an airship flies 150 km with the wind and then turn around and flies back taking 5 hour and 30 min round trip. Find the speed of the airship in calm weather is 55 mph.

To prove the converse of the Vertical Angles Theorem, we need to show that if angles LDBC and LABE are congruent and points D, B, and E are on opposite sides of line AB, then they must be collinear.

Given: ∠LDBC ≅ ∠LABE

To Prove: D, B, and E are collinear

Proof:

1. Assume that points D, B, and E are not collinear.

2. Let BD intersect AE at point X.

3. Since D, B, and E are not collinear, then X is a point on line AB but not on line DE.

4. Consider triangle XDE and triangle XAB.

5. By the Alternate Interior Angles Theorem, ∠XAB ≅ ∠XDE (corresponding angles formed by transversal AB).

6. Since ∠LDBC ≅ ∠LABE (given), we have ∠LDBC ≅ ∠XAB and ∠LABE ≅ ∠XDE.

7. Therefore, ∠LDBC ≅ ∠XAB ≅ ∠XDE ≅ ∠LABE.

8. This implies that ∠XAB and ∠XDE are congruent vertical angles.

9. However, since X is not on line DE, this contradicts the Vertical Angles Theorem, which states that vertical angles are congruent.

10. Therefore, our assumption that D, B, and E are not collinear must be false.

11. Thus, D, B, and E must be collinear. Therefore, the converse of the Vertical Angles Theorem is proven, and we can conclude that if ∠LDBC ≅ ∠LABE and D, B, and E are on opposite sides of line AB, then D, B, and E are collinear.

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Answer:

walking speed is 2 m/s

Step-by-step explanation:

given data

distance between Melissa and friend = 3 mile

total time of the trip = 2 hour

solution

we consider here

walking speed = s₁

bike speed = s₂  

so s₂ = s₁ + 4    .................1

and

time is express as

time = distance ÷ speed      .................2

so time for Melissa to friend reach = 3 ÷ s₁    

and time for return from her friend =  3 ÷ s₂  

so put this value in equation 2 we get

time = 3 ÷ s₁  + 3 ÷ s₂  

2 = \(\frac{3}{s_1} + \frac{3}{s_1 + 4}\)    

solve it and we will get

s₁² + s₁ - 6 = 0

s₁ = 2 m/s

so walking speed is 2 m/s

Answer:

Step-by-step explanation:

I think in this question we have to find slope, if so, its y = 10x.

to find the slope just pick two numbers, i chose (2,20) and (7,70) and then put them in the slope formula y2-y1/x2-x1. That gave me 10. I hope its correct. :)

-2 is the minimum value of the given set.

Assume that x is the minimum value.

The difference between the largest value and the least value is therefore what we use to determine the range:

Range = Maximum value - Minimum value

6 = 4 - x

Solving for x, we can subtract 4 from both sides:

6 - 4 = 4 - x - 4

2 = -x

Finally, we can multiply both sides by -1 to get x by itself:

x = -2

Therefore, the minimum value is -2.

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Answer:

70% of the people at the fair are students

165 people are on the ride

Step-by-step explanation:

In order to find a percentage, take the fraction given, 385/550, and divide the numerator, 385, and divide it by the denominator, 550. Once completing this, we get 0.7

Next, we multiply the result by 100, and get 70, thus, 385 is 70% of 550.

To find how many people 30% of 550 is, we take the percentage and put it in a fraction with the denominator being 100(changes with size of fraction like a decimal, 300 would be over a denominator of 1000)

With 30/100, we then multiply by 550 with the equation looking like this:

30/100*550/1

Once we finish multiplying(typically using a calculator, although you can do it manually) we get 165, the value of how many people are on rides out of the total 550.

Answer:

1. Evan

2. Stacey

Step-by-step explanation:

Answer:

C is not a function but D is

Step-by-step explanation:

For one input, you can only have one output for this to be a function. For table C, the input of 4 has 4 different outputs, so it cannot be a function.

D is a function however, because each input has only one output, even if the output is the same number.

Answer:

19/4 =12

Step-by-step explanation:

The 19/4 is a fraction, 19 being the top (numerator)

and 4 being the bottom (denominator)

(a) The firm is operating in the long run, and its supply function is determined by the profit maximization condition.

(b) The firm's input demand functions can be derived from the profit function, and their degree of homogeneity is 1/2. Changes in input prices will impact the firm's input demand.

(c) The market supply function can be derived by aggregating the supply functions of all 40 firms operating in the market.

(d) Given the market conditions and demand function, the total market supply can be calculated.

(a) The firm is operating in the long run because it has the flexibility to adjust its inputs and make decisions based on market conditions. The firm's supply function is determined by maximizing its profit, which is achieved by setting the marginal cost equal to the market price. In this case, the supply function for each firm can be derived by taking the derivative of the profit function with respect to the price of output (p).

(b) The input demand functions for the firm can be derived by maximizing the profit function with respect to each input price. The degree of homogeneity of the input demand functions can be determined by examining the exponents of the input prices. In this case, the degree of homogeneity is 1/2. Changes in the input prices will affect the firm's input demand as it adjusts its input quantities to maximize profit.

(c) The market supply function can be derived by aggregating the individual supply functions of all firms in the market. Since there are 40 identical firms, the market supply function can be obtained by multiplying the supply function of a single firm by the total number of firms (40).

(d) To determine the total market supply, we substitute the given market conditions and demand function into the market supply function. By solving for the market quantity at a given market price, we can calculate the total market supply.

In conclusion, the firm is operating in the long run, and its supply function is determined by profit maximization. The input demand functions have a degree of homogeneity of 1/2, and changes in input prices impact the firm's input demand. The market supply function is derived by aggregating the individual firm supply functions, and the total market supply can be calculated using the given market conditions and demand function.

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Answer:

G

Step-by-step explanation:

when x is inputed it will give only one answer.

True. A function whose values repeat based on positions of a point that moves around a circle is called a sinusoid, using trigonometry approach.

The sine waves oscillate in a smooth, repetitive manner, defined in terms of distance from the \(x\) axis to the point on the unit circle.

The main features of a sinusoidal function are its amplitude, its phase, and its frequency. Let us discuss the features one by one :

Amplitude specifies the maximum distance between the x axis i.e. the horizontal axis and the vertical position of the point or a the waveform. It is denoted by \(A\).

Phase of a function refers to the horizontal position of the waveform with correspondence to one rotation. The extent or angle by which, a point or a waveform is shifted, is called the phase difference or phase shift.

Frequency is the measurement which tells us about how quickly the sinusoid completes cycles i.e. it simplifies the movement of the sinusoidal wave per unit time.

The sinusoid functions play key role in modern periodic phenomena such as sound and light waves, oscillators, average temperature variations throughout the year, sunlight intensity ,etc.

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Answer:

\(y=x+3\)

Step-by-step explanation:

Using Point-Slope form: Y-y1=m(X-x1)

Slope(m) = 1, Point(x1,y1) = (-2,1)

y-1=1(x+2)

y=x+2+1

y=x+3

:]

(ps. Brainliest would be greatly appreciated lol)

Step-by-step explanation:

1.given gradient (slope) make formula of straight line

\(y = 1x + c\)

2.substitute in y and x values in order to work out c

\(1 = 1( - 2) + c\)

\(c = 3\)

3. equation of line is

\(y = 1x + 3\)

We can conclude that there is evidence to suggest that the proportion of songs on the player that were loaded by Lori is greater than 0. We are 90% confident that the true proportion is between 0.137 and 0.383.

To construct a confidence interval for the proportion of songs on the player that were loaded by Lori, we can use the following 4-step process:

Step 1: Verify Conditions

We need to verify the following conditions:

Randomization: The songs are selected randomly, and the sample is representative of the population.

Independence: The 50 songs selected are independent of each other.

Sample size: The sample size is less than 10% of the population size, so we can assume that the sampling distribution of the proportion is approximately normal.

Success-Failure Condition: Both np and n(1-p) are greater than 10, where n is the sample size and p is the proportion of songs on the player that were loaded by Lori.

Step 2: Construct the Confidence Interval

We can use the formula for a confidence interval for a proportion:

p' ± z* √(p'(1-p')/n)

where p' is the sample proportion, z* is the critical value from the standard normal distribution for the desired confidence level, and n is the sample size.

We are given that 13 out of 50 songs selected were loaded by Lori, so the sample proportion is p' = 13/50 = 0.26. We want a 90% confidence interval, so the critical value from the standard normal distribution is z* = 1.645 (from a table or calculator). The sample size is n = 50.

Plugging in the values, we get:

0.26 ± 1.645 √((0.26)(1-0.26)/50)

= 0.26 ± 0.123

= (0.137, 0.383)

So the 90% confidence interval for the proportion of songs on the player that were loaded by Lori is (0.137, 0.383). We can interpret this as: We are 90% confident that the true proportion of songs on the player that were loaded by Lori is between 0.137 and 0.383.

Step 3: Interpret the Confidence Interval

We can interpret the confidence interval as above.

Step 4: Check Assumptions and Interpret Results

We verified the necessary assumptions in Step 1. From the confidence interval, we can conclude that there is evidence to suggest that the proportion of songs on the player that were loaded by Lori is greater than 0. We are 90% confident that the true proportion is between 0.137 and 0.383.

Regarding the sampling method (with or without replacement), it is not important for the construction of the interval because the sample size is small relative to the population size.

In general, if the sample size is less than 10% of the population size, we can assume that the sampling distribution of the proportion is approximately normal regardless of whether the sampling is done with or without replacement.

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Answer:

The right answer is option D.

Step-by-step explanation:

We can easily find which one of this graph is the right answer if we look closely at the equation of this linear function. By looking at the slope, we see that it is negative which means it will have a downward trend. We also can see that the y intercept is going to be at (0. - 5). The only graph that follows both of this statements is graph D.

Answer:

Logarithms were invented in the 17th century as a calculation tool by Scottish mathematician John Napier (1550 to 1617), who coined the term from the Greek words for ratio (logos) and number (arithmos

Step-by-step explanation:

In 5040 different ways, 7 runners can places 1 through 4 be determined if in a race there are 7 runners. trophies for the race are awarded to the runners finishing in places 1 through 4.

The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations. Combinations exist when the order doesn't matter, but permutations exist when it does. A permutation could be described as an ordered combination. The following formula determines how many permutations of n objects, taken r at a time: P(n,r)=n!

Given,

Ways 7 runners can places 1 through 4 be determined:

By using permutation:

7!

7 ×6 × 5 ×4×3×2×1

5040

In 5040 different ways, 7 runners can places 1 through 4 be determined if in a race there are 7 runners. trophies for the race are awarded to the runners finishing in places 1 through 4.

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The οrdered pair that is a sοlutiοn οf the equatiοn is (-5, 0).

A value οr grοup οf values that satisfy an equatiοn οr an inequality are referred tο as sοlutiοns in mathematics. Fοr instance, if we have the equatiοn 2x + 3 = 7, the answer is x = 2 since we get the cοrrect answer when we replace x with 2: 2(2) + 3 = 7.

Similar tο the last example, if we had an inequality like x + 4 > 10 then the sοlutiοn is x > 6, meaning any value οf x greater than 6 wοuld make the inequality true.

Tο find which οrdered pair is a sοlutiοn οf the equatiοn -5x - 3y = 25, we need tο substitute values οf x and y intο the equatiοn and see if it hοlds true.

Let's try the ordered pairs one by one:

a) (-5, 0)

Substituting x = -5 and y = 0 in the equation, we get:

-5(-5) - 3(0) = 25

25 = 25

This equation is true, so (-5, 0) is a solution of the equation.

b) (0, -8)

Substituting x = 0 and y = -8 in the equation, we get:

-5(0) - 3(-8) = 25

24 = 25

This equation is not true, so (0, -8) is not a solution of the equation.

Therefore, the ordered pair that is a solution of the equation is (-5, 0).

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Complete question:

Which ordered pair is a solution of this equation?

-5x - 3y = 25

a) (-5, 0)

b) (0, -8)

Answer:

D. 29 I just know the awnser sorry

To find the value of f(−2), we substitute −2 for x in the function f(x):

f(−2) = 4(-2)^2 − 3(-2) + 7

= 4(4) − 3(2) + 7

= 16 − 6 + 7

= 11

Therefore, f(−2) = 11.

the radius of convergence (R) is ∞, and the interval of convergence (I) is (-∞, ∞).

To find the radius of convergence (R) and the interval of convergence (I) of the series given by:

∑ 7(-1)^(n-1) n^n x^n

We can apply the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is L as n approaches infinity, then the series converges absolutely if L < 1, diverges if L > 1, and the test is inconclusive if L = 1.

Let's apply the ratio test to the given series:

L = lim(n→∞) |(7(-1)^(n-1) (n+1)^(n+1) x^(n+1)) / (7(-1)^(n) n^n x^n)|

Simplifying and canceling out common factors:

L = lim(n→∞) |(7(n+1) x) / (n^n)|

Taking the absolute value:

L = lim(n→∞) |7(n+1) x / n^n|

Now, let's evaluate the limit:

L = |7x| lim(n→∞) (n+1) / n^n

The limit can be further simplified by applying the ratio test for the sequence:

lim(n→∞) (n+1) / n^n = 0

Therefore, the limit L simplifies to:

L = |7x| * 0 = 0

Since L = 0, which is less than 1, the ratio test indicates that the series converges absolutely for all values of x. Thus, the series converges for all x.

For a series that converges for all x, the radius of convergence (R) is infinite (∞), and the interval of convergence (I) is the entire real number line (-∞, ∞).

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If gasoline costs $1.95 per gallon $0.52 is its cost per liter?

One gallon of gasoline costs $1.95. To find the cost per liter, we need to convert gallons to liters. The conversion factor between gallons and liters is 1 gallon = 3.78541 liters.

So, to convert gallons to liters, we multiply the number of gallons by 3.78541.

In this case, the cost of one gallon of gasoline is $1.95. To find the cost per liter, we need to convert $1.95 from dollars per gallon to dollars per liter.

To do this, we divide $1.95 by the conversion factor between gallons and liters:

$1.95 / 3.78541

= $0.52/liter.

Therefore, the cost of one liter of gasoline is $0.52.

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Answer:

The specific vector field F is not provided in the question, making it impossible to proceed further with the calculations and verification of Stoke's Theorem.

Step-by-step explanation:

To evaluate the surface integral, let's break down the given problem step by step.

Step 1: Find the unit normal vector n to the surface:

The given surface is x² + y² − 4x + 2z = 0. We can rewrite it as:

(x - 2)² + y² + z² = 4

Comparing this to the standard equation of a sphere (x - a)² + (y - b)² + (z - c)² = r², we can see that the center of the sphere is (2, 0, 0) and the radius is 2. Hence, the unit normal vector n is (1/2, 0, 0).

Step 2: Calculate the surface area element dA:

Since the given surface is defined implicitly, we can find the surface area element dA using the formula:

dA = |∇F| dS

Here, ∇F denotes the gradient of F, and |∇F| represents its magnitude.

∇F = (∂F/∂x)i + (∂F/∂y)j + (∂F/∂z)k

    = (-2x)i + (-2y)j + (-2z)k

|∇F| = √((-2x)² + (-2y)² + (-2z)²)

     = 2√(x² + y² + z²)

Therefore, dA = 2√(x² + y² + z²) dS

Step 3: Evaluate the dot product SS V × F · n:

The cross product V × F is given by:

V × F = (1, 0, 0) × (y² + z² − x², z² + x² − y², x² + y² − z²)

      = (-(y² + z² − x²), -(z² + x² − y²), x² + y² − z²)

      = (x² - y² - z², -x² + y² - z², x² + y² - z²)

Taking the dot product of V × F with n:

(V × F) · n = (x² - y² - z²) * (1/2)

           = (x² - y² - z²) / 2

Step 4: Set up the integral:

We need to integrate (V × F) · n dA over the portion of the surface x² + y² − 4x + 2z = 0 above the plane z = 0.

Converting to cylindrical coordinates, we have:

x = r cosθ

y = r sinθ

z = z

The bounds for r and θ can be determined by analyzing the given surface equation. We have:

x² + y² − 4x + 2z = 0

r² - 4rcosθ + 2z = 0

Solving for r, we get:

r = 2cosθ ± √(4cos²θ - 2z)

To restrict the region above the plane z = 0, we take the positive square root:

r = 2cosθ + √(4cos²θ - 2z)

The bounds for θ are 0 to 2π, and for z, it is 0 to √(4cos²θ).

Therefore, the integral becomes:

∫∫(V × F) · n * 2√(x² + y²

+ z²) r dr dθ

over the region: 0 ≤ θ ≤ 2π, 0 ≤ r ≤ 2cosθ + √(4cos²θ - 2z), 0 ≤ z ≤ √(4cos²θ)

Step 5: Verify Stoke's Theorem:

To verify Stoke's Theorem, we can calculate the flux of the curl of F across the boundary curve and compare it to the value obtained from the surface integral.

The boundary curve is the intersection of the given surface x² + y² − 4x + 2z = 0 and the plane z = 0.

Setting z = 0 in the surface equation, we have:

x² + y² − 4x = 0

(x - 2)² + y² = 4

This represents a circle centered at (2, 0) with a radius of 2.

We can calculate the flux of the curl of F across this circular boundary using Stoke's Theorem and compare it to the value obtained from the surface integral.

Unfortunately, the specific vector field F is not provided in the question, making it impossible to proceed further with the calculations and verification of Stoke's Theorem.

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Answer:

There's no x in the equation pls retype it

Step-by-step explanation:

Answer:

Decimal: 0.275           Percentage: 27.5

Step-by-step explanation:

Answer:

(4,5)

Step-by-step explanation:

Since you move right 4 from the origin, then your x value would increase by 4, and since you're moving 5 units up from the origin, then your y value would increase by 5

The resultant moment about a both forces is zero. The statement is true.

A man B exerts a force on the rope, P = 30 lb

To find:

The magnitude of force, F

Consider a statement:

"The resultant moment about A of both forces is Zero."

Diagram attached at the end of the  solution

\($ \theta=\tan ^{-1}\left(\frac{3}{4}\right) \\\)

\(& \theta=36.87^0\)

To prevent the pole from rotating, so that the resultant moment is about A = 0

We will apply the equilibrium Equation \($\sum \mathrm{M}_{\mathbf{A}}=0$\)

Here force \($P \times \sin (45)$\) and \($F \times \sin (\theta)$\) will not produce the moment at A.

Taking clockwise moment as a negative and anticlockwise moment as a positive.

\(& \mathrm{P} \times \cos (45) \times(18)-\mathrm{F} \times \cos (\theta) \times 12=0 \\\)

\(& 30 \times \cos (45) \times(18)=\mathrm{F} \times \cos (\theta) \times 12 \\\)

\($ \mathrm{~F}=\frac{30 \times \cos (45) \times(18)}{\cos (36.87) \times 12} \\\)

F = 39.77 lb

Based on the given parameters,

The magnitude of force, F = 39.77 lb

So there exists the force by considering the resultant moment about an of both forces as zero.

The statement is true.

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Answer:

4(-80) = -320

Step-by-step explanation:

His elevation decreased by 80 each hour. Since he was walking for 4 hours, the equation would be

4(-80) = -320.