5. h(x)=0.5x - 1 with domain (-♾, 4) what is the range

The general solution of the given differential equation is y(t) = y_h(t) + y_p(t) = C₁e^t + C₂te^t + t^2 + 2t - 3.

To find the general solution of the given differential equation, we'll first solve the homogeneous equation y" - 2y + y = 0. The characteristic equation corresponding to this homogeneous equation is r^2 - 2r + 1 = 0, which can be factored as (r - 1)^2 = 0. Therefore, the homogeneous equation has a repeated root r = 1.

The general solution of the homogeneous equation is y_h(t) = C₁e^t + C₂te^t, where C₁ and C₂ are arbitrary constants.

Next, we'll find a particular solution to the non-homogeneous equation y" - 2y + y = 1 + t^2. Since the right-hand side is a polynomial of degree 2, we can assume a particular solution of the form y_p(t) = At^2 + Bt + C, where A, B, and C are constants.

Differentiating y_p(t) twice, we find y_p"(t) = 2A. Substituting these values into the non-homogeneous equation, we get 2A - 2(At^2 + Bt + C) + (At^2 + Bt + C) = 1 + t^2.

Simplifying the equation, we have (A - 1)t^2 + (B - 2A)t + (C - 2B) = 1.

Comparing coefficients on both sides, we get A - 1 = 0, B - 2A = 0, and C - 2B = 1.

Solving these equations, we find A = 1, B = 2, and C = -3.

Therefore, the particular solution is y_p(t) = t^2 + 2t - 3.

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Answer:

the answer is 4

Step-by-step explanation:

Answer:

13+5-14 is equaled to 4 so if i do 18-14 is will still give me 4 because 13+5 is 18 so 18- 14 is 4

9

Step-by-step explanation:

18 ÷ (9×8-7×10)

multiply 9×8

18 ÷ (72 -7 × 10)

multiply -7 × 10

18 ÷ (72 -70)

subtract 72 -70

18 ÷ 2

9

Answer:9 X 8 = 72 - 7 = 65 X 10 = 650 divided by 18 = 36.1111111111

Step-by-step explanation:

Answer:

12 type of bread 1 type of meat, 1 type of cheese and 1 type of bread.☺️☺️

Answer:

Question 1:

The letter x or any letter used when writing an expression is representative of  unit of an idea, quantity or measure, such that it can be translated in the expression to provide information about a related idea

Question 2:

The expression can be translated as two times the expression three (variable) x minus two (variable) y plus the constant 7

Question 3:

In the first expression, the like terms are;

10y and (-2y),

3x and x

In the second expression, the like terms are;

-y and -2y

3x and 4x

The first expression simplifies to 8y + 4x + 10

The second expression simplifies to  7x - 3y + 6

Question 4:

The expression is evaluated as 122

Question 5:

The equivalent expression of the expression 3(4x + 2y) + 5x, is 17x + 6y

To prove when x = 1 and y = 2 we have;

3(4×1 + 2×2) + 5×1 is 29

17×1 + 6×2 is 29 which are equivalent in value

Step-by-step explanation:

Question 1:

The letter x or any letter used when writing an expression is representative of  unit of an idea, quantity or measure, such that it can be translated in the expression to provide information about a related idea

Example;

If x is the symbol representing the average number of oranges sold in 1 hour, then the expression for the number of oranges sold per day of 24 hours  = 24·x

An expression is a written mathematical symbolic statement that shows the the finite merging together of representative symbols by the mathematical operations that govern the present constraints

An equation is a statement that two expressions are equal

Question 2:

The given expression is 2(3x - 2y) + 7

The parts are;

The coefficient of (3x - 2y) = 2

The constant term = 7

The variables are x and y

Which gives

The coefficient of the variable x = 6

The coefficient of the variable y = -4

The expression can be translated as two times the expression three (variable) x minus two (variable) y plus the constant 7

or

The expression can be translated as two times the bracket open three times (variable) x minus two times (variable) y bracket close plus the constant 7

or

The expression can be expanded as 2(3x - 2y) + 7 → 6·x - 4·y + 7 which is expressed verbally as follows;

Six times (variable) x minus four times (variable) y plus the constant 7

Question 3:

The expressions are;

10y + 3x + 10 + x  - 2y..........................(1)

3x - y + 4x + 6 - 2y,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,(2)

In the first expression, the like terms are;

10y and (-2y),

3x and x

In the second expression, the like terms are;

-y and -2y

3x and 4x

They are like terms because they can be simply added together to simplify the expressions as follows

10y + 3x + 10 + x  - 2y gives 10y - 2y + 3x + x  10  to give 8y + 4x + 10

Also

3x - y + 4x + 6 - 2y  gives  3x+ 4x - y  - 2y + 6 to give 7x - 3y + 6

Question 4:

The expression 8x² + 25·y when x = 3 and y = 2 is evaluated by replacing (putting) the value x and y (into the expression)

The expression is then evaluated as 8×3² + 25×2 which is the same as 72 + 50 or 122

Question 5:

To write the equivalent expression of the expression 3(4x + 2y) + 5x, we expand the expression as follows;

3×4x + 3×2y + 4x which is 12x + 6y + 4x

We combine like terms;

12x + 5x + 6y which is 17x + 6y

To prove we can check by substituting a value for each of the variables x and y such as x = 1 and y = 2

3(4×1 + 2×2) + 5×1 is 29

17×1 + 6×2 is 29

Answer:

the last one

Step-by-step explanation:

To ensure a zero cash flow in the portfolio, the writer needs to set up a portfolio that offsets the cash flow from selling the derivatives. The writer should have -3 underlying assets in the portfolio (meaning short sold assets)

The cash flow from selling 100 derivatives can be calculated as:

Cash Flow from selling derivatives = 100 * (Premium at time 0 - Expiry value)

Cash Flow from selling derivatives = 100 * (1.34 - 0.64) = 70

To offset this cash flow, the writer needs to include an equal and opposite cash flow from the underlying assets. Let's assume the writer buys ""x"" underlying assets.

Cash Flow from underlying assets = x * (Value at time 0 - Value at time 1)

Cash Flow from underlying assets = x * (36 - 57) = -21x

To make the cash flow from underlying assets equal to the cash flow from selling derivatives, we set up the equation:

-21x = 70

Solving this equation, we find:

x ≈ -3.33

Since the number of underlying assets must be an integer, we round -3.33 to the nearest integer, which is -3.

Therefore, the writer should have -3 underlying assets in the portfolio (meaning short sold assets).

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Step-by-step explanation:

Examples of like terms in math are x, 4x, -2x, and 7x. These are like terms because they all contain the same variable, x. The terms 8y2, y2, and -2y2 are like terms as well. These all contain the same variable, y, raised to the second power.

Answer:

Step-by-step explanation:

Multiplying x+6y=-3 with 2 so its equal to first eqn,

Eliminating,

2x + 3y = 3        (1)

2x +12y = -6       (2)                  (because subtracting)

------------------

      -9y =9

     ∴y=-1

eq. y in 1

2x -3=3

2x=3+3

x=6/2

=3

Pls mark me brainliest

The largest subset of ℝ³ on which the vector field is differentiable is ℝ³ - {(0, 0, 0)

How to determine largest subset?

To determine largest subset where the given vector field is differentiable, we need to check that all partial derivatives of each component of the vector field exist and are continuous.

Let's start by finding the partial derivatives of each component:

∂/∂x (−x² − y² − z²- 1)4/3 = −4/3(x² + y² + z² + 1)1/3 × 2x = -8x(x² + y² + z² + 1)1/3/3

∂/∂y (−x² − y² − z²- 1)4/3 = −4/3(x² + y² + z² + 1)1/3 × 2y = -8y(x² + y² + z² + 1)1/3/3

∂/∂z (−x² − y² − z²- 1)4/3 = −4/3(x² + y² + z² + 1)1/3 × 2z = -8z(x² + y² + z² + 1)1/3/3

∂/∂x (x cos(yz)) = cos(yz)

∂/∂y (x cos(yz)) = -xz sin(yz)

∂/∂z (x cos(yz)) = -xy sin(yz)

∂/∂x (xy⁴−z²) = y⁴

∂/∂y (xy⁴−z²) = 4xy³

∂/∂z (xy⁴−z²) = -2z

Now we need to check the continuity of all these partial derivatives. We can see that all of them are continuous except for the partial derivatives involving the expressions (x² + y² + z² + 1)1/3 and (yz).

The expression (x² + y² + z² + 1)1/3 involves a cube root, which is not continuous at (0, 0, 0). Therefore, the partial derivatives involving this expression are not continuous at the origin, which means that the vector field is not differentiable at the origin.

The expression yz involves the product of y and z, which is also not continuous at (0, 0, 0). Therefore, the partial derivatives involving this expression are also not continuous at the origin, which means that the vector field is not differentiable at the origin.

Therefore, the largest subset of ℝ³ on which the vector field is differentiable is ℝ³ - {(0, 0, 0).

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Correct question is "determine the largest subset of double-struck ℝ³ on which the given vector field is differentiable. f = (−x² − y² − z²- 1)4/3, x cos(yz), xy ⁴− z²".

Answer: The largest subset of ℝ³ on which the vector field is differentiable is ℝ³ itself. In summary, the given vector field is differentiable on the entire ℝ³ space.

The correct statements are:

b) Ordering costs decrease with respect to lot size,

c) It is good to have fixed interval ordering systems for products that have independent demand,

e) Taxes and insurance costs can be considered as carrying costs of inventory,

f) Costs incurred for defective products identified after the products are shipped are classified as internal failure costs,

h) Costs of repairing faulty products under warranty are limited to external failure costs, and j) Under EOQ inventory model, there is an assumption which states that there is no possibility of inventory stockout to occur.

b) Ordering costs decrease with respect to lot size: Ordering costs involve the expenses incurred when placing orders for inventory, such as administrative costs, processing fees, and transportation costs.

When the lot size increases, the frequency of placing orders decreases, resulting in lower ordering costs per unit. This is because the fixed costs associated with ordering are spread over a larger quantity of inventory.

c) It is good to have fixed interval ordering systems for products that have independent demand: Fixed interval ordering systems involve placing orders at regular intervals, regardless of the inventory level.

This approach is suitable for products with independent demand, where the demand is unpredictable or sporadic. By setting fixed intervals, the company can ensure a consistent replenishment schedule and avoid stockouts while optimizing inventory levels.

e) Taxes and insurance costs can be considered as carrying costs of inventory: Carrying costs are the expenses associated with holding and storing inventory.

They include costs such as storage fees, insurance premiums, taxes on inventory, and the opportunity cost of tying up capital in inventory. Taxes and insurance costs directly impact the financial burden of inventory holding and are considered as components of carrying costs.

f) Costs incurred for defective products identified after the products are shipped are classified as internal failure costs: Internal failure costs are expenses incurred due to quality issues discovered within the company's operations.

In the context of inventory, costs related to defective products identified after they are shipped, but before reaching the customer, fall under internal failure costs. These costs include rework, scrap, and any necessary corrective actions taken to address the quality problems.

h) Costs of repairing faulty products under warranty are limited to external failure costs: External failure costs are the expenses incurred due to quality issues discovered by customers after the products have been delivered.

When faulty products are repaired under warranty, the costs associated with the repairs are considered external failure costs. This includes the direct costs of repairing or replacing the faulty products and any associated customer service expenses.

j) Under EOQ inventory model, there is an assumption which states that there is no possibility of inventory stockout to occur: The Economic Order Quantity (EOQ) model is a widely used inventory management technique.

It assumes that demand for the product is constant and known with certainty, there are no quantity discounts or price variations, and there is no possibility of stockouts occurring.

The assumption of no stockouts simplifies the calculations and ensures that the optimal order quantity obtained from the model will meet the demand without interruptions.

However, in real-world scenarios, stockouts can occur due to unforeseen factors, variability in demand, or supply chain disruptions.

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Answer:

Factor each coefficient into primes

Step-by-step explanation:

The Factor  expression shows the greatest common factor correctly factored from the expression 12a2−36ab+18b2 is each coefficient into primes.

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Answer:

I think its  x≥3

Step-by-step explanation:

5x+4≥19

Subtract 4 from both sides.

5x+4−4≥19−4

5x≥15

Step 2: Divide both sides by 5.

5x /5  ≥ 15 /5

=x≥3

The distribution of characteristics of elements in a(n) representative sample is the same as the distribution of those characteristics among the total population of elements. A representative sample accurately reflects the larger population from which it is drawn, ensuring that the results from studying the sample can be generalized to the overall population.

The distribution of characteristics of elements in a representative sample is the same as the distribution of those characteristics among the total population of elements.

A representative sample is a subset of a population that accurately reflects the characteristics of the entire population. It is selected using a random sampling technique, which means that every member of the population has an equal chance of being included in the sample.

By selecting a representative sample, researchers can make inferences about the entire population with greater confidence, since the sample is likely to be more similar to the population as a whole.

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The fundamental theorem of arithmetic states that every natural number greater than 1 can be written as a product of primes. Using strong induction, we can prove this.

Let's proceed with the strong induction proof. We start by considering the base case, where m = 2. Since 2 is prime, it can be written as a product of primes itself.

Next, we assume that for all natural numbers k such that 2 ≤ k ≤ m, the statement holds true, i.e., k can be expressed as a product of primes. Now, we aim to prove that m+1 can also be expressed as a product of primes.

We know that m+1 is either prime itself or composite. If m+1 is prime, then it can be written as a product of a single prime, satisfying the theorem.

On the other hand, if m+1 is composite, it can be written as a product of two positive integers a and b, where 2 ≤ a ≤ b ≤ m. Since a and b are both less than or equal to m, we can apply the inductive hypothesis to express a and b as products of primes. Therefore, we can write m+1 as a product of primes by combining the prime factorizations of a and b.

By strong induction, we have shown that for any natural number m greater than 1, it can be expressed as a product of primes. This completes the proof of the fundamental theorem of arithmetic.

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Answer: true

Step-by-step explanation:

Answer:

Cost of 1 packet of biscuit=Rs 9

Cost of 1 packet of toffee=Rs 13

Step-by-step explanation:

Let

Cost of 1 packet of biscuit=x

Cost of 1  packet of toffee=y

We have to find the cost of 1 packet of  biscuit and 1 packet of toffee.

According to question

\(3x=14+y\)

\(y=3x-14\)

Now,

\(x+y=22\)

Using the value of y then, we get

\(x+3x-14=22\)

\(4x=22+14\)

\(4x=36\)

\(x=\frac{36}{4}=9\)

Substitute the value of x

\(y=3(9)-14=27-14\)

\(y=13\)

Hence, cost of 1 packet of biscuit=Rs 9

Cost of 1 packet of toffee=Rs 13

Answer:

-24

Step-by-step explanation:

The coefficients are   4    3  and  -2

 multiplied together = -24

(4)(3)(-2) = - 24

Answer:

4.5%

Step-by-step explanation:

The likelihood ratio statistic for testing the hypothesis H: P1 = P2 = ... = Pn against HA: Not H can be derived using the asymptotic distribution of the likelihood ratio test statistic.

In this scenario, we have n independent binomial random variables, X1, X2, ..., Xn, with corresponding parameters ni and Pi. We want to test the null hypothesis H: P1 = P2 = ... = Pn against the alternative hypothesis HA: Not H.

The likelihood function under the null hypothesis can be written as L(H) = Π [Bin(Xi; ni, P)], where Bin(Xi; ni, P) represents the binomial probability mass function. Similarly, the likelihood function under the alternative hypothesis is L(HA) = Π [Bin(Xi; ni, Pi)].

To derive the likelihood ratio statistic, we take the ratio of the likelihoods: R = L(H) / L(HA). Taking the logarithm of R, we obtain the log-likelihood ratio statistic, denoted as LLR:

LLR = log(R) = log[L(H)] - log[L(HA)]

By applying the properties of logarithms and using the fact that log(a * b) = log(a) + log(b), we can simplify the expression:

LLR = Σ [log(Bin(Xi; ni, P))] - Σ [log(Bin(Xi; ni, Pi))]

Next, we need to consider the asymptotic distribution of the log-likelihood ratio statistic.

Under certain regularity conditions, as the sample size n increases, LLR follows a chi-square distribution with degrees of freedom equal to the difference in the number of parameters between the null and alternative hypotheses.

In this case, since the null hypothesis assumes equal probabilities for all categories (P1 = P2 = ... = Pn), the null model has n - 1 parameters, while the alternative model has n parameters (one for each category). Therefore, the degrees of freedom for the chi-square distribution is equal to n - 1.

To test the hypothesis H at a significance level α, we compare the observed value of the likelihood ratio statistic (LLR_obs) with the critical value of the chi-square distribution with n - 1 degrees of freedom. If LLR_obs exceeds the critical value, we reject the null hypothesis in favor of the alternative hypothesis.

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Answer:

Its 0

Step-by-step explanation:ur not smart if u dont know that

\(180^{\circ} = (2x + 45)^{\circ} + x^{\circ}\\180^{\circ} = 2x^{\circ} + 45^{\circ} + x^{\circ}\\180^{\circ} - 45^{\circ} = 2x^{\circ} + x^{\circ}\\135^{\circ} = 3x^{\circ}\\x^{\circ} = 45^{\circ}\)

Answer:

x = 45

Step-by-step explanation:

The angle measurement of the line is 180 degrees because it is a straight line. Therefore, the shown two angle measurements must add up to 180 as well. So:

(2x+45) + x = 180

Combine like terms to simplify

3x + 45 = 180

-45           -45

Subtract 45 on both sides to isolate the variable

3x = 135

Divide 3 on both sides to isolate the variable as well

x = 45

*Hope this helped! : )*

The present value of the given continuous income stream is $ 37,943.55. Formula for the present value of a continuous income stream is given by:

PV = [F / r] where, F is the cash flow, and r is the discount rate.

To calculate the present value of the given income stream, we need to integrate the function F(t) over 0 to 10 years:

PV = ∫[\(40 + 5t] e^(-0.025t)\) dt from t = 0 to t = 10 years

= 1000 * ∫\([40 + 5t] e^(-0.025t)\) dt

from t = 0 to t = 10years

Let us evaluate the integral:

PV = 1000 ∫[\(40 + 5t] e^(-0.025t)\) dt

from t = 0 to t = 10years

= 1000 * [ ∫40 \(e^(-0.025t)\) dt + 5 ∫t\(e^(-0.025t)\) dt]

from t = 0 to t = 10years

= 1000 * [40 / (-0.025) (\(e^(-0.025t))\) + 5 ( -1/0.025 * \(e^(-0.025t)\) * (t-1/0.025))]

from t = 0 to t = 10years

= 1000 * [ -1600 (\(e^(-0.025*10))\) - 200 (\(-e^(-0.025*10)\) + 1) ]

= $ 37,943.55

Hence, the present value of the given continuous income stream is $ 37,943.55.

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Answer: 98/100 is .98$ or 98 cents

Step-by-step explanation:

100 cents is 1$

you have to put a decimal point in front of any number less than 100 in terms of money.

so you would put .98$ or 98 cents

Answer: Look at stwp by step

Step-by-step explanation:

Basically we can compare both equations to get that x = √7 and y = √2 so we can substitute that into 2x + 10y to get 2√7 + 10√2

Answer:

280 trees on a 1.5 acre plot

Step-by-step explanation:

It has more trees with less acres already without any calculations.

Answer:

1/8 of an hour

Step-by-step explanation:

3/4 x 1/6 = 3/24 = 1/8

Hope this helps!

Answer:

sin(2x)

Step-by-step explanation:

The given trigonometric expression is:

sin(x)cos(x) + cos(x)sin(x)

We can simplify this expression by using the following identity:

sin(x)cos(x) + cos(x)sin(x) = sin(2x)

Simplified Expression is: sin(2x)

We can also write this expression in terms of sine and cosine as follows:

sin(2x) = 2sin(x)cos(x)

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