what is 4(1+0.5m)=7m

Answer:

Step-by-step explanation:

answer is A. n is parallel to both l and m

The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

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The outcome is random if we know the possible values it can have, but not which particular value it takes.

Randomness refers to the property of a process or system where the outcome is uncertain, unpredictable, and not predetermined. In a random process, we know the set of possible outcomes.

But we cannot determine which particular outcome will occur until it actually happens. For example, when flipping a fair coin, the possible outcomes are heads or tails.

But we do not know which one will come up until the coin is flipped. Randomness is a fundamental concept in probability theory and is used to model and analyze a wide range of phenomena.

Including games of chance, genetics, and quantum mechanics.

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If a function f is differentiable at a point a and f(a) is not equal to zero, then the absolute value function |f| is also differentiable at that point.

The proof involves considering two cases based on the sign of f(a) and showing that the limit of the difference quotient exists for |f| at point a in both cases. However, it is important to note that |f| is not differentiable at the point where f(a) equals zero.

To prove that if f is differentiable at a, then |f| is also differentiable at a, provided that f(a) ≠ 0, we need to show that the limit of the difference quotient exists for |f| at point a.

Let's consider the function g(x) = |x|. The absolute value function is defined as follows:

g(x) = {

x if x ≥ 0,

-x if x < 0.

Since f(a) ≠ 0, we can conclude that f(a) is either positive or negative. Let's consider two cases:

Case 1: f(a) > 0

In this case, we have g(f(a)) = f(a). Since f is differentiable at a, the limit of the difference quotient exists for f at point a:

lim (x→a) [(f(x) - f(a)) / (x - a)] = f'(a).

Taking the absolute value of both sides, we have:

lim (x→a) |(f(x) - f(a)) / (x - a)| = |f'(a)|.

Since |g(f(x)) - g(f(a))| / |x - a| = |(f(x) - f(a)) / (x - a)| for f(a) > 0, the limit on the left-hand side is equal to the limit on the right-hand side, which means |f| is differentiable at a when f(a) > 0.

Case 2: f(a) < 0

In this case, we have g(f(a)) = -f(a). Similarly, we can use the same reasoning as in Case 1 and conclude that |f| is differentiable at a when f(a) < 0.

Since we have covered both cases, we can conclude that if f is differentiable at a and f(a) ≠ 0, then |f| is also differentiable at a.

Note: It's worth mentioning that at the point where f(a) = 0, |f| is not differentiable. The proof above is valid when f(a) ≠ 0.

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Answer:

Answer: ∫ (x +1 + 1 x. )dx = 1. 2 x2 + x + ln|x| + C. 3. Evaluate the following integrals. (a) ∫. 2. 0 √4 − y2 dy.

The simplified expression for (f ∘ g)(x) is 2 + x (option d).

To find and simplify (f ∘ g)(x), we need to substitute the expression for g(x) into f(x) and simplify.

Given:

f(x) = log₃(9x)

g(x) = \(3^x\)

Substituting g(x) into f(x):

(f ∘ g)(x) = f(g(x)) = log₃\((9 * 3^x)\)

Now, we simplify the expression:

log₃\((9 * 3^x)\) = log₃(9) + log₃\((3^x)\)

Since logₓ(a * b) = logₓ(a) + logₓ(b), we have:

log₃(9) + log₃\((3^x)\) = log₃\((3^2)\) + x

Using the property logₓ\((x^a)\) = a * logₓ(x), we get:

log₃\((3^2)\) + x = 2 * log₃(3) + x

Since logₓ\((x^a)\) = a, where x is the base, we have:

2 * log₃(3) + x = 2 + x

Therefore, (f ∘ g)(x) simplifies to:

(f ∘ g)(x) = 2 + x

So, the correct answer is (d) 2 + x.

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Complete Question:

Given f(x)=log₃(9x) and g(x)=\(3^x\). Find and simplify (f ∘ g)(x)

(a) 2x

(b) x

(c) \(27^x\)

(d) 2+x

(e) None of these.

Answer:

0

Step-by-step explanation:

no mo explanation for this next time

Answer:

Step-by-step explanation:

1.In the equation there is no y-intercept so it will be at 0

2.The slope or rise over run is 3/1 and is positive because there are no negative signs. Going up 3 and to the right 1 is how to mark the points on your graph and the opposite side will be doing a -3 and -1 by going down three from the 0 points and to the left 1.

3.As seen in the graph there are the points given and the line directed on them.

4.We already determined that our slope is positive

m=3

b=0

Answer:

Hopes this helps

Step-by-step explanation:

Simplifying

10 + -13x = -8x + 25

Reorder the terms:

10 + -13x = 25 + -8x

Solving

10 + -13x = 25 + -8x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '8x' to each side of the equation.

10 + -13x + 8x = 25 + -8x + 8x

Combine like terms: -13x + 8x = -5x

10 + -5x = 25 + -8x + 8x

Combine like terms: -8x + 8x = 0

10 + -5x = 25 + 0

10 + -5x = 25

Add '-10' to each side of the equation.

10 + -10 + -5x = 25 + -10

Combine like terms: 10 + -10 = 0

0 + -5x = 25 + -10

-5x = 25 + -10

Combine like terms: 25 + -10 = 15

-5x = 15

Divide each side by '-5'.

x = -3

Simplifying

x = -3

Answer:

- 3

Step-by-step explanation:

Step 1:

10 - 13x = - 8x + 25    Equation

Step 2:

10 = 5x + 25    Add 13x on both sides

Step 3:

- 15 = 5x    Subtract 25 on both sides

Step 4:

- 15 ÷ 5   Divide

Answer:

x = - 3

Hope This Helps :)

Answer:

C

Step-by-step explanation:

The probability that a randomly selected housefly has a wing length between 4mm and 5mm is 0.7941 .

We have the following information from the question is:

Suppose a study finds that the wing lengths of houseflies are normally distributed with a mean of \(\mu=\) 4.55 mm

and standard deviation is: \(\sigma=\) 0.392 mm.

We have to find the probability that a randomly selected housefly has a wing length between 4 mm and 5 mm.

Now, According to the question:

Let X be the random variable that represents the wing lengths of a randomly selected housefly.

We use the formula :

z = \(\frac{x-\mu}{\sigma}\)

We have to calculate for x = 4 mm

\(z=\frac{4-4.55}{0.392}\) ≈ -1.40

Now, Calculate for x = 5mm

\(z=\frac{5-4.55}{0.392}\) ≈ 1.15

Therefore, the probability that a randomly selected housefly has a wing length between 4mm and 5mm is given by :

P(4 < X < 5) = P( -1.40 < X < 1.15)

P(1.15) - P(-1.40)  =  0.8749281 - 0.0807567

=> 0.7941714 ≈ 0.7942

Hence, the probability that a randomly selected housefly has a wing length between 4mm and 5mm is 0.7941 .

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Answer: get smart bro

you would know it if you was smart

Step-by-step explanation:

you wont do your work, you always cheat, and you don't listen to the teacher

you need to find the answer out on your own.

P.S. i hope you have a good day :)

Answer:

y = -1/3x + 4

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals of each other.  The equation for line y1 is 3x - 4  The slope is the coefficient of x, which is 3.  That means the slope of line y2 is -1/3, because it's the negative reciprocal.  As for the y-intercept, just look for the point on the y-axis that the line intercepts.  If we look closely, we can see it intercepts point (0,4) on the y-axis.  Therefore, the slope-intercept form equation for line y2 is:  y = -1/3x + 4.

Answer:

y=5-x/3

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

one apple and another equals to 2.

Answer: 11

Step-by-step explanation: you put one and one together lol

The name of every month ends in the letter y is the given statement. February is a counterexample to this statement. This is because February does not end with the letter 'y'. So the right  option is (c) February.

What is a counterexample?

In mathematics, a counterexample is an example that opposes or disproves a statement, proposition, or theorem. It is a scenario, an instance, or an example that goes against the given statement.

Therefore, a counterexample demonstrates that the given statement is false or invalid.In this case, the statement is: "The name of every month ends in the letter y." We have to find which of the months listed does not end in "y."February is the only month in the options listed that does not end in the letter "y."

Thus, it is a counterexample to the given statement. Therefore, the correct option is C, February.

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Answer:

Step-by-step explanation:

Hey mate I guess for this Question The Answer is "A"

Hope you Get it right!

Hey there! I'm happy to help!

How many times does 12 minutes go into 60 minutes?

60/12=5

Therefore, we are traveling 18 miles 5 times!

18(5)=90

Therefore, the boat will travel 90 miles in one hour!

Have a wonderful day! :D

The speedboat will go 90 miles in an hour.

What are the relations between time, speed and distance ?

Distance = Time x Speed.

Speed = (Distance/Time)

Time = (Distance/Speed)

Distance is the length we have travelled generally measured in kilo meters or in Miles.

Speed is the rate of change of position of an object with respect to time.

Time we all know what it is can in seconds, minutes, hour or in days.

In the given question

The speed boat travels 18 miles in 12 minutes

So, It will travel (18 x 60)/12 miles = 90 miles.

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No, nominal data is not rank ordered.

Nominal data, also known as categorical data, is a type of data that is used to label and classify groups of items based on characteristics and attributes.

It does not involve any measurement or numerical value and typically does not follow any order.

Nominal data is not measured in any way, so it does not have a ranking system.

In contrast, data that is rank-ordered, such as ordinal data, is measured and can be ranked from lowest to highest.

If you had a list of test scores from a group of students, the scores would be rank-ordered from lowest to highest.  

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3 kg of the drug costs Rs 18,000.

Using the provided information, we can put up a proportion to resolve this issue.

Assume that x is the price for 3 kg of the commodity.

The cost of 0.06 kg of the material, according to the information provided, is Rs 360.

The ratio can be set up as follows:

0.06 kg/Rs 360 equals 3 kg/x

We can cross-multiply and then solve for x to find the answer:

Rs 360 * 3 kg = 0.06 kg * x

0.06x = Rs 1080

We divide both sides of the equation by 0.06 to separate out x:

x = Rs 1080 / 0.06

x = Rs 18,000

Consequently, 3 kg of the drug costs Rs 18,000.

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Answer:

1445

Step-by-step explanation:

hey

\(4\frac{1}{6} +a=5\frac{2}{3}\) is the equation that has a=\(1\frac{1}{2}\) as its solution.

Two or more expressions with an Equal sign is called as Equation.

we need to find the equation which gives a=\(1\frac{1}{2}\)

Convert the mixed fraction to the improper fraction

a=3/2

\(4\frac{1}{6} +a=5\frac{2}{3}\)

Convert the mixed fraction to the improper fraction

25/6+a=17/3

Now take the variable on one side and constants on other sides

a=17/3-25/6

LCM of 3 and 6 is 6

a=34-25/6

a=9/6

The numerator and denominator are multiples of 3.

a=3/2

Hence, \(4\frac{1}{6} +a=5\frac{2}{3}\) is the equation that has a=\(1\frac{1}{2}\) as its solution.

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The circle can be illustrated by its equation, and the equation that represents the circle is (x + 4)² + (y - 9)² = 5²

The center of the circle is given as:

Center, (a,b) = (-4,9)

The diameter is given as:

d = 10

Calculate the radius (r)

r = 10/2 = 5

The circle equation is then calculated using:

(x - a)² + (y - b)² = r²

So, we have:

(x + 4)² + (y - 9)² = 5²

Hence, the equation that represents the circle is (x + 4)² + (y - 9)² = 5²

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Answer:

B on edge

Step-by-step explanation:

(x + 4)^2 + (y – 9)^2 = 25

Answer:

Length = 7 cm

Width = 2 cm

Step-by-step explanation:

Perimeter of rectangle = 18 cm

Let length of rectangle = \(l\) cm

Let width of rectangle =  \(w\) cm

As per given statement, length is 3 cm more than the twice of its width:

Writing equation:

\(l = 2\times w +3 ....... (1)\)

Formula for perimeter of a rectangle is given as:

\(P = 2 \times (Length + Width)\)

OR

\(P = 2 \times (l + w)\)

Putting values of P as given and \(l\) by using equation (1):

\(18 = 2 \times (2w +3 + w)\\\Rightarrow \dfrac{18}2 = 3w +3 \\\Rightarrow 9 = 3w +3\\\Rightarrow 3w = 9 -3\\\Rightarrow w = \dfrac{6}{3}\\\Rightarrow w = 2\ cm\)

Putting value of \(w\) in equation (1):

\(l = 2\times 2 +3 \\\Rightarrow l = 4+3\\\Rightarrow l = 7\ cm\)

So, the dimensions are:

Length = 7 cm

Width = 2 cm

Answer:

\(x^2 - 8x + 7 = 0\)

Step-by-step explanation:

Let the boy's present age be x.

Let his dad's present name be y.

Last year, his dad was 8 times as old as him. Subtract one year from each their ages and multiply the son's age by 8:

(y - 1) = 8(x - 1) ______ (1)

Now, his dad's age is the square of his age:

y = \(x^2\) _________(2)

From (1):

y = 8x - 8 + 1

y = 8x -7

Put this in (2):

\(8x - 7 = x^2\\\\=> x^2 - 8x + 7 = 0\)

This problem has been represented in the form of a quadratic equation.

Answer:

3/4

Step-by-step explanation:

When converting time from 12 hour to 24 hour format, you need to make sure if it's AM or PM and add or not 12 hours accordingly. To convert 16:00 p.m. to military time, you need to add 12 hours to the time.

Military time, also known as 24-hour time, is a way of expressing time that is commonly used in the military, but is also used in other settings such as transportation and emergency services. It is different from the 12-hour time that is typically used in everyday life.

To convert 16:00 p.m. to military time, you need to add 12 hours to the time. This is because 16:00 p.m. is the 16th hour of the day, but military time starts counting at 00:00 and goes up to 23:59. So, 16:00 p.m. in 12-hour time would be the same as 16+12=28 in military time. However, since military time uses only two digits to represent the hour, we need to subtract 24 from the result. This gives us 28-24=04:00.

So, 16:00 p.m. in 12-hour time would be equivalent to 04:00 in military time.

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The parametric equation of the circle of radius 4 centered at (4,3), traced counter-clockwise starting on the y-axis when t=0 is x = 4*cos(t) + 4 and y = 4*sin(t) + 3. This circle can be traced out by varying the parameter t from 0 to 2π.

To find the parametric equation of the circle of radius 4 centered at (4,3), we can use the following formula:
x = r*cos(t) + a
y = r*sin(t) + b
where r is the radius, (a,b) is the center of the circle, and t is the parameter that traces out the circle.
In this case, r = 4, a = 4, and b = 3. We also know that the circle is traced counter-clockwise starting on the y-axis when t=0.
Plugging in these values, we get:
x = 4*cos(t) + 4
y = 4*sin(t) + 3
This is the parametric equation of the circle of radius 4 centered at (4,3), traced counter-clockwise starting on the y-axis when t=0. The parameter t ranges from 0 to 2π in order to trace out the entire circle.
Answer: The parametric equation of the circle of radius 4 centered at (4,3), traced counter-clockwise starting on the y-axis when t=0 is x = 4*cos(t) + 4 and y = 4*sin(t) + 3. This circle can be traced out by varying the parameter t from 0 to 2π.

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P2, P3, P1 is a safe sequence according to the banker's algorithm.

The banker's algorithm gets its name from the fact that it determines whether or not a person should be granted a loan amount in order to assist the bank system in securely simulating resource allocation. In this part, we'll go through the Banker's Algorithm in depth. The Banker's Algorithm is primarily used in the banking system to avoid stalemate. It assists you in determining whether or not a loan will be granted. This procedure is used to assess the allocation for securely replicating the maximum amount available for all resources.

Here,

According to the banker's algorithm, the sequence P2, P3, P1 is secure.

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