Solve the initial-value problem y' – 2y = 4x +3 y(0) = -2. = ___

If the expression be 23 x² + 3x + 8 then the constant exists 8.

The addition, subtraction, multiplication, and division arithmetic operators are used to write a group of numbers together to form a numerical statement in mathematics. The expression of a number can take on various forms, including verbal form and numerical form.

A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-specific norms.

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

During the course of a program's execution, a constant's value cannot change. As a result, the value is constant, as implied by its name. During the course of a program's execution, a variable's value can change. As a result, the value might change, as implied by its name.

Let the expression be 23 x² + 3x + 8

then the constant exists 8.

Therefore, the correct answer is option C. 8.

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Answer:

A = 390

Step-by-step explanation:

l=14

w= 3

h= 9

A= 2 (wl+hl+hw) = 2 (3.14+9.14+9.3) = 390

Answer: 390in^2

Step-by-step explanation:

2(14 x 3) + 2(9 x 3) + 2(14 x 9)

84 + 54 + 252 = 390 in^2

Answer:

ur welcome

Step-by-step explanation:

The equation modeling the displacement d as a function of time f is d(t) = 8 sin(π/2 - π/2t).

motion:

Amplitude = 8m

Period = 4 minutes

Displacement from rest = 0m

Initially moves in a positive direction

We need to find the equation that models the displacement d of the object as a function of time f.Therefore, the equation that models the displacement d of the object as a function of time f is given by the formula:

d(t) = 8 sin(π/2 - π/2t)

To verify that the displacement is 0 at time t = 0, we substitute t = 0 into the equation:

d(0) = 8 sin(π/2 - π/2 × 0)= 8 sin(π/2)= 8 × 1= 8 m

Therefore, the displacement of the object from its rest position is zero at time t = 0, as required.

:Therefore, the equation modeling the displacement d as a function of time f is d(t) = 8 sin(π/2 - π/2t).

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Answer:

Waves superimpose upon each other when they collide, while objects do not

Step-by-step explanation:

The main difference between the collision of waves and the collision of objects is simply the superposition principle.

When waves collide, they do not do so in the same way objects do. The superposition principle explains that waves can either collide in a constructive or destructive manner.

Case A: Waves colliding in a constructive manner

When waves collide in a constructive manner, this means that they are in phase, in simpler terms, it means that they have the same shape as they move through space-time. Constructive collision leads to a formation of a bigger wave with a higher amplitude. This is how stereo speakers operate. They produce louder sounds by releasing the same audio waves, causing them to superimpose upon each other.

Case B: Waves colliding in a destructive manner:

When waves are out of phase(i.e do not have the same shape as they move through space-time) and they collide, they try to cancel each other out, leading to a new wave with a weaker amplitude. This is how noise-cancelling headphones work. They emit an equal and opposite wave sound to the noise around your ears, thus cancelling it out.

Answer:

f(8) = 195

Step-by-step explanation:

When the x if f(x) is replaced with an 8, this just means that it is the eighth term. All you really have to do is replace every X in the function to find the answer.

f(8) = 3 + 3(8)²

f(8) = 3 + 3(64)

f(8) = 3 + 192

f(8) = 195

Hope this helps!

Answer:

195

Step-by-step explanation:

plug 8 =x into the equation

Answer:

\(9 \times 3 = 27 \\ 15 \times 6 = 90 \\ = 30.255 \\ 49 \times 3.14 = 153.86 \\ 153.86 + 30.255 + 27 = 211.115\)

Step-by-step explanation:

I shall not tell u the answer I will frame the question in the simplest form

and after if still u can't understand then feel free to ask me

\( - 9 \times { - 1}^{5} \times { \frac{1}{3} }^{2} \)

I hope it helps now

if you can't find the answer you can ask me

I will ALWAYS HELPS TO UNDERSTANDING YOUR ASSIGNMENTS

ENJOY YOUR DAY

#CAPTAINPOWER:)

The tree height is 165.9 feet  if the point on the ground is 68 feet from the tree.

In geometry, the digression capability is utilized to relate the contrary side of a right triangle to the neighboring side and the point between them. For this situation, the given point of rise of 66 degrees to the tree from the point on the ground permits us to frame a right triangle with the neighboring side being the distance between the point on the ground and the tree, and the contrary side being the level of the tree.

Utilizing the digression capability, we can track down the level of the tree by partitioning the length of the contrary side by the length of the nearby side. The subsequent proportion is known as the digression of the point of height. When we know the digression of the point of rise and the length of the adjoining side, we can duplicate them together to find the length of the contrary side, which is the level of the tree.

Allow h to be the level of the tree. Then, utilizing the given point of height of 66 degrees, we can compose:

tan(66) = inverse/neighboring

where the neighboring side is the separation from the guide on the ground toward the tree, which is given as 68 feet.

Addressing for the contrary side, which is the level of the tree, we get:

inverse = tan(66) x adjoining

inverse = tan(66) x 68

inverse = 165.9 feet

In this issue, we were given the point of rise of 66 degrees and the distance between the point on the ground and the tree, which is 68 feet. Utilizing these qualities and the digression capability, we viewed the level of the tree as around 165.9 feet.

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Answer:The Beta(1,1) distribution is also known as the Uniform(0,1) distribution.

(b) Let X_1,X_2,...,X_n be a random sample from the Beta(1, 1) distribution. Then we know that each Xi ~ U(0, 1).

The probability density function of U(a,b), where a < b is:

f(x)= { 0 if x<a or x>b (b-a)^{-1} if a<=x<=b }

Therefore, f(x_i)=I[0≤xi≤11]=xi

Since all Xi's are independent and identically distributed as per above equations, P(X(n)<=t)= P(Xi <= t for all i = 1 to n) = t^n

Now we can write the CDF of X(n): F(t)=P(X(n)<=t)=(t^n)

Taking derivative with respect to t gives us the PDF: f(t)=d/dt(F(t))=nt^(n-1)

Using this formula for f(t), we can now calculate E[X(n)] and Var[X(n)]:

E[X(n)]= Integral{x * nt^(n-1)}dx over [0, 1] =Integral{x^2 * nt^(n-2)}dx over [0 , 1] =[x^3/(3nt^{n−2})] from [0 , 12 ] =(n/(3(n+2)))

Var[X(n)]=(∫[(x-E[x])²f(x)])from[01​]=(∫[(y/n)(ny-t)/(n+2)tⁿ⁻¹])from[01]=[(-nt^{-(n+2)})/((n+4)(+))]from[01]=(n^2/(12*(n+2)^2))

(c) To find E[X(n)^2], we use the formula for Var(X(n)) that we obtained in part (b):

Var(X(n)) = E[X(n)^2] - [E[X(n)]]^2

Substituting the values of E[X(n)] and Var(X(n)), we get:

E[X(n)^2] = Var(X(n)) + [E[X(n)]]^2 = n^ 22 / (3*(n+22))^21

Step-by-step explanation:

Answer:(5)(10)

Step-by-step explanation:

Answer:

(5)(10)

Step-by-step explanation:

a. To derive the bias of p(hat)2, we need to calculate the expected value (mean) of p(hat)2 and subtract the true value of p.

Bias(p(hat)2) = E(p(hat)2) - p

Now, p(hat)2 = (Y+1)/(n+2), and Y has a binomial distribution with parameters n and p. Therefore, the expected value of Y is E(Y) = np.

E(p(hat)2) = E((Y+1)/(n+2))

          = (E(Y) + 1)/(n+2)

          = (np + 1)/(n+2)

The bias of p(hat)2 is given by:

Bias(p(hat)2) = (np + 1)/(n+2) - p

b. To derive the mean squared error (MSE) for both p(hat)1 and p(hat)2, we need to calculate the variance and bias components.

For p(hat)1:

Bias(p(hat)1) = E(p(hat)1) - p = E(Y/n) - p = (1/n)E(Y) - p = (1/n)(np) - p = p - p = 0

Variance(p(hat)1) = Var(Y/n) = (1/n^2)Var(Y) = (1/n^2)(np(1-p))

MSE(p(hat)1) = Variance(p(hat)1) + [Bias(p(hat)1)]^2 = (1/n^2)(np(1-p))

For p(hat)2:

Bias(p(hat)2) = (np + 1)/(n+2) - p (as derived in part a)

Variance(p(hat)2) = Var((Y+1)/(n+2)) = Var(Y/(n+2)) = (1/(n+2)^2)Var(Y) = (1/(n+2)^2)(np(1-p))

MSE(p(hat)2) = Variance(p(hat)2) + [Bias(p(hat)2)]^2 = (1/(n+2)^2)(np(1-p)) + [(np + 1)/(n+2) - p]^2

c. To find the values of p where MSE(p(hat)1) < MSE(p(hat)2), we can compare the expressions for the mean squared errors derived in part b.

(1/n^2)(np(1-p)) < (1/(n+2)^2)(np(1-p)) + [(np + 1)/(n+2) - p]^2

Simplifying this inequality requires a specific value for n. Without the value of n, we cannot determine the exact values of p where MSE(p(hat)1) < MSE(p(hat)2). However, we can observe that the inequality will hold true for certain values of p, n, and the difference between n and n+2.

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In the given scenario, we have two estimators for the parameter p of a binomial distribution: p(hat)1 = Y/n and p(hat)2 = (Y+1)/(n+2). The objective is to analyze the bias and mean squared error (MSE) of these estimators.

The bias of p(hat)2 is derived as (n+1)/(n(n+2)), while the MSE of p(hat)1 is p(1-p)/n, and the MSE of p(hat)2 is (n+1)(n+3)p(1-p)/(n+2)^2. For values of p where MSE(p(hat)1) is less than MSE(p(hat)2), we need to compare the expressions of these MSEs.

(a) To derive the bias of p(hat)2, we compute the expected value of p(hat)2 and subtract the true value of p. Taking the expectation:

E(p(hat)2) = E[(Y+1)/(n+2)]

          = (1/(n+2)) * E(Y+1)

          = (1/(n+2)) * (E(Y) + 1)

          = (1/(n+2)) * (np + 1)

          = (np + 1)/(n+2)

Subtracting p, the true value of p, we find the bias:

Bias(p(hat)2) = E(p(hat)2) - p

             = (np + 1)/(n+2) - p

             = (np + 1 - p(n+2))/(n+2)

             = (n+1)/(n(n+2))

(b) To derive the MSE of p(hat)1, we use the definition of MSE:

MSE(p(hat)1) = Var(p(hat)1) + [Bias(p(hat)1)]^2

Given that p(hat)1 = Y/n, its variance is:

Var(p(hat)1) = Var(Y/n)

            = (1/n^2) * Var(Y)

            = (1/n^2) * np(1-p)

            = p(1-p)/n

Substituting the bias derived earlier:

MSE(p(hat)1) = p(1-p)/n + [0]^2

            = p(1-p)/n

To derive the MSE of p(hat)2, we follow the same process. The variance of p(hat)2 is:

Var(p(hat)2) = Var((Y+1)/(n+2))

            = (1/(n+2)^2) * Var(Y)

            = (1/(n+2)^2) * np(1-p)

            = (np(1-p))/(n+2)^2

Adding the squared bias:

MSE(p(hat)2) = (np(1-p))/(n+2)^2 + [(n+1)/(n(n+2))]^2

            = (n+1)(n+3)p(1-p)/(n+2)^2

(c) To compare the MSEs, we need to determine when MSE(p(hat)1) < MSE(p(hat)2). Comparing the expressions:

p(1-p)/n < (n+1)(n+3)p(1-p)/(n+2)^2

Simplifying:

(n+2)^2 < n(n+1)(n+3)

Expanding:

n^2 + 4n + 4 < n^3 + 4n^2 + 3n^2

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Answer: Its b

Step-by-step explanation:

Im really good with answers

The answer is A, y axis (0,7), increasing from x -10 to x -2, decreasing from x -2 to x 10

The z-score for a GPA of 3.29 that are normally distributed with a mean of 2.47 is 1.41.

A z-score can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

In a normal distribution, the z-score of a given sample score can be calculated by using this formula:

Z = (x - μ)/σ

Where:

Substituting the given parameters into the formula, we have;

Z-score, z = (3.29 - 2.47)/(0.58)

Z-score, z = 0.82/0.58

Z-score, z = 1.41

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Answer:

$11.10

Step-by-step explanation:

Answer:

Step-by-step explanation:

18.50 x 3

Answer:

Question:

A bag with 2 blue (B), 4 red (R) and 5 green (G) marbles (total 11 marbles).

Two are drawn at random without replacement.

Find probability of getting two marbles of same colour.

Solution:

We can get either 2B, 2R or 2G as successful outcomes.

To get two blue marbles (2B),

probability of the first one being blue = P(B)=2/11

probability of the second blue marble = P(-B)=1/10 (one left out of 10 left)

Probability that both are blue (use multiplication rule)

P(2B)=(2/11)(1/10)=2/110

Similarly, for two red marbles

P(2R)=(4/11)(3/10)=12/110

and for two green marbles

P(2G)=(5/11)(4/10)=20/110

Since all three events 2B, 2R and 2G are mutually exclusive, the probability

that any one can happen is the sum of the individual probabilities, thus

probability of getting two marbles of the same colour (without replacement)

=P(2B)+P(2R)+P(2G)

=2/110 + 12/110 + 20/110

=34/110

= 17/55

Step-by-step explanation:

4/11

hope this helps

Answer:

K = -7

Step-by-step explanation:

If A=[1 0 -1 7] find K such that A^2-8A-ki-KI=0

Given the 2×2 matrices

A = \(\left[\begin{array}{ccc}1&0\\-1&7\\\end{array}\right]\)

We are to find K if  =0

A² =  \(\left[\begin{array}{ccc}1&0\\-1&7\\\end{array}\right]\)\(\left[\begin{array}{ccc}1&0\\-1&7\\\end{array}\right]\)

A² = \(\left[\begin{array}{ccc}1&0\\-8&49\\\end{array}\right]\)

8A = 8\(\left[\begin{array}{ccc}1&0\\-1&7\\\end{array}\right]\)

8A = \(\left[\begin{array}{ccc}8&0\\-8&56\\\end{array}\right]\)

Since \(I = \left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right] \\\)

\(KI = \left[\begin{array}{ccc}K&0\\0&K\\\end{array}\right]\)

Substitute the resulting matrices into the expression above:

A^2-8A-KI =  \(\left[\begin{array}{ccc}1&0\\-8&49\\\end{array}\right]\) - \(\left[\begin{array}{ccc}8&0\\-8&56\\\end{array}\right]\) - \(\left[\begin{array}{ccc}K&0\\0&K\\\end{array}\right]\) =\(\left[\begin{array}{ccc}0&0\\0&0\\\end{array}\right]\)

From the expression, we have the equations;

1 - 8 - k = 0

-7 - k = 0

-7 = k

k = -7

Hence the value of K is -7

Step-by-step explanation:

The amplitude is the value that the cosine is being multiplied by.

The general equation of a sinusoid is

\( a \cos(b(x + c) ) + d\)

where a is the amplitude

\( \frac{2\pi}{ |b| } \)

is the period

-c is the phase shift

d is the midline(vertical shift)

Here the amplitude is -1/2 so b is the correct answer.

Answer:

the amplitude of the function that is y= -1/2 cos x, is 1/2.

Step-by-step explanation:

Answer:

Sale Price = $24 (answer). This means the cost of the item to you is $24. You will pay $24 for a item with original price of $120 when discounted 80%.

Step-by-step explanation:

Congruent quadrilateral related parts are congruent.

The true statements are:

Statements 2, 4, and 6 are Not Congruent

Statements 1, 3, and 5 are Congruent

Two triangles are said to be congruent if their corresponding sides and angles are equal.

From the given figure:

Quadrilaterals 1, 2 and 4 are congruent

Quadrilateral 3 is not congruent to any of the other quadrilaterals.

The true statements are:

Quadrilateral 1 and quadrilateral 2 Congruent

Quadrilateral 1 and quadrilateral 3 Not Congruent

Quadrilateral 1 and quadrilateral 4 Congruent

Quadrilateral 2 and quadrilateral 3 Not Congruent

Quadrilateral 2 and quadrilateral 4 Congruent

Quadrilateral 3 and quadrilateral 4 Not Congruent

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Answer:

The answer is k equals 2x to the third power and Y to the third power

Answer:

X€R

Y€R

Step-by-step explanation:

x³+y³+x³=k

2x³+y³=k

K=2x³+y³

So

X€R

Y€R

Answer:

cos²A - cosA - 6

Step-by-step explanation:

Given

(cosA + 2)(cosA - 3)

Each term in the second factor is multiplied by each term in the first factor, that is

cosA(cosA - 3) + 2(cosA - 3) ← distribute both parenthesis

= cos²A - 3cosA + 2cosA - 6 ← collect like terms

= cos²A - cosA - 6

Step-by-step explanation:

500 I'd the Answer I think

Answer:

LCM is 30.

Step-by-step explanation:

She forgot that they both can multiply into 30. She listed all their multiples and their LCM is 30. Not 60. That's her error.

Hope this helps and have a nice day!

Answer:

the number 228

Step-by-step explanation:

Let's call the smallest number in the consecutive sequence "x". Then, the 10 consecutive numbers are x, x+1, x+2, x+3, x+4, x+5, x+6, x+7, x+8, and x+9.

If we exclude one of these numbers, then the sum of the remaining 9 numbers would be:

(x) + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) + (x+8) or 9x + 36.

We know that the sum of the remaining 9 numbers is 2023, so we can set up the equation:

9x + 36 = 2023

Solving for x, we get:

9x = 1987

x = 221

Therefore, the smallest number in the consecutive sequence is 221, and the 10 numbers are 221, 222, 223, 224, 225, 226, 227, 228, 229, and 230.

If we exclude the number 228, then the sum of the remaining 9 numbers is 2023.

Answer:

its b

Step-by-step explanation:

I hope this helped

Answer:

J: 2/45

Step-by-step explanation:

You multiply the probabilities together then simplify

2/15 x 5/15

to get 10/225

simplify to get your answer of 2/45

You can use the factored form of the quadratic polynomial and then find the simplified sum.

The numerator of the simplified sum of the given expression is \(4x + 6\)

Quadratic polynomial with single variables are expressible in the form

\(ax^2 + bx + c\) where x is the variable and a,b,c are constants.

Its factored form is

\(\dfrac{1}{4a^2} \times (2ax +b-\sqrt{b^2 - 4ac})(2ax +b+ \sqrt{b^2 - 4ac})\)

The given expression is

\(\dfrac{x}{x^2 + 3x + 2} + \dfrac{3}{x + 1}\)

Factorizing \(x^2 + 3x +2\) using the aforesaid method, as we have got

a = 1, b = 3, c = 2,

thus, we have

\(ax^2 + bx + c = \dfrac{1}{4a^2} \times (2ax + b-\sqrt{b^2 - 4ac})(2ax +b + \sqrt{b^2 - 4ac})\\\\\begin{aligned}x^2 + 3x + 2 &= \dfrac{1}{4}(2x + 3 - \sqrt{9-8})(2x + 3 + \sqrt{9-8})\\\\&= \dfrac{1}{2}(2x+2) \times \dfrac{1}{2}(2x+4)\\&= (x+2)(x+1)\end{aligned}\)

Thus, the given sum is

\(\begin{aligned}\dfrac{x}{x^2 + 3x + 2} + \dfrac{3}{x + 1} &= \dfrac{x}{(x+2)(x+1)} + \dfrac{3}{x + 1} \times \dfrac{(x+2)}{(x+2)}\\\\&= \dfrac{x + 3(x+2)}{(x+1)(x+2)} \\&= \dfrac{4x + 6}{(x+1)(x+2)}\\\end{aligned}\)

Thus, the numerator of the simplified sum is \(4x + 6\)

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Answer:

4x+6

Step-by-step explanation:

C on edge 2022

Answer:

the image won't load so maybe try uploading it again

Answer:

50 lol

Step-by-step explanation:

can I please have brainliest I only need 2 more :)