Write the expression in the standard form a + bi. (1 + i)20

The far that can it glide in terms of distance measured along the ground is 15,400 ft.

The length of the line segment connecting the two sites is used to measure the distance between them. The shortest line segment between a point and a line will be used to determine the distance between them.

Given that,

World War I Sopwith Camel was 7.7.

If the aircraft is in flight at 2000 ft when the engine fails.

Based on the above information, the calculation is as follows:

lift/drag = distance/height

7.7 = distance / 2000

So, the distance is 15,400 ft.

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When the patient recovery time from a specific surgical procedure is normally distributed, with a mean of 5.2 days and a standard deviation of 2.3 days, the probability of spending more than 2 days in recovery will be 0.61.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. Information about the likelihood that something will happen is provided by probability. For instance, meteorologists use weather patterns to forecast the likelihood of rain. Probability theory is used in epidemiology to comprehend the connection between exposures and the risk of health effects.

Here,

z=(X-μ)/σ

X=2

μ=5.2

σ=2.3

Z=(2-5.2)/2.3

Z=-1.39

-1.39+1

=0.39

1-0.39=0.61

The probability of spending more than 2 days in recovery will be 0.61 when the patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.2 days and a standard deviation of 2.3 days.

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Answer:

y=18-5x

Step-by-step explanation:

Answer:

0.52 cubic inches

Step-by-step explanation:

Given: circumference of a basketball is 31.4 inches.

\(\pi =3.14\)

To find: basketball's volume to the nearest cubic inches

Solution:

circumference of a basketball (sphere) = 6.28(radius)

Also, circumference of a basketball = 31.4 inches.

So, 6.28(radius) = 3.14

radius = \(\frac{3.14}{6.28}=\frac{1}{2}\) inch

Volume of the basketball (sphere) = \(\frac{4}{3}(\pi )(radius)^3=\frac{4}{3}(3.14)(\frac{1}{2})^3=0.52\,\,cubic\,\,inches\)

Answer:  See the image below.

The value of the additional data point is 36

To find the value of the additional data point, we can use the concept of the sample mean.

Given the data set: 23, 28, 20, 33, 42, 12, 19, 50, 36, 25, 19.

The sample mean of this data set is 26.5.

To find the value of the additional data point, we can use the formula for the sample mean:

(sample mean) = (sum of all data points) / (number of data points)

In this case, we have 11 data points in the original data set. Let's denote the value of the additional data point as x.

Therefore, we can set up the equation:

26.5 = (23 + 28 + 20 + 33 + 42 + 12 + 19 + 50 + 36 + 25 + 19 + x) / 12

Multiplying both sides of the equation by 12 to eliminate the fraction, we have:

318 = 282 + x

Subtracting 282 from both sides of the equation, we find:

x = 318 - 282

x = 36

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.

The value of the expression using PEDMAS is 7.

The acronym PEMDAS, which can alternatively stand for "Please Forgive My Dear Aunt Sally," is a mnemonic tool for remembering the order of operations in mathematical and algebraic formulas. Its acronym is:

P - Parenthesis (operations inside parentheses are done first)

E: Exponents (operations involving exponents are done next)

Divide and multiply is abbreviated MD (these operations are done left to right, whichever comes first)

AS stands for addition and subtraction (these operations are done left to right, whichever comes first). No matter how they approach it or how they understand it, PEMDAS helps to ensure that the same statement is assessed in the same way by various people. In mathematics, it is crucial to understand this idea, especially when working with complicated expressions or formulae.

The given expression is 1/2 x (48 ÷ 6) – 2 + 5.

Simplifying the expressions we have:

1/2 x (48 ÷ 6) – 2 + 5

= 1/2 x 8 - 2 + 5

= 4 - 2 + 5

= 7

Hence, the value of the expression using PEDMAS is 7.

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Answer:

\(y = \frac{6}{7}x - 1\)

Explanation:

\(Point 1: (-7, -7)\\Point 2: (7, -5)\)

\(\frac{y_{2} - y_{1} }{x_{2} - x_{1}}\)

\(\frac{(-5) - (-7)}{(-7) - (7)}\)

\(\frac{-12}{-14}\)

\(\frac{12}{14}\)

\(m = \frac{6}{7}\)

\(y - y_{1} = m(x - x_{1})\)

\(y - (-7) = \frac{6}{7}(x - (-7))\)

\(y + 7 = \frac{6}{7}(x + 7)\)

\(y = \frac{6}{7}x + \frac{42}{7} - 7\)

\(y = \frac{6}{7}x + (\frac{42}{7} - \frac{49}{7})\)

\(y = \frac{6}{7}x - 1\)

Answer: 83900

Step-by-step explanation:

N100 x 2.5 = N250

33560 x 2.5 = 83900

Using shell method, the volume of the solid generated by revolving the shaded region about the line y is 200π cubic units.

A solid of revolution is divided into cylindrical shells and its volume is calculated using the shell method. We cut the solid perpendicular to the axis of revolution that produces the shells. The volume of the cylindrical shell is calculated by multiplying the cylinder's surface area by the thickness of the cylindrical wall.

The Shell Method Formula: What Is It?

Let R be the area enclosed by the lines x = a and x = b.

Consider the case when we rotate a solid about a vertical axis to create a solid. Let h(x) be the height of the shell and r(x) be the separation between the rotational axis and x.

V=2bar(x)h(x)dx is a formula for calculating the solid's volume.

How to solve?

The area is enclosed by a horizontal parabola with the equation y = (5x)12, which has its vertex at x=0 and its extremum at x=5. Make a narrow vertical slice with thickness dx and location x.

This thin slice may be rotated about the y-axis to create a cylindrical shell with the dimensions x, dx, and 2y. The shell's volume is as follows:

dV = 2π (x) (2y) (dx)

dV = 4π xy dx

dV = 4π x (5x)^½ dx

dV = 4π√5 (x^³/₂) dx

The total volume is the sum of all the shell volumes from x=0 to x=5.

V = ∫₀⁵ dV

V = ∫₀⁵ 4π√5 (x^³/₂) dx

Evaluating the integral:

V = 4π√5 ∫₀⁵ (x^³/₂) dx

V = 4π√5 (⅖ x^⁵/₂) |₀⁵

V = 4π√5 [(⅖ 5^⁵/₂) − (⅖ 0^⁵/₂)]

V = 200π

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The signal f(t) = cos(6t) + sin(8t) + e(j2t) is not periodic.

To determine if a signal is periodic, we need to check if there exists a fundamental period T₀ such that f(t + T₀) = f(t) for all t.

Let's analyze each component separately:

1. cos(6t): The fundamental period of cos(6t) is 2π/6 = π/3. This means that cos(6t + π/3) = cos(6t) for all t. Therefore, the fundamental frequency ω₀ for cos(6t) is 6.

2. sin(8t): The fundamental period of sin(8t) is 2π/8 = π/4. This implies that sin(8t + π/4) = sin(8t) for all t. Hence, the fundamental frequency ω₀ for sin(8t) is 8.

3. e(j2t): The exponential term e(j2t) has a frequency of ω = 2. However, it does not have a fundamental period since e(j2(t + T₀)) ≠ e(j2t) for any T₀.

Since the three components have different fundamental periods, there is no common fundamental period T₀ that satisfies f(t + T₀) = f(t) for all t. Hence , it is not periodic.

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The expected number of votes for Miss Frizzle in the election is 4725

The data that completes the question is as follows:

Miss Frizzle = 45

Miss Reynolds = 75

The expected number of votes for Frizzle is:

Frizzle = 45/120 * 12600

Evaluate

Frizzle = 4725

Hence, the expected number of votes for Miss Frizzle in the election is 4725

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Answer:

♡ madeline here ♡

by factor grouping, it is (3n+13) (n-7)

your amazing by the way!

goodnight/goodday

✧･ﾟ: *✧･ﾟ:･ﾟ✧*:･ﾟ✧･ﾟ

Step-by-step explanation:

Answer:

The Percentage change of the price was $1

Step-by-step explanation:

$2.25 - $1.25 = $1

The percentage change in the price of milk is 80%, meaning the price has increased by 180%.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
To find the percentage change in price, you can use the following formula:

Percentage change = (New Price - Old Price) / Old Price × 100

Percentage change = (2.25 - 1.25) / 1.25 × 100

= 80%

So, the percentage change in the price of milk is 80%, meaning the price has increased by 180%.

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The solution to the equation \((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\) is 10.3891

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

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\)

Using the following trigonometry ratio

sin²(x) + cos²(x) = 1

We have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = (\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + 1 + e^2\)

The sum to infinity of a geometric series is

S = a/(1 - r)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = \frac{1/2}{1 - 1/2} + \frac{9/10}{1 - 1/10} + 1 + e^2\)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 1 + 1 + 1 + e^2\)

Evaluate the sum

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 3 + e^2\)

This gives

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 10.3891\)

Hence, the solution to the equation is 10.3891

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Answer:

The closest measurement is 69 meters.

Step-by-step explanation:

We already know that 22 meters is the diameter and to find the circumference you need to multiply the diameter with π. We don't know π, so we are going with 3.14. When you multiply 22 and 3.14 together, you get 69.08 meters. You round the answer to the nearest meter, so it's 69 meters. So, the closest measurement is 69 meters.

Which expression is equivalent to (4x⁵ + 11)² ?

O 16x^5 + 121

O 16x^10 + 121

⊙ 16x^10 +88x^5 + 121

O 16x^25 +88x^5 + 121

Step-by-step explanation:

Using formula :

(a + b)² = a² + 2ab + b²

so that…

(4x⁵ + 11)²

= (4x⁵)² + 2(4x⁵)(11) + 11²

= 16x¹⁰ + 88x⁵ + 121

\(16x^{10} +88x^{5} +121\) expression is equivalent to \((4x^{5} +11)^{2}\).

An expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it.

Given expression

\((4x^{5} +11)^{2}\)

It is in the form of \((a+b)^{2} =a^{2} + 2ab+b^{2}\)

\((4x^{5} +11)^{2}\) = \((4x^{5}) ^{2} +2\times 4x^{5}\times11+11^{2}\)

= \(16x^{10} +88x^{5} +121\)

\(16x^{10} +88x^{5} +121\) expression is equivalent to \((4x^{5} +11)^{2}\).

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The Braille system uses two vertical columns of three dots each to represent characters. There are 8 possible combinations for each column, giving a total of 64 distinct Braille characters.

The Braille system of representing characters was developed by Louis Braille in the early nineteenth century. This system is used by blind people and consists of raised dots that represent characters. The positions for the dots are selected from two vertical columns of three dots each. At least one raised dot must be present to represent a character.

To determine the number of distinct Braille characters possible, we need to consider the number of ways we can arrange the dots in the two vertical columns. Each column has three dots, and we need to choose which of these three dots to raise to represent a character. This gives us a total of 2^3 = 8 possible combinations for each column.

Since we have two columns, we can multiply the number of possible combinations for each column to get the total number of distinct Braille characters. This gives us 8 x 8 = 64 possible characters.

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Answer:

168.5 m/s^2

Step-by-step explanation:

Answer:

25° and 65°

Step-by-step explanation:

1. 65°-25°= 40°

2. 90°-65°=25°

3. 90°-25°=65°

Therefore 25° and 65° fit the criteria, make sure to add the degrees symbol :)

Complementary angles have a sum of 90° thus measure of the first and the second angle is 25° and 65° respectively.

Angle is the measurement of the angular distance for example for linear motion we have a meter inch but for angular rotation, we don't have the measurement so the angle is useful to measure the angular rotation.

Let's suppose the first angle is x while the second is y.

If two angles have a sum of 90° then they will be called as complementary angles since x and y are complementary.

x + y = 90

Now given that,

The measure of the first angle is 40° less than the measure of the second.

x = y - 40

x - y = -40

By adding both equations,

(x + y) + (x - y) = 90 + (-40)

2x = 50

x = 25

y = 90 - 25 = 65

Hence "The first and the second angle is 25° and 65° respectively".

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The number of steps he would have to take to make the cut for the top 5% for his distribution is 12,031.5.

The number of steps he would have to take to make the cut for the top 5% for his distribution is 12,031.5.

Suppose that the distribution of the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. So, the population parameters are:

Mean=μ=10,000

Standard Deviation=σ=1,500

We need to find the number of steps he would have to take to make the cut for the top 5% for his distribution.

Step 1: We need to find out the z-score for the top 5% of the distribution.

We can find out the z-score for the top 5% of the distribution using the standard normal distribution table. The table value of z for 0.05=1.645. Check the attachment.

Step 2: We can use the z-score formula to find out the value of X for the top 5% of the distribution.

z=(X-μ)/σ

Rearranging the above equation, we get:

X=μ+z.σ

X=10,000+1.645×1,500

X=12,031.5

Therefore, It would take him 12,031.5 steps to make the top 5% for his distribution.

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The expression \(8x^{6} \sqrt{200x^{13} } /2x^{5} \sqrt{32x^{7} }\) can be simplified as 10x⁴.

Simply said, a radical expression is a mathematical expression that contains the radical sign (√).

Given: \(8x^{6} \sqrt{200x^{13} } /2x^{5} \sqrt{32x^{7} }\)

Rewrite as a fraction using \(\sqrt[n]{a} .\sqrt[n]{b} =\sqrt[n]{ab}\):

\(\frac{8x^{6} \sqrt{200x^{13} }}{2x^{5} \sqrt{32x^{7} }}\) =  \(\frac{8x^{6} }{2x^{5} } . \sqrt{\frac{200x^{13} }{32x^{7} } }\)

Cancel out the common factor.

\(4x.\sqrt{\frac{25x^{6} }{4} }\)

Now, using \(\sqrt[n]{ab}=\sqrt[n]{a} .\sqrt[n]{b}\) rewrite the expression

\(4x.\frac{\sqrt{25x^{6}} }\sqrt{4}\)

Simplifying, we get

\(4x \frac{\sqrt{(5^{2} ) (x^{3}) ^{2} )} }{\sqrt{(2^{2} )} } = 4x \frac{5x^{3} }{2}\)

Canceling out the common factor from denominator and numerator,

= 2x.5x³

=10x⁴

Therefore, the given expression can be solved as 10x⁴.

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Answer:

58.3°

Step-by-step explanation:

Missing Information:

In this question the diagram is missing Following are the attachment of diagram of the given question.

As we seen that the vertex c is making the right angle i,e 90°  also there is an acute angle the Hypotenuse: 20 cm and the perpendicular is 10.5 cm

Now we have find the best approximation of the angle ABC used the cosx  trigonometric function.

\(cos\ x\ =\ \frac{perpendicular}{Hypotenuse} \\\)

Putting the value of perpendicular and hypotenuse in the previous formula we get

\(cos\ x\ =\ \frac{10.5\ cm}{20\ cm} \\\)

\(x\ =cos^{-1}\ 0.525\\x \ = \ 58.33\)

Answer:

58.3

Step-by-step explanation:

jus did the test review on EDGE! :)

Answer:

\(\sf The \: answers\: are \:attached\)

_________________

Answer:

Step-by-step explanation:

\(100x^2-20x+1=0\\\\(10x)^2-2\cdot10x\cdot1+1^2=0\\\\(10x-1)^2=0\\\\10x-1=0\\\\10x=1\\\\x=0.1\)

Answer:

D. 1.49

Step-by-step explanation:

_________________

Answer:

D. 1.49

Step-by-step explanation:

That is the answer, I have no explanation why.

Answer:

4%  = 0.04

4000 = 0.04

6 years = 0.04

Step-by-step explanation:

Hope this helps!

Answer:

Explain how to use the distributive property to find an expression that is equivalent to 20 + 16. First, I would find that the GCF of 20 and 16 is 4. Then, I would divide both 20 and 16 by 4. Last, I would use the distributive property to write the sum as 4(5 + 4).