scientific value for n that will make the equation (4.8 × 10^(-3))(n) = 9.6 × 10^9 true is given by: Option D: 2.0 × 10^(12)

The number is written in the form  \(a \times 10^b\)  where we have \(1 \leq a < 10\)

The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).

Scientific notations have some of the profits as:

Better readability due to compact representation

Its value in terms of power of 10 is known, which helps in easy comparison of quantities differing by a large value.

Finding the value of n from the given equation:

\((4.5 \times 10^{-3}) \times n = 9.6 \times 10^9\\\\\text{Dividing both the sides by } (4.5 \times 10^{-3}) \\\\n = \dfrac{9.6 \times 10^9}{4.5 \times 10^{-3}} = \dfrac{9.6}{4.5} \times \dfrac{10^{9}}{10^{-3}}\\\\n \approx 2.1333 \times 10^{9-(-3)} = 2.1333 \times 10^{12} \approx 2.0 \times 10^{12}\)

Thus, the scientific value for n that will make the equation (4.8 × 10–3)(n) = 9.6 × 10^9 true is given by: Option D: \(2.0 \times 10^{12}\)

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Answer: D

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

u don't need pemdas for this one

The expression that represents the relationship between the step number n and the total number of small squares in the pattern is this: (n-1)^2.

From the given information, we can see that the pattern starts with 0 squares at step 1, and each subsequent step adds a square to the pattern. However, the lower right square is always missing. Therefore, the total number of small squares in the pattern at step n can be represented by the expression: (n-1)^2

The reason we subtract 1 from n is that we started counting from step 1, whereas the expression (n-1)^2 assumes that we start counting from 0. Then we square (n-1) to account for the number of squares in the pattern, excluding the missing square in the lower right corner.

Complete Question:

Which expression represents the relationship between the step number n and the total number of small squares in the pattern?

A pattern of small squares. Step 1 has 0 squares. Step 3 has 3 squares: 2 by 2 but missing the lower right square. Step 3 has 8 squares: 3 by 3 but missing the lower right square.

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Answer:

6:22 and 9:33

Step-by-step explanation:

You multiple 3 by 2 and you get 6 then 11 by 2 and you get 22. The same for the second one and any other one you do.

Answer:

6:22, 9:33

Step-by-step explanation:

Answer:

Step-by-step explanation:

455

Answer:

A.  2 units left and 3 units up

Step-by-step explanation:

2 from x is taken away and thus shifts 2 to the left

3 is added to the eventual y value and thus shifts 3 upward

Answer:

37

Step-by-step explanation:

Good Luck! I double checked my answer!

Answer:

37

Step-by-step explanation:

Hey There!

They want us to find the hypotenuse using the Pythagorean Theorem

The Pythagorean Theorem says

\(a^2+b^2=c^2\)

or that the two legs ( shorter side) square, added together equal the hypotenuse square

Note: This only works with right triangles

so basically

\(hypotenuse^2=35^2+12^2\\35^2=1225\\1262=144\\144+1225=1369\\\sqrt{1369} =37\)

Therefore the missing side length equals 37

hope this helps!

Answer:

Step-by-step explanation:

The radius is approximately . 96 ft.

We will use the formula Circumference = 2pi(radius)

=> C=2pi(r)

=> Substitute 3.14 for pi, and 6 for C

=> 6 = 2(3.14)r

=> 6 = 6.28r

=>  .955 =r

=>  The radius is approximately .96 ft.