Find the general solution of the given differential equation (you can use either undetermined coefficients or variation of parameters) y" - y" + y' - y = 2e-sin (D)

Answer:

-8

Step-by-step explanation:

-12r+4=100

100-4=96

-12r=96

96/-12=-8

Answer: \(10\frac{2}{3}\pi\)

Step-by-step explanation:

Do you really need it? If so, reply, if not, mark brainliest.

With 90% confidence that the true proportion of voting adults in the community who support the city ordinance is between 0.646 and 0.714.

To construct a confidence interval for the true proportion, we can use the following formula:

CI = p ± z√(p(1-p)/n)

where:

p = sample proportion = 0.68

z = z-score for the desired confidence level = 1.645 (from a z-table for a 90% confidence level)

n = sample size = 805

Plugging in the values, we get:

CI = 0.68 ± 1.645 x [√((0.68)(1-0.68)/805)]

CI = 0.68 ± 0.034

CI = (0.646, 0.714)

Therefore, we can say with 90% confidence that the true proportion of voting adults in the community who support the city ordinance is between 0.646 and 0.714.

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Answer:

15 steps

Step-by-step explanation:

Answer:

-579

Step-by-step explanation:

The range of x are;

1. x < -30

2. x > 8

3. x > 15

4. x < -2

A relationship between two expressions or values that are not equal to each other is called 'inequality.

1. -130 > 50x +20

-130-20> 50x

-150 > 50x

-150/50 > x

-30 > x

x < -30

2. -8(x-3) < -40

-8x +24< -40

collect like terms

-8x < -64

x > -64/-8

x > 8

3. 2x - 22 > 8

collect like terms

2x > 30

divide both sides by 2

x > 30/2

x > 15

4. -35 < -5(x+9)

-35 < -5x -45

collect like terms

10 < -5x

-2 > x

x < -2

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The equation of the tangent line to the curve y = 2x³ - 5x + 1 at the point where x = 0 is y - 1 = -5x + 5 or 5x + y - 6 = 0.

The given curve is y = 2x³ - 5x + 1. We are required to find an equation of the tangent line to the curve at the point where x = 0.

To find the equation of the tangent line to the curve at x = 0, we need to follow the steps given below:

Step 1: Find the first derivative of y with respect to x.

The first derivative of y with respect to x is given by:

dy/dx = 6x² - 5

Step 2: Evaluate the first derivative at x = 0.

Now, substitute x = 0 in the equation dy/dx = 6x² - 5 to get:

dy/dx = 6(0)² - 5

= -5

Therefore, the slope of the tangent line at x = 0 is -5.

Step 3: Find the y-coordinate of the point where x = 0.

To find the y-coordinate of the point where x = 0, we substitute x = 0 in the given equation of the curve:

y = 2x³ - 5x + 1

= 2(0)³ - 5(0) + 1

= 1Therefore, the point where x = 0 is (0, 1).

Step 4: Write the equation of the tangent line using the point-slope form.

We have found the slope of the tangent line at x = 0 and the coordinates of the point on the curve where x = 0. Therefore, we can write the equation of the tangent line using the point-slope form of a line:

y - y1 = m(x - x1)

where (x1, y1) is the point on the curve where x = 0, and m is the slope of the tangent line at x = 0.

Substituting the values of m, x1 and y1, we get:

y - 1 = -5(x - 0)

Simplifying, we get:

y - 1 = -5xy + 5 = 0

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The amount of money in Iris's checking account can be modeled by a linear function of the form:

y = mt + b

where y is the amount of money in the account, t is the time (measured in years), m is the rate of interest, and b is the initial amount in the account.

In this case, we have m = 0.04 (since the interest rate is 4% per year) and b = 180 (since that's the initial amount in the account). Therefore, the linear function that models the amount of money in Iris's checking account at any time t is:

y = 0.04t + 180

For example, if t = 5 (years), then the amount of money in Iris's checking account is 0.04 * 5 + 180 = 198 dollars.

Answer: V≈9.42 yd^3

the formula to use for a cylinder is V=πr^2h. The radius is 0.5 since the diameter is 1. The height is 12. Plug them in and you get that answer.

Hope it helps!

Answer:

121

Step-by-step explanation:

Because every one of them shook with each other and one person shook 11 times so 11 into 11 is 121.

Answer:

55 handshakes.

Step-by-step explanation:

  n(n-1)

   ----------

         2

= 11(11-1) / 2

= 11* 10 / 2

= 110 / 2

= 55

Answer:

Division!

Step-by-step explanation:

(1/6) ÷ (3/7)

(1/6)(7/3)

= 7 / 18

Ken bought a total of 91 bags of apples and oranges combined.

What is Statistics?

The branch of mathematics dealing with data collection, organization, analysis, interpretation and presentation.

Ken bought 7 bags of apples. To find out how many bags of oranges he bought, we need to use the information that he bought 12 times as many bags of oranges as apples.

So, we can start by multiplying the number of bags of apples by 12:

7 x 12 = 84

This means that Ken bought 84 bags of oranges.

To find the total number of bags he bought, we just need to add the bags of apples and oranges together:

7 + 84 = 91

Therefore, Ken bought a total of 91 bags of apples and oranges combined.

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The control limits for the mean chart are 7.76821 (LCL) and 8.34595 (UCL), while the control limits for the range chart are 0 (LCL) and 0.86566 (UCL).

To calculate the exact control limits for the mean and range charts, we will use the formulas provided:

Calculate the mean and range for each sample:

Sample 1:

Mean = (7.98 + 8.34 + 8.02 + 7.94 + 8.44 + 7.68 + 7.81 + 8.11) / 8 = 8.055

Range = 8.44 - 7.68 = 0.76

Sample 2:

Mean = (8.33 + 8.22 + 8.08 + 8.51 + 8.41 + 8.28 + 8.09 + 8.16) / 8 = 8.275

Range = 8.51 - 8.08 = 0.43

Sample 3:

Mean = (7.89 + 7.77 + 7.91 + 8.04 + 8.00 + 7.89 + 7.93 + 8.09) / 8 = 7.9475

Range = 8.09 - 7.77 = 0.32

Sample 4:

Mean = (8.24 + 8.18 + 7.83 + 8.05 + 7.90 + 8.16 + 7.97 + 8.07) / 8 = 8.055

Range = 8.24 - 7.83 = 0.41

Sample 5:

Mean = (7.87 + 8.13 + 7.92 + 7.99 + 8.10 + 7.81 + 8.14 + 7.88) / 8 = 7.9925

Range = 8.14 - 7.81 = 0.33

Sample 6:

Mean = (8.13 + 8.14 + 8.11 + 8.13 + 8.14 + 8.12 + 8.13 + 8.14) / 8 = 8.1325

Range = 8.14 - 8.11 = 0.03

Calculate the overall mean and overall average range:

Overall Mean = (8.055 + 8.275 + 7.9475 + 8.055 + 7.9925 + 8.1325) / 6 = 8.05708

Overall Average Range = (0.76 + 0.43 + 0.32 + 0.41 + 0.33 + 0.03) / 6 = 0.37833

Construct the control charts:

Mean Chart:

Upper Control Limit (UCL) = Overall Mean + (A2 * Overall Average Range)

Lower Control Limit (LCL) = Overall Mean - (A2 * Overall Average Range)

For a sample size of 8, A2 = 0.729.

UCL = 8.05708 + (0.729 * 0.37833) = 8.34595

LCL = 8.05708 - (0.729 * 0.37833) = 7.76821

Range Chart:

Upper Control Limit (UCL) = D4 * Overall Average Range

Lower Control Limit (LCL) = D3 * Overall Average Range

For a sample size of 8, D3 = 0 and D4 = 2.282.

UCL = 2.282 * 0.37833 = 0.86566

LCL = 0 * 0.37833 = 0

Therefore, the control limits for the mean chart are 7.76821 (LCL) and 8.34595 (UCL), and the control limits for the range chart are 0 (LCL) and 0.86566 (UCL).

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--The given question is incomplete, the complete question is given below " Webster Chemical Company produces mastics and caulking for the construction industry. The product is blended in large mixers and then pumped into tubes and capped. Management is concerned about whether the filling process for tubes of caulking is in statistical control. Several samples of eight tubes were taken, each tube was weighted, and the weights in the following table were obtained.

Assume that only six samples are sufficient and develop the control charts for the mean and the range. "--

The two different ways to write four thirty includes:

The expression "four thirty" can be represented in two different ways: "4:30" and "16:30". The first format follows the standard convention for representing time using a colon to separate the hours and minutes.

The second format a period as a separator which is common in some countries or contexts. Both notations convey the same meaning of indicating half-past the hour of 4.

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Answer:

3 17/30

Step-by-step explanation:

In order to do this problem, we have to get the two fractions to have the same denominator

So we change 2 8/15 into 2 16/30 (multiplying both the numerator by 2, if you don't know why this works then ask me) and then we just add. So 2 16/30 + 1 1/30 = 3 17/30

The probability that the prize goes to a woman is 9/19.

To calculate the probability that the prize goes to a woman, we need to determine the number of women present at the party and divide it by the total number of guests.

Given:

Number of men present = 200

Number of women present = 180

Total number of guests = Number of men + Number of women

Total number of guests = 200 + 180 = 380

The probability that the prize goes to a woman is the number of women divided by the total number of guests:

Probability = Number of women / Total number of guests

= 180 / 380

= 9 / 19

Therefore, the probability that the prize goes to a woman is 9/19.

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Answer:

1) (3,5) is the new point

2) P(-1,-4) U(-5,0) N (-2,1)

Step-by-step explanation:

hope this helps. good luck

The alpha level for a hypothesis test is a value that defines the concept of "significance level" or "level of significance".

The significance level, denoted as α, represents the threshold at which the null hypothesis is rejected in favor of the alternative hypothesis. It is a predetermined value chosen by the researcher to determine the level of confidence required to reject the null hypothesis.

The critical region, also known as the rejection region, consists of the extreme or unlikely values of the test statistic that would lead to the rejection of the null hypothesis.

These values are determined based on the chosen alpha level. If the calculated test statistic falls within the critical region, the null hypothesis is rejected in favor of the alternative hypothesis.

The critical region is defined by the alpha level, and it represents the probability of observing extreme test statistics under the assumption that the null hypothesis is true.

In other words, it defines the values of the test statistic that would be considered statistically significant, and that would lead to the rejection of the null hypothesis if observed.

The specific values that define the critical region are determined by the nature of the hypothesis test and the type of test being conducted, such as one-tailed or two-tailed test.

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a) If the true rate of rejection is 10%, then the probability that the production will be suspended based on a sample of 15 bearings is 10%.

b)  The assumptions made in part a are that the sample of 15 bearings is representative of the population of bearings produced, and that each bearing is independent of the others.

To ensure that the production process is producing quality products, samples of 15 bearings are taken periodically and carefully inspected. If more than 2 bearings in a sample of 15 fail to meet the required specifications, production is suspended for necessary adjustments.

a) If the true rate of rejection is 10%, what is the probability that the production will be suspended based on a sample of 15 bearings? To answer this question, we need to use the binomial distribution. The binomial distribution is used to calculate the probability of a certain number of successes in a fixed number of independent trials. In this case, the number of trials is 15, and the probability of success (i.e., a bearing not meeting the required specifications) is 10%.

b) The assumptions allow us to use the binomial distribution to calculate the probability of having a certain number of bearings fail to meet the required specifications in a sample of 15. Additionally, we assume that the true rate of rejection is 10%, which may not always be the case.

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The range of speeds at which a car can safely make the curve is approximately 70 km/h to 130 km/h.


When a car moves along a banked curve, the friction force plays a crucial role in preventing the car from slipping. To determine the safe range of speeds, we consider two scenarios: when the car goes too slow and when it goes too fast.
1. When the car goes too slow: If the car moves slower than the required speed, the friction force points uphill, away from the center of the curve. In this case, the static friction force needs to provide the centripetal force. Using the equation F_friction = μ_s * N, where μ_s is the coefficient of static friction and N is the normal force, we can find the minimum speed at which the friction force can supply the required centripetal force.

2. When the car goes too fast: If the car moves faster than the required speed, the friction force points downhill, toward the center of the curve. The static friction force is not needed for the centripetal force in this case. Instead, the vertical component of the normal force provides the necessary centripetal force. Again, we can use the equation F_friction = μ_s * N to find the maximum speed at which the friction force is still within the limit.
Considering these scenarios, with a coefficient of static friction of 0.40, we find that the safe range of speeds for the car to make the curve is approximately 70 km/h to 130 km/h, rounded to two significant figures.

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a percent using the form % to represent the following word problem is x=12

What do u mean by percent?

percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity. percentage. Related Topics: mathematics percentile.

60 % of 20

60/100 = x/20

cross product

60 * 20 = 100x

divide by 100

1200/100 =x

12=x

60/100 = x/20    x= 12

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The time it will take for the rocket to hit the ground is given as follows:

4.5 seconds.

The quadratic function modeling the rocket's height after x seconds is given as follows:

y = -2x² + 5x + 18.

The rocket hits the ground when y = 0, that is:

-2x² + 5x + 18 = 0

2x² - 5x - 18 = 0.

The discriminant is given as follows:

D = (-5)² - 4(2)(-18) = 169.

Hence the positive root is given as follows:

x = [5 + sqrt(169)]/4

x = 4.5 seconds.

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Answer:

y= -3/2x + 2

Step-by-step explanation:

slope intercept form is y=mx+b, solve for formula

Answer:

y= -3/2x+2

Step-by-step explanation:

y=mx+b

m= slope

b= y-intercept

Answer:

Step-by-step explanation:

5, 5, 5, 16, 16, 28, 29, 32, 35, 48

Mode: 5, 16

Median: 44/2 = 22

range: 48 - 5 = 43

mean: (5 + 5 + 5 + 16 + 16 + 28 + 29 +32 + 35 + 48)/10 = 219/10 = 21.9

Answer:

She must sell 1026.66666667 kites

Step-by-step explanation:

15,400/15

The number of kites that Ellen needs to sell to complete her annual goal is 1027.

The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

Given that Ellen can make a $15 profit on each kite she sells. Also, Ellen's annual income goal is to have $15,400. Therefore, the number of kites that Ellen needs to sell is,

Number of kites that Ellen will sell = Annual income goal/Profit on each kite

Number of kites that Ellen will sell = $15,400 / $15

                                                     = 1026.6667

Since Ellen can not sell half kites, therefore, she needs to sell 1027 kites to complete her annual income goal.

Hence, the number of kites that Ellen needs to sell to complete her annual goal is 1027.

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Answer:

The fear of a local outbreak of the virus, limited staffing due to health concrens from the administration who run the school.

Step-by-step explanation:

The point R has an abscissa 9 and ordinate 5