A dragon flew 300 miles from his castle to visit a friend. Flying with the wind, his trip took 2 hours. His return trip against the wind took 3 hours. What was the speed of the wind and the speed of the dragon in still air?

The area of Maria’s circle is 18π square units option fourth is correct.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

The figure is missing.

Please refer to the attached picture for the figure.

We have given the radius of the circle as 3 units

r = 3 units

Area of circle = πr² = π(3)² = 9π square units

The area of Maria’s circle = 2(9π) = 18π square units

Thus, the area of Maria’s circle is 18π square units option fourth is correct.

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We have that O(n²) is the theta notation for 7n² + 4n + 2.

Let's give big-Oh a formal definition:

O(g(n)) = {the set of all f such that 0 [tex]\leq[/tex] f(n) [tex]\leq[/tex] cg(n) for any n >= n₀ fulfilling positive constants c and n₀}

To show this

We need to find c and n₀ such that:

7n² + 4n + 2 <= cn² for all n >= n₀ .

Divide both sides by n², getting:

7 + 4/n + 2/(n²) <= c for all n >= n₀ .

If we choose n₀ equal to 1, then we need a value of c such that:

7 + 4 + 2 <= c

We can set c equal to 13. Now we have:

7n² + 4n + 2 <= 13n² for all n >= 1 .

Hence, 7n² + 4n + 2=O(n²)

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The correct answer is option B which is g(x)= 1/2f(-x).

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

As we can see in the graph that the value of the function g(x) will be calculated by the distance formula:-

[tex]g(x) = \dfrac{ 0 + 2}{2 - 0 }=\frac{2}{2}=1[/tex]

The value of the function f(x) will be:-

[tex]f(x) =\dfrac{2-0}{-4+0}=\dfrac{-1}{2}[/tex]

So g(x) = ( -1/2) f(x)

Therefore the correct answer is option B which is g(x)= 1/2f(-x).

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The second derivative of the first function is s"(x) = = -[8e^(x/5) - 2]e^(x/5)/25(e^(x/5) + 2)³.

The second derivative of the second function is; k''(t) = (36t² - 6)e^(-3t²)

1)  We are given the function;

s(x) = 4/(1 + 2e^(-0.2x)

First derivative is;

ds/dx = [8e^(x/5)]/5(e^(x/5) + 2)²

Second Derivative is;

d²s/dx² = -[8e^(x/5) - 2]e^(x/5)/25(e^(x/5) + 2)³

At x = 0;

d²s/dx² = -[8e^(0/5) - 2]e^(0/5)/25(e^(0/5) + 2)³

d²s/dx² = 8/675

B) We are given the function;

k(t) = e^(-3t²)

The first derivative is;

dk/dt = -6te^(-3t²)

The second derivative is;

k''(t) = (36t² - 6)e^(-3t²)

At t = 1, we have;

k''(t) = (36(1)² - 6)e^(-3(1²))

k"(t) = 1.494

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The trigonometry ratios are cos(θ) = -7/√58, sec(θ) = -√58/7 and cot(θ) = -7/3

The point on the terminal side is given as:

(x, y) = (-7, 3)

Start by calculating the hypotenuse using:

[tex]h= \sqrt{x^2 + y^2[/tex]

So, we have:

[tex]h= \sqrt{(-7)^2 + 3^2[/tex]

Evaluate

[tex]h= \sqrt{58[/tex]

The cosine is then calculated using:

cos(θ) = x/h

This gives

cos(θ) = -7/√58

The secant is then calculated using:

sec(θ) = 1/cos(θ)

This gives

sec(θ) = -√58/7

The cotangent is then calculated using:

cot(θ) = cos(θ)/sin(θ)

Where

sin(θ) = y/h

So, we have:

sin(θ) = 3/√58

So, we have:

cot(θ) = (-7/√58)/(3/√58)

This gives

cot(θ) = -7/3

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The expression for length and breadth of the rectangle garden in terms of the side of the square tomato patch.

l=3x+2

b=x+5

The linear equation is the equation where the highest degree of the variables is 1.

Here given that the garden is rectangular in shape and the tomato patch is square in shape.

the length of the side of the square tomato patch is x.

Asuume the length of the rectangle garden is l

and the breadth of the rectangle garden is b.

Given that

the length of the garden is greater than the 3 times of the length of the rectangular garden by 2 feet.

3 times of the length of the rectangular garden is 3x

2 feet greater than 3 times of the length of the rectangular garden= 3x+2

so from above, it is clear that l=3x+2

similarly, the breadth of the garden is greater than the length of the rectangular garden by 5 feet.

then the breadth of the garden = b= x+5

Therefore the expression for length and breadth of the rectangle garden in terms of the side of the square tomato patch.

l=3x+2

b=x+5

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The doctor recommends rest if the patient has the flu. Then the correct option is A.

Determining the proper option, acquiring evidence, and exploring various options are all steps in the decision-making process.

Read the following two statements.

Then, if possible, use the Law of Detachment to draw a conclusion.

Then the correct option is A.

The doctor recommends rest if the patient has the flu.

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Answer:

7.5mph

Step-by-step explanation:

Let the average speed of the boat to be x mph.

Total Distance = Avg. Speed x Total Time

60 = ((x+6) + (x-6))(4)

60 = (x+6+x-6)(4)

(2x)(4)=60

2x=60/4

2x = 15

x = 15 /2

x = 7.5mph

Answer:

  15 +√261 ≈ 31.155 mph

Step-by-step explanation:

The time for the trip can be found by dividing the distance by the speed.

__

The relation between time, speed, and distance is ...

  time = distance/speed

The speed for the downstream leg was the sum of the boat speed (b) and 6 mph. The speed for the upstream leg was the difference. So the total trip time was ...

  4 = 60/(b +6) +60/(b -6) . . . total  time is the sum of the times for the legs

__

Multiplying by the product of the denominators, we have ...

  4(b +6)(b -6) = 60(b -6) +60(b +6)

  b² -36 = 30b . . . . divide by 4 and simplify

  b² -30b = 36 . . . . put in a form useful for completing the square

  (b -15)² = 36 +15² . . . . . complete the square

  b -15 = √261 . . . . . . . . take the square root (negative root is extraneous)

  b = 15 +√261 ≈ 31.155 . . . . add 15

The average speed of the boat was about 31.155 mph.

Answer:

7/4 meters

Step-by-step explanation:

the tallest plant is 19/8

since they have all the same denominaters we can just compare the top numbers

so

the smallestp lant is 5/8

19/8 - 5/8 = 14/8

7/4 is your final answer after simplifying

Answer:

x-23=.55

Step-by-step explanation:

Answer: 0.55 = x - 23

Step-by-step explanation:

let his savings = x

Answer: 9516793/9765625

Step-by-step explanation:

We can subtract the probability none of them have been vaccinated from 1.

If 52% of people are vaccinated, then 48% of people are not vaccinated.

Thus, the probability is [tex]1-(0.48)^{5} =\frac{9516793}{9765625}[/tex]

Answer:

5/6

Step-by-step explanation:

4/3-1/2

1) make the denominators the same on both fractions

8/6-3/6=?

2) subtract numerators

5/6

3) simplify

cannot simplify

Answer:

5/6

Step-by-step explanation:

4/3  -1/2

The first step is to get a common denominator of 6

4/3 *2/2 = 8/6

1/2 * 3/3 = 3/6

8/6  -3/6

5/6

Answer:

Step-by-step explanation:

The total distance travelled is 1075.91 km.

The average speed is the total distance traveled by the object in a particular time interval. The average speed is a scalar quantity.

45 * (x +12)= 50* 1/5 + 1/2 *x

45x + 540= 10+ 0.5 x

44.5 x = 530

x= 11.91 (neglect the negative sign cause time can't be negative)

So, distance= 45* 23.91 = 1075.91 Km

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The number of cars that have passed through the intersection is 245.

Direct variation is when two variables move in the same direction. If one variable increases, the other variable increases.

The equation that represents direct variation is; c = wk

Where:

1085 = k31

k = 1085 / 31

k = 35

c = 7 x 35

c = 245

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Let's prove that (sec x)(csc x) is equal to cot x + tan x

[tex]\Longrightarrow \sf (sec(x) )(csc(x))[/tex]

[tex]\Longrightarrow \sf \dfrac{1}{\cos \left(x\right)\sin \left(x\right)}[/tex]

[tex]\Longrightarrow \sf \dfrac{\cos ^2\left(x\right)+\sin ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)}[/tex]

[tex]\Longrightarrow \sf \dfrac{\cos ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)} + \dfrac{\sin ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)}[/tex]

[tex]\Longrightarrow \sf \dfrac{\cos\left(x\right)}{\sin \left(x\right)} + \dfrac{\sin \left(x\right)}{\cos \left(x\right)}[/tex]

[tex]\Longrightarrow \sf cot(x) + tan(x)[/tex]

Hence student A did correctly prove the identity properly.

Also Looking at student B's work, he verified the identity properly.

So, Both are correct in their own way.

Identities used:

[tex]\rightarrow \sf sin^2 (x) + cos^2 (x) = 1[/tex]       (appeared in step 3)

[tex]\sf \rightarrow \dfrac{cos(x) }{sin(x) } = cot(x)[/tex]               (appeared in step 6)

[tex]\rightarrow \sf \dfrac{sin(x )}{cos(x) } = tan(x)[/tex]               (appeared in step 6)

Answer:

[tex]y=-\dfrac{1}{2}x+2[/tex]

Step-by-step explanation:

Define two points on the line:

  [tex]\textsf{let}\:(x_1,y_1)=(0,2)[/tex]

  [tex]\textsf{let}\:(x_2,y_2)=(4,0)[/tex]

Use the slope formula and the defined points to find the slope:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-2}{4-0}=-\dfrac{1}{2}[/tex]

Substitute the found slope and one of the points into the point-slope form of a linear equation:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-2=-\dfrac{1}{2}(x-0)[/tex]

Simplify:

[tex]\implies y-2=-\dfrac{1}{2}x[/tex]

[tex]\implies y=-\dfrac{1}{2}x+2[/tex]

Answer:

[tex]\boxed{\sf x = 1, \ x = -5}[/tex]

Explanation:

[tex]\rightarrow \sf 4x^2 + 16x - 20 = 0[/tex]

[tex]\rightarrow \sf 4(x^2 + 4x - 5) = 0[/tex]

[tex]\rightarrow \sf x^2 + 4x - 5 = 0[/tex]

[tex]\rightarrow \sf x^2 + 5x -x- 5 = 0[/tex]

[tex]\rightarrow \sf x(x + 5) -1(x+ 5) = 0[/tex]

[tex]\rightarrow \sf (x-1)(x+ 5) = 0[/tex]

[tex]\rightarrow \sf x = 1, \ x = -5[/tex]

The asnwer is C

for finding domain look at just x-axis from left to right , because there are arrows , so domain is all real numbers or from negative infinity to positive infinity

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The average salary of sanitation workers in the city of Euonymus is overpaid from the one-tail test and the average salary of sanitation workers in the city of Euonymus is not 24230 from the two-tail test.

The null and alternative hypotheses are two generalizations about a population that are strictly contradictory. The null hypothesis can be denoted by H₀ and the alternative hypothesis can be denoted by H₁.

We have:

Average x = 24375

u = 24230

SD = 523

n = 105

Null hypothesis and alternative hypothesis for one-tail test:

H0: the average salary of sanitation workers in the city of Euonymus is not overpaid.

u = 24230

H1:  the average salary of sanitation workers in the city of Euonymus is overpaid.

u > 24230

Assume significance level = 0.05

From the Z-table:

Z(critical) = 1.645

Now,

Z = (x-u)/(SD/√n)

Z = (24375-24230)/(523/√105)

Z = 2.84

Z > Z(critical)

So, reject the null hypothesis.

The average salary of sanitation workers in the city of Euonymus is overpaid.

Now, from the two-tail test:

Null hypothesis and alternative hypothesis for one-tail test:

H0: the average salary of sanitation workers in the city of Euonymus is 24230

u = 24230

H1:  the average salary of sanitation workers in the city of Euonymus is not 24230

u ≠ 24230

Assume significance level = 0.05

From the Z-table for the two-tail test:

Z(critical) = ±1.96

Now,

Z = 2.84

Z > z(critical)

∴ The average salary of sanitation workers in the city of Euonymus is not 24230.

Thus, the average salary of sanitation workers in the city of Euonymus is overpaid from the one-tail test and the average salary of sanitation workers in the city of Euonymus is not 24230 from the two-tail test.

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Answer:

56

Step-by-step explanation:

all your doing is removing the .053 to get your whole number

Answer:

[tex]3 \frac{7}{8}[/tex]

Step-by-step explanation:

Answer: He have to pay $172.5 if he buys 150 such articles.

72 articles for --> $82.80
1 article for - - - > 82.80/72

150 articles for --> (82.80/72)*150
                           = $172.5

Answer:

$172.5

Step-by-step explanation:

Given:

Shopkeeper buys = 72 articles

Price = $ 82.8

To Find:

The amount he'll need to pay If he buys 150 articles.

Solution:

Amount if he buys 150 articles

[tex] \boxed{\rm \: No. \: of \: articles \: he \:will \: buy × \cfrac{Cost \: of \: that \: article \: he \: has}{Number \: of \: articles \: he \: has}} [/tex]

[tex] = \$ \bigg(\rm150 * \cfrac{82.80}{72}\bigg) [/tex]

[tex]= \$ (150* 1.15)[/tex]

[tex] = \$172.5[/tex]

So we can conclude that:

$172.5 he will have to pay if he buys 150 such articles.

Answer:

25%

Step-by-step explanation:

In the sentence "15 is 25% of 60.", 25% is the percentage.

15 is the partial amount and 60 is the total amount.

15/60 = .25

convert a decimal to a percentage by multiplying by 100

.25 × 100 = 25

Some people use a shortcut of moving the decimal two places to the right. This is the same as multiplying by 100.

15/60 is 25%

Answer: B. (2,2)

Step-by-step explanation:

The vertex of the parabola in the form [tex](x-h)^2 = 4p(y-k)[/tex] is (h, k).

The coordinate of C( a+c , b) ,  AC are ((a+c)/2 , b/2) , BD are ((a+c)/2 , b/2)

Coordinates is the value assigned to a point in a x-y graph to determine its location.

The coordinates of parallelogram is

A ( 0,0) B (a,0) , C ( __ , ___) , D ( c , b)

The y coordinate is same as D as b

and the x coordinate will be a+c

C( a+c , b)

The coordinate of the mid point of AC are ((a+c)/2 , b/2)

The coordinate of the mid point of BD are ((a+c)/2 , b/2)

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Answer:

D.

Step-by-step explanation:

It is the only one that contains all the x-values of the points. (Domain is the set of x-values).