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Substituting the given values in the equation, we get:

y[n] = u[n] * h[n]y[n] = u[n] * [δ[n+1]−2δ[n]+δ[n−1]]y[n] = u[n+1] − 2u[n] + u[n-1]For n < 0, u[n] = 0For n >= 0,

Substituting the given values in the equation, we get:

y[n] = x[n] * h[n]y[n] = [δ[n+1]+δ[n]+δ[n−1]] * [δ[n+1]−2δ[n]+δ[n−1]]y[n] = δ[n+2] − 2δ[n+1] + δ[n+1] + δ[n] − 2δ[n] + δ[n-1] + δ[n] - 2δ[n-1] + δ[n-2]y[n] = δ[n+2] - δ[n+1] - δ[n-1] + δ[n-2]

Putting the value of n as 0 in the above equation we get; y[0] = δ[2] - δ[1] - δ[-1] + δ[-2]Since δ[-1] = 0 and δ[-2] = 0,

we have: y[0] = δ[2] - δ[1]

Similarly, for n = 1, we have: y[1] = δ[3] - δ[2] - δ[0] + δ[-1] = δ[3] - δ[2]

Similarly, for n = -1, we have: y[-1] = δ[1] - δ[0] - δ[-2] + δ[-3] = δ[1] + δ[-3]

For any other values of n, the output y[n] is 0

(ii) The output of the system in response to x[n]=u[n] is given by y[n] = x[n] * h[n]

Substituting the given values in the equation, we get:

y[n] = u[n] * h[n]y[n] = u[n] * [δ[n+1]−2δ[n]+δ[n−1]]y[n] = u[n+1] − 2u[n] + u[n-1]For n < 0, u[n] = 0For n >= 0,

we have: y[n] = u[n+1] − 2u[n] + u[n-1]

For n = 0, we have:\(y[0] = u[1] - 2u[0] + u[-1] = u[1] - 2u[0\)]

For n = 1, we have: \(y[1] = u[2] - 2u[1] + u[0]\)

For n > 1, we have: \(y[n] = u[n+1] - 2u[n] + u[n-1]\)

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The probability that a randomly selected student used acrylic paint given that the student chose to create a portrait is 3/5 or 60%.

To find the probability that a randomly selected student used acrylic paint given that the student chose to create a portrait, you can use the conditional probability formula:

P(Acrylic Paint | Portrait) = P(Acrylic Paint and Portrait) / P(Portrait)

From the given data:

- There were 3 students who used acrylic paint and created a portrait.
- There were a total of 5 students who created a portrait (3 with acrylic paint and 2 with oil paint).

So, the probability calculation would be:

P(Acrylic Paint | Portrait) = (3/5) / (5/5) = 3/5

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The likelihood of finding that the sample mean is between 59,050 and 60,950 miles can be determined by calculating the probability using the normal distribution with a sample size of 90, a population mean of 60,000 miles, and a population standard deviation of 4,000 miles.

To find out the probability of getting a sample mean between 59,050 and 60,950, a simulator is used to determine the tread life of tires mounted on light-duty trucks that follows a normal probability distribution.

Here, the population mean is 60,000 miles and the standard deviation is 4,000 miles. The given sample size is 90.

We can use the formula for standardizing the score. The standardized score for the lower limit of 59,050 is -2.78, and that of the upper limit of 60,950 is 2.78. Now, we need to find the probability of getting the mean value between -2.78 and 2.78.

We can use the standard normal distribution table to find the value, which is 0.9950 for z = 2.78 and 0.0050 for z = -2.78. Hence, the required probability is 0.9900.

Therefore, the likelihood of finding that the sample mean is between 59,050 and 60,950, for a sample size of 90 tires, is 0.9900.

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the BEST statement is: The serving costs about 40 cents.

To determine the cost of the optimal serving, we need to calculate the cost per serving based on the quantities of chicken and tomatoes used.

Given that an optimal serving contains 0.89 ounces of chicken and 0.52 ounces of tomatoes, we can calculate the cost as follows:

Cost of chicken =\(0.89 ounces * $0.40/ounce\)

Cost of tomatoes = \(0.52 ounces * $0.08/ounce\)

Total cost = Cost of chicken + Cost of tomatoes

Total cost =\((0.89 * $0.40) + (0.52 * $0.08)\)

Total cost =\($0.356 + $0.0416\)

Total cost ≈\($0.3976\)

Rounding to the nearest cent, the cost of the optimal serving is about 40 cents.

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Answer:

14,641.

Step-by-step explanation:

214,358,881 ÷ 14,641 = 14,641.

Answer:

1. The formula used to the find distance formula is: \(Distance\:Formula=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

2. The distance between the points (-3,8) and (-4, -2) is 10.04

Step-by-step explanation:

1. Which of the following is the correct form of the distance formula?

The formula used to the find distance formula is: \(Distance\:Formula=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

2. Use the distance formula to find the distance between the points (-3.8) and (-4. -?)

Note: Since the y-term in (-4,-) is missing So, I am using -2 to solve the question and find distance. You can use the term given in question and replace it with -2 and use this solution as reference to solve and find the correct answer.

We have points (-3,8) and (-4,-2)

Putting values in distance formula and finding result:

\(Distance\:Formula=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

We have x_1=-3, y_1=8, x_2=-4, y_2=-2

\(Distance=\sqrt{(-2-(-3))^2+(-2-8)^2}\\Distance=\sqrt{(-2+3)^2+(-2-8)^2}\\Distance=\sqrt{(1)^2+(-10)^2}\\Distance=\sqrt{1+100}\\Distance=\sqrt{101}\\Distance=10.04\)

So, the distance between the points (-3,8) and (-4, -2) is 10.04

2 hours after administration 20 mg of the drug will remain in the client's system.

To determine how much of the drug will remain 2 hours after administration, we need to consider the concept of half-life.

The half-life of a drug is the time it takes for half of the initial amount of the drug to be eliminated from the body.

The half-life of the drug is 2 hours.

Let's break down the problem:

Initial amount of the drug: 40 mg

Half-life of the drug: 2 hours

After 2 hours, half of the initial amount of the drug will remain.

So we can calculate it as follows:

Remaining amount = \(Initial amount \times (1/2)^{(time elapsed / half-life)\)

The time elapsed is 2 hours, and the half-life is also 2 hours.

Substituting these values into the formula:

Remaining amount = \(40 mg \times (1/2)^{(2 / 2)\)

Simplifying the calculation:

Remaining amount = 40 mg × (1/2)¹

Remaining amount = 40 mg × (1/2)

Remaining amount = 20 mg

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Answer:

-243

Step-by-step explanation:

Each value is multiplied by -3. 3 x -3 = -9, -9 x -3 = 27, and the rest goes the same

Answer:

The common ratio of the sequence is -3
The sum of the first five terms of the sequence is 183

Step-by-step explanation:

I got it right, but -3*3= -9 and you just keep multiplying by -3 to get 183

Answer:

All of them

Step-by-step explanation:

The ratios equivalent to 6:8 would be:

21:28

9:12

36:48

All of these answer choices would be correct because they are all multiples of 6

He will have to mix 3 pounds of cashews and 7 pounds of peanuts .

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Let c be denoted as cashew and p be denoted as peanuts

c + p = 10  ⇒ (1)

5.6c + 2.3p = 3.29*10 ⇒ (2)

Multiply eq(1) by 560

Multiply eq(2) by 100

560c + 560p = 5600

560c + 230p = 3290

Subtract and solve for "p":

330p = 2310

p = 7  (amt. of peanuts needed)

substitute  the value of p in eq(1)

c + 7 = 10

c = 3  (amt. of cashews needed)

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The shortest length of fence that the rancher can use is 6000 ft.

What is meant by length?

The measuring of one thing from finish to finish or on its longest aspect, or a measuring of a selected a part of one thing is known as length.

Main Body:

x = width of rectangle

y = length of rectangle

A = area of rectangle = xy = 1500000 ft^2

L = length of fencing needed = 2(x + y) + x = 3x + 2y

L = 3x + 2(1500000/x) = 3x + 3(10^6)x^(-1)

As x –> 0+, L –> +inf.

As x –> +inf, L –> (3x)+.

Sketch and see that there will be a minimum in Quadrant I.

dL/dx = 3 - 3(10^6)x^(-2)

Extrema occur when dL/dx = 0:

3 - 3(10^6)x^(-2) = 0

(10^6)x^(-2) = 1

x^2 = 10^6

x > 0, so x = 1000 feet for shortest length.

Hence,Shortest L = 3000 + 3(10^6)(10^3)^(-1) = 6000 feet.

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the point equidistant from the points (0, 0, 0), (0, 4, 0), (3, 0, 0), and (2, 2, -3) are (1/2, 1, 3/2).

Equidistant is a synonym for "equally distant," which is the state of two points being at the same distance from one another. Equidistant implies at the same distance from a location. The term "equidistant" is commonly used in reference to circles, perpendicular bisectors, parallel lines, and other geometrical concepts .Equidistant refers to the relationship between two or more objects or points that are situated at the same distance from one another. A point is considered to be equidistant from two other points when they are both located at the same distance from it. In the middle of the two starting points is a midway. The distance formula or the halfway formula can be used to demonstrate this.

Equation of sphere passes through origin is given by

x2 + y2 + z2 + ax + by+ cz =0

Given, it also passes through (1,0,0), (0,2,0),(0,0,3)

1+ a = 0,                                a = -1

4+2b =0,                             b=-2

And, 9+3c = 0,                       c= -3

The equation of the sphere becomes x2 +y2+ z2 -x -2y -3z = 0

Comparing with x2 +y2+ z2+ 2gx +2fy +2kz +C =0

Therefore the point that is equidistant from all the given points will be the centre of the sphere passing through all these points.

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The two points that would lie on the graph of function g(x) = 3f(x) are (-2, -12) and (1, 30).

To find the points that would lie on the graph of function g(x) = 3f(x)

we need to multiply the y-coordinates of the given points on the graph of f by 3.

Given points on the graph of f:

(-2, -4) and (1, 10)

Applying the multiplication by 3:

(-2, -4) -> (-2, -4×3) -> (-2, -12)

(1, 10) -> (1, 10×3) -> (1, 30)

Therefore, the two points that would lie on the graph of function g(x) = 3f(x) are (-2, -12) and (1, 30).

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Given, Two vertical poles of length 6 feet and 8 feet, respectively, stand 10 feet apart.

A cable reaches from the top of one pole to some point on the ground between the poles and then to the top of the other pole. We need to express the amount of cable used, f, as a function of the distance from the 6-foot pole to the point where the cable touches the ground, x.

[asy]
size(200);
draw((0,0)--(8,0)--(8,10)--(0,6)--cycle);
draw((0,6)--(8,8));
label("$6$",(0,0)--(0,6),W);
label("$8$",(8,0)--(8,8),E);
label("$x$",(0,0)--(0,6),NW);
label("$10-x$",(0,6)--(0,10),W);
label("$y$",(8,0)--(8,8),NE);
label("$10$",(0,0)--(8,0),S);
[/asy]

Let the height of the point where the cable touches the ground be y. Then the distance from the 6-foot pole to the point where the cable touches the ground, x = 10 - y.

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Step-by-step explanation:

enjoyyyyyyyyyyyy broooooooo

Answer:

33m

Step-by-step explanation:

If the ratio of the new length to the old length is 11:8 (simplified ratio)

I like to set up a proportion, like this,

x/24 = 11/8, where x is the undefined new length

x*8 = 24*11 (cross multiply)

8x = 264 (multiply)

x = 33 (divide 8 by both sides)

The new length is 33m.

Hope I helped! Good Luck!

Answer:

33m

Step-by-step explanation:

The 8 part of the ratio refers to the old length 24m

Divide by 8 to find the value of one part of the ratio

24m ÷ 8 = 3m ← value of 1 part of the ratio, then

11 parts = 11 × 3 = 33m

Thus

33m : 24m = 11 : 8

Answer:

a=14

b=166

c=166

d=166

e=166

f=14

x=5

The dots in the patterns are illustrations of a sequence or progression

From the pattern, we have:

So, we have the following pattern

\(T_n = (n -1)^2+ 3\)

When n = 10, we have:

\(T_{10} = (10 -1)^2+ 3\)

T10 = 84

This means that, there will be 84 dots in step 10 and there will be (n -1)^2+ 3 dots in step n

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Given that 3/5 of the people who attended the concert live closer than 50 miles from the venue, we can find the total number of people who live closer than 50 miles by multiplying 3/5 with the total number of people who attended the concert:

Total number of people who live closer than 50 miles = 3/5 x 4800 = 2880

We are also given that 0.3 of the people who live closer than 50 miles from the venue spent more than $560 per ticket. To find the number of people who attended the concert and live closer than 50 miles from the venue and spent more than $560 per ticket, we can multiply the total number of people who live closer than 50 miles by 0.3:

Number of people who attended the concert and live closer than 50 miles from the venue and spent more than $560 per ticket = 0.3 x 2880 = 864

Therefore, 864 people who attended the concert live closer than 50 miles from the venue and spent more than $560 per ticket.

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Answer:

z= 63 degrees

x≈16

Step-by-step explanation:

90+27=117

180-117=63 (bc all angles in a triangle have to add up to 180)

so the angle opposite from the 27 is 63 degrees.

Because of opposite interior angles, z=63.

sin 63= \(\frac{14}{x}\)

xsin63=14

x=\(\frac{14}{sin63}\)

x≈16

(1) -5 + -9 is simplified as - 14.

(2) (-7)(-8) is simplified as 56.

(3) 17 - (-8) is simplified as 25.

(4) i. 9 + 9 = 18, ii. 9 - 9 = 0, iii. -9 - 9 = -18, iv. 9 - (-9) = 18, v. -9 - (-9) = 0

(5) The evaluation of  -5 + 4 - 8 is determined as -9.

(6) The evaluation of  4 + 3² + 9 ÷  3/2² is determined as 13.75.

(7) The evaluation of  (-4)² - (-4) + 10 x  3 + 2 is determined as 52.

(8) The LCM of the numbers 2, 6, and 9 is 18

9b. False. All natural numbers are integers.

9a. π is an irrational number.

The given expressions is simplified as follows;

Question 1, is simplified as;

-5 + -9 = -14

Question 2, is simplified as;

(-7)(-8) = 56

Question 3, is simplified as;

17 - (-8) = 25

Question 4, is simplified as;

i. 9 + 9 = 18

ii. 9 - 9 = 0

iii. -9 - 9 = -18

iv. 9 - (-9) = 18

v. -9 - (-9) = 0

Question 5, the evaluation of  -5 + 4 - 8 is determined as;

-5 + 4 - 8 = -9

Question 6, the evaluation of  4 + 3² + 9 ÷  3/2² is determined as;

4 + 3² + 9 ÷  3/2²

= 4 + 9 + 3 / 4

= 4 + 9 + 0.75

= 13.75

Question 7, the evaluation of  (-4)² - (-4) + 10 x  3 + 2 is determined as;

(-4)² - (-4) + 10 x  3 + 2

= 16 + 4 + 30 + 2

=  52

Question 8, the LCM of the numbers 2, 6, and 9 is 18

Question 9,

b. False. All natural numbers are integers.

a. π is an irrational number.

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the derivative of f(x) is: f'(x) = 5ln(7x) + 5 = 35ln(7x) + 35 , To differentiate f(x) = 5xln(7x) - 5x, we can use the product rule and the chain rule of differentiation:

Product rule: (fg)' = f'g + fg'

Chain rule: (f(g(x)))' = f'(g(x)) * g'(x)

Using the product rule, we get:

f'(x) = (5x)'ln(7x) + 5x * (ln(7x))'

= 5ln(7x) + 5x(1/x)

= 5ln(7x) + 5

Using the chain rule, we get:

f'(x) = 5x * ((ln(7x))' * 7 + ln(7x)' * 7x')

= 5x * (1/x * 7 + ln(7x) * 7)

= 35ln(7x) + 35

Thus, the derivative of f(x) is:

f'(x) = 5ln(7x) + 5 = 35ln(7x) + 35

This means that the rate at which f(x) is changing with respect to x is given by the function f'(x). We can interpret this result as follows: if x increases by a small amount, f(x) will increase by approximately 35ln(7x) + 35 times that amount. This rate of change is influenced by both the logarithm and the constant term in the function, and it can be either positive or negative depending on the value of x.

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Answer: 2 3/7

Step-by-step explanation:

The requirements for a hypothesis test are satisfied.

To test the claim that the rate of polio is less for children given the Salk vaccine, we need to check if the requirements for a hypothesis test about two population proportions are met. The requirements are:

1. The samples are simple random samples and independent.
2. For each of the two groups, the sample size is at least 1000.

In this case, the study involved 401,974 children who were randomly assigned to two groups: the treatment group with 201,229 children and the placebo group with 200,745 children. This satisfies the first requirement, as the samples are simple random samples and independent. The sample size for both groups is also larger than 1000, meeting the second requirement.

Therefore, the requirements for a hypothesis test are satisfied, and we can proceed with testing the claim that the rate of polio is less for children given the Salk vaccine.

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(a) The derivative of f(x) with respect to x at x = -1 is -6.

(b) The product of (2x) and f'(x) at x = -1 is 12.

(c) The sine of the expression f(x) + 2x² - 2x + 2 at x = -1 is sin(4).

(a) To find df(x)/dx at x = -1, we need to differentiate the given function f(x) = 2x² - 2x + 2 with respect to x. Taking the derivative of f(x), we get f'(x) = 4x - 2. Now, substitute x = -1 into the derivative equation to find f'(-1): f'(-1) = 4(-1) - 2 = -6. Therefore, df(x)/dx at x = -1 is -6.

(b) To find the product (2x)f'(x) at x = -1, we multiply the given function f'(x) = 4x - 2 by 2x. Substitute x = -1 into the expression to get (2(-1))f'(-1): (2(-1))f'(-1) = -2(-6) = 12.

(c) To find sin(f(x) + 2x² - 2x + 2) at x = -1, substitute x = -1 into the given function f(x) = 2x² - 2x + 2. We get f(-1) = 2(-1)² - 2(-1) + 2 = 2 + 2 + 2 = 6. Now, substitute f(-1) into sin(f(x) + 2x² - 2x + 2) to find sin(6 + 2x² - 2x + 2). At x = -1, this becomes sin(6 - 2 - 2 + 2) = sin(4). Hence, sin(f(x) + 2x² - 2x + 2) at x = -1 is sin(4).

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If X is a radom variable for amount you win, Then the excepted value of game or expected income i.e E(X) is 8/13.

Expected Income is the result of multiplying your income by the probability of earning it. This expected revenue can be subtracted by the expected cost to get the expected profit.

Mathematically, E(X) = X₁p₁ + X₂p₂ + ---+ Xₙpₙ

where Xᵢ are observation and pᵢ probability of Xᵢ.

We have given that,

Total number of cards in standard card deck = 52

i.e total possible outcomes = 52

One card is drawn from deck.

Total number of king cards in 52-card deck = 4

Favourable outcomes that drawn card is king = 4

Probability of getting a king card , p = 4/52 = 1/13

Probability of not getting a king ,q = 1 - p

= 1 - 1/13 = 12/13

let X be the amount you win . You win $20 if a king is drawn and lose $1 if king is not drawn . So, probability distribution is

Xᵢ pᵢ

$20 1/13

-$1 12/13

So, E(X) = ∑ Xᵢpᵢ = 20× 1/13 + (-1)× 12/13 = 20/13 - 1/13 = 8/13

Hence, required excepted value is 8/13.

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Answer:

8⁻¹

Step-by-step explanation:

1/x = x⁻¹

Answer:

Nina has drove 80 mph.

Step-by-step explanation:

400 miles 5 hours

400 dived by 5= 80

Answer: 19 gallons

Step-by-step explanation:

Conversion factor is 1 gallon is to 128 fluid ounces.

If 2,432 fluid ounces leaked out, to find out the amount of gallons this was, you need to divide the fluid ounces by the number of fluid ounces in a gallon. This is what is done when moving from a smaller unit to a larger one.

= 2,432 / 128

= 19 gallons