Complex numbers [tex]z[/tex] and [tex]w[/tex] satisfy [tex]|z|=|w|=1, |z+w|=\sqrt{2}[/tex].
What is the minimum value of [tex]P = |w-\frac{4}{z}+2(1+\frac{w}{z})i|[/tex]?

In both cases, the subject term (S) and the predicate term (P) are distributed, which means that the proposition makes a claim about the entire class of S and the entire class of P.

Traditional categorical logic, a proposition with both of its terms (subject and predicate) distributed is called a universal proposition.

Stronger claim than a particular proposition.

A universal proposition is a statement that applies to all members of a category or class.

Asserts that the subject term is either entirely included or entirely excluded from the predicate term.

There are two types of universal propositions:

Universal affirmative proposition (A): All S are P.

Universal negative proposition (E): No S are P.

"All mammals are warm-blooded" is a universal affirmative proposition (A) because it claims that the subject term (mammals) is entirely included in the predicate term (warm-blooded).

It distributes both terms and claims the most knowledge.

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The power series method can be used to solve a nonhomogeneous differential equation about an ordinary point by finding both a homogeneous and particular solution using a series expansion and the method of undetermined coefficients.

The power series method is a technique used to find a series solution of a differential equation. When applied to a nonhomogeneous differential equation, the method involves finding both a homogeneous solution and a particular solution.

Assuming that the nonhomogeneous differential equation has the form

y''(x) + p(x)y'(x) + q(x)y(x) = f(x)

where p(x), q(x), and f(x) are functions of x, we can begin by finding the solution to the associated homogeneous equation

y''(x) + p(x)y'(x) + q(x)y(x) = 0

Using the power series method, we can assume a solution of the form:

y(x) = a0 + a1(x - x0) + a2(x - x0)^2 + ...

where a0, a1, a2, ... are constants to be determined, and x0 is the ordinary point of the differential equation.

Next, we can find the coefficients of the power series by substituting the series solution into the differential equation and equating coefficients of like powers of (x-x0). This leads to a system of equations for the coefficients, which can be solved iteratively.

After finding the homogeneous solution, we can find a particular solution using a similar method. Assuming a particular solution of the form:

y(x) = u(x) + v(x)

where u(x) is a solution to the associated homogeneous equation, and v(x) is a particular solution to the nonhomogeneous equation, we can use the method of undetermined coefficients to find v(x). This involves assuming a form for v(x) based on the form of f(x), and then solving for its coefficients using the same technique as before.

Once we have found both the homogeneous and particular solutions, we can combine them to obtain the general solution to the nonhomogeneous differential equation.

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Positive divisors does n2 have are 5.

If an integer n has exactly three positive divisors, including 1 and n, it means that n is a perfect square of a prime number.

The reason for this is that a prime number has only two divisors: 1 and itself. Therefore, if n has exactly three positive divisors, n must be a perfect square of a prime number, since the only divisors of a perfect square are the divisors of its square root, and its square root must be a prime number.

Let's say that n is equal to p², where p is a prime number. The positive divisors of n are 1, p, and n (which is p²).

Now, to find the number of positive divisors of n², we can use the fact that any positive divisor of n² can be expressed in the form [tex]p^k[/tex], where 0 ≤ k ≤ 4 (since n² = p⁴).

Therefore, the positive divisors of n² are:

1, p, p², p³, and p⁴ (which is n²)

So, n² has 5 positive divisors: 1, p, p², p³, and n².

Hence, the answer is 5.

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Part A:

The correct answers are:

The data set is numerical data

The data in this set can be quantified in the form of numbers.

The set has an outlier

An outlier is an extreme value that differs from the rest of the set. The outlier in this set is 5.

A box plot is an appropriate data display for this data

A box plot is great for showing distribution of data. A circle chart would not be good for this set because circle charts are better for part-to-whole data.

Part B:

A: Students in his class have between 5 to 950 photos stored on their cell phones.

The text at the top explains that this data was gathered from students in Shamar's class, and the data ranges from 5 to 950.

If Alice has $50 and spends 4/5 of her money, she spends $40.

A fraction is a mathematical expression that represents a part of a whole or a ratio between two quantities. Fractions are commonly represented using two numbers separated by a horizontal line, where the top number is called the numerator and the bottom number is called the denominator.

Alice spends 4/5 of her money, which is equivalent to 0.8 of her money.

To find out how much Alice spends, we can multiply her total money ($50) by 0.8

= $50 x 0.8

Multiply the numbers

= $40

Therefore, Alice spends $40.

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I have solved the question in general, as the given question is incomplete.

The complete question is:

Alice has $50 and spends 4/5 of her money. How much does Alice spend?

The surface area of the two solids are listed below:

Case 1 - 232 square centimeters

Case 2 - 240 square centimeters

The surface area of a solid is the sum of the areas of all its faces. There are two cases of solids whose surface areas must be determined. The area formulas for triangle and rectangle are, respectively:

Triangle

A = 0.5 · b · h

Rectangle

A = b · h

Case 1

A = (6 cm) · (8 cm) + 2 · 0.5 · (6 cm) · (12 cm) + 2 · 0.5 · (8 cm) · (14 cm)

A = 232 cm²

Case 2

A = 2 · 0.5 · (8 cm) · (3 cm) + (8 cm) · (12 cm) + 2 · (5 cm) · (12 cm)

A = 24 cm² + 96 cm² + 120 cm²

A = 240 cm²

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It is important to test for interactions in a two-way ANOVA to ensure that the main effects of each variable are not being confounded by the presence of an interaction.

In a two-way ANOVA test, if the effect of one variable depends on the value of another variable, then there is an interaction between the two variables. An interaction occurs when the effect of one independent variable on the dependent variable changes depending on the level of the other independent variable. It is important to test for interactions in a two-way ANOVA to ensure that the main effects of each variable are not being confounded by the presence of an interaction.

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In a two-way ANOVA test, if the effect of one variable depends on the value of another variable, "interaction".

In a two-way ANOVA test, interaction occurs when the effect of one independent variable on the dependent variable

depends on the level of another independent variable.

This means that the effect of one variable is not constant across all levels of the other variable, and it is important to

consider this interaction effect in interpreting the results of the ANOVA test.

Correlation and multicollinearity are not directly related to ANOVA tests, while "group of answer choices" is not a

relevant term in this context.

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Answer:47

7•7

Step-by-step explanation:

Answer:

15+17+12

=44 subscriptions altogether

S=(15+17)+12

S=32+12

S=44

The combined fraction in the context of this problem is given as follows:

(4x² + 12x - 9)/(x² + 8x + 15).

The fractional expression in the context of this problem is given as follows:

(x + 6)/(x² + 8x + 15) + 3x/(x + 5) - (x - 3)/(x + 3).

(x + 5)(x + 3) = x² + 8x + 15, hence the denominator of the simplified expression is given as follows:

x² + 8x + 15.

Applying the least common factor, the numerator of the simplified expression is given as follows:

x + 6 + 3x(x + 3) + (x - 3)(x + 5) = x + 6 + 3x² + 9x + x² - 3x + 5x - 15

x + 6 + 3x(x + 3) + (x - 3)(x + 5) = 4x² + 12x - 9

Hence the combined expression is given as follows:

(4x² + 12x - 9)/(x² + 8x + 15).

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In this instance, the three trigonometric ratios are:

Sinx = 15/17

Cosx =  8/17

Tanx = 15/8

Mathematical trigonometric functions connect the angle of a right-angled triangle to the ratios of its two side lengths.

In all areas of study that involve geometry, such as geodesy, solid mechanics, celestial mechanics, and many others, they are widely used.

Review the trigonometric ratios for sine, cosine, tangent, cotangent, secant, and cosecant.

So, the 3 trigonometric ratios in the given situation would be:

Sinx = O/H = 15/17

Cosx = A/H = 8/17

Tanx = O/A = 15/8

Therefore, in this instance, the three trigonometric ratios are:

Sinx = 15/17

Cosx =  8/17

Tanx = 15/8

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The total distance Brown family drove this morning at the speed of  65 miles per hour in 2.5 hours is equal to 162.5 miles.

Let 's' represents the speed of the moving object.

And 't' represents the time to cover distance.

The speed was 65 miles per hour.

And the time they drove was 2.5 hours.

The distance the Brown family drove this morning

=  Multiplying their speed by the time they drove.

This implies,

distance = speed x time

Substitute the values we have,

The distance they drove this morning is equal to,

⇒ distance = 65 miles per hour x 2.5 hours

⇒ distance = 162.5 miles

Therefore, the distance drove by Brown family this morning is 162.5 miles at the speed of 65 miles per hour.

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Answer:

use desmos or they work pretty well

The solution of the inequality is -4<x≤1 where x≠-1

A relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is x²-1/x²+5x+4 ≤0

Let us factor the terms in inequality to find the solution

(x+1)(x-1)/(x+1)(x+4) ≤0

(x-1)/(x+4)  ≤0

Find the critical values where the inequality changes sign

Interval 1: x < -4

Interval 2: -4 < x < 1

Interval 3: x > 1

Test each interval to see where the inequality is true or false

For interval 1, we can choose x = -5 as a test point:

(x-1)/(x+4) = (-5-1)/(-5+4) = -6 < 0

Since the inequality is true for x = -5, it is also true for all x < -4.

For interval 2, we can choose x = 0 as a test point:

(x-1)/(x+4) = (0-1)/(0+4) = -1/4 < 0

Since the inequality is true for x = 0, it is also true for all -4 < x < 1.

For interval 3, we can choose x = 2 as a test point:

(x-1)/(x+4) = (2-1)/(2+4) = 1/6 > 0

Since the inequality is false for x = 2, it is also false for all x > 1.

Combine the intervals where the inequality is true -4<x≤1 where x≠-1 is the solution

Hence, the solution of the inequality is -4<x≤1 where x≠-1

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Answer:

The missing side of the right triangle is 8, and it is one of the legs.

Step-by-step explanation:

Step 1: Write down the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. In equation form, it looks like this:

a^2 + b^2 = c^2

where a and b are the lengths of the legs (the shorter sides) and c is the length of the hypotenuse.

Step 2: Identify which sides are the legs and which is the hypotenuse.

In our triangle, we are given the lengths of two sides, 10 and 6. We don't know which one is the hypotenuse and which one is a leg. However, we can use the fact that the hypotenuse is always the longest side to figure it out. Since 10 is longer than 6, we know that 10 is the hypotenuse.

Step 3: Apply the Pythagorean theorem to find x.

Now that we know which side is the hypotenuse, we can use the Pythagorean theorem to find x. We substitute the values we know into the formula and solve for x:

a^2 + b^2 = c^2

6^2 + x^2 = 10^2

36 + x^2 = 100

x^2 = 100 - 36

x^2 = 64

x = √64

x = ±8

Step 4: Choose the positive value of x.

Since x represents a length of a side of a triangle, it must be a positive value. Therefore, x = 8.

Step 5: Verify that the answer is correct.

We can check that our answer is correct by substituting x = 8 into the Pythagorean theorem and seeing if it holds true:

6^2 + 8^2 = 10^2

36 + 64 = 100

100 = 100

Answer:

1

Step-by-step explanation:

First of all we use the "law of sines"

to get the measure/length we need the opposing angle of it of the side, now in this case the missing side is x

and its opposing angle is missing so using common sense, the sum of angles in the triangle is 180°

180°=70°+51°+ x

x = 180°-121°

=59°

Using law of sines:

(sides are represented by small letters/capital letters are the angles)

a/sinA= b/sinB= c/sinC

We have one given side which is "9"

so,

9/sin70= x/sin59

doing the criss-cross method,

9×sin59=sin70×x

9×sin59/sin70=x

x=8.2 (answer 1)

I hope this was helpful <3

Therefore, the probability of drawing a white marble followed by a striped marble is 0.18, the probability of drawing a white marble followed by a black marble is 0.06, and the probability of drawing two striped marbles in a row is 0.09.

Probability is the measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event will not occur, and 1 indicates that the event is certain to occur. The probability of an event is determined by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is widely used in fields such as mathematics, statistics, economics, and science to analyze and predict the likelihood of events.

Here,

Since the first marble is put back in the bag before the second one is drawn, the probability of each event remains the same for both draws. We can use the multiplication rule of probability which states that the probability of two independent events occurring together is the product of their individual probabilities.

Given: white=6, striped=3, black=1

P(white, then striped) = P(white) × P(striped)

= (6/10) × (3/10)

= 0.18

P(white, then black) = P(white) × P(black)

= (6/10) × (1/10)

= 0.06

P(striped, then striped) = P(striped) × P(striped)

= (3/10) × (3/10)

= 0.09

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The probability that the flight will leave on time when it is not raining is approximately 0.83.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents impossibility (the event will not occur) and 1 represents certainty (the event will definitely occur).

According to the given information:

To find the probability that the flight will leave on time when it is not raining, we need to subtract the probability of the flight being delayed due to rain from 1 (since the sum of all probabilities in a given event space is equal to 1).

Let:

P(rain) = 0.07 (probability of rain)

P(delayed) = 0.17 (probability of delay)

P(rain and delayed) = 0.02 (probability of rain and delay)

We can use the formula for conditional probability:

P(A|B) = P(A and B) / P(B)

In this case, we want to find P(on time | not raining), which can be expressed as:

P(on time | not raining) = P(on time and not raining) / P(not raining)

Since rain and not raining are mutually exclusive events (i.e., they cannot occur simultaneously), we have:

P(on time | not raining) = P(on time) / (1 - P(rain))

We can now substitute the given probabilities to calculate the required probability:

P(on time | not raining) = P(on time) / (1 - P(rain))

P(on time | not raining) = (1 - P(delayed)) / (1 - P(rain))

P(on time | not raining) = (1 - 0.17) / (1 - 0.07)

P(on time | not raining) = 0.83

So, the probability that the flight will leave on time when it is not raining is approximately 0.83 (rounded to the nearest thousandth).

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Fred should use a critical value of 2.145 and a standard error of the mean of 2.84 to construct a 95% confidence interval for the average length of movies he watches

To construct a confidence interval for the population mean length of movies watched by Fred, we can use the following formula

Confidence interval = sample mean +/- (critical value) x (standard error)

where the standard error of the mean (SE) is calculated as:

SE = sample standard deviation / sqrt(sample size)

Since Fred's sample size is 15 and he wants a 95% confidence interval, we need to find the critical value for a t-distribution with 14 degrees of freedom (n-1), which can be obtained from a t-distribution table or calculator.

Using a t-distribution calculator with 14 degrees of freedom and a 95% confidence level, we find the critical value to be 2.145.

Next, we can calculate the standard error of the mean as

SE = 11 / sqrt(15) = 2.84

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The total amount of meals in dollars served by Jerome is equals to $1150.

Total amount Jerome earned this weekend = $252.50.

Jerome earned every weekend = $80.

Jerome earned cost of meals as tips by serving them = 15%

Let us consider the dollar amount of the meals that Jerome served 'x'.

Jerome earned a total of $252.50 for the weekend,

which consists of his earnings from the meals and his flat rate earnings.

Set up an equation to represent this,

x × 0.15 + 80 = 252.50

Simplifying this equation by subtracting 80 from both sides, we get,

⇒ 0.15x = 172.50

⇒ x = 1150

Therefore, the dollar amount of the meals that Jerome served was $1150.

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The above question is incomplete, the complete question is:

The weekend Jerome earned 252. 50 in all. What was the dollar amount of the meals that Jerome served? Jerome served worth meals this weekend. Jerome earns 15%percent off all the costs of meal on all meals and he earns 80 dollars every weekend

Answer:

2.36 miles

Step-by-step explanation:

radius, r = 3 miles∅ = 45°Length of an arc = ∅/360 * 2πr= 45/360 * 2 * 3.14 * 3= 2.36 miles

Answer:

Yo, my dude is bringing half a crate of popsicles to the picnic. When we split it up into 6 ice buckets, each bucket gonna get a fair share, man. It's gonna be like dividing the remaining popsicles evenly among the buckets, so each bucket gonna have like a fraction of the crate, you feel me? It's gonna be all chill, bro! Each ice bucket gonna get like 1/6 of the crate, straight up! Easy peasy, lemon squeezy!

The radius of the circle is approximately 22.9 meters when rounded to the nearest tenth.

To find the radius of the circle, we need to use the formula:

arc length = radius x central angle (in radians)

Since the central angle is given in degrees, we need to convert it to radians by multiplying it by π/180.

First, let's convert the central angle:

258° x π/180 ≈ 4.5 radians

Now we can plug in the values into the formula and solve for the radius:

102.9 = r x 4.5

r = 102.9 / 4.5

r ≈ 22.9

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The circumference of the circle given the radius as 11 cm in terms of π is 22π cm.

Circumference of a circle = 2πr

Where,

Radius, r = 11 cm

Circumference of a circle = 2πr

= 2 × π × 11

= 22π cm

Ultimately, the circumference in terms of π is 22π.

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The ratio of LM to FG is 3:4, so correct option is A.

A triangle is a polygon with three sides, three vertices, and three angles. It is one of the basic shapes in geometry and has many properties that make it a useful and interesting shape to study.

The sum of the interior angles of a triangle is always 180 degrees, which is a fundamental property of triangles.

Triangles also have many interesting properties related to their sides, angles, and areas. For example, the Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. The area of a triangle can be calculated using the formula 1/2(base x height) or by using various trigonometric functions.

Triangles are important in many areas of mathematics and science, such as in geometry, trigonometry, calculus, and physics. They are also commonly used in architecture, engineering, and design.

If LMN and FGH are similar triangles, then the ratio of their areas is equal to the square of the ratio of their corresponding side lengths.

Let x be the ratio of LM to FG. Then the ratio of their areas is (x²).

So we have:

LMN / FGH = 18 / 32

(x²) = 18 / 32

x² = 9 / 16

x = (3 / 4)

Therefore, the ratio of LM to FG is 3:4, which is option A.

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The distance from A to B is  724.64 ft

Consider the following figure.

In right triangle CDA, the sine of angle DAC would be,

sin(∠DAC) = CD/CA

sin(32°) = CD/1540

CD = 816.1 ft

Consider the tangent of angle DAC.

tan(∠DAC ) = CD/AD

tan(32°) = 816.1 / AD

AD = 816.1/ 0.63

AD = 1295.4

Let us assume that distance AB = x feet

In right triangle CDB, the tangent of angle CBD would be,

tan(∠CBD) = CD/DB

tan(∠CBD) = CD/(DA + AB)

tan(22°) = 816.1 / (1295.4+ x)

1295.4 + x = 816.1 / 0.4040

1295.4 + x = 2020.04

x = 2020.04 -  1295.4

x = 724.64 ft

Therefore, the required distance is  724.64 ft

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Find the complete question below.

An expression that is equivalent to the product of 146 is just 146 itself.

Two or more fractions are said to be equivalent fractions if they are equal to the same value irrespective of their numerators and denominators. For example, 2/4 and 8/16 are equivalent fractions because they get reduced to 1/2 when simplified.

We can either multiply or divide both the numerator and the denominator of the given fraction by the same number to generate equivalent fractions to the given fraction.

None of the choices provided is equivalent to the product 146.

The product of 146 is simply 146.

So, an expression that is equivalent to the product of 146 is just 146 itself.

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