___1.which of the following illustrate the union of two sets
___2.which of the following represent the intersection of two sets
___3.which of the following is the factored form x³ + 4x²+4x+16​

The solution to the initial-value problem is y(t) = sin(t) - [e^(-πt) - e^(-2πt)] × u(t-π)/2, 0 ≤ t < ∞.

To solve this initial-value problem using Laplace transform, we will apply the Laplace transform to both sides of the differential equation and use the initial conditions to find the Laplace transform of y.

Taking the Laplace transform of both sides of the differential equation, we get

Ly'' + Ly = Lf(t)

Using the properties of Laplace transform, we can find Ly' and Ly as follows

Ly' = sLy - y(0) = sLy - 0 = sLy

Ly'' = s^2Ly - s*y(0) - y'(0) = s^2Ly - 1

Substituting these expressions into the differential equation, we get:

s^2Ly - 1 + Ly = Lf(t)

Simplifying, we get

Ly = Lf(t) / (s^2 + 1) + 1/s

Now we need to find the Laplace transform of f(t). Using the definition of Laplace transform, we get

Lf(t) = ∫[0,π] 0e^(-st) dt + ∫[π,2π] 1e^(-st) dt + ∫[2π,∞) 0*e^(-st) dt

= 1/s - (e^(-πs) - e^(-2πs))/s

Substituting this expression into the equation for Ly, we get

Ly = [1/s - (e^(-πs) - e^(-2πs))/s] / (s^2 + 1) + 1/s

Now we need to find y(t) by taking the inverse Laplace transform of Ly. We can use partial fraction decomposition to simplify the expression for Ly

Ly = [(1/s)/(s^2 + 1)] - [(e^(-πs) - e^(-2πs))/s]/(s^2 + 1) + 1/s

Using the inverse Laplace transform of 1/(s^2 + 1), we get

y(t) = sin(t) - [e^(-πt) - e^(-2πt)]*u(t-π)/2

where u(t) is the unit step function.

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Below is the answer

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assistant professors on the business faculty at state-supported institutions in Ohio make, on average, between $69,263 and $74,737 for nine months.

In Ohio's state-supported institutions, the

average incom for a sample of assistant professors in the business faculty for nine months is $72,000.

Since the sample size is unknown, it is difficult to draw any definitive conclusions based on this statistic

. However, we can use this mean to estimate the probable range of incomes for assistant professors at these institutions by calculating a confidence interval.For example, if we use a 95 percent confidence level, we can assume that the real average income for assistant professors in the business faculty at Ohio's state-supported institutions falls within a certain range of values

. Based on the sample mean of $72,000 and a standard deviation of $5,000, the 95 percent confidence interval is $69,263 to $74,737. This means that we are 95 percent confident that the real average income for assistant professors falls within this range.The interval reflects the range of values that the true average could fall within, given the uncertainty of the sample data.

Therefore, we can infer that assistant professors on the business faculty at state-supported institutions in Ohio make, on average, between $69,263 and $74,737 for nine months.

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The mean income for sample assistant professors on the business faculty at state-supported institutions in Ohio is $72,000 for 9 months.

Based on the information provided, the mean income for sample assistant professors on the business faculty at state-supported institutions in Ohio is $72,000 for 9 months.

To better understand this, let's break it down step by step:

1. The mean income refers to the average income earned by assistant professors on the business faculty in Ohio.
2. The sample represents a group of assistant professors who were surveyed or studied.
3. The business faculty refers to the department or area of expertise these assistant professors specialize in.
4. State-supported institutions in Ohio are public universities or colleges that receive funding from the state government.
5. The $72,000 represents the average income earned by assistant professors on the business faculty in Ohio over a period of 9 months. It does not include income earned during the summer months.
6. It's important to note that this figure may vary for different individuals based on factors such as experience, qualifications, and position within the faculty.

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Answer:

  b)  -3

Step-by-step explanation:

You want the value of 'a' when the quadratic y = –3x² – 15x – 11 is written in the form y = a(x – h)² + k.

The leading coefficient in either form is the coefficient of x². It is the same in both forms: -3.

Single Sampling Plan: AQL = 0, LTPD = 3.41, AOQ = 1.79 Double Sampling Plan: AQL = 0, LTPD = 2.72, AOQ = 1.48

The values for the ASN (Average Sample Number) curves for the given single sampling plan and double sampling plan are:

Single Sampling Plan (n=80, c=3):

ASN curve values: AQL = 0, LTPD = 3.41, AOQ = 1.79

Double Sampling Plan (n1=50, c1=1, r1=4, n2=50, c2=4, r2):

ASN curve values: AQL = 0, LTPD = 2.72, AOQ = 1.48

The ASN curves provide information about the performance of a sampling plan by plotting the average sample number (ASN) against various acceptance quality levels (AQL). The AQL represents the maximum acceptable defect rate, while the LTPD (Lot Tolerance Percent Defective) represents the maximum defect rate that the consumer is willing to tolerate.

For the single sampling plan, the values n=80 (sample size) and c=3 (acceptance number) are used to calculate the ASN curve. The AQL is 0, meaning no defects are allowed, while the LTPD is 3.41. The Average Outgoing Quality (AOQ) is 1.79, representing the average quality level of outgoing lots.

For the equally effective double sampling plan, the values n1=50, c1=1, r1=4, n2=50, c2=4, and r2 are used. The AQL and LTPD values are the same as in the single sampling plan. The AOQ is 1.48, indicating the average quality level of outgoing lots in this double sampling plan.

These ASN curve values provide insights into the expected performance of the sampling plans in terms of lot acceptance and outgoing quality.

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Answer:

8

Step-by-step explanation:

2x + 7 = 23

2x = 16

X = 8

The time it take until 2000 people know about the rumor is 16 days.

The square root of a variety of is described because the value, which offers the variety while it's miles increased with the aid of using itself. The radical symbol √ is used to suggest the square root.  Radical is any other call given to the square root symbol. It is likewise called the surds. While Radicand is the variety gift beneath neath the square root symbol.

Find t, when N=200

N=5OO t^1/2

2000=500 t^1/2

t^1/2=4

t=16 days

Thus, the time it take until 2000 people know about the rumor is 16 days.

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The number of cookies in the jar initially was 42

To find out how many cookies were in the jar initially, we can use algebra to represent the problem. Let x be the number of cookies in the jar initially. After Latoya took half of the cookies, Mark took 1/3 of the remaining cookies, Kandi took 1/4 of the remaining cookies, and Shannon took 1 cookie, there are 2 cookies left in the jar.

We can use this information to set up the equation:

x/2 - (x/2)/3 - (x/2)/4 - 1 - 2 = 0.

By solving this equation, we get x = 42. This means there were 42 cookies in the jar initially. To find out how many cookies were there before Latoya came, we just add the 2/3 of a cookie that was left over to the 2 whole cookies we know of.

So, 42+2/3 = 42.67 which means 42 cookies were there before Latoya came.

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The general solution of the differential equation is `y = Ce^(-2x) - 2x + 5/2`, where `C` is a constant and the differential equation is `dy/dx = -2y + 3x + 4`.

The given differential equation is: `dy/dx = -2y + 3x + 4`. To solve this differential equation, we first need to solve the homogeneous part and then the particular part. The homogeneous part of the differential equation is: `dy/dx = -2y`.This can be rewritten as:`dy/y = -2dx`Now integrating both sides, we get:`ln|y| = -2x + C_1`where `C_1` is the constant of integration.Solving for `y`, we get:`y = Ce^(-2x)`where `C = ±e^(C_1)`.

Thus, the general solution of the homogeneous part is given by:`y_h = Ce^(-2x)`where `C` is the constant of integration.The particular part of the differential equation is given by:`dy/dx = 3x - 2y + 4`To solve this, we need to use the method of undetermined coefficients. For this, we assume the particular solution to be of the form:`y_p = Ax + B`where `A` and `B` are constants.Using this particular solution, we have:`dy_p/dx = A`Plugging this into the differential equation, we get:`A = 3x - 2(Ax + B) + 4`Simplifying and solving for `A` and `B`, we get:`A = -2` and `B = 5/2`.

Therefore, the particular solution is:`y_p = -2x + 5/2`Hence, the general solution of the given differential equation is:`y = y_h + y_p` `= Ce^(-2x) - 2x + 5/2`Where `C` is the constant of integration.Answer: The general solution of the differential equation is `y = Ce^(-2x) - 2x + 5/2`, where `C` is a constant and the differential equation is `dy/dx = -2y + 3x + 4`.

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Answer:

a) 7³

b) \(11^{20}\)

c) \(4^{8}\)

d) \(6^9\)

e) \(12^{14}\)

f) \(3^9\)

g) \((0.173)^{11}\)

h) 0.87²

i) (\(\frac{5}{2}\\\))²

Step-by-step explanation:

The exponents are subtracted when they are dividing, are summed when it's multiplication, and are multiplied when it's between parenthesis.

Answer:

Follow the steps below

Step-by-step explanation:

a. When dividing with the same base, (7 in this case), subtract the exponents. So, 7^6 / 7^2 = 7^6-2 = 7^4

b. (11^4)^5 becomes 11^4*5 = 11^20

c. Once again, same base (4 this time), so add the exponents. 4^2 * 4^6 = 4^2+6 = 4^8

d. So, 6 is technically 6^1, so 6 * 6^8 = 6^1 * 6^8 = 6^9

e. (12^2)^7 is 12^2*7 = 12^14

f. (3^10) / 3 = 3^10 / 3^1 = 3^10-1 = 3^9

g. (0.173)^9 * (0.173)^2 = 0.173^9+2 = 0.173^11

h. (0.87^5) / (0.87^3) = 0.87^5-3 = 0.87^2

i. (5/2)^8 / (5/2)^6 = (5/2)^8-6 = (5/2)^2

Let's take the subspace (X,T) of (Y,T*), where (Y,T*) is a subspace of (Z,T**). Here, we are required to show that (X,T) is also a subspace of (Z,T**). Let's start our proof.

To show that (X,T) is a subspace of (Z,T**), we must show that (X,T) satisfies the subspace axioms. The subspace axioms that must be satisfied are:

1. The zero vector, 0, is in (X,T).

2. If u and v are in (X,T), then u + v is also in (X,T).

3. If u is in (X,T) and a is a scalar, then au is also in (X,T).

So, let's prove each axiom for (X,T) to be a subspace of (Z,T**):

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Answer:

6

Step-by-step explanation:

The formula to find the area of a triangle is length times height (12) and divide by 2.

The solution is, the probability that it is not a king given that it is a face card =2/3

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

Total number of cards in a deck = 52

Number of face cards = 12  ( 4 King + 8 others)

The probability that a card is face card P(Face card)= 12//52

                                                                                     =3/13

Number of cards are not king = 8

The probability that a card is face card are not King :

P( Face card and not king )= 8/52

                                            =2/13

Using conditional probability formula ,

P = 2/13/3/13

  =2/3

Hence, the probability that it is not a king given that it is a face card =2/3.

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Given:

Equation is:

Find-:

Solve the equation

Explanation-:

Simplify the equation then,

Taking ln both sides then,

Use logarithmic property

Then the value is:

The value of "x" is:

So, the value of "x" is 1.601

The total cost of the camera with sales tax included is $811.47.

The total cost refers to the summation of all the cost involved from the manufacturing to sales, it majorly involves the fix cost and variable cost.

To find the total cost we need to derive a formula

total cost = listed price + ( listed price x sales tax rate)

now by placing the values given in the question we can calculate the the total cost

listed price = $761. 98

sales tax rate = 6. 5%

then,

total cost = 761.98 + (761.98 x 0.065)

total cost = 761.98 + 49.49

total cost = $811.47

The total cost of the camera with sales tax included is $811.47.

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Answer:

200 candles

Step-by-step explanation:

20*10 = 200

The slope of the line is 8, which represents the rate at which the amount of money in the account is increasing per week.

An equation is a mathematical statement that asserts that two expressions have the same value. It typically consists of two parts: the left-hand side, which contains one expression, and the right-hand side, which contains another expression. The two sides are separated by an equal sign. The goal of solving an equation is to find the value(s) of the variable(s) that make the equation true.

Here,

The graph is not shown, but based on the given information, we can determine the slope of the line using the slope-intercept form of a linear equation:

y = mx + b

where y is the amount of money in the account, x is the number of weeks, m is the slope (the rate at which the money in the account is changing), and b is the y-intercept (the initial amount of money in the account). We know that Fred starts with 6 dollars in the account (y-intercept), and deposits 8 dollars each week (slope). Therefore, the equation for the line is:

y = 8x + 6

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Complete question:

Fred starts with 6 dollars in a bank account. He deposits exactly 8 dollars each week, and does not take any money out. The graph below represents the relationship between the number of weeks and the amount of dollars in the account. What is the slope of the line?

Answer:

B: Subtraction property of equality

Answer:

ASA

Step-by-step explanation:

Answer:

1 1/20

Step-by-step explanation:

I'm not sure how to explain this but it's the correct answer. Plz mark brainliest.

Answer:

1 1/20

Step-by-step explanation:

2/5 * 10 = 20/50

0.22 as a fraction 11/50

20/50 is the same as 40/100

11/50 is the same as 22/100

multiply

880/10000

which is 22/250

I will demonstrate two different ways to solve the equation 5^(2x+1) = 25.

Method 1: Taking the logarithm of both sides

Step 1: Start with the equation: 5^(2x+1) = 25

Step 2: Take the logarithm of both sides. We can use any logarithm base, but let's use the natural logarithm (ln) for this example:

ln(5^(2x+1)) = ln(25)

Step 3: Apply the logarithmic property to bring down the exponent:

(2x+1) * ln(5) = ln(25)

Step 4: Divide both sides by ln(5) to solve for x:

2x+1 = ln(25) / ln(5)

Step 5: Subtract 1 from both sides:

2x = (ln(25) / ln(5)) - 1

Step 6: Divide both sides by 2 to isolate x:

x = ((ln(25) / ln(5)) - 1) / 2

Now you can evaluate the right side of the equation to find the numerical value of x.

Method 2: Using the properties of exponents

Step 1: Start with the equation: 5^(2x+1) = 25

Step 2: Rewrite 25 as a power of 5:

5^2 = 25

Step 3: Set the exponents equal to each other:

2x+1 = 2

Step 4: Subtract 1 from both sides:

2x = 2 - 1

Step 5: Divide both sides by 2 to solve for x:

x = (2 - 1) / 2

Simplifying further:

x = 1/2

So, the solutions for the equation 5^(2x+1) = 25 are x = ((ln(25) / ln(5)) - 1) / 2 and x = 1/2.

Answer:

3

Step-by-step explanation:

division go brrrrrrrrrr

Answer:

x = 3

Step-by-step explanation:

The scale factor of A to B is \(\frac{18}{9}\) = 2

then

2x = 6  ( divide both sides by 2 )

x = 3

Answer:

55°

Step-by-step explanation:

A straight line equals 180 so all you have to do is subtract what you have from 180 to get x

180-125=55

Answer:

x=55

Step-by-step explanation:

180-125=55 since it is a straight angle

Answer:

As per the moment I cannot answer this due to know screenshot and lack of informatio

Step-by-step explanation:

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

No buddy you are wrong .

Look ;

(( Left table )) :

\( \frac{y}{x} = 6 \\ \)

\( \frac{48}{8} = 6 \\ \)

\( \frac{60}{10} = 6 \\ \)

\( \frac{72}{12} = 6 \\ \)

Thus it is proportional .

_________________________________

(( Right table )) :

\( \frac{y}{x} = \: .... \\ \)

\( \frac{12}{6} = 2 \\ \)

\( \frac{28}{7} = 4 \\ \)

\( \frac{68}{8} = 8 \\ \)

_________________________________

Thus the left table is proportional and

y is 6 times x in it.

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

15/19 + 14/19 = 29/19

Step-by-step explanation:

Add the number of balls in the basket together.

Subtract the number of white balls from the sample space ( the total amount of balls) your answer is written over the sample space and the same process is done for the green ball

The investment grows to $4,493.29 at 2% interest, $4,558.56 at 3% interest, $4,625.05 at 4% interest, $4,692.79 at 5% interest, and $4,761.81 at 6% interest after 4 years of continuous compounding.

To solve this problem, we need to use the formula for continuous compound interest:
A = Pe^(rt)

Where A is the amount after t years, P is the initial principal, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate, and t is the time in years.

Using the given information, we can fill in the table as follows:

Interest Rate | Amount after 4 years
--------------|---------------------
2%            | $4,493.29
3%            | $4,558.56
4%            | $4,625.05
5%            | $4,692.79
6%            | $4,761.81

To find the amount after 4 years at each interest rate, we plug in the values of P, r, and t into the formula and simplify:

2%: A = $4000 * e^(0.02*4) = $4,493.29
3%: A = $4000 * e^(0.03*4) = $4,558.56
4%: A = $4000 * e^(0.04*4) = $4,625.05
5%: A = $4000 * e^(0.05*4) = $4,692.79
6%: A = $4000 * e^(0.06*4) = $4,761.81

Therefore, the investment grows to $4,493.29 at 2% interest, $4,558.56 at 3% interest, $4,625.05 at 4% interest, $4,692.79 at 5% interest, and $4,761.81 at 6% interest after 4 years of continuous compounding.

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The given function f(x) = 25e^(-2x) represent the exponential decay.

According to th egiven question.

We have an exponential function.

f(x) = 25e^(-2x)

As we know that

If \(P = P_{o} e^{-kt}\) be an exponential function, then it will represent

Where,

P is the final amount

\(P_{o}\) is the intial amount

t is the time interval

k is the constant of proportionality

For the given question if we compare the given exponential function with the standard exponentential function we get

\(P_{o}\) = 25

k = 2

and t = x

Now,

e^(-2) = 0.13

Since, e^(-2) < 1.

Hence, the given function f(x) = 25e^(-2x) represent the exponential decay.

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