Plot the values on a graph​

Step-by-step explanation:

(y2-y1)/(x2-x1)=(y-y1)/(x-x1)

(-21-15)/(-2-4)=( y-15)/(x-4)

6(x-4)=y-15

6x-y-9=0

Given the n™ term of a number sequence, the first three terms of the sequence are 0, 2 and 6

The sequence is given as:

n^2 - n​

To write down the first three terms of the sequence, we set n =1, 2 and 3

So, we have:

When n = 1

n^2 - n​ = 1^2 - 1

Evaluate

n^2 - n​ = 0

When n = 2

n^2 - n​ = 2^2 - 2

Evaluate

n^2 - n​ = 2

When n = 3

n^2 - n​ = 3^2 - 3

Evaluate

n^2 - n​ = 6

Hence, the first three terms of the sequence are 0, 2 and 6

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The required probability is 0.4408.

The operating characteristics of the loading gate problem are:

L = λ/ (μ - λ)

W = 1/ (μ - λ)

Lq = λ^2 / μ (μ - λ)

Wq = λ / μ (μ - λ)

ρ = λ / μ

P0 = 1 - λ / μ

Where, L represents the average number of cars either being loaded or waiting.

W represents the average time a car spends either being loaded or waiting.

Lq represents the average number of cars waiting.

Wq represents the average waiting time of a car.

ρ represents the utilization factor.

ρ = λ / μ represents the ratio of time the worker spends loading cars to the total time the system is busy.

P0 represents the probability that the system is empty.

The probability that there will be more than six cars either being loaded or waiting is to be determined. That is,

P (n > 6) = 1 - P (n ≤ 6)

Now, the probability of having less than or equal to six cars in the system at a given time,

P (n ≤ 6) = Σn = 0^6 [λ^n / n! * (μ - λ)^n]

Putting the values of λ and μ, we get,

P (n ≤ 6) = Σn = 0^6 [(6/ 48)^n / n! * (8/ 48)^n]

P (n ≤ 6) = [(6/ 48)^0 / 0! * (8/ 48)^0] + [(6/ 48)^1 / 1! * (8/ 48)^1] + [(6/ 48)^2 / 2! * (8/ 48)^2] + [(6/ 48)^3 / 3! * (8/ 48)^3] + [(6/ 48)^4 / 4! * (8/ 48)^4] + [(6/ 48)^5 / 5! * (8/ 48)^5] + [(6/ 48)^6 / 6! * (8/ 48)^6]P (n ≤ 6) = 0.5592

Now, P (n > 6) = 1 - P (n ≤ 6) = 1 - 0.5592 = 0.4408

Therefore, the required probability is 0.4408.

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The formula for the matrix of the projection onto Null(A) can be found using the concept of orthogonal projection. It is given by P = I - A(A^T A)^(-1) A^T, where A^T represents the transpose of matrix A,

To find the matrix of the projection onto Null(A), we can use the concept of orthogonal projection. The projection matrix P projects vectors onto the null space of A.

The formula for the projection matrix is P = I - A(A^T A)^(-1) A^T, where A^T represents the transpose of matrix A, I is the identity matrix, and (A^T A)^(-1) denotes the inverse of the matrix product A^T A.

The matrix A has independent rows, which implies that its columns are linearly independent. This means that the matrix A^T A is invertible.

Using the formula for the projection matrix P, we can find the matrix that projects vectors onto the null space of A. By subtracting the projection matrix from the identity matrix I, we obtain the desired matrix.

Therefore, the formula for the matrix of the projection onto Null(A) is P = I - A(A^T A)^(-1) A^T.

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Let's solve your inequality step-by-step.

\(2<2x+4<10\)

\(2 + -4 < 2x + 4 + -4 < 10 + -4\) (Add -4 to all parts)

\(-2 < 2x < 6\)

\(\frac{-2}{2} < \frac{2x}{2} < \frac{6}{2}\) (Divide all parts by 2)

\(-1 < x < 3\)

So the answer is : \(-1 < x < 3\)

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

3π=3×3.14 =9.42

7π=7×3.14=21.98

Step-by-step explanation:

so the distance around window , in feet be

3π=3×3.14=9.42

7π=7×3.14=21.98

Hey there!

f(x) = g(x) = h(x) = y

Since, you have the value of x (8), you can substitute it in the equation to make it easier to solve. We just have to find your f(x) value (also known as the y-value)

f(x) -0 -3 * x^2 - 2

f(x) = -3x^2 - 2

y = -3x^2 - 2

y = -3(8)^2 - 2

y = -3(8^2) - 2

y = -3(8 * 8) - 2

y = -3(64) - 2

y = -192 - 2

y = -194

Therefore, your answer should be:

f(x) = -194

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer: 2/x+4x^2

Step-by-step explanation:

Do distrubitive property.

SO mutiply 2/5 to 5/x which is 10/5x or 2/x

then 2/5 times 10x^2

10*2/5=20/5 or 4

Done.

Have a nice day! :)

Answer:

Step-by-step explanation:

So the equation is y = 4x + 9 is indeed y - 4x = 8.

To find the equation of a line parallel to the line y = 4x + 9 and passing through the point (-2, 0), we can use the fact that parallel lines have the same slope.

The given line has a slope of 4, so the parallel line will also have a slope of 4.

Using the point-slope form of a linear equation, we can write the equation for the parallel line:

y - y1 = m(x - x1),

where (x1, y1) is the given point (-2, 0), and m is the slope, which is 4.

Substituting the values into the equation:

y - 0 = 4(x - (-2)),

y = 4(x + 2),

y = 4x + 8.

This equation is in the slope-intercept form (y = mx + b), where the slope is 4 and the y-intercept is 8.

However, the answer provided, y - 4x = 9, is in a different form called the standard form of a linear equation. To convert the equation y = 4x + 8 to the standard form, we can move the 4x term to the left side:

y - 4x = 8.

So, the equation for the line passing through the point (-2, 0) and parallel to y = 4x + 9 is indeed y - 4x = 8.

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The ratio of impressions to fans is a measure of fan acquisition.

Given is to find the ratio of impressions to fans.

The ratio of impressions to fans is a measure of fan acquisition. Social marketing campaigns begin with fan acquisition, which involves using any of a variety of means, from display ads to News Feed and page pop-ups, to attract people to your Web page.

Therefore, the ratio of impressions to fans is a measure of fan acquisition.

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The length of line segment BC in this particular kite is 14 units, which is equal to the length of AB.

In the given kite ABCD, we know that sides AB and BC are congruent, and the length of AB is 14 units. Additionally, sides CD and AD are congruent, and the length of CD is 22 units.

To find the length of BC, we can use the properties of a kite. Since AB and BC are congruent, we can conclude that BC is also 14 units long.

This is because a kite has two pairs of congruent adjacent sides. Therefore, the length of line segment BC in this particular kite is 14 units, which is equal to the length of AB.

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Answer:

The length of line segment BC in this particular kite is 14 units, which is equal to the length of AB.

Step-by-step explanation:

just took test

The forecast for week 6 if Y is forecast for demand of chips sale and X is the week 18. The correct answer is 1) 18 KD.

This forecast assumes a linear relationship between the demand for chips sale and time. To use the equation Y=2X+6 for forecasting the demand of chips sale, we need to plug in the value of X, which is the week for which we want to create the forecast. Here, we want to forecast for week 6, so X=6.

Substituting the value of X=6 in the equation, we get:

Y=2(6)+6

Y=12+6

Y=18

Therefore, the forecast for week 6 using the given equation is 18.

Hence, option 1) 18 KD is the correct answer.

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The function in terms of its partial fractions. The inverse Laplace transform of 2/(s^2+81)^2 is 2te^(-9t)cos(9t) - 2te^(9t)cos(9t).

To apply the convolution theorem to find the inverse Laplace transform of the function 2/(s^2+81)^2, we first need to express the function in terms of its partial fractions.

The given function can be written as: 2/(s^2+81)^2 = A/(s+9i)^2 + B/(s-9i)^2 Where A and B are constants. Now, we need to find the values of A and B. To do this, we can multiply both sides of the equation by (s+9i)^2 and substitute s = -9i: 2 = A + B/(s-9i)^2 2 = A + B/(-18i)^2 2 = A + B/324 From this equation, we can find A = 2 and B = -324.

Now, we can find the inverse Laplace transform of each term separately. The inverse Laplace transform of A/(s+9i)^2 is 2te^(-9t)cos(9t), and the inverse Laplace transform of B/(s-9i)^2 is -2te^(9t)cos(9t).

Therefore, the inverse Laplace transform of 2/(s^2+81)^2 is 2te^(-9t)cos(9t) - 2te^(9t)cos(9t).

In summary, the inverse Laplace transform of the given function is 2te^(-9t)cos(9t) - 2te^(9t)cos(9t).

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Answer:

A

Step-by-step explanation:

Notice that its y-intercept is (0,-5), so it crosses the y-axis at (0,-5)

Then, we notice that it is going doing from [-10,-2] and remains the same from[-2, 10]. Thus, the best choice is A

Answer: The large rectangle boxes all have the property of 2

This is because 2 large boxes are equivalent to 4 and one of the rectangular boxes has to fill in the gap which is the 2  -1 boxes which would make them equivalent to each other.

Answer:

g

Step-by-step explanation:

g

Answer:

33:21

Step-by-step explanation:

The way I look at it is that 11:7 is 18 parts of 54. So I divide 54 by 18 and get 3 per. Then multiply, 11 * 3 is 33 and 7 * 3 is 21.

The expression is 12 x 2 / 7 will be 24/7. And the number 54 into the ratio 11:7 will be 33 and 21.

The utilization of two or more additional numbers that compares is known as the ratio.

The expression is given below.

⇒ 12 x 2 / 7

⇒ 24 / 7

Divide 54 into the ratio 11:7.

⇒ 54 x 11 / (11 + 7)

⇒ 594 / 18

⇒ 33

⇒ 54 x 7 / (11 + 7)

⇒ 378 / 18

⇒ 21

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The particular solution for the given non-homogeneous system of first-order linear differential equations is:

\(Y = 54x - (5/3)x^3 + 3x^2 + 25x + 16\)

To find the particular solution for the non-homogeneous system of first-order linear differential equations, we need to substitute the given values into the system and solve for the unknown coefficients.

The given system is:

\(Y' = 54 - 5x^2 + 6x + 25\\Y(0) = 12 - x^2 + 2x + 4\)

Differentiating the second equation, we have:

\(Y'(0) = -2x + 2\)

Now, let's substitute these values into the first equation:

\(Y' = 54 - 5x^2 + 6x + 25\)

Since there are no derivatives of Y in the equation, we can integrate both sides with respect to x to find the particular solution:

\(\int Y' dx = \int (54 - 5x^2 + 6x + 25) dx\)

Integrating each term separately, we get:

\(Y = 54x - (5/3)x^3 + 3x^2 + 25x + C\)

Now, using the initial condition\(Y(0) = 12 - x^2 + 2x + 4\), we can substitute x = 0 and \(Y = 12 - x^2 + 2x + 4\) into the equation to solve for the constant C:

\(12 - 0 + 2(0) + 4 = 54(0) - (5/3)(0^3) + 3(0^2) + 25(0) + C\)

16 = C

C= 16

Therefore, the particular solution for the given non-homogeneous system of first-order linear differential equations is:

\(Y = 54x - (5/3)x^3 + 3x^2 + 25x + 16\)

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Answer:

simplified = 8x - 8

Step-by-step explanation:

trust me :)

Step-by-step explanation:

1 kg = 1000 grams (hence the name : "kilo" means 1000).

so, 2kg = 2×1000 = 2000 grams.

now, how many CDs are in 2000 grams, when 1 weighs 10 grams ?

in other words : how often does 19 grams fit into 2000 grams ?

that is what division is for :

2000/10 = 200

so, you would need 200 CDs to reach 2kg.

There are four ways for four kings can be next to each other and four queens can be next to each other.

The first way is by positioning the kings and queens diagonally opposite each other.

The second way is by arranging them in a cross shape, with two kings on the top, two queens on the bottom, two queens on the left, and two kings on the right.

This means that in total, there are four possible ways that four kings and four queens can be placed next to each other.

The kings and queens on a card set are four in number. Hence, the probability of their arrangement next to each other would be four.

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Latrell would need to pay 105 to replace the felt on his pool table.

Latrell has a pool table that is 3 feet wide and 7 feet long.

The pool table's felt needs to be replaced, and the cost of the felt per square foot is $5.00.

Let's find out how much it would cost Latrell to replace the pool table's felt.

What is the surface area of the pool table.

To determine the surface area of the pool table,

we need to multiply the length by the width, as shown below:

Surface area = length × width

Surface area = 7 ft × 3 ft

Surface area = 21 square feet

Now that we know the surface area of the pool table, we can determine the cost of the felt.

Latrell will need 21 square feet of felt, and it costs $5.00 per square foot.

We can use the following formula to determine the total cost of the felt:

Total cost of felt = cost per square foot × surface area.

Total cost of felt = $5.00 × 21 square feet.

Total cost of felt = $105

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The total number of arrangements is 1,152.

There are 4 husband-wife pairs, which we can treat as units. We can first arrange the wives in any order, which can be done in 4! = 24 ways. Once the wives are arranged, we can arrange the husbands to the right of their wives. The first husband can take any of the 4 available slots to the right of his wife, the second husband can take any of the remaining 3 slots, and so on.

Therefore, the total number of arrangements is:

4! x 4 x 3 x 2 x 1 = 1,152.

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Answer:

B) -2

Step-by-step explanation:

Hope this helps. Good luck...

Answer:

B

Step-by-step explanation:

Answer:

Domain: All real numbers

Range:  f(x) ≥ 5 or f(x) < 2

Step-by-step explanation:

The given graph is a graph of a piecewise function.

Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.

When graphing piecewise functions:

Domain

The domain of a function is the set of all possible input values (x-values).

From inspection of the graph, the arrows show that the function continues indefinitely in both the positive and negative directions.

The value of x = 1 is not included in the left part of the graph, but it is included in the right part of the graph.

Therefore, the domain of the function is all real values of x:  

Range

The range of a function is the set of all possible output values (y-values).

From inspection of the graph, there is an open circle at y = 2 and a closed circle at y = 5.  Therefore, there are no y-values in the interval:
2 ≤ y < 5.

Therefore, the range of the function is f(x) < 2 or f(x) ≥ 5:

Answer:

Step-by-step explanation:

−2/9x+2.7=4

subtract 2.7 from both sides

-2.9x = 1.3

divide -2.9 from both sides

x= -.4482 or x= -.45

The value of c for which f '(/4) = 1 in the function f(x) = cx ln(cos x) is approximately c = -2.

To find the value of c, we first need to calculate the derivative of f(x) with respect to x. Using the product rule and the chain rule, we obtain:

f '(x) = c ln(cos x) - cx tan(x).

Next, we substitute x = π/4 into f '(x) and set it equal to 1:

f '(/4) = c ln(cos(/4)) - c(/4) tan(/4) = 1.

Simplifying the equation, we have:

c ln(√2/2) - c(1/4) = 1.

ln(√2/2) can be simplified to ln(1/√2) = -ln(√2) = -ln(2^(1/2)) = -(1/2) ln(2).

Now, rearranging the equation and solving for c:

c ln(2) = -1 + c/4.

c(ln(2) - 1/4) = -1.

c = -4/(4ln(2) - 1).

Calculating the approximate value, c ≈ -2.

Therefore, the value of c for which f '(/4) = 1 in the function f(x) = cx ln(cos x) is approximately c = -2.

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There are different ways to approach this question, but one possible method is to conduct a one-sample t-test using the formula t = (M - μ) / (s / sqrt(n)), where M is the sample mean, μ is the population mean (null hypothesis), s is the sample standard deviation, and n is the sample size. With the given information, the t-value is (1.6 - 0) / (0.8 / sqrt(16)) = 8.

The degrees of freedom is n - 1 = 15. Using a t-table or a calculator, the p-value for a one-tailed test with 15 degrees of freedom and a t-value of 8 is much smaller than .05 (e.g., < .0005). Therefore, we can reject the null hypothesis and conclude that women find a sense of humor to be important in a long-term relationship at a .05 level of significance. The correct answer is b.

Test 2 is associated with smaller critical values. The critical values for a t-test depend on the level of significance, the degrees of freedom, and whether the test is one-tailed or two-tailed. In general, a smaller level of significance or a larger sample size leads to smaller critical values (i.e., it becomes easier to reject the null hypothesis). Since Test 2 has a larger sample size than Test 1, it is more likely to detect a significant effect (i.e., have a smaller Type II error rate), and therefore requires smaller critical values to achieve a .05 level of significance. The correct answer is b.

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