If a plane can travel 510 miles per hour with the wind and 410 miles per hour against the​ wind, find the speed of the wind and the speed of the plane in still air.​

The value of ACD of a trapezium is 26.56°.

Let ABCD be a trapezoid with BCǀǀAD and AB=BC=CD= ½ AD.

ACD can be determined by using the Pythagorean theorem or using the theorem of Pythagoras.

The theorem of Pythagoras states that if you draw a right-angled triangle with the hypotenuse as c and the legs a and b.

The sum of squares of the legs (a and b) equals the square of the hypotenuse (c).

Therefore, by using the Pythagorean theorem ; AC² = AB² + BC²

=> AC² = (1/2 AD)² + (1/2 AD)²

=> AC² = 1/4 AD² + 1/4 AD²

=> AC² = 1/2 AD².

Hence,AC² = 1/2 AD²

ACD is a right-angled triangle where AC is the hypotenuse.

Thus, using the theorem of Pythagoras, we can write: AD² = AC² + CD²

=> AD² = [√(1/2 AD²)]² + (AD/2)²

=> AD² = 1/2 AD² + 1/4 AD²

=> AD² = 3/4 AD²=> AD = √4/3 AD

Thus, ACD=ACD = tan¯¹(√1/2 AD²/AD/2) = tan¯¹(√2/4) = 26.56°

Therefore, ACD is 26.56°.

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Answer:

\( \frac{7}{17} \)

Step-by-step explanation:

(-14) ÷ (-34)

14/34

= ⁷/17

The quotient of the division will be 0.41. And the solution of the division (−14) by (−34) would be 7/17  as a simplified fraction.

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division, thus, can be interpreted as equally dividing the number that is being divided in total x parts, where x is the number of parts the given number is divided.

We need to divide the mixed fraction with integers, So

(-14) ÷ (-34)

The common denominator we can calculate as the least common multiple of the denominators then we get

14/34

= 7/ 17

= 0.41

Thus, the quotient of the division will be 0.41

Therefore, the solution of the division (−14) by (−34) would be 7/ 17  as a simplified fraction.

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The particular solution that satisfies the differential equation and the initial condition f(0) = a is: f(x) = -sin(x) + C1x + a.

To find the particular solution that satisfies the differential equation f''(x) = sin(x) and an initial condition, we need to integrate the equation twice and apply the initial condition.

1. First Integration:

Integrating the differential equation f''(x) = sin(x) with respect to x once gives us:

f'(x) = -cos(x) + C1

where C1 is the constant of integration.

2. Second Integration:

Integrating f'(x) = -cos(x) + C1 with respect to x again gives us:

f(x) = -sin(x) + C1x + C2

where C2 is another constant of integration.

3. Applying the Initial Condition:

To apply the initial condition, we need to use the given information about the problem. Let's say the initial condition is given as f(0) = a, where 'a' is a specific value.

Substituting x = 0 and f(x) = a into the equation, we get:

a = -sin(0) + C1(0) + C2

a = 0 + 0 + C2

C2 = a

Therefore, the particular solution that satisfies the differential equation and the initial condition f(0) = a is:

f(x) = -sin(x) + C1x + a

In this particular case, the initial condition f(0) = a determines the value of the constant C2, which becomes C2 = a. The resulting particular solution incorporates the constant C1 from the first integration and the constant a from the initial condition.

Note that without a specific initial condition or boundary condition, the constants C1 and C2 remain arbitrary and can be adjusted to fit different situations or additional information if provided.

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The new coordinates that define the figure after dilation with a center at the origin by the given scale factor are;

1) (1, 0)

2) (1, 4/3)

3) (0, 4/3)

4) (9/2, 0)

5) (9/2, 6)

6) (0, 6)

When we dilate a shape or coordinate by a scale factor, it means that we are going to multiply the dimensions of the coordinates by that scale factor. Thus;

1) (3, 0) dilated by a scale factor of 1/3 is;

1/3 *3, 0 * 1/3 = (1, 0)

2) (3, 4) dilated by a scale factor of 1/3 is;

1/3 *3, 4 * 1/3 = (1, 4/3)

3) (0, 4) dilated by a scale factor of 1/3 is;

1/3 *0, 4 * 1/3 = (0, 4/3)

4) (3, 0) dilated by a scale factor of 3/2 is;

3 *3/2, 0 * 3/2 = (9/2, 0)

5) (3, 4) dilated by a scale factor of 3/2 is;

3 *3/2, 4 * 3/2 = (9/2, 6)

6) (0, 4) dilated by a scale factor of 3/2 is;

0 *3/2, 4 * 3/2 = (0, 6)

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Therefore, the height of each tent pole is approximately 8.07 meters.

Trigonometry is a branch of mathematics that deals with the study of the relationships between the sides and angles of triangles. It is used to solve problems involving triangles, such as finding the length of a side or the measure of an angle. Trigonometry is based on the use of trigonometric functions, which are ratios of the sides of a right triangle.

Here,

We can use trigonometry to solve this problem. Let's call the height of the tent pole "h" and the length of the rope "r". Then, we can use the tangent function to find the height:

tan(52°) = h/r

Rearranging this equation, we get:

h = r * tan(52°)

We know that the length of each rope is equal, so we can choose any arbitrary length for r. For simplicity, let's assume that each rope is 10 meters long. Then, we can plug in the values into the equation:

h = 10 * tan(52°)

Using a calculator, we get:

h ≈ 8.07 meters

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Answer:

5x-30

Step-by-step explanation:

x+15+4x-45

5x+14-45

5x-30

Answer:

1. 2

2. 7

3. 17

4. 18

5. 83

6. 79

7. 7

8. 7

9. 19

10. 54

11. 26

12. 16

13. 9

14. 4

15. 3

16. 7

17. 5

18. 5

19. 30

20. 14

21. 20

22. 27

Step-by-step explanation:

Hope this helps!

The least possible value of the area of square T is 49 i.e., the correct answer is option (C) 49, representing the least possible value of the area of square T.

The least possible value of the area of square T can be determined by analyzing the relationship between the two squares and their perimeters.

Let's denote the side length of square S as 'a'.

Since the perimeter of square S is 40, each side of the square has a length of 10 (40 divided by 4).

Square T is inscribed in square S, which means that its corners touch the sides of square S.

To find the least possible value of the area of square T, we need to consider the scenario where square T is the smallest possible square that can be inscribed in square S.

In this case, the sides of square T are parallel to the sides of square S, and the corners of square T coincide with the midpoints of the sides of square S.

Since square T is inscribed in square S, the diagonal of square T is equal to the side length of square S.

Using the expression of Pythagorean theorem, we can calculate the length of the diagonal of square T:

Diagonal of square T = √(\(10^2 + 10^2\)) = √200 = 10√2

The side length of square T can be found by dividing the diagonal length by √2:

Side length of square T = 10√2 / √2 = 10

Therefore, the area of square T is (side length)^2 = \(10^2\) = 100.

However, we are looking for the least possible value of the area of square T.

Since the answer choices are given, we can see that the smallest possible area is 49, which corresponds to option (C).

Hence, the correct answer is option (C) 49, representing the least possible value of the area of square T.

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The probability that the mean of a sample of 55 families will be between 17 and 18 pounds is approximately 71.55%.

σ_sample = σ / sqrt(n)

σ_sample = 2.5 / sqrt(55)

σ_sample ≈ 0.336

Now, we can standardize the values of 17 and 18 pounds using the Z-score formula. This will tell us how many standard deviations away from the population mean these values are:

Z = (X - μ) / σ_sample

Z_17 = (17 - 17.2) / 0.336 ≈ -0.595

Z_18 = (18 - 17.2) / 0.336 ≈ 2.381

Now we will use the standard normal distribution (Z-distribution) to find the probabilities corresponding to these Z-scores. You can use a Z-table, statistical software, or an online calculator to find these probabilities.

P(Z < -0.595) = 0.2760

P(Z < 2.381) = 0.9915

To find the probability that the mean of a sample of 55 families will be between 17 and 18 pounds, we will find the difference between the probabilities corresponding to the two Z-scores:

P(17 < X < 18) = P(Z < 2.381) - P(Z < -0.595)

P(17 < X < 18) = 0.9915 - 0.2760

P(17 < X < 18) ≈ 0.7155

So, the probability that the mean of a sample of 55 families will be between 17 and 18 pounds is approximately 71.55%.

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Answer:

\(\frac{(x+2)}{(x-1)}\)

Step-by-step explanation:

\(\frac{x^2 + x -2}{x^2 -2x+1}\) =

\(\frac{(x+2)(x-1)}{(x-2)(x-1)}\) =

\(\frac{(x+2)}{(x-1)}\)

Answer:

(-14, 4)

Step-by-step explanation:

I graphed it on Desmos Graphing calculator. This is a great resource. Hope this helps!

Step-by-step explanation:

( - 14, -4)

is a right answer

The duration of shoot would be 2 hours and Either stylist would cost $282 if the shoot lasted 2 hours.

A fashion photographer needs to hire a stylist to prepare his models.

Let the number of hours stylist take = x

Jayla charges $156 for showing up, plus $63 per hour. So, this can be mathematically written as ,

156 + 63x                                                  equation 1

Sally charges $158 plus $62 per hour.  So, this can be mathematically written as ,

158 + 62x                                                  equation 2

As per the question, the expected duration of his photo shoot, either stylist would cost him the same amount. So we can equate equation 1 and equation 2. On equating equation 1 and equation 2 , we will get

156 + 63x  = 158 + 62x

⇒  x = 2

So, the duration would be 2 hours.

Jayla cost = Sally cost = 156 + 63x  = 156 + (63 × 2) = 282

Either stylist would cost $282 if the shoot lasted 2 hours.

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Sam's experimental probability of getting heads in 30 coin flips was 20 out of 30, while the theoretical probability of getting heads is 1/2 or 0.5.

Sam's experimental probability of getting heads in the 30 coin flips was 20 out of 30, which can be written as 20/30 or simplified to 2/3. This means that in the experiment, heads appeared in approximately two-thirds of the flips. On the other hand, the theoretical probability of getting heads in a fair coin flip is 1/2 or 0.5. This is because there are two equally likely outcomes (heads or tails) and only one of them is heads.

Comparing the experimental and theoretical probabilities, we can see that Sam's results deviate slightly from the expected outcome. The experimental probability of getting heads is higher than the theoretical probability. This could be due to chance or random variation, as 30 coin flips may not be enough to perfectly represent the true probability. With a larger number of trials, the experimental probability would tend to converge towards the theoretical probability. However, in this specific experiment, Sam's results suggest a slightly biased coin favoring heads.

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Answer:

*12 and *6

Step-by-step explanation:

5*12/6*12=10*6/10*6

60/72=60/72

60=60

true

Step-by-step explanation:

The price of the lot measuring 120' x 200', selling for $300 a front foot is $192,000.

To find out the price of a lot measuring 120' x 200', selling for $300 a front foot, you need to use the formula given below;

Price = Front Footage × Price per Front Foot

First, you need to calculate the front footage of the lot, which can be obtained by adding up the length of all the sides of the rectangular lot.

Front footage = 120 + 120 + 200 + 200

                       = 640 ft

Then you can find the price of the lot by multiplying the front footage by the price per front foot.

Price = 640 ft × $300/ft

        = $192000

Therefore, the price of the lot measuring 120' x 200', selling for $300 a front foot is $192,000.

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Answer:

Step-by-step explanation:

2 easy ways:

1. Divide 7 by 3 then multiply by 2

7/3= seven thirds or 2.333

Now multiply by two to get 14 thirds

or 4.666

2. Multiply 7 by 2/3, or 0.666

This way is a lot easier with a

calculator

The weight of the box is 14/3’s or 4.666

Answer: y = 3x + 2

Step-by-step explanation:

Let's start with what we know. To calculate the slope, we do:
(y1 - y2)/(x1 - x2)

So, for this equation we get:

(5 - 2)/(3-0)

We get 3/3, so the slope = 1. So far, we have:

y = 3x + b

Let's use one of our coordinates to plug this in:

2 = 0 + b

So b = 2.

So our final equation is:
y = 3x + 2

Answer:

multiples of 50:   50, 450, 500

not multiples:   515, 410, 555, 540

Step-by-step explanation:

\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$110\\ r=rate\to 3.7\%\to \frac{3.7}{100}\dotfill &0.037\\ t=years\dotfill &1 \end{cases} \\\\\\ A=110[1+(0.037)(1)]\implies A=110(1.037)\implies A=104.07\)

Answer:

Explanation:

Given:

Qd = 479 - 3P

where:

Qd = the quantity of residential landscape cleanings per week that people in the local area would be willing to purchase

P = monthly price in dollars

We plug in the given price of 39 dollars per month into Qd = 479 - 3P. So,

Therefore, the quantity demanded at a price of 39 dollars per month is 362.

Let:

After a reflection across the line y = x:

Answer:

-8j+5

Step-by-step explanation:

the answer is -8j+5

The domain of the quadratic function f(x) = x² - 10x + 22 include the following: D. all real numbers.

In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are always read and written from smaller to larger numerical values, and from the left of the graph to the right.

Generally speaking, the domain of a quadratic function (parabola) is always all the real numbers that are located on the x-axis of a cartesian coordinate.

In conclusion, the domain of this quadratic function are all the x-values (independent value) that are located on the x-axis of the graph, which include {-∞, ∞} or all real numbers.

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Answer:

the fee at sunset bank will always be more than fee at Oceanview bank.

Answer:

D

Step-by-step explanation:

i got it correct and go to k-12

Answer:

Step-by-step explanation:

4 - 0.4 = 3.6

3.6 - 0.4 = 3.2

2.8 - 0.4 = 2.4

2.4 - 0.4 = 2

2 - 0.4 = 1.6

so the next numbers in the pattern are: 2.4, 2 and 1.6

Answer:

55 to 70

Step-by-step explanation:

The first quartile is the left-most region of the graph, from 55 to 70.  The second quartile stretches from 70 to 80.