what angle is opposite the longest side?
I will mark as brainliest​

The inverse Laplace transform of F(s) = (s + 3)² (s + 5) is given by L⁻¹{F} = 1/2 * e^(-3t) - t * e^(-3t) + 1/2 * e^(-5t).

To determine the inverse Laplace transform of F(s) = (s + 3)² (s + 5), we can use the properties and formulas of Laplace transforms.

The inverse Laplace transform of F(s) can be obtained by applying partial fraction decomposition, followed by looking up the corresponding inverse Laplace transform in a table of Laplace transforms.

Let's first factorize F(s):

F(s) = (s + 3)² (s + 5)

Next, we perform partial fraction decomposition. We express F(s) as the sum of simpler fractions:

F(s) = A/(s + 3) + B/(s + 3)² + C/(s + 5)

To find the values of A, B, and C, we can equate the numerator of F(s) with the sum of the numerators in the partial fraction decomposition:

(s + 3)² (s + 5) = A(s + 3)(s + 5) + B(s + 5) + C(s + 3)²

Expanding the equations and collecting like terms, we get:

s² + 8s + 15 = (A + C)s² + (8A + 3C + B)s + (15A + 5B)

Equating the coefficients of the terms on both sides, we have the following system of equations:

A + C = 1

8A + 3C + B = 8

15A + 5B = 15

Solving this system of equations, we find A = 1/2, B = -1/2, and C = 1/2.

Now, we can rewrite F(s) in terms of the partial fractions:

F(s) = 1/2/(s + 3) + (-1/2)/(s + 3)² + 1/2/(s + 5)

Looking up the inverse Laplace transform of each term in the table, we find:

L⁻¹{1/2/(s + 3)} = 1/2 * e^(-3t)

L⁻¹{(-1/2)/(s + 3)²} = -t * e^(-3t)

L⁻¹{1/2/(s + 5)} = 1/2 * e^(-5t)

Therefore, the inverse Laplace transform of F(s) is:

L⁻¹{F} = 1/2 * e^(-3t) - t * e^(-3t) + 1/2 * e^(-5t)

This is the desired result for the inverse Laplace transform of F(s).

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Answer:

12 discs

Step-by-step explanation:

Sheet metal has dimensions of 56 cm by 33 cm. This indicates that it is a rectangle.

A_rectangle = length × width

A_rect = 56 × 33

A_rect = 1848 cm²

It is now melt down and recast into disc's of 7 cm radius and similar thickness.

Thus;

Area of one disc = πr² = π × 7² = 49π

Thus,number of disc's cast = 1848/49π

number of disc's cast = 12

Answer:

answer is y = 3/4x - 5

Step-by-step explanation:

picture below.

The 3/4 comes from the line. You would use rise over run to find the slope, which in this case is 3/4. and the -5 is basically the y-intercept

Answer:

I was unable to see this link. Sorry.

Step-by-step explanation:

While playing, they move, but still maintain the sinusoidal function, ... 5.At the end of the performance, the band marches off the field to the ... Asa grabs his camera to takes a picture of the entire football field. At the instant he takes the picture, the first person forming the curve now stands at the 5 yard line.

Answer:

26 cents

Step-by-step explanation:

S0, lets just subtract the 10 by the 9.74 to get our answer:

10-9.74

=

0.26

So, lets remember that there are 100 cents in 1 dollar.

So 1 cent would be: 0.01

Our answer we got above is 0.26

So that must be 26 cents.

Answer:

26

Hope this helps! ;)

Answer:

No

Step-by-step explanation:

By multiplying each ratio by the second number of the other ratio, you can determine if they are equivalent.

Answer:

x = 6

11/2x + 2/3x = 37

37/6x = 37

Step-by-step explanation:

these are correct since when you evaluate the equation, you only get 6 being the value for x. And all these three options I wrote above lead to x = 6

Hope this helped :)

Answer:

175

Step-by-step explanation:

140

140/4=35

140+35=175

Answer:

1000

Step-by-step explanation:

volume of prism formula=b*w*h(base times width times height)

10*10*10(10^3)=1000

Answer: 1,000 m

Step-by-step explanation:

To find volume you have to multiply: LengthxWidth,Height so you would do 10x10x10 and get 1,000 m

HOPE THIS HELPS ^^

If a normal distribution with a mean of 7.5 and a standard deviation of 1.2. (a) The probability that a cookie has less than 9 chips is 0.8944. (b) The probability that a random sample of 4 cookies has an average of fewer than 9 chips per cookie is 0.9938.

As μ = 7.5, σ = 1.2. The number of chips in a given cookie is in a normal distribution. We need to estimate the following probabilities:

(a) For this, we need to identify the probability of a Z-score when X=9. We can calculate it using the formula,

Z = (X-μ)/σ.

Therefore,

Z = (9-7.5)/1.2 = 1.25.

Now we can use the standard normal distribution table or calculator to identify the probability associated with the Z-score of 1.25. Using the calculator, P(Z < 1.25) = 0.8944.

(b) For this, we need to identify the probability of the Z-score when X = 9, n=4. We can calculate it using the formula,

Z = (X-μ)/(σ/√n).

Therefore,

Z = (9-7.5)/(1.2/√4) = 2.5.

Now we can use the standard normal distribution table or calculator to identify the probability associated with the Z-score of 2.5. Using the calculator, P(Z < 2.5) = 0.9938.

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The required answer is The literature review should be completed before developing a research hypothesis or research questions for a quantitative study.

Explanation :

The role of literature review in the qualitative study.To examine the problem of attrition from an online doctoral program in a qualitative study, a literature review is essential to identifying the theoretical frameworks and practices for reducing attrition. Researchers need to review the current theories on student retention, persistence, and attrition to examine the factors contributing to these trends.

By reviewing related literature, researchers gain insight into how student attrition is approached in existing literature. Additionally, literature review helps in developing the research problem and objectives, identifying gaps in the current literature that the study can fill. This provides a solid foundation for conducting qualitative research and enables the researcher to identify the gaps and the direction the study should take.

When should you complete a literature review for a quantitative study?For a quantitative study of the factors that predict attrition from a doctoral program, a literature review should be completed before determining your research hypothesis or research questions.

A literature review is essential as it helps researchers to identify the current literature, theories, and research studies conducted in the area of attrition in doctoral programs.

By conducting a literature review, the researcher can identify gaps, inconsistencies, and areas that require more attention. This allows researchers to develop an appropriate research design, research questions, and hypotheses that address the identified gaps in the literature.

Thus, the literature review should be completed before developing a research hypothesis or research questions for a quantitative study.

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Answer:

a)b=4

b)x=-9

c)r=6

Step-by-step explanation:

Question 2.

a)5b+6=26

5b=26-6

5b=20

b=4

b)6-x=15

-x=15-6

-x=9

x=-9

c)r/2+2=5

r/2=5-2

r/2=3

Multiply both sides by 2 to remain with r

r/2×2=3×2

r=6.

Answer:

143 ft2

Step-by-step explanation:

Formula for parrallelogram: A= BxH

13x11= 143

Answer: 216, 343, 512, 729, 1000, 1331, 1728, 2197, 2744

Step-by-step explanation: The terms are the cubes of the numbers 1, 2, 3, 4, 5...

Answer:

The 16ᵗʰ term of this sequence is 82

Step-by-step explanation:

Here,

First Term = a₁ = 9

Common Difference = (d) = 2

Now, For 16ᵗʰ term, n = 16

aₙ = a + (n - 1)d

a₁₆ = 7 + (16 - 1) × 2

a₁₆ = 7 + 15 × 5

a₁₆ = 7 + 75

a₁₆ = 82

Thus, The 16ᵗʰ term of this sequence is 82

-TheUnknownScientist

The margin of error for a 97% confidence interval for (p1 - p2) is 0.159.

To find the margin of error (E) for a 97% confidence interval for (p1 - p2), we can use the following formula:

E = Z * sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))

Where:

Z is the z-score corresponding to the desired confidence level. For a 97% confidence level, the z-score is approximately 2.170.

p1 and p2 are the sample proportions for populations 1 and 2, respectively.

n1 and n2 are the sample sizes for populations 1 and 2, respectively.

To calculate p1 and p2, we divide the sample counts (x1 and x2) by their respective sample sizes (n1 and n2).

p1 = x1 / n1 = 62 / 108 ≈ 0.574

p2 = x2 / n2 = 235 / 723 ≈ 0.325

Substituting the values into the formula, we have:

E = 2.170 * sqrt((0.574 * (1 - 0.574) / 108) + (0.325 * (1 - 0.325) / 723))

Calculating this expression, we find:

E ≈ 2.170 * sqrt(0.004957 + 0.000443)

≈ 2.170 * sqrt(0.005400)

≈ 2.170 * 0.073486

≈ 0.159

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Answer:

volume in cubic centimeters = 30 cm³

Step-by-step explanation:

Ratio of mass to volume = 27 g : 10 cm³

what is the volume in cubic centimeters of the sample of metal if mass = 81 g

Let

volume in cubic centimeters = v

Ratio of mass to volume = 81 g : v

Equate both ratios

27 g : 10 cm³ = 81 g : v

27/10 = 81/v

Cross product

27 * v = 10 * 81

27v = 810

v = 810/27

v = 30 cm³

volume in cubic centimeters = 30 cm³

Answer:

increase by 10%.

In the first question, based on the given regression equation, if a student spends 5 hours studying for a test, the predicted test score would be 50 + 7(5) = 85.

In the second question, the information provided is unclear and incomplete. The given text appears to contain multiple unrelated statements and lacks sufficient context or specific details to answer the question regarding the critical value for hypothesis testing.

1. For the first question, the regression equation is given as y = 50 + 7x, where y represents the test score and x represents the number of hours studied. To find the test score when a student spends 5 hours studying, we substitute x = 5 into the equation: y = 50 + 7(5) = 85.

2. However, the second question is unclear and does not provide sufficient information or context to determine the intended calculation or answer. It mentions something about applicant interviews, regression output, and ANOVA, but the information is not well-defined or organized. Without specific details and clear instructions, it is not possible to provide a meaningful response.

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Answer: So, 8%3 = 2

Step-by-step explanation:

Answer:

2 and 5

Step-by-step explanation:

2×5 = 10 or visa versa

10 ÷5=2

10 ÷2 =5

Answer:

2.8 feet

Step-by-step explanation:

tan(29)=x/5

5tan(29)=x

2.8=x

Answer:

5.7

Step-by-step explanation:

2(3a + 5) + 8(a - 1)

= 6a + 10 + 8a - 8

= 6a + 8a + 10 - 8

= 14a + 2

Answer:

the answer is X = 40 Y=50

Step-by-step explanation: