Introduction
Scientists have established a timeline of events after the Big Bang, based on astronomical observations and our understanding of the physical laws of the universe, such as gravity and the speed of light. In this lab activity, you will gather evidence to support the Big Bang theory.
Problem:
How can models demonstrate theories of our expanding universe?
Hypothesis:
Review the virtual lab demonstration in the lesson and stop the video when prompted to formulate a hypothesis. Hypothesize (or predict) what will happen to the distances between the labeled circles when you blow up the balloon ¼ full, ½ full, and ¾ full. Remember to include independent and dependent variables in your hypothesis.
The carbon dioxide represents how galaxies will spread out.
Materials:
Watch the virtual lab demonstration video within the lesson. No additional materials are needed.
Variables:
For this investigation:
List the independent variable(s):
List the dependent variable(s):
List the controlled variable(s):
Procedures:

1. Watch the virtual lab demonstration video within the lesson and record your observations in Table 1.
2. Using your expanding universe data from Table 1, construct a line graph using the volume of the below on the X axis and the distance between points on the Y axis. Be sure to include units and add titles to the graphs. Refer to the graph example and graphing tutorial in the lesson if needed.
3. Complete the Questions and Conclusion section of the lab report.
Data and Observations:
Table 1: Expanding Universe Observations


Galaxies Distance: Uninflated balloon (centimeters)
Distance: ¼ full (centimeters) Distance: ½ full (centimeters) Distance: ¾ full (centimeters)
A to B
A to C
A to D
B to C
B to D
C to D

Construct a line graph using the expanding the universe data from table 1. The volume will be plotted on the x-axis. The distance between the points will be plotted on the y-axis. Be sure to include units and add titles to the graph. Refer to the graph example and graphing tutorial in the lesson if needed.
Place your graph here.
Questions and Conclusion
1. How does the density and distribution of your “stars” change as the balloon expands?
2. How does your expanding balloon model represent an expanding universe?
3. What are some shortcomings of using this model as a replica of universe expansion?
4. How does the model you created help to show that the Steady State theory is inaccurate?
5. Suggest a way that a scientist could create an even more accurate model of universe expansion.
6. What will happen to the gravitational force between stars as the universe continues to expand?
In conclusion, how did your prediction of distances between points compare to your experimental results? All I truly need is the variables question 3 and 5 and I’m good :) thank you <3 this is for science but I didn’t know which one to pick so I picked a random one lol

The curvature of y = sin(–1x) at x = pi/4 is 2√2/3.

Curvature is the measure of how much a curve bends. It is the rate at which the unit tangent vector changes with respect to arc length. It is given by the formula,K = |dT/ds|Where K is curvature, T is the unit tangent vector, and s is arc length.So, the first step is to find the first derivative of y, which is given by,dy/dx = -1/√(1-x²)Now, we find the second derivative of y which is given by,d²y/dx² = x/(1-x²)^(3/2)At x = pi/4, we have,d²y/dx² = (π/4)/(1-(π/4)²)^(3/2) = 2√2/3Therefore, the curvature of y = sin(–1x) at x = pi/4 is 2√2/3.

Know more about curvature here:

https://brainly.com/question/30106465

#SPJ11

Answer:

each friend ate 1/4 of pizza

Step-by-step explanation:

3/4 ÷ 3

= 1/4

The theorem states that for positive natural numbers a and n, the statements "GCD(a, n) = 1" (a and n are relatively prime), "a is not a zero divisor," and "there exists a natural number b such that ab ≡ 1 (mod n)" are all equivalent.

The theorem establishes the equivalence of three statements concerning positive natural numbers a and n. Firstly, if the greatest common divisor (GCD) of a and n is 1, it indicates that a and n are relatively prime.

This means that they have no common factors other than 1.

The second statement states that if a is not a zero divisor, then it implies that a multiplied by any nonzero element b is not equal to zero. In other words, a does not "annihilate" any nonzero element in multiplication.

Lastly, the theorem asserts that if there exists a natural number b such that ab ≡ 1 (mod n), it signifies the existence of a multiplicative inverse of a modulo n.

This means that a and n have a modular inverse, which is a natural number that, when multiplied by a, gives a remainder of 1 when divided by n.

The theorem shows that these three statements are equivalent, meaning that if one statement is true, then the other two statements will also hold.

The proof of this theorem involves establishing the logical connections between these statements and demonstrating that they are always true under the given conditions.

Learn more about greatest common divisor (GCD)

brainly.com/question/32552654

#SPJ11

Answer:

C.

Step-by-step explanation:

Since the slope is 1 meaning it goes up and over by 1 the GPA would increase by 1 every hour

Answer:

c

Step-by-step explanation:

The probability of event E is 0.20, the probability of event F is 0.45, and the probability of both E and F occurring is 0.10. Therefore, the probability of either event E or event F occurring, denoted as P(E or F), is 0.65.

Given that P(E) = 0.20 and P(F) = 0.45, we also know that P(E and F) = 0.10. Using the formula P(E or F) = P(E) + P(F) - P(E and F), we can substitute the values and calculate the probability of either event E or event F occurring.

P(E or F) = P(E) + P(F) - P(E and F)

P(E or F) = 0.20 + 0.45 - 0.10

P(E or F) = 0.65

Therefore, the probability of either event E or event F occurring, denoted as P(E or F), is 0.65.

The concept behind this formula is that when we add the individual probabilities of E and F, we count their intersection (P(E and F)) twice. Since we want to avoid double-counting the intersection, we subtract P(E and F) from the sum of P(E) and P(F). This gives us the probability of either event E or event F occurring.

In this case, the probability of either event E or event F occurring is 0.65, indicating a relatively high likelihood of one of the events happening.

Learn more about probability here:

https://brainly.com/question/32117953

#SPJ11

9514 1404 393

Answer:

  a) ∆RLG ~ ∆NCP; SF: 3/2 (smaller to larger)

  b) no; different angles

Step-by-step explanation:

a) The triangles will be similar if their angles are congruent. The scale factor will be the ratio of any side to its corresponding side.

The third angle in ∆RLG is 180° -79° -67° = 34°. So, the two angles 34° and 67° in ∆RLG match the corresponding angles in ∆NCP. The triangles are similar by the AA postulate.

Working clockwise around each figure, the sequence of angles from lower left is 34°, 79°, 67°. So, we can write the similarity statement by naming the vertices in the same order: ∆RLG ~ ∆NCP.

The scale factor relating the second triangle to the first is ...

  NC/RL = 45/30 = 3/2

__

b) In order for the angles of one triangle to be congruent to the angles of the other triangle, at least one member of a list of two of the angles must match for the two triangles. Neither of the numbers 57°, 85° match either of the numbers 38°, 54°, so we know the two triangles have different angle measures. They cannot be similar.

Answer:

B

Step-by-step explanation:

got it right on edg

Answer:

3 dots

Step-by-step explanation:

This should be correct due to there only being 3 100% on the table

a. Null hypothesis (H0): The average caloric intake among female Canadian athletes is equal to or greater than the recommended amount (µ ≥ 2811.5 kcal/day).

Alternative hypothesis (H1): The average caloric intake among female Canadian athletes is less than the recommended amount (µ < 2811.5 kcal/day).

b. The value of n that should be used is 201

c. SEM = 880 / √201

d. To sketch the normal curve and label the test statistic, we need the test statistic value and the critical region corresponding to the significance level α = 0.05

e. Without the test statistic or critical region, we cannot calculate the p-value.

f. Since we don't have the test statistic, critical region, or p-value, we cannot make a decision to reject or fail to reject the null hypothesis at this point.

g. Without the test statistic, critical region, or p-value, we cannot draw a conclusion regarding the evidence for or against the deficiency in caloric intake among female Canadian athletes.

a. The appropriate null and alternative hypotheses to test whether female Canadian athletes are deficient in caloric intake can be stated as follows:

Null hypothesis (H0): The average caloric intake among female Canadian athletes is equal to or greater than the recommended amount (µ ≥ 2811.5 kcal/day).

Alternative hypothesis (H1): The average caloric intake among female Canadian athletes is less than the recommended amount (µ < 2811.5 kcal/day).

b. The value of n that should be used is 201, which represents the number of female athletes in the study. The key word in the last sentence of the paragraph ("n=201 women") indicates that the information provided specifically pertains to the female athletes, not the entire sample of 324 athletes.

c. To calculate the test statistic, we need to determine the standard error of the mean (SEM) using the formula:

SEM = σ / √n

where σ is the population standard deviation and n is the sample size. In this case, the population standard deviation is given as 880 kcal/day, and the sample size is 201.

SEM = 880 / √201

d. To sketch the normal curve and label the test statistic, we need the test statistic value and the critical region corresponding to the significance level α = 0.05. However, the critical region is not provided in the given information.

e. The p-value represents the probability of obtaining a test statistic as extreme as or more extreme than the observed value, assuming the null hypothesis is true. Without the test statistic or critical region, we cannot calculate the p-value.

f. Since we don't have the test statistic, critical region, or p-value, we cannot make a decision to reject or fail to reject the null hypothesis at this point.

g. Without the test statistic, critical region, or p-value, we cannot draw a conclusion regarding the evidence for or against the deficiency in caloric intake among female Canadian athletes. Further analysis is required to obtain the missing information and make a conclusive statement.

Visit here to learn more about alternative hypotheses brainly.com/question/28331914

#SPJ11

The probability of event B given event A P(B|A) is approximately 0.2857

P(B|A), the probability of event B given event A, we use the formula:

P(B|A) = P(A and B) / P(A)

P(B|A) denotes conditional probability the probability of event B depends on another event A.

Given the following probabilities:

Probability of event A P(A) = 0.35

Probability of event B P(B) = 0.55

Probability of event  A  and B (A and B) = 0.10

We can calculate P(B|A) as follows:

P(B|A) = P(A and B) / P(A)

P(B|A) = 0.10 / 0.35

P(B|A) ≈ 0.2857

Therefore, P(B|A) is approximately 0.2857.

To know more about probability click here :

https://brainly.com/question/32004014

#SPJ4

The solution to the differential equation y' + 3y = f(t), y(0) = α using Laplace transforms is y(t) = αe⁻³ᵗ + F(s)/(s+3), where F(s) is the Laplace transform of f(t).

We use the Laplace transform on both sides of the problem in order to solve the given differential equation. Let Y(s) and F(s) represent the Laplace transforms of y(t) and f(t), respectively. Taking the Laplace transform of both sides of the equation, we have:

sY(s) - y(0) + 3Y(s) = F(s)

Substituting y(0) = α, we get,

sY(s) - α + 3Y(s) = F(s)

Rearranging the equation and solving for Y(s), we have,

Y(s) = (F(s) + α)/(s + 3)

Now, we need to find the inverse Laplace transform of Y(s) to obtain y(t). Using the properties of Laplace transforms, we know that the inverse Laplace transform of Y(s) is y(t) = L⁻¹{Y(s)}. Applying the inverse Laplace transform, we find,

y(t) = αe⁻³ᵗ + L⁻¹{F(s)/(s+3)}

The term αe⁻³ᵗ corresponds to the initial condition y(0) = α. The remaining term L⁻¹{F(s)/(s+3)} represents the inverse Laplace transform of F(s)/(s+3), which depends on the specific function f(t) and its Laplace transform.

Therefore, the solution to the differential equation is y(t) = αe⁻³ᵗ + F(s)/(s+3), where F(s) is the Laplace transform of f(t).

To know more about Laplace transform, visit,

https://brainly.com/question/29583725

#SPJ4

To show that the relation T defined on the set of integers Z is an equivalence relation, we need to prove three properties: reflexivity, symmetry, and transitivity.

1. Reflexivity: For any integer a, we need to show that aTa (mod). In modular arithmetic, a is congruent to itself modulo any integer, so this property holds.

2. Symmetry: For any integers a and b, if aTb (mod), then we need to show that bTa (mod). In modular arithmetic, if a is congruent to b modulo some integer, then b is also congruent to a modulo the same integer. Therefore, the symmetry property holds.

3. Transitivity: For any integers a, b, and c, if aTb (mod) and bTc (mod), then we need to show that aTc (mod). In modular arithmetic, if a is congruent to b modulo some integer and b is congruent to c modulo the same integer, then a is also congruent to c modulo that integer. Therefore, the transitivity property holds.

Since the relation T satisfies all three properties (reflexivity, symmetry, and transitivity), we can conclude that T is an equivalence relation.

To  know more about Equivalence relations:

https://brainly.com/question/30956755

#SPJ4

Answer:

The train is more reliable.

Step-by-step explanation:

The train is more reliable. The bus is on-time 87.5% of the time, while the train is on-time 90% of the time.

Answer:

m = - 6 :)

Step-by-step explanation:

Answer:

w=8

Step-by-step explanation:

[tex]72=7w+2w\\72=9w\\\frac{72}{9} =w\\w=8[/tex]

proof:

[tex]72=7(w)+2(w)\\72=7(8)+2(8)\\72=56+16\\72=72[/tex]

Answer:

Simplest-9w=72, w=8

Step-by-step explanation:

7w+2w=9w

72/9=8

w=8

Step-by-step explanation:

2 would be the answer .

hope it helps u .

2 cubed = 8

equasion; 2 Cubed = [tex]2^{3}[/tex] = 2 × 2 x 2 = 8

i hope this helps <3

Answer:

the answer is B on USA Prep

Step-by-step explanation:

"A potential outlier at (50, 12)" is the statement that best describes the data shown in the scatter plot.

A straight line that minimizes the gap between it and certain data is called a line of best fit. In a scatter plot containing several data points, a relationship is expressed using the line of best fit. It is a result of regression analysis and a tool for forecasting indicators and price changes.

Given:

The scatter plot shows the relationship between backpack weight and student weight.

From the given choices:

An outlier is a value that nowhere near the range of the data set.

From the scatter plot:

A potential outlier at (50, 12).

Therefore, a potential outlier at (50, 12).

To learn more about the line of the best fit;

https://brainly.com/question/14279419

#SPJ6

The population at time n=9 is approximately 11.95. The term "population" refers to the entire set of individuals, objects, or events that are of interest to a researcher or analyst.

Based on the given information, we have:

Initial population (P0) = 10

Growth rate (r) = 0.2

To find an explicit formula for Pn, we can use the formula for exponential growth:

Pn = P0 * (1 + r)^n

Substituting the given values:

Pn = 10 * (1 + 0.2)^n

Simplifying the formula, we have:

Pn = 10 * 1.2^n

Using this formula, we can find P9:

P9 = 10 * 1.2^9 ≈ 11.95

Therefore, the population at time n=9 is approximately 11.95.

Visit here to learn more about population brainly.com/question/31598322

#SPJ11

Answer:

95 < 75 + 0.80m 20 < m Company A will charge less than Company B for mileages less than 20.

Answer:

I believe

D. Pyramid

Is the answer I did it in 6th or 7th grade

Step-by-step explanation:

Square is flat so no height.  

Line segment is a flat line so no height  

point is a literal dot  

pyramid is a 3d figure so it would have all of the attributes

We both helped right?

Answer:

Pyramid

Step-by-step explanation:

Square is flat so no height.

Line segment is a flat line so no height

point is a literal dot

pyramid is a 3d figure so it would ahve all of the attributes

Answer:

It would be 4 quarts.

Step-by-step explanation:

The answer is 2 quarts

Answer:

1. 4 less than x

2. v = 15.00n

Answer:

4 minus x and v = 15.00n

Step-by-step explanation:

Answer:

umm, i think the question is incomplete

Step-by-step explanation:

Given Info : What is the difference of the value of Lily's expression , 6x-3, when x=5 and the value of Pedro's expression when x=5 .

To Find :- Show or explain how you got your answer.

Solution:-

The expression is 6x-3 , and we need to find its value at x = 5 , On putting x =5 we have

6*5-3 = 30-3 = 27.

This value will come same in case of Pedro, therefore our required answer is 5

Answer : 1/2 gallon

Explanation:

There were a total of 5 gallons collected, as the question states.

There are 3 x's above 1/4, 2 x's above 3/8, 4 x's above 5/8 and 1 x above 1. This is a total of

3+2+4+1 = 10 x's. This means there were 10 trees.

If 5 gallons is evenly distributed among 10 trees, this would give us the ratio 5/10, which simplifies to 1/2 gallon per tree.

....this answer is not from me. The same question was asked on brainy and I've copy pated it, it is the right answer tho. Credit goes to "MsEHolt" for answering.

Answer:

131.92ft²

Step-by-step explanation:

okay, so we have to find the area of both circles, and the circumference then multiply that with the height, it's confusing, so:

3² x 3.14 = 28.26 x 2 = 56.52 so that the area of the bases

3 x 2 x 3.14 = 18.85 x 4 = 75.4

75.4 + 56.52 = 131.92

So the surface area of the cylinder is 131.92ft²