Andrea has 2 times as many stuffed animals as Tyronne. Put together, their collections have 42 total stuffed animals. How many stuffed animals does Andrea have? How many stuffed animals are in Tyronne's collection?

Answer:

23

13

13/23

Step-by-step explanation:

The solution to the given differential equation with initial condition y(1) = 2 is y = x/2 + (ln(x)/x) - (1/(2x)) + Ce^(-x).

Given differential equation is dx + y= x + 25x²ln(x)

We have to find the solution to the first-order linear differential equation by using the Integrating Factor Technique.

Solution:

We can write the given differential equation in the form of dy/dx + p(x)y = q(x),where p(x) = 1 and q(x) = x + 25x²ln(x)

Now, we need to calculate the integrating factor (I.F), which is given by I.F = e^(∫p(x)dx).

We have p(x) = 1.

I.F = e^(∫ dx)

I.F = e^(x)

Now, we need to multiply both sides of the given differential equation by the integrating factor (I.F), we get I.F

dy/dx + I.F

y = I.F(x + 25x²ln(x)).

Substitute the values of I.F, p(x), and q(x).

We have I.F = e^(x)

And, p(x) = 1 and q(x) = x + 25x²ln(x).

Therefore, e^(x)dy/dx + e^(x)y = xe^(x) + 25x²ln(x) e^(x)

Multiply the integrating factor e^(x) with the given differential equation.

dx e^(x)dy + e^(x)ydx = xe^(2x)dx + 25x²ln(x)e^(x)dx

Integrating both sides, we get,

e^(x)y = ∫xe^(2x)dx + ∫25x²ln(x)e^(x)dx

Integrating the first integral by the substitution method.

Substitute u = 2x, du = 2 dx, and dx = du/2.

The integral becomes

(1/2) ∫ue^(u)du = (1/2)ue^(u) - (1/2) ∫e^(u)du

= (1/2)ue^(u) - (1/2)e^(u)

= (u - 1/2)e^(u)

Substituting back the value of u, we get,

(1/2) ∫ue^(u)du = (x - 1/2)e^(2x)

The second integral, we can solve by parts method.

Let u = ln(x), dv = e^(x)dxdu/dx = 1/xv = e^(x)

So, the integral becomes

∫ln(x)e^(x)dx = ln(x) e^(x) - ∫(1/x) e^(x)dx

= ln(x) e^(x) - e^(x)/x + C

Now, substituting the values of both integrals in the solution obtained above,

e^(x)y = (x - 1/2)e^(2x) + ln(x) e^(x) - e^(x)/x + C

On simplifying and solving for y, we get

y = x/2 + (ln(x)/x) - (1/(2x)) + Ce^(-x)

This is the solution to the given differential equation with initial condition y(1) = 2.

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Given statement 'a local variable is a variable defined inside a function that can only be used inside its function' is False

A local variable is a type of variable that we declare inside a block or a function, unlike the global variable. They can be used only by the statements that are inside the function or the block of the code. Local variables are not known to functions outside their own.

The variable declared is local within that function that is the declared variable is accessible inside that block itself, it cannot be accessible outside the given function.

Consider the following multiplication function:

ex - void multi()

{

int a = 10,  b = 2, c ;

c = a * b ;

cout << c ;

}

int main()

{

cout << "value for c is :"<< c ;

return 0;

}

Here inside the multi function variable a, b, c are declared and initialized inside the function.

Thus, a local variable is defined inside the body of the function and is not accessible outside of the function.

Therefore, given statement 'a local variable is a variable defined inside a function that can only be used inside its function' is False

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Answer:

0.15

Step-by-step explanation:

Answer:

1 1/24

Step-by-step explanation:

Pls give brainly if right :) also not 11 its 1u 1/24

Answer: Area = x^2 + 12x + 35

Step-by-step explanation:

The area of the entire rectangle can be found by adding the areas of the four rectangles:

Area = (x)(x) + (x)(7) + (5)(x) + (5)(7)

Simplifying each term, we get:

Area = x^2 + 7x + 5x + 35

Combining like terms, we get:

Area = x^2 + 12x + 35

So the area of the entire rectangle is a polynomial in standard form given by x^2 + 12x + 35.

The area of the entire rectangle is found by multiplying the length (x + 5) by the width (x + 7), which gives a polynomial in the standard form of x^2 + 12x + 35.

The area of a rectangle is calculated by the formula: Area = length ✖ width. Here, the length is expressed as 'x + 5' and the width as 'x + 7'.

To find the area, we need to multiply the length by the width.

(x + 5)(x + 7) = x^2 + 7x + 5x + 35 = x^2 + 12x + 35

The area of the entire rectangle is thus x^2 + 12x + 35, which is a polynomial in standard form.

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The prime factorization of the radicand 2 is 9√15.

A number can be expressed as the product of its prime components through the process of prime factorization. A number with precisely two elements, 1 and the number itself, is said to be a prime number.

As an illustration, let's use the number 30. We know that 30 = 5 × 6, but 6 is not a prime number. The number 6 can further be factorized as 2 × 3, where 2 and 3 are prime numbers. Therefore, the prime factorization of 30 = 2 × 3 × 5, where all the factors are prime numbers.

Given that,

x= 3√135

Solving the equation further using the rule √A*B = √A*√B

x= 3√9*15

x= 3√9*√15

x=3*3*√15

x= 9√15

Therefore, the prime factorization of the radicand 2 is 9√15.

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The probability distributions whose graphs can be approximated by bell-shaped curves are commonly known as normal distributions or Gaussian distributions.

These distributions are characterized by their symmetrical shape and the majority of their data falling within a certain range around the mean. The normal distribution is widely used in statistics and is a fundamental concept in many fields of study, including psychology, economics, and engineering. The normal distribution is also known for its many practical applications, such as predicting test scores, stock prices, and medical diagnoses. In summary, the bell-shaped curve is a useful tool in probability theory that can help us understand and make predictions about a wide range of phenomena. The probability distributions whose graphs can be approximated by bell-shaped curves are called Normal Distributions or Gaussian Distributions. They have a symmetrical shape and are characterized by their mean (µ) and standard deviation (σ), which determine the central location and the spread of the distribution, respectively.

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Answer:

×=4

y=4

Step-by-step explanation:

simplify then multiply both sides

The correct answer is A. The standard error of the sample proportion will become larger as the sample size increases.

The standard error is a measure of the variability or uncertainty associated with an estimate. In the case of the sample proportion, it measures the spread or variability in the proportion of successes observed in the sample compared to the true population proportion.

As the sample size increases, the standard error decreases, indicating greater precision in estimating the true population proportion. This is because a larger sample provides more information and reduces the impact of sampling variability.

On the other hand, options B, C, and D are incorrect. The standard error is not affected by the population proportion itself but rather by the sample size. The population proportion approaching 0.50, 1.00, or 0 does not directly impact the standard error, although it may affect other measures such as the margin of error or confidence intervals. The primary factor influencing the standard error is the sample size, with larger samples leading to smaller standard errors.

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Y in represents the following in this linear regression Y = α₀+α₁X+α₂X₂+ε: C. dependent variable.

In Mathematics and Geometry, a regression line is a statistical line that best describes the behavior of a data set. This ultimately implies that, a regression line simply refers to a line which best fits a set of data.

In Mathematics and Geometry, the general functional form of a linear regression can be modeled by this mathematical equation;

Y = α₀+α₁X+α₂X₂+ε

Where:

In conclusion, Y represent the dependent variable or response variable in a linear regression.

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Answer:

\(x\geq 3\)

Step-by-step explanation:

Answer:

\(\frac{2t-4}{3}\)

Step-by-step explanation:

\(\frac{2}{3}\)\((t-2)\\\)
=> \((\frac{2}{3} * t ) + (\frac{2}{3} * -2)\)
=> \(\frac{2t}{3} + (-\frac{4}{3})\)
=> \(\frac{2t-4}{3}\)

Hope you understood!!

Answer:

X = 5

Step-by-step explanation:

multiply what is in the ( )

-2 ( -2)

-2 ( 9)

3x -5 +2x -18 = 2

combine like terms

5x -23 = 2

add 23 to both sides

5x = 25

divide 25 by 5

X = 5

Answer:

40

Step-by-step explanation:

Once you plot the data, the middle values will be 39 and 41. To calculate the median, you add them up and divide by two, which will result in 40!

Median is the middle value.

Write the numbers out from smallest to largest:

35, 38, 38, 39, 39, 41, 42, 43, 43, 44

There are 10 total numbers, find the middle two:

39 and 41

Add them Together and divide by 2:

39 + 41 = 80

80/2 = 40

Median = 40

Answer:

$ 612 is her monthly payment

Step-by-step explanation:

$3,600/6 = 600

600 + 12 = 612

Answer:600

Step-by-step explanation:

Answer:

Step-by-step explanation:

originally she had to put in 3 cups

she accidentally put in 3

the amount of extra cups is 6-3

=3

-12 + _ = -20

-12 + (-18) = -20✔

so the answers is = -18

The normal vector, f, to the surface of the inner conductor is a unit vector in the radial direction, pointing away from the conductor.

a. The normal vector, f, to the surface of the inner conductor is a unit vector in the radial direction, pointing away from the conductor.

b. The boundary condition at the surface of the conductor (medium 2) is that the normal component of the electric field is equal to the surface charge density.

c. The boundary condition in the dielectric (medium 1) is that the tangential component of the electric field is equal to zero.

d. The surface charge density, Ps, at the surface of the conducting cylinder is P.

The complete question is:

An infinitely long conducting cylinder of radius a (medium 2) has a surface charge density P. The cylinder is surrounded by a dielectric (Er = 4, medium 1) that contains no free charges (that is to say p = 0 inside the dielectric). Defining 2 as the axis of the conducting cylinder, the electric field, E, inside the dielectric medium (whenra) is found as: E = Er*sin(θ)/r.

a. What is the normal vector, f, to the surface of the inner conductor?

b. What is the boundary condition at the surface of the conductor (medium 2)?

c. What is the boundary condition in the dielectric (medium 1)?

d. What is the surface charge density, Ps, at the surface of the conducting cylinder?

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f(x) represents the long-term average temperature in degrees Celsius at the Willburn Airport and x represents the month of the year. The temperature will be 17°C at two specific months of the year .

To determine the months when the temperature is 17°C, we need to solve the equation f(x) = 17, where f(x) represents the long-term average temperature in degrees Celsius at the Willburn Airport and x represents the month of the year. The specific form of the equation is not provided in the question, so we cannot determine the exact months without further information about the equation or temperature data.

The equation f(x) = 17 represents the condition for the temperature to be 17°C, and by solving this equation, The specific form of the equation is not provided in the question, so we cannot determine the exact months without further information about the equation or temperature datawe can identify the corresponding months. However, without the specific form of the equation or additional information, we cannot provide a definitive answer regarding which months temperature will be 17°C at the Willburn Airport.

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#Complete Question

They have a $30 advertising budget. A front-page ad is more effective than an ad inside the paper. They want to advertise at least 20 times. The best strategy is to use as many front-page ads as possible. They can place 15 front-page ads and five inside page ads within their budget.

Math Club members have a $30 advertising budget, and they want to advertise their fundraiser each week in the school paper. They know that a front-page ad is more effective than an ad inside the paper. It cost $2 for each front-page ad and $1 for each inside page ad. The club wants to advertise at least 20 times.

The club can decide to use inside page ads for the remaining five ads. The cost for each inside page ad is $1. Therefore, they can purchase five inside page ads for a total cost of $5. The remaining $5 in their budget will not be used.To summarize, the Math Club members will advertise their fundraiser each week in the school paper.

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Answer:

17.3

Step-by-step explanation:

I had a test and this is what they had as the answer.

Answer:

Angle c = 118 degrees

Step-by-step explanation:

c is 118 because c is congruent to <A and it is verticle from <A

Calculate (4 + 10i)²To calculate (4 + 10i)², we can use the formula (a + bi)² = a² + 2abi + (bi)²: (4 + 10i)²

= 4² + 2(4) (10i) + (10i)²

= 16 + 80i - 100= -84 + 80i(ii) Hence, and without using a calculator, determine all solutions of the quadratic equation z² +6iz + 12 – 20i= 0.

Now, we can substitute z = a + bi and separate the real and imaginary parts: z² + 6iz + 12 - 20i

= 0 (a + bi)² + 6i(a + bi) + 12 - 20i

= 0 a² + 2abi - b² + 6ai + 6bi² + 12 - 20i

= 0 Now, we can equate the real and imaginary parts to get a system of two equations: a² - b² + 6a + 12

= 0 ...(1) 2ab + 6b - 20

= 0 ...(2)From equation (2), we get:b(2a + 6)

= 20b

= 10 / (a + 3)Substituting b into equation (1):a² - (10 / (a + 3))² + 6a + 12 = 0We can simplify by multiplying everything by (a + 3)²: (a + 3)²a²(a + 3)² - 10² + 6a(a + 3)² + 12(a + 3)² = 0 (a + 3)²a⁴ + 6a³ + 9a² - 100 + 18a³ + 54a² + 36a + 108

= 0a⁴ + 24a³ + 81a² + 36a + 8

= 0

Now, we can solve this equation using the Rational Root Theorem and synthetic division. The only rational roots are ±1, ±2, ±4, and ±8. By testing these roots, we get that a = -1 is a root. Dividing a⁴ + 24a³ + 81a² + 36a + 8 by a + 1 using synthetic division gives us:(a + 1)(a³ + 23a² + 58a + 8) = 0

Now, we can use the cubic formula to solve the cubic equation a³ + 23a² + 58a + 8 = 0. However, this is a tedious and time-consuming process, so we can instead use the fact that there is a root close to -3. Substituting a = -3 + x, we get:(x - 1)(x² + 20x + 2) = 0Now, we can solve the quadratic equation x² + 20x + 2 = 0 using the quadratic formula. This gives us:x

= -10 + 2√23 or x

= -10 - 2√23Therefore, the solutions of the quadratic equation z² + 6iz +   12 - 20i

= 0 are:-3 - 5i + √23i and -3 + 5i - √23i(b)Determine all solutions of z² + 6z + 5 = 0.Now, we can use the quadratic formula to solve the quadratic equation z² + 6z + 5

= 0. This gives us:z

= (-6 ± √(6² - 4(1)(5))) / (2(1))= (-6 ± √16) / 2

= -3 ± 2Therefore, the solutions of the quadratic equation z² + 6z + 5

= 0 are:-1 and -5.

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The graph of f(x)=−x^2 is a downward-opening parabola.

The graph of f(x)=−x^2 represents a quadratic function.

In this case, the coefficient of is -1, indicating that the parabola opens downwards. The negative sign in front of reflects the reflection of the graph across the x-axis.

The vertex of the parabola is located at the point (0, 0), which is the origin of the coordinate system. As we move to the left or right from the vertex, the function values decrease since the coefficient of is negative.

The graph is symmetrical with respect to the y-axis, meaning that for every x-value to the right of the vertex, there is a corresponding x-value to the left of the vertex that produces the same function value.

As x approaches positive or negative infinity, the function values also approach negative infinity. This indicates that the graph decreases without bound as x moves further away from the vertex in either direction.

Overall, the graph of f(x)=−x^2 is a downward-opening parabola that is symmetrical with respect to the y-axis and has its vertex at the origin (0, 0). It represents a quadratic function with a negative coefficient of resulting in a decreasing graph as x moves away from the vertex.

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To shoot a 20-cm-long arrow parallel to the axle and through the wheel without hitting any spokes, the arrow should be aimed at a point on the circumference of the wheel that is 4 cm away from any spoke.

The diameter of the wheel is 60 cm (2 x radius), so the circumference is 188.5 cm (π x diameter). Since the arrow is 20 cm long, it must pass through the wheel at a point that is at least 20 cm away from any spoke. To find this point, divide the circumference of the wheel by the number of spokes (which is not given in the problem).

Since the spokes are equally spaced, this will give the minimum distance between any two spokes. For example, if there are 6 spokes, the distance between each spoke is 31.4 cm (188.5 / 6). Therefore, the arrow should be aimed at a point on the circumference of the wheel that is 4 cm (20 / 5) away from any spoke.

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Answer:3/5

Step-by-step explanation:

(y2-y1)/(x2-x1)

(2-(-1))/(6-1)=3/5

2. The exact value of sin (185° - 65°) is (√3/2)(cos (65°)) - (1/2)(sin (65°)).

3. The exact value of tan 255° is (1/√3 - √3)/2.

The sine function has a range of values between -1 and 1, and it is a periodic function that repeats every 2π radians or 360 degrees.

We can use the difference identity for sine to find the exact value of sin (185° - 65°):

sin (185° - 65°) = sin 185° cos 65° - cos 185° sin 65°

Since sin (180° + x) = -sin x and cos (180° + x) = -cos x to simplify the expression:

sin (185° - 65°) = sin (120°) cos (65°) + cos (120°) sin (65°)

= (√3/2)(cos (65°)) + (-1/2)(sin (65°))

= (√3/2)(cos (65°)) - (1/2)(sin (65°))

Therefore, the exact value of sin (185° - 65°) is (√3/2)(cos (65°)) - (1/2)(sin (65°)).

Here,

tan 255° = tan (225° + 30°)

Using the tangent sum identity, we get:

tan (225° + 30°) = (tan 225° + tan 30°)/(1 - tan 225° tan 30°)

Since tan 225° = tan (225° - 180°) = tan (-45°) = -1 and tan 30° = (√3)/3, we can substitute these values:

tan 255° = (-1 + (√3)/3)/(1 + 1/√3)

Simplifying the denominator by rationalizing the denominator, we get:

tan 255° = (-1 + (√3)/3)/(√3 + 1)

Multiplying the numerator and denominator by (√3 - 1), we get:

tan 255° = [(-1 + (√3)/3)(√3 - 1)]/[(√3 + 1)(√3 - 1)]

= [(√3 - 1 - 1 + 1/√3)]/(2)

= [√3 - 2 + 1/√3]/2

= (1/√3 - √3)/2

Therefore, the exact value of tan 255° is (1/√3 - √3)/2.

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Considering the conditions given in the question, the appropriate assignments of digits would be, let 0 and 1 = winner. let 2-5 = not a winner. skip 6-9.

The likelihood of an event occurring is defined by probability. There are numerous instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not. In general, probability has many wonderful uses in games, in business to make forecasts based on likelihood, and in this emerging branch of artificial intelligence.

Information about the possibility that something will happen is provided by probability. For instance, meteorologists utilize weather patterns to forecast the likelihood of rain. Probability theory is utilized in epidemiology to comprehend the connection between exposures and the risk of health outcomes.

An appropriate assignment of digits would be:

let 0 and 1 = winner. let 2-5 = not a winner. skip 6-9.

This assignment is appropriate because it accurately reflects the probability of the wheel landing on "winner." There is a 1 in 5 chance that the wheel will land on "winner," so assigning 2 digits (0 and 1) to represent "winner" and the other 3 digits (2, 3, 4, and 5) to represent "not a winner" accurately reflects this probability. Skipping the digits 6 through 9 is also appropriate because they are not needed for this simulation.

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