Consider a mass spring system with m = 1 kg, B = 8 kg/s and k = 16 N/m. The external force applied to the mass is F(t) = sint + 2e-4t. Find the equation for the displacement of the mass. x(t).

Answer:

a) yes, because they both increase by the same increments each time. Tis can be represented by the equation y=5x+2

b) y=5x+2

c) The y-intercept represents the amount of units there were initially and the slope represents the amount of units for every worker.

SA= 2 (4)(5) + 2(5)(9) + 2(4)(9)

SA= 202in^2

If the box contains confetti, how much cubic inches of confetti are needed to fill the box?

V= lwh

= 4*5*9

= 180 in^3

Answer:

Step-by-step explanation:

The solution to the system of equations is x1 = -(9/7)x4, x2 = (2/7)x4, x3 = -(1/7)x4, and x4 is a free variable.

a) xy + 2x2 + 2x3 = 1 X1 - 2x2 + 2x3 = -3 3x1 - x2 + 5x3 = 7

We can solve the system of equations using both inverse matrix (if possible) and reduced row echelon forms.

We begin by converting the above equations into matrix form as follows:

[xy+2x2+2x3=1] [X1-2x2+2x3=-3] [3x1-x2+5x3=7] = [1] [-3] [7]

We represent the coefficient matrix by A and the variable matrix by X.

Then we have AX = B where B = [1] [-3] [7]

To find the inverse of A.

If the inverse of A exists, we can use it to find X = A^(-1)B.

We can find the inverse of A using the formula A^(-1) = adj(A)/|A| where adj(A) is the adjugate of A and |A| is the determinant of A.

We have: det(A) = |[1,2,2;-1,-2,2;3,-1,5]| = 9adj(A) = [11,6,-4;19,9,-5;-7,-4,3]

Therefore, A^(-1) = adj(A)/|A| = [11/9,2/3,-4/9;19/9,1/3,-5/9;-7/9,-4/3,1/9]

We can use A^(-1) to find X as follows:

X = A^(-1)B = [11/9,2/3,-4/9;19/9,1/3,-5/9;-7/9,-4/3,1/9][1;-3;7] = [-5/3;1/3;2/3]

Therefore, the solution to the system of equations is x = -5/3, y = 1/3, z = 2/3.

We can also solve the system of equations using the reduced row echelon form of the augmented matrix as follows:[1,2,2,1;-1,-2,2,-3;3,-1,5,7] [R2+R1,R3-3R1] [1,2,2,1;-4,-3,4,-2;0,-7,-1,4] [R2/(-4),R3/(-7)] [1,2,2,1;1/4,1,-1,1/2;0,1,1/7,-4/7] [R1-2R2, R3-(1/7)R2] [1,0,3/2,-1/2;0,1,1/7,-4/7;0,0,0,0]

The last row of the above matrix represents the equation 0x1 + 0x2 + 0x3 + 0x4 = 0, which is an identity.

The system of equations is consistent, and we can solve for x, y, and z using the first two rows of the above matrix as follows:

x + (3/2)z = (-1/2)y + (1/7)z = (4/7)

Solving for z, we have: z = 2/3

Substituting z into the first equation, we have:

x + (3/2)(2/3) = (-1/2)x = -5/3

Substituting z into the second equation, we have:

y + (1/7)(2/3) = (4/7)y = 1/3

Therefore, the solution to the system of equations is x = -5/3, y = 1/3, z = 2/3.b) x1 + 2xy + 2x3 + 5x4 = 0 *1 - 2x2 + 2x2 - 4x4 = 0 3x1 - x2 + 5x3 + 2x4 = 0 3x, -2x2 + 6x3 - 3x4 = 0

To solve this system of equations, we begin by converting it into matrix form as follows:[1,2y,2,5;0,-2,2,-4;3,-1,5,2;3,-2,6,-3] [x1;x2;x3;x4] = [0;0;0;0]

We represent the coefficient matrix by A and the variable matrix by X.

Then we have AX = 0. Our task is to find the reduced row echelon form of the augmented matrix [A|0].

We perform the following elementary row operations to the above matrix to obtain the reduced row echelon form:[1,2y,2,5,0;0,-2,2,-4,0;3,-1,5,2,0;3,-2,6,-3,0] [R1-2yR2, R3-3R2, R4-3R2] [1,0,-2y-1,2y+5,0;0,-2,2,-4,0;0,-7,-1,14,0;0,-8,0,9,0] [R3/(-7), R4/(-8)] [1,0,-2y-1,2y+5,0;0,-2,2,-4,0;0,1,1/7,-2/7,0;0,1,0,-9/8,0] [R1+(2y+1)R3] [1,0,0,9/7,0;0,-2,0,-2/7,0;0,1,1/7,-2/7,0;0,0,0,0,0]

The last row of the above matrix represents the equation 0x1 + 0x2 + 0x3 + 0x4 = 0, which is an identity.

The system of equations is consistent, and we can solve for x1, x2, x3, and x4 using the first three rows of the above matrix as follows:

x1 = -(9/7)x4x2 = (2/7)x4x3 = -(1/7)x4

Therefore, the solution to the system of equations is x1 = -(9/7)x4, x2 = (2/7)x4, x3 = -(1/7)x4, and x4 is a free variable.

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Answer:

the answer is 3,107.21

The answer to that question is that one

The conclusions are as follows:

a. We reject the null hypothesis.

b. The p-value for this test is approximately 0.001.

To complete parts a and b, we can follow the steps for hypothesis testing.

a. The z-test statistic can be calculated using the formula:

z = ([tex]\bar{X}[/tex] - μ) / (σ / √n)

Given:

[tex]\bar{X}[/tex] = 49

σ = 11

n = 32

Substituting these values into the formula, we get:

z = (49 - 47) / (11 / √32) ≈ 2.90

The z-test statistic is approximately 2.90 (rounded to two decimal places).

To determine the critical z-score(s), we need to find the z-value that corresponds to the significance level α = 0.10. Since the alternative hypothesis is one-sided (μ > 47), we are performing a right-tailed test.

Using a standard normal distribution table or a calculator, the critical z-score for a right-tailed test at α = 0.10 is approximately 1.28 (rounded to two decimal places).

Because the test statistic z = 2.90 is greater than the critical z-score of 1.28, we reject the null hypothesis.

b. The p-value represents the probability of obtaining a test statistic as extreme as the observed value (or more extreme) assuming the null hypothesis is true. Since the alternative hypothesis is μ > 47, we are looking for the probability in the right tail of the distribution.

Using a standard normal distribution table or a calculator, we can find the p-value corresponding to the z-test statistic z = 2.90. The p-value is the area under the curve to the right of 2.90.

The p-value is approximately 0.001 (rounded to three decimal places).

Therefore, the conclusions are as follows:

a. We reject the null hypothesis.

b. The p-value for this test is approximately 0.001.

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Answer:

C. 333.14

Step-by-step explanation:

Both the basketball and baseball has got the shape of a sphere. So that;

volume of a sphere = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]

where r is the radius

i. Volume of the baseball = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]

                           =  [tex]\frac{4}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex](9.25)^{3}[/tex]

                           = 3315.5655

volume of the baseball = 3316.57 cube inches

ii. Volume of the basketball =  [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]

                            = [tex]\frac{4}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex](9.55)^{3}[/tex]

                            = 3649.8372

Volume of the basketball = 3649.84 cube inches

The required difference = volume of basketball - volume of baseball

                                  = 3649.84 - 3316.57

                                  = 333.27 cube inches

The difference of the volumes of the basketball and baseball is 333.27 cube inches.

Answer:

The ratio is [tex]\frac{2}{3}[/tex].

Step-by-step explanation:

The ratio of the perimeters of Quad ABCD to Quad WXYZ = [tex]\frac{perimeter of ABCD}{perimeter of WXYZ}[/tex]

But considering sides AB and WX,

representative factor for both figures = [tex]\frac{12}{8}[/tex]

So that;

WX = 12

XY = 1.5 x 6 = 9

YZ = 1.5 x 7 = 10.5

WZ = 1.5 x 7 = 10.5

Thus,

perimeter of Quad ABCD = 6 + 7 + 7 + 8

                                           = 28

perimeter of Quad WXYZ = 9 + 10.5 + 10.5 + 12

                                           = 42

The ratio of the perimeters of Quad ABCD to Quad WXYZ = [tex]\frac{28}{42}[/tex]

                                                         = [tex]\frac{2}{3}[/tex]

As the lower bound of the 90% confidence interval is below 0, there is not enough evidence to conclude that  the proportion of overweight kids aged 6-11 among boys is greater than the proportion of overweight kids aged 6-11 among girls.

The sample proportions are given as follows:

The difference is then given as follows:

0.1367 - 0.1245 = 0.0122.

The standard error for each sample is given as follows:

Then the standard error for the distribution of differences is given as follows:

[tex]s = \sqrt{0.0153^2 + 0.0145^2}[/tex]

s = 0.0211.

The critical value for a 90% confidence interval is given as follows:

z = 1.645.

The lower bound of the interval is:

0.0122 - 1.645 x 0.0211 = -0.0225.

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Answer:

Following are the responses to the given question:

Step-by-step explanation:

[tex]French \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Mathematics\\\\X= 85\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ X= 80\\\\\mu=72\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \mu =70\\\\\sigma=12 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sigma= 7.8\\\\[/tex]

Formula:

[tex]\bold{Z-Score=\frac{x-\mu}{\sigma}}\\\\French \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Mathematics\\\\Z=\frac{85-72}{12} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Z=\frac{80-70}{7.8}\\\\=1.0833 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =1.2820\\\\[/tex]

In the french exam Z value is 1.0833 and in the maths exam Z value is 1.2820 that's why we can say that  in maths exam, she does better than french exam.

To find the distance from point Q=(-28, 41) to the line represented by the equation (x, y) = (2, 1) + t(4, 3), we can use the formula for the distance between a point and a line in the coordinate plane. Therefore, the distance from point Q to the line is 233/5.

The distance between a point (x0, y0) and a line Ax + By + C = 0 is given by the formula:

d = |Ax0 + By0 + C| / √(A^2 + B^2)

In this case, we have the line represented parametrically as (x, y) = (2, 1) + t(4, 3), where t is a parameter. To use the formula, we need to convert this parametric representation to the standard form Ax + By + C = 0.

Expanding the parametric equation, we have:

x = 2 + 4t

y = 1 + 3t

From these equations, we can rearrange them to isolate t:

t = (x - 2) / 4

t = (y - 1) / 3

Setting the two expressions for t equal to each other, we get:

(x - 2) / 4 = (y - 1) / 3

Simplifying, we have:

3x - 6 = 4y - 4

4y - 3x = 2

Now we have the equation of the line in standard form. The coefficients A, B, and C are 4, -3, and 2, respectively.

To find the distance between point Q=(-28, 41) and the line, we can substitute the values into the distance formula:

d = |4(-28) + (-3)(41) + 2| / √(4^2 + (-3)^2)

Calculating the numerator and the denominator, we have:

d = |-112 - 123 + 2| / √(16 + 9)

d = |-233| / √25

d = 233 / 5

Therefore, the distance from point Q to the line is 233/5.

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Answer: 3 buses

Step-by-step explanation:

Answer:

Simply multiply 21 until you get a number greater than 47. In this case, 3, even though there is only a little remainder of 5 kids on one bus by themselves.

Step-by-step explanation:

The overall runtime of the algorithm is O(|V|+|E|). The DFS algorithm has a runtime of O(|V|+|E|), as does the main algorithm, which runs DFS for each vertex.Therefore, the algorithm has a total runtime of O(|V|+|E|).

a) Algorithm to determine if a graph has a cycle:The algorithm is implemented using DFS (Depth First Search) traversal, which starts from every vertex in the graph. During the DFS traversal, we maintain a set of vertices on the current path. We continue DFS traversal of each unvisited neighbor vertex, and if a neighbor is already on the path set, then we have found a cycle.

The algorithm to determine if a graph has a cycle is given below -Graph G(V, E)Start DFS from each vertex v in VIf DFS utility detects a cycle, then return true.

Else, return false.Let's take a look at the DFS algorithm below -DFS(vertex u)

1. Mark u as visited.

2. For every unvisited neighbor v of u, doDFS(v)

3. If v is already on the current path, return true to denote the existence of a cycle.

4. If there is no cycle, return false to denote that the graph does not contain a cycle.

The overall runtime of the algorithm is O(|V|+|E|).

The DFS algorithm has a runtime of O(|V|+|E|), as does the main algorithm, which runs DFS for each vertex.

b) Justification of the correctness and runtime of the algorithm:The algorithm provided uses a DFS traversal.

Therefore, the algorithm can detect a cycle in an undirected connected graph. If there is a cycle, then the algorithm will correctly detect it.

Since the algorithm starts DFS from each vertex, it will detect the cycle even if it starts from a vertex other than the one containing the cycle.

Therefore, it's correct.The overall runtime of the algorithm is O(|V|+|E|). The DFS algorithm has a runtime of O(|V|+|E|), as does the main algorithm, which runs DFS for each vertex.

Therefore, the algorithm has a total runtime of O(|V|+|E|).

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The expected value is 0, which means that, on average, you neither gain nor lose points over the long run. This suggests that after playing the game for a long time, we would expect to have a point total close to zero.

To determine whether you would expect to have a positive or negative point total after a long time playing the game, we can calculate the expected value or average point gain/loss per roll.

Let's calculate the expected value for each outcome:

Rolling an even number:

Probability = 3/6 = 1/2,

Point gain/loss = -1

Rolling a 1:

Probability = 1/6,

Point gain/loss = 1

Rolling a 3:

Probability = 1/6,

Point gain/loss = 3

Rolling a 5:

Probability = 1/6,

Point gain/loss = -4

The expected value, we multiply each outcome's point gain/loss by its probability and sum them up

Expected Value = (1/2) × (-1) + (1/6) × 1 + (1/6) × 3 + (1/6) × (-4)

Expected Value = -1/2 + 1/6 + 1/2 - 2/3

Expected Value = 0

The expected value is 0, which means that, on average, you neither gain nor lose points over the long run. This suggests that after playing the game for a long time, you would expect to have a point total close to zero.

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Null and alternative hypothesis: The null hypothesis is that the mean weight of the diabetics insured by two employers is similar.

In contrast, the alternative hypothesis is that the mean weight of the diabetics insured by two employers is not equal. Level of significance: The level of significance

(α) is the probability of rejecting the null hypothesis when it is valid. The commonly used level of significance is 0.05.

Test statistic: Assuming the population variances are equal, the test statistic is the t-distribution.

Decision Rule: Reject H0 if the t-value is greater than 2.060 or less than -2.060 and accept H0 if the t-value is between 2.060 and -2.060.

State Output: Assuming equal variances, the p-value associated with a two-tailed t-test for equality of means is 0.2682.Statistical decision: Since the p-value is greater than 0.05, we accept the null hypothesis and conclude that the mean weight of diabetics insured by the two employers is equal.

Conclusion: Therefore, there is no considerable difference in the mean weight of diabetics insured by two employers in the City of Asheville and Mission-St. Joseph’s Health System. Linear regression model and interpretation (if necessary): A linear regression model was not necessary in this study.

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Answer: Justin earns a base salary of $1500 per month at

the jewelry shop. He also earns a 3% commission

on all sales. If Just sold $82,975 worth of jewelry

last month, how much would he make for the

month including his base salary and commission?

Step-by-step explanation: $1500 + 3% + $82,975 = 84475. 03 or 84475

Answer:

Zx = 131

Step-by-step explanation:

The angles will equal to 180, so therefore you will do 180-49=Zx

Answer:

342

Step-by-step explanation:

Given

Shape: Rectangular prism

The missing dimensions are:

[tex]Length = 5 ft[/tex]

[tex]Width = 6 ft[/tex]

[tex]Height = 12 ft[/tex]

Required

Determine the surface area

The surface area is calculated as:

[tex]Area = 2(Length * Width + Length * Height + Width *Height)[/tex]

This gives:

[tex]Area = 2(5ft* 6ft+ 5ft * 12ft+ 6ft*12ft)[/tex]

[tex]Area = 2(30ft^2+ 60ft^2+ 72ft^2)[/tex]

[tex]Area = 324ft^2[/tex]

Answer:

36+25= 61

61/600 x 100 = 10.1 %

Step-by-step explanation:   Hope This helped!!!!

Answer:

see in the picture mark brainliest if correct

Answer:

B.490

Step-by-step explanation:

Correct me if im wrong

Answer: 490

Step-by-step explanation:

Answer:

(-2, 4)

Step-by-step explanation:

Hopes this helps!

Answer: -g - 10h

Step-by-step explanation:

(5g - 3h) - (6g + 7h)

= 5g - 3h - 6g - 7h

= 5g - 6g - 3h - 7h

= -g - 10h

Answer: The estimate is not valid based on the given sample.

Explanation:

The given information can be used to determine if the estimate is valid or not. It is estimated that at a certain college, at most 25% of the students ride bicycles to class, and a random sample of 90 college students is taken. The number of students who ride bicycles to class in the sample is 28.                                                                                            Therefore, to determine if the estimate is valid, the proportion of students who ride bicycles to class in the sample must be calculated.                                                                                                                                                                   The proportion of students who ride bicycles to class in the sample is 28/90 = 0.31 ≈ 31%.The proportion of students who ride bicycles to class in the sample is greater than the estimated proportion of students who ride bicycles to class, which is 25%.

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Answer:

-21 Feet

Step-by-step explanation:

-336/16

The balloon's elevation during the second minute will be 21 feet.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

A sight-seeing balloon pilot starts to land her inflatable. In the main moment the inflatable rise - 336 feet. In the subsequent moment, the inflatable's height changes by 1/16 of that sum.

Then the balloon's elevation during the second minute is given as,

⇒ - 336 x (1/16)

⇒ - 336 / 16

⇒ - 21 feet

The balloon's elevation during the second minute will be 21 feet.

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Answer:

22.7 km

Step-by-step explanation:

The Pythagorean Theorem is:

a² + b² = c²

where a and b are legs and c is the hypotenuse.

The hypotenuse is the longest side of a right triangle and can be identified as being across from the right angle. The legs are interchangeable between the variables a and b.

Because it's clear that x is the hypotenuse:

15² + 17² = x²

225 + 289 = x²

514 = x²

√514 = √x²

x = √514

Because we can't simplify √514 anymore, we can keep it as radical 514 or round it:

22.6715681 ≈ 22.7