oh god does anyone understand this? I need help it’s for a test and I wanna do good!!

Answer:A

Step-by-step explanation:

The existence and uniqueness theorem in the ordinary differential equations are explained below.

(a) "Existence" in the context of the existence and uniqueness theorem for ordinary differential equations (ODEs) refers to the guarantee that a solution to the ODE exists for a certain interval or range of values.

(b) "Uniqueness" means that there is only one solution to the ODE that satisfies certain initial conditions or constraints. It ensures that there are no multiple solutions that meet the given criteria.

(c) The equation x' = f(t, x) represents a first-order ODE, where the derivative of the function x with respect to t is equal to the function f, which depends on both t and x.

(d) The notation x(to) = xo represents the initial condition of the ODE. It specifies the value of the function x at a particular initial time to, which is equal to xo.

(e) The graph of R = {(t, x): 0 ≤ |t - to| ≤ a, 0 ≤ |x - xo| ≤ b} represents a rectangular region in the t-x plane. It includes all points (t, x) that satisfy the conditions: the absolute difference between t and to is less than or equal to a, and the absolute difference between x and xo is less than or equal to b. The point (to, xo) is included in this region.

(f) The symbol u(t) is not mentioned in the given context. Without additional information, it is not possible to provide a specific interpretation or meaning for u(t).

(g) "On some interval |t - to| < h contained in |t - to| < a" implies that there exists a smaller interval, represented by |t - to| < h, which is fully contained within the larger interval |t - to| < a. The value of h represents the size or length of the smaller interval. In the graph, h can be added as a smaller length within the interval defined by a.

The relationship between a and h is that h is a subset of a. This means that h is smaller or equal to a and is fully contained within a. In other words, h represents a sub-interval of the larger interval a.

(h) The significance of the existence and uniqueness theorem in layman's terms is that it provides a mathematical assurance that a specific type of differential equation has a unique solution that satisfies certain conditions. It gives confidence that a solution exists and is unique within a specified range or interval. This is valuable for various scientific and engineering applications, as it allows for the prediction and understanding of systems described by differential equations.

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The probability that Andy chooses red and his boss approves is 6.4%

The correct option is option c.

Let A be the probability that Andy chooses red

Let B be the probability that his boss approves

probability of A = 0.32

probability of B = 0.20

\(P (A and B) = P(A) \times P(B)\\P (A and B) = 0.32 X 0.20 P\\P (A and B) = 0.064\)

Convert the 0.064 to percentage, multiply it by 100.

=0.064 x 100

=6.4%

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Answer:

if its easy then answer it .-.

Step-by-step explanation:

Answer:

u =-3

Step-by-step explanation:

Answer:

Step-by-step explanation:

1). m³ + 4  

   By substituting m = 4 in the given expression,

   (4)³ + 4 = 68

2). 3r ÷ 2

   By substituting r = 8 in the expression,

   3(8) ÷ 2 = 12

3). 5w²- 3w

   By substituting w = 2 in the expression,

   5(2)² - 3(2) = 20 - 6

                      = 14

4). 7x¹. x⁰

   = 7x(1) [Since, 0 power of any number = 1]

   = 7x

   By substituting x = 3

   7x = 7(3) = 21

You will be able to withdraw approximately $3,076.32 at the end of 5 years.

To calculate the amount you will be able to withdraw at the end of 5 years, we can use the future value formula for compound interest.

The formula for calculating the future value (FV) of a present value (PV) invested at an annual interest rate (r) for a certain number of years (t) is:

\(FV = PV * (1 + r)^t\)

Given:

PV = $2,300

r = 6% = 0.06 (decimal representation)

t = 5 years

Substituting these values into the formula, we get:

FV = $2,300 * \((1 + 0.06)^5\)

Calculating the expression inside the parentheses:

\((1 + 0.06)^5 = 1.338225\)

Multiplying the present value by this factor:

FV = $2,300 * 1.338225

FV ≈ $3,076.32

Therefore, you will be able to withdraw approximately $3,076.32 at the end of 5 years.

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You deposit $2,300 into an account that pays 6% per year. Your plan is to withdraw this amount at the end of 5 years to use for a down payment on a new car. How much will you be able to withdraw at the end of 5 years? Do not round intermediate calculations. Round your answer to the nearest cent

a) Speed = distance/time

From the information given,

Distance = 3.75

time = 0.3

Thus, her speed would be

Speed = 3.75/0.3 = 12.5 miles per hour

b) Given that

Distance = 4.5 miles

Speed = 12.5 miles per hour,

Time = distance/speed = 4.5/12.5

Time = 0.36 hours

It will take her 0.36 hours to go 4.5 miles

Answer:

256

Step-by-step explanation:

Given. :

2⁴ / 2^-4

2⁴ = 2 * 2 * 2 * 2 = 16

2^-4 = 1/2⁴ = 1 / (2 * 2 * 2 * 2) = 1 / 16

16 ÷ (1 /16)

16 * 16 /1

= 256

Answer:

Step-by-step explanation:

1/256 i believe

Polynomials are algebraic expressions consisting of terms that include real numbers, variables, and positive integer exponents. Each term in a polynomial has a variable raised to a non-negative integer power, and the coefficient of each term is a real number. Polynomials are classified by the degree of their highest power. If two or more terms in a polynomial have the same variable raised to the same power, they can be combined into a single term.

1. -x² + x - x² + 1

Combine like terms: -x² + x - x² + 1 = -2x² + x + 1

This polynomial has degree 2 because the highest power of the variable is 2.

2. x² + x + 2x³ - x

Rearrange terms: 2x³ + x² + x - x = 2x³ + x²

This polynomial has degree 3 because the highest power of the variable is 3.

3. 4x + x + x - 2

Combine like terms: 4x + x + x - 2 = 6x - 2

This polynomial has degree 1 because the highest power of the variable is 1.

4. 3x² + 4 - 3x² - 1

Combine like terms: 3x² - 3x² + 4 - 1 = 3

This polynomial has degree 0 because there is no variable term.

Therefore, the four given polynomials have degrees 2, 3, 1, and 0, respectively.

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Answer:

y=1.25x+5

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

We can start by dividing 3.5 and 0.75.

3.5/0.75 is 4.67.

Now, we multiply 4.67 by 1 since we are finding how much she walks in 1 hour.

1*4.67 is 4.67.

Answer:

^7 squroot5^3

Step-by-step explanation:

5x2= 10

7÷ 3= 2.5

Answer:

C is the correct answer

Answer:

67 degrees

Step-by-step explanation:

Calculator!

Answer:

7

Step-by-step explanation:

if you add 7 to -5 you get 2

Answer:

(−1/6)÷(−5/6) which when you cancel gets 0.2 or also 1/5.

Step-by-step explanation:

Answer:

Linear functions change at a constant rate per unit interval. An exponential function changes by a common ratio over equal intervals.

Answer:

C. 150

Step-by-step explanation:

The given angle and angle x are supplementary. This means that when added together they add to 180. So, to solve you can set up an algebraic equation like 180=x+30. Then, subtract 30 from both sides to get 150=x.

A :

Call the number of appointments Maci had as x (x > 0)

-> The amount of money she earned from her appointments = 60x (dollars)

Since she earned $60 in tips, we have the equation : 60x + 60 = 300.

Solve for x : x = (300-60)/4 = 4.

B :

Call the number of appointments Logan had as x (x > 0)

Since he charged $55 per appointment, but have to pay a rental fee of $10 per appointment, he made a total of (55-10)x = 45x (dollars)

Because he received $35 in tips, the total amount he made was 45x + 35.

So, we have the equation : 45x + 35 = 350

Solve for x : 45x = 315 -> x = 7.

This is a geometric sequence with a common ratio of 2. So the predicted order quantity for September is 1376 copies.

In a geometric sequence, each term is found by multiplying the previous term by a fixed number called the common ratio. In this case, we can see that each month's order quantity is double the previous month's order quantity. This makes it a geometric sequence with a common ratio of 2.

To verify, we can divide any term by its preceding term and see that we always get the same ratio of 2. For example:

June order / May order = 172 / 86 = 2

July order / June order = 344 / 172 = 2

August order / July order = 688 / 344 = 2

Knowing that this is a geometric sequence with a common ratio of 2, we can use the formula for the nth term of a geometric sequence to find the order quantity for any given month:

an = a1 * r^(n-1)

where:

an = the nth term

a1 = the first term

r = the common ratio

n = the number of terms

For example, to find the order quantity for September (the 5th month), we can plug in the values:

a5 = 86 * 2^(5-1) = 86 * 16 = 1376

So the predicted order quantity for September is 1376 copies.

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Answer: 180ft squared

Step-by-step explanation:

A = 10+18*6/2 = 84

B = 12*4 = 48

C= 12*4 = 48

Add

84+48+48 = 180

Answer:-17

Step-by-step explanation:

45-28=17

Answer:

C

Step-by-step explanation:

A. is wrong because having a different height for each seedling and not trying to keep it equal is simply worse than making sure the heights are identical.

B. Completely wrong because it would likely result in 1 plot having more melon seedlings than the other.

C. Correct because it makes sure the seedlings are the same height at the beginning of the experiment, allowing less randomness in the experiment.

D. Putting the taller of a each pair for 1 plot makes it the experiment rigged in favor of the plot with taller seedlings

E. Same issue as D.

Answer:

B.

Step-by-step explanation:

Answer:

(2 , 4) this is the answer off your question

Answer:

98 feet

Step-by-step explanation:

divide 48 by 2.

Then do pythag

c2=a2+b2, which is the formula to find c2 = 25

then add all together which is perimeter

Answer: 98 feet

Step-by-step explanation:

First, you need to find the hypotenuse, which is always opposite from the right angle.

Because this isosceles triangle consists of 2 right triangles, they are congruent which means that you can simply just divide 48 by 2 to find the base of one of the triangles, 24.

Next, use a^2 + b^2 = c^2

7^2 + 24^2 = c^2

49 + 576 = c^2

625 = c^2

25 = c

Now, you can find the perimeter.

48 + 25 + 25 = 98 feet

Hope this helped :)

The following are the statements with explanation whether the statement is true or false, using rank-nullity theorem and invertible matrix theorem.

a. False. According to the rank-nullity theorem, the rank of a matrix plus its nullity equals the number of columns. As a result, a 7 x 4 matrix can only have a rank of 4, because the nullity cannot be negative.

b. False. According to the rank-nullity theorem, the nullity of a matrix plus its rank equals the number of columns. As a result, because the rank cannot be negative, a 4 x 7 matrix can have a maximum nullity of 3.

c. True. According to the rank-nullity theorem, the nullity of a matrix plus its rank equals the number of columns. As a result, a 7 x 4 matrix has a maximum nullity of 3, implying that it can have a nullity 5.

d. True. According to the rank-nullity theorem, the rank of a matrix plus its nullity equals the number of columns. As a result, if A is a 7 x 4 matrix, rank(A) + nullity(A)= 4 + nullity(A) = 7. When we solve for nullity(A), we get nullity(A) = 3, therefore rank(A) + nullity(A) = 4 + 3 = 7.

e. False. According to the rank-nullity theorem, the nullity of a matrix plus its rank equals the number of columns. As a result, if A is a 6 x 8 full-rank matrix, its nullity is 8 - 6 = 2, rather than nullity(A) = 2² = 4.

f. True. According to the invertible matrix theorem, a full-rank matrix has a unique solution for any non-zero right-hand side vector b. As a result, the system Ax = b is always consistent for every non-zero b.

g. True. According to the invertible matrix theorem, a full-rank matrix has a unique solution for each right-hand side vector b. As a result, the system Ax = b will always have a distinct solution for any b.

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To detect a 20% improvement in median survival from 5 to 6 months with 80% power and a significance level of 0.05, following patients for 1 year, the required sample size can be calculated using power analysis formulas.

To determine the number of patients needed for the survival study, we can use power analysis calculations based on the specified parameters. In this case, we want to detect a 20% improvement in the median survival time from 5 months to 6 months, with 80% power at a significance level of 0.05. The study will follow patients for 1 year (12 months) assuming an exponential distribution for survival.

To calculate the required sample size, we can use statistical software or power analysis formulas. One common approach is to use the formula:

n = (2 * (Zα + Zβ)^2 * σ^2) / (δ^2)

where n is the required sample size, Zα is the Z-value for the chosen significance level (0.05), Zβ is the Z-value for the desired power (80%), σ is the standard deviation of the survival times (assumed to be equal for both treatment groups), and δ is the desired difference in survival times.

In conclusion, to detect a 20% improvement in median survival from 5 to 6 months with 80% power and a significance level of 0.05, following patients for 1 year, the required sample size can be calculated using power analysis formulas. By plugging in the appropriate values for Zα, Zβ, σ, and δ into the formula, the specific number of patients needed for the study can be determined.

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