What is the median and mean of 18,15, 11, 3, 8, 4, 13, 12, 3, 18

The general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is: y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

To solve this differential equation, we can use separation of variables.

First, we can rearrange the equation to get dy/dx on one side and the rest on the other side:

dy/dx = 1/3(sin x − xy^2)

dy/(sin x - xy^2) = dx/3

Now we can integrate both sides:

∫dy/(sin x - xy^2) = ∫dx/3

To integrate the left side, we can use substitution. Let u = xy^2, then du/dx = y^2 + 2xy(dy/dx). Substituting these expressions into the left side gives:

∫dy/(sin x - xy^2) = ∫du/(sin x - u)

= -1/2∫d(cos x - u/sin x)

= -1/2 ln|sin x - xy^2| + C1

For the right side, we simply integrate with respect to x:

∫dx/3 = x/3 + C2

Putting these together, we get:

-1/2 ln|sin x - xy^2| = x/3 + C

To solve for y, we can exponentiate both sides:

|sin x - xy^2|^-1/2 = e^(2C/3 - x/3)

|sin x - xy^2| = 1/e^(2C/3 - x/3)

Since the absolute value of sin x - xy^2 can be either positive or negative, we need to consider both cases.

Case 1: sin x - xy^2 > 0

In this case, we have:

sin x - xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(sin x - 1/e^(2C/3 - x/3))/x]

Note that the initial condition y(0) = 5 only applies to the positive square root. We can use this condition to solve for C:

y(0) = √(sin 0 - 1/e^(2C/3)) = √(0 - 1/e^(2C/3)) = 5

Squaring both sides and solving for C, we get:

C = 3/2 ln(1/25)

Putting this value of C back into the expression for y, we get:

y = √[(sin x - e^(x/2)/25)/x]

Case 2: sin x - xy^2 < 0

In this case, we have:

- sin x + xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(e^(2C/3 - x/3) - sin x)/x]

Again, using the initial condition y(0) = 5 and solving for C, we get:

C = 3/2 ln(1/25) + 2/3 ln(5)

Putting this value of C back into the expression for y, we get:

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x]

So the general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is:

y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x], if sin x - xy^2 < 0 and y(0) = 5

Note that there is no solution for y when sin x - xy^2 = 0.

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Answer:

Step-by-step explanation:

There are a total of 35 questions on a test:

Points from multiple choice answers = 2m

Points from short answers = 5s

There are a total of 100 points on the test:

The condition is

\(\\ \sf\longmapsto m+s=35\)

\(\\ \sf\longmapsto 2m+5s=100\)

The required regular singular points are x = -6, x = 0.

In mathematics, a singular point typically refers to a point where a function, curve, or surface fails to behave as expected or becomes undefined. The precise definition of a singular point can vary depending on the context in which it is used.

In the study of differential equations, a singular point is a point where the solution to a differential equation is not well-defined or becomes infinite.

Singular points can have different classifications, such as regular singular points, irregular singular points, or apparent singular points, depending on the behavior of the solutions near those points.

To classify the singular points of the given differential equation as regular or irregular, we need to analyze the behavior of the equation near each point.

The given differential equation is:

(x² + 2x - 24)y'' + (8x + 48)y' - 6x³y = 0

To determine the singular points, we need to find the values of x for which the coefficients of y'', y', and y become zero or infinite.

1. Singular points due to (x² + 2x - 24) = 0:

  Solving this quadratic equation, we find:

  x² + 2x - 24 = 0

  (x + 6)(x - 4) = 0

  x = -6, 4

2. Singular points due to (8x + 48) = 0:

  This linear term becomes zero at x = -6.

3. Singular points due to -6x³ = 0:

  This term becomes zero at x = 0.

Now, let's classify each singular point as regular or irregular:

A regular singular point is one where the coefficients of y'' and y' can have at most a pole of order 1, while the coefficient of y can have at most a pole of order 2.

1. x = -6:

  The coefficient (8x + 48) becomes zero at this point.

  Since this is a linear term, it can have at most a pole of order 1.

  The coefficient (x² + 2x - 24) is non-zero at this point.

  The coefficient of y is non-zero at this point.

  Therefore, the singular point x = -6 is a regular singular point.

2. x = 0:

  The coefficient (-6x³) becomes zero at this point.

  Since this is a cubic term, it can have at most a pole of order 3.

  The coefficient (x² + 2x - 24) is non-zero at this point.

  The coefficient of y is non-zero at this point.

  Therefore, the singular point x = 0 is a regular singular point.

In conclusion, the regular singular points of the given differential equation are:

A. x = -6

B. x = 0

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\(\begin{cases} x = -4 &\implies x +4=0\\ x = 3 &\implies x -3=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +4 )( x -3 ) = \stackrel{0}{f(x)}} \hspace{5em}\textit{we also know that } \begin{cases} x ~~ ~~ = ~~ 2\\ f(x)=-6 \end{cases} \\\\\\ a ( 2 +4 )( 2 -3 ) = -6\implies a(6)(-1)=-6\implies -6a=-6 \\\\\\ a=\cfrac{-6}{-6}\implies a=1 \\\\[-0.35em] ~\dotfill\\\\ 1( x +4 )( x -3 ) =f(x)\implies {\Large \begin{array}{llll} ( x +4 )( x -3 ) =f(x) \end{array}}\)

Answer:

E. The student scored 1.3 standard deviations lower on the second exam than the class average on the second exam.

Step-by-step explanation:

Whenever we have a negative z-score, this means that the raw score is a certain standard deviation below the mean average.

From the above question, we are told that:

An AP Statistics teacher grades using z-scores. On the second major exam of the grading period, a student receives a grade with a z-score of -1.3.

This means the students score in the second major exam is 1.3 standard deviations below the average score in the second major exam.

Hence, according to the options given in the above question, the correct interpretation of this grade is

The student scored 1.3 standard deviations lower on the second exam than the class average on the second exam.

Option E is the correct option.

Answer:

A. x < 2

Step-by-step explanation:

2x - 8 < 12

2x < 12 + 8

2x < 20

x < 20/10

x < 2

Answer:

A) the probability of winning is 0.24%.

B) Yes i will play the game

C) Despite the fact that the probability of winning is very low, one should play the game because the expected value of the game is positive.

Step-by-step explanation:

Expected value of X is denoted by;

E(X) = x1•p1 + x2•p2 +..... xn•pn

Where;

xi is the observation and pi is the probability of xi

Now, let's make p the probability of the winning bet and 1 - p be the probability of losing the game

If the bet is win, the net gain is $98,800 and if the bet is lose, the loss is -$1200.

Hence the probability distribution will be;

For xi = $98,800, pi = p

For xi = -$1,200, pi = 1 - p

So;

E(X) = Σxi.pi

Thus;

1200 = 98800p - 1200(1 - p)

1200 = 98800p - 1200 + 1200p

1200 + 1200 = 100000p

2400 = 100000p

p = 2400/100000

p = 0.024

Thus, the probability of winning is 0.24%.

Despite the fact that the probability of winning is very low, one should play the game because the expected value of the game is positive.

The value of KL for the similar triangle ∆JKL is derived to be equal to 10.92

The triangles XYZ and JKL are similar, this implies that the length XY of the smaller triangle is similar to the length JK of the larger triangle

similarly, YZ is similar to KL so;

8.7/12.18 = 7.8/KL

KL = (7.8 × 12.18)/8.7 {cross multiplication}

KL = 95.004/8.7

KL = 10.92

Therefore, the value of KL for the similar triangle ∆JKL is derived to be equal to 10.92.

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Answer: 10.92

Step-by-step explanation:

I am in the middle of taking the test is this would be the best answer choice in my opinion. Im not sure if it is correct or not yet but just let me know if it is or isn't!

The largest value that f(4) can possibly be is 29.

The mean value theorem states that for a function f(x) that is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), there exists a number c in the open interval (a, b) such that:

f(b) - f(a) = f'(c)(b - a)

In this case, we are given that f(0) = -3 and that f'(x) ≤ 8 for all values of x. To determine how large f(4) can possibly be, we can use the mean value theorem with a = 0 and b = 4:

f(4) - f(0) = f'(c)(4 - 0)

Substituting the given values:

f(4) - (-3) = f'(c)(4)

f(4) + 3 = 4f'(c)

Since f'(x) ≤ 8 for all values of x, we can say that f'(c) ≤ 8. Therefore:

f(4) + 3 ≤ 4f'(c) ≤ 4(8) = 32

Therefore, we have:

f(4) ≤ 32 - 3 = 29

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Answer:yooob 123vv

Step-by-step explanation:212345ggg

gcj  bbbbb

Answer: Option 4 - 1440

Step-by-step explanation:

2 Square Sides : Take 12 times 12 and times by two for both sides.

12 x 12 = 144     144 x 2 = 288

4 rectangular sides : The multiplication of 12 times 24

12 x 24 = 288    288 x 4 = 1152

Added All Together : 288 + 1152 = 1440

Answer:

its 373248

Step-by-step explanation:

I got this by 2squared 9 and 3squared 6

Answer:

Step-by-step explanation: T20 = (-1)^20 3520(c)^15(d)^20

= 35c20c^15 d^20

The most likely object to weigh 4 tons will be Helicopter

The correct option is (D) Helicopter

1 ton = 1000 Kg

First, a watermelon weigh= 0.001 to 0.003  tons(i.e., 1-3 Kg)

then, A man weigh= 0.09 to 0.1 tons (i.e., 90 - 100kg)

A clothes dryer weigh= 0.07 to 0.09 tons (i.e., 70- 90 Kg)

lastly, a Helicopter weigh= 0.275- 56 tons (i.e., 275 - 56,000 Kg)

The closest is Helicopter weight 0.275- 56 tons

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Answer:

Divide  172.75 by 348.79

Step-by-step explanation:

Answer:

58.68

Step-by-step explanation:

348.79- 172.75=176.04

176.04/3= 58.68

The correct conversion of the number 0.0000783 to scientific notation is:7.83 x 10⁻⁶

The general form of scientific notation is: a x 10n, where a is the coefficient and n is the exponent.In this case, Tyler converted 0.0000783 to scientific notation as 78.3 x 10⁻⁶, which is incorrect. Tyler's mistake is that he did not shift the decimal point to the right one place to get the coefficient of 7.83, which is the correct coefficient. Therefore, the main answer is No, the coefficient should be 7. 83.The correct conversion should be:0.0000783 = 7.83 x 10⁻⁶

In conclusion, Tyler made an error when he converted 0.0000783 to scientific notation. Instead of 78.3 x 10⁻⁶, the correct scientific notation for 0.0000783 is 7.83 x 10⁻⁶.

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The probability that the body is attempting to reject the kidney when the new urine test has a positive result is 74.19%.

In about 30% of kidney transplants, the body tries to reject the organ. The new urine test is not perfect and it is known that 20% of people who do reject the transplant test negative, and 7% of people who do not reject the transplant test positive.

According to Baye’s theorem:

The probability that the body is attempting to reject the kidney when the new urine test has a positive result P(A) = P (Trying to reject | Positive test)

Now, we have to find P (Trying to reject | Positive test)

P(Trying to reject) = 30%

P(Not Trying to reject) = 70%

P(Positive test | Trying to reject) = 80%

P(Negative test | Trying to reject) = 20%

P(Positive test | Not trying to reject) = 7%

P(Negative test | Not trying to reject) = 93%

Let's calculate the probability of a positive result

P(Positive result) = P(Trying to reject) x P(Positive test | Trying to reject) + P(Not Trying to reject) x P(Positive test | Not trying to reject)

P(Positive result) = 0.3 × 0.8 + 0.7 × 0.07

P(Positive result) = 0.314

We can now calculate the probability that the body is attempting to reject the kidney when the new urine test has a positive result using Baye’s theorem.

P(Trying to reject | Positive test) = P(A) = P(Positive test | Trying to reject) x P(Trying to reject) / P(Positive result)

P(A) = 0.8 × 0.3 / 0.314P(A) = 0.7419 ≈ 74.19%

Therefore, the probability that the body is attempting to reject the kidney when the new urine test has a positive result is 74.19%.

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Answer:

it it 2 3/4

Step-by-step explanation:

35/8-13/8=2 3/4

Answer: 2³/₄

Step-by-step explanation:

\(\displaystyle\\4\frac{3}8} -1\frac{5}{8}=\\\\\frac{4(8)+3}{8}-\frac{1(8)+5}{8}=\\\\ \frac{32+3}{8} -\frac{8+5}{8}=\\\\\frac{35}{8} - \frac{13}{8} =\\\\\frac{35-13}{8}=\\\\\frac{22}{8} =\\\\\frac{2(11)}{2(4)} =\\\\\frac{11}{4} =\\\\2\frac{3}{4}\)

Answer:

c

Step-by-step explanation:

The period is 1 complete cycle of the wave, before repeating.

1 cycle is from - 6 to - 2 , then

period = 4  → c

The area of the computer monitor display is approximately 0.103 square meters, with three significant figures.

The area of the monitor display in square meters is found by converting the measurements from inches to meters and then calculate the area.

The conversion factor from inches to meters is 0.0254 meters per inch.

Width in meters = 14.60 inches * 0.0254 meters/inch

Height in meters = 10.95 inches * 0.0254 meters/inch

Area = Width in meters * Height in meters

We calculate the area:

Width in meters = 14.60 inches * 0.0254 meters/inch = 0.37084 meters

Height in meters = 10.95 inches * 0.0254 meters/inch = 0.27813 meters

Area = 0.37084 meters * 0.27813 meters = 0.1030881672 square meters

Now, we determine the number of significant figures.

The measurements provided have four significant figures (14.60 and 10.95). However, in the final answer, we should retain the least number of significant figures from the original measurements, which is three (10.95). Therefore, the answer should have three significant figures.

Thus, the area of the monitor display in square meters is approximately 0.103 square meters, with three significant figures.

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Answer:

t = 1.23 hours

Step-by-step explanation:

Given that,

Distance between two stations is 204 miles

One train travels at 90 miles per hour while the other travels at 75 (let) miles per hour.

We need to find how long will it take for the two trains to meet.

As both cars travel toward each other, it means they approach with a speed of 90 mph + 75 mph = 165 mph.

Let t is the time when they meet. So,

\(t=\dfrac{d}{v}\\\\t=\dfrac{204}{165}\\\\t=1.23\ h\)

It will take 1 hour 23 minutes for the trains to meet.

Answer:

x = √76

Step-by-step explanation:

in upper triangle :

7² - 3² =40 so the third side of the upper triangle is : √40

in the biggest triangle :

(3+3)² + 40 = 76 so the another side of the biggest triangle is : √76

Answer:

C

Step-by-step explanation:

yards and feet would take to long, miles would be the most efficient

Answer:

its C

Step-by-step explanation:

Answer:

16/3 pounds

Step-by-step explanation:

We are give that each friend took 2/3 pound of grapes from the bowl. Therefore, to know the total amount taken by the four friends, we will simply do cross multiplication as follows:

1 friend .................> 2/3 pounds

4 friends ...............> ?? pounds

Amount taken by the 4 friends = [4*(2/3)] / 1 = 8/3 pounds

The bowl originally had 8 pounds and 8/3 pounds were taken, therefore:

remaining amount = 8 - 8/3 = 16/3 pounds                                                                           hope this helps!

Answer:

3 groups of 17, or 7-17 groups of 3

Step-by-step explanation:

52 - 1 = 51

3(17) = 51

Answer:

Dee divided her bears into 3 groups of 17 bears, OR 17 groups of 3 bears

Step-by-step explanation:

If Dee had 1 bear left over after she divided her collection, then the number of bears in the groups = 52 - 1 = 51

To find the groups, we need to find the factors of 51.

(a factor is a number that divides another number evenly, with no remainder)

As 51 is an odd number, we can say that all multiples of 2 (even numbers) cannot be a factor.

Factors of 51:

1 and 51

3 and 17

We are told that Dee divided her collection into equal groups (not one group), so we can discard 1 and 51.  Therefore, Dee divided her bears into 3 groups of 17 bears, OR 17 groups of 3 bears (both solutions are correct)

Tn = a + ( n- 1 ) d

T 26 = -33 + ( 26 - 1 ) 4

T 26 = -33 + ( 25 x 4 )

= -33 + 100

= 67.............. Option D

The equation of line d is perpendicular to line c is y=-4/3 x+5.

The equation of line is y=3/4 x-2.

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line.

In the equation of line is y=3/4 x-2, slope=m=3/4

The slope of a line perpendicular to given line is m1=-1/m2

So, the slope of a perpendicular line is -4/3

Substitute m=-4/3 and (x, y)=(6, -3) in y=mx+c, we get

-3=-4/3 (6)+c

⇒ -3=-8+c

⇒ c=5

Now, substitute m=-4/3 and c=5 in y=mx+c, we get

y=-4/3 x+5

Therefore, the equation of line d is perpendicular to line c is y=-4/3 x+5.

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