The seesaw moves and the angle created by the left side of the seating board and the central support is now 80 degrees. Create and use a model, to find the distance from point Q to the ground when the angle created by the left side of the seating board and the central support is 80 degrees. Show your work or explain your answer. Round your final answer to the nearest tenth of a foot. Enter your model, your answer, and your work or explanations in the space provided. ​

Answers

Answer 1

Answer:5.7

Step-by-step explanation:

Answer 2

The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. The distance between the point Q and the ground is h-[L cos(80°)].

What is Tangent (Tanθ)?

The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,

[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The Base is the adjacent smaller side of the angle θ.

Let the height of the support be h and the height between the point q and the ground is x. Also, the distance between point Q and the support of the seesaw is L.

Now if we look at the ΔQAR, the measure of the ∠QRA is 80°, therefore, the sine of ∠QRA can be written as,

[tex]\rm Cos(\theta)=\dfrac{Base}{Perpendicular}\\\\Cos(\angle QRA) = \dfrac{AR}{QR}\\\\Cos(\angle QRA) = \dfrac{h-x}{L}\\\\L \times Cos(80^o)=h-x\\\\x=h-[L\ Cos(80^o)][/tex]

Hence, the distance between the point Q and the ground is h-[L cos(80°)].

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The Seesaw Moves And The Angle Created By The Left Side Of The Seating Board And The Central Support

Related Questions

4th grade math helplolll

Answers

Answer:

175 dollars

Step-by-step explanation:

from that word problem the equation that i was able to get out of it was

1225/ 7

^ the travel allowance and how much days they are going to be there

i dont know if you are allowed to use a calculator in your class but puting 1225/ 7 does give you a answer of a positive number of 175 dollars

meaning that they can only use 175 dollars a day so they dont go over the allowance

i hope this helps you! please stay safe and have a good day :)

Answer:

Um, the answer for that is 175.

Step-by-step explanation:

all you need to do is divide $1,225 by 7 which is 175.

help me bros, this question is a big part of my grade!!

Answers

Answer:

6.

m1 : 61

m2 : 61

m3 : 29

7.

m1 : 87

m2 : 45

m3 : 45

m4 : 52

(50 POINTS) Write out each sum.

Answers

Step-by-step explanation:

12. n^2+2n

if you insert 1 for k and then work up by inserting 2 for k and adding those together and stoping at n.

13. 8-2(2^n)

if you insert 3 for k and then work up by inserting 4 for k and adding those together and keep on going but stopping at n.

Hope that helps :)

Find the volume of this triangular pyramid.

Answers

Answer:

v = 340 cm³

Step-by-step explanation:

base area = 12 x 10 x 0.5 = 60 cm²

v = 60 x 17 x 1/3 = 340 cm³

A spinner has five equal sections labeled 1-5. In 60 spins, how often can you expect to spin a 3?

Answers

ok so lets say that you have a pizza cutted out in 5 sections and want to pick up only a certain piece, let's say pepperoni. If you took a piece at random, the chances of getting that certain piece of pepperoni in 60 spins is:    12 / 60

At the 90% Confidence Interval, what are the (lower bound; upper bound)?

Answers

The lower bound of the interval is given as follows:

28.1.

The upper bound of the interval is given as follows:

29.9.

What is a t-distribution confidence interval?

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

The variables of the equation are listed as follows:

[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.

The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 30 - 1 = 29 df, is t = 1.6991.

The lower bound of the interval is given as follows:

[tex]39 - 1.6991 \times \frac{3}{\sqrt{30}} = 38.1[/tex]

The upper bound is given as follows:

[tex]39 + 1.6991 \times \frac{3}{\sqrt{30}} = 39.9[/tex]

Missing Information

The complete problem is:

"If n=30, (x-bar)=39, and s=3, at the 90% Confidence Interval, what are the (lower bound; upper bound)".

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A rectangular hall is 55 feet long and 48 feet wide. How long is a walkway along the diagonal?​

Answers

Answer:

[tex]73[/tex]

Step-by-step explanation:

[tex]73=\sqrt{55^{2} +48^{2} }[/tex]

Event A: You roll a double. Event B: The sum of the two scores is even. Event C: The score on the blue die is greater than the score on the red die. Event D: You get a 6 on the red die. Complete the following as a group. Discuss each question together and enter your answers. When you are done, be sure to finish the last few steps of the meeting agenda ("reflect" and "share recording"). = 1. Circle the pairs of events for which PIX and Y) = P(X) x P(Y) A&B A&C A&D B&C B&D C&D

Answers

Among the pairs of events A&B, A&C, A&D, B&C, B&D, and C&D, the pairs A&C and B&D satisfy the condition P(A∩B) = P(A) × P(B), indicating that they are independent events.

To determine if two events are independent, we compare the product of their individual probabilities to the probability of their intersection. If the product of the individual probabilities is equal to the probability of the intersection, then the events are independent.

Let's examine each pair of events:

A&B: Rolling a double and getting a sum of even scores are not independent events. The occurrence of one event does not guarantee the occurrence of the other.

A&C: Rolling a double and having the score on the blue die greater than the score on the red die are independent events. The probability of rolling a double is solely dependent on the outcome of the dice roll, while the probability of the blue die having a greater score than the red die is independent of the outcome of rolling a double.

A&D: Rolling a double and getting a 6 on the red die are not independent events. The occurrence of rolling a double does not affect the probability of getting a 6 on the red die.

B&C: Getting a sum of even scores and having the score on the blue die greater than the score on the red die are not independent events. The occurrence of one event does not guarantee the occurrence of the other.

B&D: Getting a sum of even scores and getting a 6 on the red die are independent events. The probability of getting a sum of even scores is solely dependent on the outcome of the dice roll, while the probability of getting a 6 on the red die is independent of the sum of the scores.

C&D: Having the score on the blue die greater than the score on the red die and getting a 6 on the red die are not independent events. The occurrence of one event does not guarantee the occurrence of the other.

In summary, the pairs of events A&C and B&D are the only pairs that satisfy the condition P(A∩B) = P(A) × P(B), indicating that they are independent events.

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For each of the following questions, draw the phase portrait as function of the control parameter μ. classify the bifurcations that occur as μ varies, and find all the bifurcation values of μ .
1. θ = μ sin θ - sin 2θ
2. θ = sin θ/ μ+cos θ
3. θ = sin θ / μ + sin θ
4. θ = μ + cos θ + cos 2 θ
5. θ = μ sin θ + cos 2θ
6. θ = sin 2θ/ 1 + μ sin θ

Answers

Phase portrait as a function of the control parameter μ and the classification of bifurcations that occur as μ varies in the following questions are:

1. θ = μ sin θ - sin 2θA) μ<0, stable equilibrium at θ = nπ, where n is an odd integerB) μ>0, stable equilibrium at θ = 0, unstable equilibrium at θ = nπ, where n is a non-zero even integer. Hence, we have homoclinic bifurcation at μ = 0.

2. θ = sin θ/ μ+cos θA) μ<1, stable equilibrium at θ = nπ, where n is an integerB) μ>1, stable equilibrium at θ = sin−1 (μ) + nπ, where n is an integer. Hence, we have a pitchfork bifurcation at μ = 1.

3. θ = sin θ / μ + sin θA) μ<−1, stable equilibrium at θ = nπ, where n is an integerB) μ>−1, stable equilibrium at θ = 0, unstable equilibrium at θ = nπ, where n is a non-zero integer. Hence, we have homoclinic bifurcation at μ = −1.

4. θ = μ + cos θ + cos 2θA) μ>−1, stable equilibrium at θ = nπ, where n is an even integerB) μ<−1, no equilibrium point exists. Hence, we have fold bifurcation at μ = −1.

5. θ = μ sin θ + cos 2θA) μ>0, stable equilibrium at θ = sin−1 (−μ) + 2nπ, where n is an integerB) μ<0, stable equilibrium at θ = sin−1 (−μ) + (2n+1)π, where n is an integer. Hence, we have pitchfork bifurcation at μ = 0.

6. θ = sin 2θ/ 1 + μ sin θA) μ<−1, unstable equilibrium at θ = nπ/2, where n is an odd integerB) μ>−1, unstable equilibrium at θ = 0, stable equilibrium at θ = π. Hence, we have pitchfork bifurcation at μ = −1.

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Help ASAP! Find The Area Of A Circle With R =20.5

Answers

Answer:

Step-by-step explanation:

Pi*r^2 = Area

20.5^2 * Pi = 1320.25

A new experimental tank is in the shape of a cone, cylinder and sphere. All of the tanks have a volume of 10,000 cm3 . One condition to this tank is that the Radius should be 10 cm. Follow up the questions below based on this scenario.
Find the height of cylinder . Keep the answer in terms of π

Answers

Answer:

100/π cm

Step-by-step explanation:

Volume of a cylinder = πr²h

Volume = 10,000cm³

Radius = 10cm

The formula for the height of a cylinder is obtained as:

V = πr²h

h = V/ πr²

h = 10000 /π × 10²

h = 10000 /π × 100

h = 100/π cm

The height of the cylinder in terms of π = 100/π cm

Over which interval does f(t) have positive average rate of change?

A) -8,-2
B) -5,-1
C) -9,-8
D) 2,4

Answers

Answer:

D) 2,4

Step-by-step explanation:

The only answer with positive numbers

Answer:

D) 2,4

Step-by-step explanation:

Students plant 148 flowers at a community park. Seventy-eight percent of the flowers are pansies. Use
rounding to estimate how many flowers are pansies

Answers

About 115 are pansies when you round down from the original number (115.44)

Can someone pleaseeee helppp i dont know how to do this

Answers

Answer:

C=3e

Step-by-step explanation:

Slope=

can someone pls simplify this
[tex] \frac{105}{12} [/tex]

Answers

25/3..................

What is the simple interest on $4,000 for 2 and a half years at 4 percent a year?

Answers

Answer:

Step-by-step explanation:

You can't receive money if you withdraw in the midst of a year.

So 4000 * 1/25 * 2 = $4320

Gary is 4 years less than three times his brothers age, \displaystyle bb. The sum of Gary and his brothers' age is 52. Write an equation to represent this relaitonship.
(PLS HELP ME WITH THAT QUESTION! IF YOU HELP ME I GIVE YOU BRAINLIEST I SWEAR)

Answers

Let x be the age of Gary’s brother.
x + (3x - 4) = 52

Find a solution, an, for the recurrence relation given below where ao = 7, a1 = 8 and for n > 2 an = -20 x an-1-90 x an 2

Answers

The solution an for the recurrence relation is given by the formula,an = (25/19)*(10)^n + (102/19)*(-9)^n for n > 1.

Given the recurrence relation,ao = 7, a1 = 8 and for n > 2 an = -20 x an-1-90 x an 2.

To find the solution, an, of the recurrence relation we need to follow the below steps.

Step 1:Find the general formula for the recurrence relation. We have an = -20 x an-1-90 x an 2. This is a second-order recurrence relation.

To solve a recurrence relation of this order, we assume the solution of the form an = r^n.Then substituting this value of an in the given relation we have r^n = -20r^(n-1) - 90r^(n-2).

Dividing both sides by r^(n-2), we have the characteristic equation r^2 = -20r - 90.On simplifying the above equation we get, r = 10 and r = -9.

Now, the general solution for an is given by, an = c1 * (10)^n + c2 * (-9)^n.

Step 2:Find the value of constants c1 and c2. We have a0 = 7 and a1 = 8.

Substituting n = 0 in the above general formula for an, we get c1 + c2 = 7.

 Substituting n = 1 in the above general formula for an, we get 10c1 - 9c2 = 8.

On solving the above two equations we get, c1 = (25)/19 and c2 = (102)/19.

Hence, the solution to the given recurrence relation is,an = (25/19)*(10)^n + (102/19)*(-9)^n.

The solution is valid for n > 1.

Therefore, the solution an for the recurrence relation is given by the formula,an = (25/19)*(10)^n + (102/19)*(-9)^n for n > 1. This is the required answer.

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You surveyed the number of tree species along the American River watershed, and obtain the following data set. Please respond to the following questions. Species a b Forest A Number 10 8 3 Forest B Number 5 6 0 7 10 Forest C Number 8 8 5 2 NINO d 1 e 1 2 Which forest has the lowest species richness, A, B, or c?

Answers

After considering the given data and analysing the information carefully we conclude that the lowest species richness observed is Forest A with only 18 species.

Let us get into the explanation part by first keeping in mind that to determine this, we need to evaluate the total number of species in each forest.

From the given data set, we clearly see that Forest A has 18 species, Forest B has 28 species, and Forest C has 25 species.

Hence, Forest A has the lowest species richness with only 18 species then Forest A has the lowest species richness among the three forests.

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Solve the system using substitution: x = -4y and x + 5y = 2
Please and thank you.

Answers

Answer:

x = - 8, y = 2

Step-by-step explanation:

[tex]x = - 4y......(1) \\ x + 5y = 2....(2) \\ plug \: x = - 4y \: in \: equation \: (2) \\ - 4y + 5y = 2 \\ y = 2 \\ plug \: y = 2 \: in \: equation \: (1) \\ x = - 4(2) \\ x = - 8\\[/tex]

pls helpppppp !!
tysmmmm <33

Answers

Answer:

180

Step-by-step explanation:

From basic rules of a triangle we know that the interior angles of a triangle have to add up to equal 180°

But here is a formula for future references for finding the sum of the interior angles

interior angle sum = (n-2)180

where n = number of sides

and here is an example:

a triangle has 3 sides so we plug in 3 for n

(3-2)180

3-2=1

1*180 = 180

so the interior angles add up to equal 180

If $120.99 is charged for 654 units of electricity used,find the cost of one unit of electricity

Answers

divide 654 by 120.99
which equals $5.41

Answer:

$5.41

Step-by-step explanation:

654 divided by 120.99=5.405... therefore the answer is $5.41

tricia runs 520 meters each day for 3 days. how many total kilometers does tricia run in these 3 days?

Answers

Answer: 1.56 kilometers

Step-by-step explanation:

you multiply 520 by 3 because she ran for three days

so she ran 1560 meters

1000 meters= 1 kilometer

that makes it 1.56 kilometers

Eu tenho um ovo de páscoa que custa 24,99 e tem 185 gramas, tbm tenho uma barra de chocolate q custa 5,10 e tem 90 gramad. Qual da mais vantagem para mim?

Answers

Answer:

A maior vantagem para mim é a barra de chocolate.

Step-by-step explanation:

Temos que encontrar o custo de 1 grama de ovo de Páscoa e barra de chocolate

Para o ovo de páscoa

Tenho um ovo de Páscoa que custa 24,99 e tem 185 gramas.

185 gramas = 24,99

1 grama = x

Multiplicação cruzada

185 gramas × x = 1 grama × 24,99

x = 1 grama × 24,99 / 185 gramas

x = 0,1612258065

Aproximadamente = 0,16

O custo de 1 grama de ovo de Páscoa = 0,15

Para a barra de chocolate

Também tenho uma barra de chocolate que custa 5,10 e tem 90 gramas.

90 gramas = 5,10

1 grama = x

Multiplicação cruzada

90 gramas × x = 1 grama × 5,10

x = 1 grama × 5,10 / 90 gramas

x = 0,0566666667

Aproximadamente = 0,06

O custo de 1 grama de barra de chocolate = 0,06

A maior vantagem para mim é a barra de chocolate.

Problem 8-28 The exponential distribution applies to lifetimes of a certain component. Its failure rate is unknown. Find the probability that the component will survive past 5 years assuming:
(a) lambda=.5
Pr=
(b) lambda=0.9
Pr=
(c) lambda=1.1
Pr=

Answers

The exponential distribution applies to the lifetimes of a certain component. Its failure rate is unknown. The probability that the component will survive the past 5 years assumes:

(a) lambda=.5

Pr= 0.082

(b) lambda=0.9

Pr= 0.082

(c) lambda=1.1

Pr= 0.036

In the exponential distribution, the failure rate is a degree of the way fast the factor is expected to fail. It is regularly denoted through the parameter lambda (λ).

The opportunity that a thing will continue to exist beyond a positive time may be calculated using the exponential survival function, which is given by:

[tex]Pr(X > t) = e^(-λt)[/tex]

where X represents the random variable denoting the life of the thing, t is the specific time, and e is the bottom of the herbal logarithm.

Now let's calculate the possibilities for each case:

(a) lambda = 0.5, t = 5

Pr(X > 5) = [tex]e^(-0.5 * 5)[/tex] ≈ 0.082

In this example, with a lambda of 0.5, the element has a notably low failure price. The opportunity of the thing surviving beyond 5 years is about 0.082, or 8.2%.

(b) lambda = 0.9, t =5

Pr(X > 5) = [tex]e^(-0.9 * 5)[/tex] ≈ 0.082

With a lambda of 0.9, the issue has a slightly higher failure rate as compared to the previous case. The probability of the aspect surviving beyond 5 years stays at about 0.082, or 8.2%.

(c) lambda = 1.1, t = 5

Pr(X > five) = [tex]e^(-1.1 * 5)[/tex]≈ 0.036

In this situation, with a lambda of one.1, the factor has a better failure fee. The possibility of the element surviving beyond 5 years decreases to approximately 0.036, or 3.6%.

In precis, the possibility of a component surviving the past five years in an exponential distribution relies upon the failure price parameter lambda.

A lower failure price ends in a higher chance of survival, at the same time as a higher failure price decreases the opportunity of survival. It is essential to don't forget these chances when assessing the reliability and toughness of additives in diverse packages.

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The star running back on our football team got most of his total yardage running. The rest was catching passes. He caught passes for 60 yards. His total yardage was 150 yards. The running back for the other team got 200 yards. How many yards did the star running back on our football team get running?

Answers

Answer: The other team is extra information. 150 – 60 = 90

He got 90 yards running.

Step-by-step explanation:

Find the volume of a cylinder with a diameter 4 mm and a height 8 mm.

Answers

Answer:100.53mm

Step-by-step explanation:

How to divide 49 yd in the ratio 1:6?​

Answers

Answer:

7:42

Step-by-step explanation:

First off you add the ratio together-

6+1=7

Then you divide-

49÷7= 7

7 is equal to 1 in this ratio.

To write out the ratio you need to multiplicate-

7×1=7

and

6×7= 42

Leaving the as-

7:42

Answer:

7:42  

Step-by-step explanation:

First, add up the two numbers in the ratio to get 49.

Next, divide the total amount by 49, i.e. divide £16 by 8 to get £5. £5 is the amount of each 'unit' in the ratio.

Then you need to divide the total amount using that number i.e. 49/16 = 7/42.

To work out how much each person gets, you then multiply their share by the ratios. Therefore, the answer is 7 yd and 42 yds.

Solve the word problem using the plotted points on the graph.

Answers

Answer:

In the graph, we can see that the relation between length and weight is given by the adjusted line, which passes through the points (24, 16) and (28, 25)

Remember that a linear relation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If this line passes through the points (x₁, y₁) and (x₂, y₂) the slope can be calculated as:

a = (y₂ - y₁)/(x₂ - x₁)

Then in our case, the slope will be:

a = (25 - 16)/(28 - 24) = 9/4

y = (9/4)*x + b

Knowing that this line passes through (24, 16), we know that when x = 24, y must be equal to 16.

If we replace these in the equation, we can find the value of b.

16 = (9/4)*24 + b

16 = 54 + b

16 - 54 = b - 38

Then the equation is:

y = (9/4)*x - 38

Now that we know the equation, we can simply replace y by 34 pounds to find the value of x.

34 = (9/4)*x - 38

34 + 38 = (9/4)*x

72*(4/9) = x = 32

So we can estimate that the length of a fish that weighs 34 pounds is 32 (I do not know the unit of length, I can't see the horizontal axis on the image)

Consider the following scenario. Suppose that
1000 people are involved in a conspiracy.
Suppose that every single individual involved in
the conspiracy can be trusted 99.9%, that is,
there is a 0.01% probability they reveal the
secrets of the conspiracy to the media within 50
years. This probability is the same for everyone
involved, and never changes over the course of
the 50 years. Moreover, suppose that the event
where anyone goes to the media (or not) is
independent if anyone else has (or hasn't)
already.
What is the probability that at least one
person involved in the conspiracy reveals their
involvement to the media within 50 years?

Answers

The probability that at least one person involved in the conspiracy reveals their involvement to the media within 50 years is approximately 0.994.

Consider the following scenario: There are 1000 individuals involved in a conspiracy.

Every person involved in the conspiracy can be trusted 99.9%, which means that there is a 0.01% probability that they will reveal the secrets of the conspiracy to the media within 50 years.

The probability of revealing the conspiracy is the same for everyone involved and remains constant throughout the 50 years.

Additionally, the probability of someone revealing the conspiracy is independent of whether anyone else has already done so or not.

What is the likelihood that at least one person will reveal their involvement to the media within 50 years? We can use the binomial distribution to determine the probability that at least one person in the conspiracy will reveal their involvement in the media in 50 years.

We'll use the following formula for the binomial distribution: P(X ≥ 1) = 1 - P(X = 0) where X is the number of individuals that reveal the secrets of the conspiracy.

In this situation, we know that there are 1000 people in the conspiracy, and the probability that each person will reveal the conspiracy is 0.01%.

We can therefore use the formula for the binomial distribution to solve for the probability of at least one person revealing the conspiracy:

P(X ≥ 1) = 1 - P(X = 0) P(X ≥ 1) = 1 - [tex](0.999)^{1000}[/tex] P(X ≥ 1) ≈ 0.994

Therefore, The probability that at least one person involved in the conspiracy reveals their involvement to the media within 50 years is approximately 0.994.

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Suppose the isoquants are drawn with capital on the vertical axis. The firm pays $10 per unit of labour and $8 per unit of capital. In order to minimise the cost of producing the current output level, the firm should: a) not change its input mix because the current input mix already minimises costs. b) increase K and reduce L. c) increase L and reduce K. d) reduce both K and L. e) increase both K and L. be uploaded on Moodie immediately after completing the test) Gestion 15 23 Assume that females have put rates the normally with mean of 73.25 Then a. If 4 adult females are randomly selected, find the probability that they have pulse rates with a sample sans sem The probability to (Round to four decimal places as needed.) b. Why can the normal distribution be used in part (a), even though the sample size does not exceed 30? O A. Since the distribution of sample means, not individuals, the distribution is a normal distribution for any vargle uze. 3. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size C. Since the mean pulse rate exceeds 30, the distribution of sample means is a normal distribution for any sample size D. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size be ed on g the test.) use pseudocode to show a reusable module which would make an inappropriate value appropriate Trading skills of institutional investors. Managers of stock portfolios make decisions as to what stocks to buy and sell in a given quarter. The trading skills of these institutional investors were quantified and analyzed in The Journal of Finance (April 2011). The study focused on "round-trip" trades, i.e., trades in which the same stock was both bought and sold in the same quarter. Consider a random sample of 200 round trips made by institutional investors. Suppose the sample mean rate of return is 2.95% and the sample standard deviation is 8.82%. If the true mean rate of return of round-trips is positive, then the population of institutional investors is considered to have preformed successfully.a) Specify the null and alternative hypotheses for determining whether the population of institutional investors preformed successfully.b) Find the rejection region for the test using alpha=0.05.c) Interpret the value of alpha in the words of the problem.d) Give the appropriate conclusion in the words of the problem. Refer to Passage 2 Excerpt from Letter From Birmingham Jail.Reread paragraph 43 from Passage 2. I hope the church as a whole will meet the challenge of this decisive hour. But even if the church does not come to the aid of justice, I have no despair about the future. I have no fear about the outcome of our struggle in Birmingham, even if our motives are at present misunderstood. We will reach the goal of freedom in Birmingham and all over the nation, because the goal of America is freedom. Abused and scorned though we may be, our destiny is tied up with America's destiny. Before the pilgrims landed at Plymouth, we were here. Before the pen of Jefferson etched the majestic words of the Declaration of Independence across the pages of history, we were here. For more than two centuries our forebears labored in this country without wages; they made cotton king; they built the homes of their masters while suffering gross injustice and shameful humiliation and yet out of a bottomless vitality they continued to thrive and develop. If the inexpressible cruelties of slavery could not stop us, the opposition we now face will surely fail. We will win our freedom because the sacred heritage of our nation and the eternal will of God are embodied in our echoing demands.Dr. King offers his thoughts on the future of freedom for African Americans.Based on this paragraph, what is Dr. King's perspective on the future of the freedom movement?Question 29 options:The future of the freedom movement is uncertain if he remains in jail.Freedom in Birmingham can only be achieved with the support of the church.There will be freedom in Birmingham even without the support of the church.The church's involvement in the freedom movement will hinder the movement's efforts. Which of the following statements about cloud computing is incorrect? Software-a5-a-Service (Sa:S) is the lowest layer in cloud computing. The cloud provider in Infrastructure-as-a-Service (laaS) model ensures the underlying cloud infrastructure is always available. Cloud computing is the use of the internet to access applications, data, or services that are stored or run on a remote server. In a Platform-as-a-Service (PaaS) model, the cloud provider is responsible for providing a complete managed platform, for user's application to run.Previous questionNext question dr. istrati spent his whole working life selflessly helping sick and low-income people in developing countries around the world. this example illustrates if you were interested in being part of an emergency crew with knowledge and practice in the fundamentals of emergency medical care, to which area would you apply? responses paramedic paramedic emt-i/99 emt-i/99 ambulance driver ambulance driver emt-b xpropriation of corporate assets without prompt and adequate compensation is an example of which class of amines can form intermolecular hydrogen bonds? a profit-maximizing, competitive firm for which the marginal product of labor is diminishing also experiences group of answer choices a perfectly inelastic supply of labor. a perfectly elastic supply of labor. a downward-sloping demand for labor. an upward-sloping demand for labor. .An ideal gas in a sealed piston is allowed to expand isothermally and reversibly against an external pressure of 1.0 atm. What can be said of the change in the entropy of the surroundings, Ssurr, for this process?a) Ssurr > 0b) Ssurr = 0c) Ssurr < 0 in a single-slit diffraction experiment, a beam of monochromatic light of wavelength 573 nm is incident on a slit of width of 0.312 mm. if the distance between the slit and the screen is 2.30 m, what is the distance between the central axis and the first dark fringe (in mm)? You are the owner of a motorbike company that currently has two different factories, an old one and a new one. The old factory uses an old technology that requires large amounts of labor to produce motorbikes. The production technology for the old firm is given by Fo(L) = m*L^1/2 . The new factory uses a much more modern production technology given by Fn(L) = n*L^1/2 .a. What are costs as a function of output for each individual factory?b. Suppose that you want to produce 1000 motorbikes. How many motorbikes will you produce at the old factory and how many will you produce at the new factory?c. Derive an expression for the total cost of producing y motorbikes (assuming that you always divide production between the factories in the optimal way). How does this cost function compare to the individual factory cost functions?