Find the solution of the initial-value problem y" - 55" +9y' - 45y = sec 3t, y(0) = 2, 7(0) = 0, "(0) = 33. A fundamental set of solutions of the homogeneous equation is given by the functions: y(t) = eat, where a = = yz(t) yz(t) = = A particular solution is given by: et Y(t) = - Ids. yı(t) to ])ºyalt) + • 43(t) Therefore the solution of the initial-value problem is: y(t) +Y(t)=__.

Answer:

829.2 miles

Step-by-step explanation:

To find how far they traveled in total, add together all of the distances:

417 + 45.3 + 366.9

= 829.2

So, all together, they traveled 829.2 miles

The statement |A ∪ B ∪ C| = |A| + |B| + |C| is true, which means the statement is proven.

Let A, B, and C be sets with finite cardinalities that satisfy A ∩ B ∩ C = ∅.

We have to prove that |A ∪ B ∪ C| = |A| + |B| + |C|.

The addition law of sets states that the cardinality of a union of two finite sets is equal to the sum of the cardinalities of the sets minus the cardinality of their intersection.

Thus, we get: |A ∪ B ∪ C| = |A ∪ B| + |C| − |(A ∩ B) ∪ C| = (|A| + |B| − |A ∩ B|) + |C| − |(A ∩ B) ∩ C| = |A| + |B| + |C| − |A ∩ B ∩ C|.Since A ∩ B ∩ C = ∅, we get |A ∪ B ∪ C| = |A| + |B| + |C|.

Thus, the statement is proven.

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Answer:

[tex]1\frac{3}{4}[/tex]

Step-by-step explanation:

[tex]\frac{10}{12} +\frac{11}{12} \\\\\frac{21}{12} \\\\1\frac{9}{12} \\\\1\frac{3}{4}[/tex]

Answer:

heres the answer I think

Step-by-step explanation:

-3 < x < 1/2

To find a primitive root modulo a given integer, we can use Corollary 5.15 and Proposition 5.17. For (a) 7, a common primitive root r can be found by using these results. Similarly, for (b) 11m, (c) 13m, and (d) 17m, the same approach can be applied to find primitive roots modulo each integer.

(a) To find a primitive root modulo 7 and 72, we can use Corollary 5.15, which states that if r is a primitive root modulo n, then r is also a primitive root modulo any power of n. Since 7 is a prime number, we can easily find a primitive root modulo 7. Let's say r is a primitive root modulo 7. Using Proposition 5.17, which guarantees that a primitive root modulo a prime number remains a primitive root modulo any positive integral power of the prime, we can conclude that r is a primitive root modulo 7 for all positive integral m.

(b) Similarly, for 11m, we can find a primitive root modulo 11 and use Proposition 5.17 to prove that it is a primitive root modulo 11m for all positive integral m.

(c) The same approach can be applied to find a primitive root modulo 13m.

(d) Finally, for 17m, we can find a primitive root modulo 17 and use Proposition 5.17 to prove its primitiveness modulo 17m for all positive integral m.

By using Corollary 5.15 and Proposition 5.17, we can find a common primitive root for all the given integers modulo their corresponding powers.

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Answer:

171

Step-by-step explanation:

6x6x4.75 is 171

Answer:

25 tickets

Step-by-step explanation:

If the answer is wrong, I don't know what to say because the answer I got is 25

The would be 25 more gift card raffle ticket than shopping spree raffle tickets if there are 500 total raffle tickets

An equation is an expression that shows the relationship between two or more numbers and variables.

The shopping spree raffle tickets is 35% while the gift card tickets is 40%. Hence for 500 tickets:

Difference = (40% - 35%) * 500 = 25 tickets

The would be 25 more gift card raffle ticket than shopping spree raffle tickets if there are 500 total raffle tickets

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Answer:

The answer is 21 units²

Step-by-step explanation:

To find the area of a right triangle you use the formula A=ab/2

So

A=6×7/2 = 21

If we fail to reject the null hypothesis, we cannot conclude that the means are significantly different.

To check whether the means of the samples from different states are significantly different or if the difference is just by chance, we can use the one-way analysis of variance (ANOVA).

The premise is that the ANOVA assumption of normality and homogeneity of variance has been satisfied.

Here, the null hypothesis is that the means of all the samples are equal while the alternative hypothesis is that at least one mean is different.

The significance level is 5%.

To perform the ANOVA test, we can follow these steps:

Step 1: State the null and alternative hypotheses

H0: μ1 = μ2 = μ3 = ... = μk (where k is the number of groups)

Ha: At least one mean is different

Step 2: Set the significance level (α)α = 0.05

Step 3: Calculate the test statistic

The test statistic used in ANOVA is the F-statistic, which is the ratio of the between-group variance to the within-group variance.

If the F-statistic is large and the p-value is less than the significance level, we can reject the null hypothesis and conclude that at least one mean is different. If the F-statistic is small and the p-value is greater than the significance level, we fail to reject the null hypothesis and conclude that the means are not significantly different.

Step 4: Calculate the p-value

Using the F-statistic and the degrees of freedom for the between-group and within-group variance, we can calculate the p-value. If the p-value is less than the significance level, we can reject the null hypothesis. If the p-value is greater than the significance level, we fail to reject the null hypothesis.

Step 5: State the conclusion

Based on the p-value, we can either reject or fail to reject the null hypothesis. If we reject the null hypothesis, we can conclude that at least one mean is different. If we fail to reject the null hypothesis, we cannot conclude that the means are significantly different.

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The method that begins with a matrix or table describing the characteristics of a target population is quota sampling.

Quota sampling is a non-probability sampling method in which the researcher first creates a matrix or table describing the characteristics of the target population. Once the matrix is created, the researcher then selects a certain number of people from each category in the matrix until the desired sample size is reached.

For example, if the researcher is interested in studying the political views of college students, they might create a matrix with the following categories:

Gender: Male, Female

Age: 18-21, 22-25, 26-30

Political affiliation: Democrat, Republican, Independent

Once the matrix is created, the researcher might then select 100 students from each category, for a total sample size of 300.

Quota sampling is a quick and easy way to obtain a sample of a population. However, it is not a probability sampling method, which means that the sample may not be representative of the population. This is because the researcher is not randomly selecting participants from the population. Instead, they are selecting participants based on their characteristics.

As a result, quota sampling can lead to bias in the results of a study. For example, if the researcher selects more students from one political affiliation than another, the results of the study may be biased in favor of that political affiliation.

Overall, quota sampling is a useful tool for researchers who need to obtain a sample of a population quickly and easily. However, it is important to be aware of the limitations of this method and to take steps to minimize bias in the results of the study.

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a) The GCD of 27,720 and 58,212 is 1.

b) Integers r = 3 and s = -1 satisfy the equation 27720r + 58212s = GCD(27720, 58212).

(a) To find the greatest common divisor (GCD) of 27,720 and 58,212, we can use the Euclidean Algorithm.

Divide 58,212 by 27,720.

58,212 ÷ 27,720 = 2 remainder 2

Divide the previous divisor (27,720) by the remainder (2).

27,720 ÷ 2 = 13,860

Divide the previous remainder (2) by the new remainder (2).

2 ÷ 2 = 1

Since the remainder is now 1, the GCD is found.

Therefore,  the greatest common divisor (GCD) of 27,720 and 58,212 is 1.

(b) To find integers r and s such that 27720r + 58212s = GCD(27720, 58212), we can use the Extended Euclidean Algorithm.

Using the Euclidean Algorithm from part (a), we can backtrack to find the coefficients r and s:

2 = 27,720 - 13,860

Substituting the values:

2 = 27,720 - (58,212 - 2 * 27,720)

Simplifying:

2 = 3 * 27,720 - 58,212

Comparing with the form 27720r + 58212s = GCD(27720, 58212):

r = 3

s = -1

Therefore, we substitute r = 3 and s = -1 into the equation 27720r + 58212s, it will result in the greatest common divisor (GCD) of 27720 and 58212.

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Answer:

56 oz or 3 1/2 lbs

Step-by-step explanation:

1 1/4 + 1 1/2 = 2 3/4lbs = 44 oz

44 oz + 12 oz = 56 oz

Answer:

81/4

Step-by-step explanation:

the answer is not sure

Answer:

32

Step-by-step explanation:

Answer:

The answer to this question is $14,916

Step-by-step explanation:

18,469 - 3,553 = 14916

As he already has money for the car.

A bar model is shown in the linked picture.

Answer:

If the triangle is similar then their ratio is also same

x = 8

6 4.8

X =8×6

4.8

x = 10 cm

hope this helps

good day mate

(a) R4= 61.4626 and (b) L4= 61.4626.

In order to estimate the area under the graph of f(x) = 10 sqrt x from x = 0 to x = 4 using four approximating rectangles and right endpoints, we need to use the formula:

Rn = Δx [f(x1) + f(x2) + f(x3) + ... + f(xn)], where Δx is the width of each rectangle and f(xi) is the height of the rectangle at the right endpoint of the ith interval.

Step 1: Calculation of ∆x.∆x = (4 - 0)/4 = 1

Step 2: Calculation of xi for i = 1, 2, 3 and 4.x1 = 1, x2 = 2, x3 = 3, x4 = 4

Step 3: Calculation of f(xi) for i = 1, 2, 3 and 4.f(x1) = 10√(1) = 10f(x2) = 10√(2) ≈ 14.1421f(x3) = 10√(3) ≈ 17.3205f(x4) = 10√(4) = 20

Step 4: Calculation of R4.R4= ∆x [f(x1) + f(x2) + f(x3) + f(x4)]R4= 1[10 + 14.1421 + 17.3205 + 20]= 61.4626Area ≈ 61.4626 square units.

Step 5: Calculation of L4.Ln = ∆x [f(x0) + f(x1) + f(x2) + ... + f(xn-1)]

Where x0 is the initial value.

Here, we can find the value of L4 by using the left endpoints.

So, x0 = 0L4 = ∆x [f(x0) + f(x1) + f(x2) + f(x3)]L4 = 1 [f(0) + f(1) + f(2) + f(3)]L4 = 1 [10 + 14.1421 + 17.3205 + 20]L4 = 61.4626

Therefore, (a) R4= 61.4626 and (b) L4= 61.4626.

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Answer:

Top:(4r⁹+3r³-5)

Bottom: r⁵

Step-by-step explanation:

Answer:

24 IN.

Sorry for all caps

Step-by-step explanation:

Answer:

2d) d = 60°

3a) x = 50°

Step-by-step explanation:

2d) both of the diagonals pass through the centre of the circle and divide the rectangle into 4 triangles,then it means that;

30 + d = 90°

d = 90 - 30

d = 60°

3a) since O is the centre of the circle, and we can see that the 2 chords directly above and below the centre are parallel to each other, it means that angle x = 50° since the two sides projecting from the centre to form x° and 50° are equal and in essence used to form isosceles triangle.

Answer:

20%

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

19.99 - 3.998(20%) = 15.992 which when rounded is 15.99

Answer: i think its 10

Step-by-step explanation:

The p-value (0.0208) is less than the significance level (0.05), we reject the null hypothesis. This indicates that there is sufficient evidence to suggest the case.

Null hypothesis (H0): The population means are equal, μ1 = μ2.

Alternative hypothesis (Ha): The population means are different, μ1 ≠ μ2.

Select the significance level (α): In this case, α = 0.05.

Now, The test statistic for a two-sample t-test is given by:

  t = (sample mean 1 - sample mean 2) / √((s1² / n1) + (s2² / n2))

  where s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Here X₁ = 10, X₂ = 14, s= 3, n₁ =12, n₂ = 18

So, t= (10-14) / √(3²/12) + (3²/18) et:

t= (-4)/ √(3/4 + 1/2)

t= -4 / (5/4)

t= -2.7931

Now, degrees of freedom (df):

= (9/12 + 9/18)² / (((9/12)² / 11) + ((9/18)² / 17))

= 25.164

So, the p value will be 0.0208.

As, p-value is less than α (0.0208 < 0.05), we reject the null hypothesis.

Since the p-value (0.0208) is less than the significance level (0.05), we reject the null hypothesis. This indicates that there is sufficient evidence to suggest the case.

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This is the answer

I hope if you get it correct or right

Good luck everyone

The total vertical change from the start of the ride for the roller coaster after the 20 seconds 76 m.

The rise is the vertical difference between two points called vertical change.

Thus, the total vertical rise will be,

100 (upward) - 72 (downward) = 28(upward)

So, the total rise will become,

28(upward) + 48(upward) = 76(upward)

Therefore, the total vertical rise of the roller is 76 meter during the time of 20 seconds.

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Answer:

a complementary angle adds up to 90 degrees.So 90 minus 64 and the measure of the other angle is 26

Step-by-step explanation:

Hope it helped ;)

Answer:

A small box of the same cereal has 19 ounces and costs 4.19.

Step-by-step explanation:

In the first case, you have $3.37 per 15.3 ounces

Thus take 3.37 / 15.3 and you get $0.2203 per ounce or 22 cents per ounce

In the second case, you have $4.59 per 20 ounces

Thus take 4.59 / 20 and you get $0.2295 per ounce or almost 23 cents per ounce

So the smaller box actually has a slightly cheaper cost per ounce associated with it.