What percentage of the total number of microstates are in one of the three most likely macro states of 100 coins being tossed (49 heads and 51 tails, 50 heads and 50 tails, or 51 heads and 49 tails)

Answer:

a) [tex]\Delta A \approx 26.389\,cm^{2}[/tex], b) [tex]r_{A} \approx 0.019[/tex], c) [tex]\delta = 1.9\,\%[/tex]

Step-by-step explanation:

a) The area of the circular disk is modelled after this expression:

[tex]A = \pi \cdot r^{2}[/tex]

The total differential is given by the following formula:

[tex]\Delta A = 2\pi r \cdot \Delta r[/tex]

The maximum absolute error in the calculated area of the disk is:

[tex]\Delta A = 2\pi \cdot (21\,cm)\cdot (0.2\,cm)[/tex]

[tex]\Delta A \approx 26.389\,cm^{2}[/tex]

b) The relative error is given by:

[tex]r_{A} = \frac{\Delta A}{A}[/tex]

[tex]r_{A} = \frac{26.389\,cm^{2}}{\pi \cdot (21\,cm)^{2}}[/tex]

[tex]r_{A} \approx 0.019[/tex]

c) The percentage error is:

[tex]\delta = r_{A}\times 100\,\%[/tex]

[tex]\delta = 0.019 \times 100\,\%[/tex]

[tex]\delta = 1.9\,\%[/tex]

Answer:

Step-by-step explanation:

WITH THE GIVEN DATA

A ) using regression to investigate the relationship between the number of fatal accidents and the percentage of drivers under the age pf 21

to fit into a regression line we must have ∝ and β

where β = [tex]\frac{S_{xy} }{S_{xx} }[/tex]   = 0.2871

and ∝ = y - βx   =  - 1.5974

regression line = ∝ + β * x

insert values into regression line equation

regression line = -1.5974 + 0.2871 * x

we can conclude that for every single unit of : x, y would be increased by 0.2871.  and intersection of x and y will be through =1.5974

B ) conclusion and recommendations can you derive from your analysis

it  can be  concluded that they are strongly positively correlated. There is strong and positive correlation between them. i.e the number of fatal accidents and the drivers under the age of 21

using the correlation coefficient  ( r ) = [tex]\frac{S_{xy} }{\sqrt{S_{xx}*S_{xy} } }[/tex]    = 0.8394

Answer:

0.8394

Step-by-step explanation:

.

Answer:

  10.5 ft high

  5.3 ft horizontally

Step-by-step explanation:

The equation can be written in vertex form to answer these questions.

  f(x) = -0.2(x² -10.5x) +5

  f(x) = -0.2(x² -10.5x +5.25²) +5 +0.2(5.25²)

  f(x) = -0.2(x -5.25)² +10.5125

The vertex of the travel path is (5.25, 10.5125).

The maximum height is 10.5 feet, which occurs 5.3 feet (horizontally) from the point of release.

Answer:

x or slope: 3

y-intercept: 7

x      y

0     7

1      10

Explanation:

Answer:

rounded to 3 decimal places ...

Step-by-step explanation:

The function can be put into vertex form:

  h(t) = -4.92(t -(1769/984))^2 +575 +4.92(1769/984)^2

  h(t) ≈ -4.92(t -1.79776)^2 +590.90122

The value of h(t) is zero for ...

  t = √(590.90122/4.92) +1.79776 ≈ 12.75686

For practical purposes, the domain of the function is those values of t between the time the object is tossed and the time it hits the ground. That is, the domain is ...

  0 ≤ t ≤ 12.75686

The range is the set of useful vertical heights, so extends from 0 to the maximum height, given by the vertex.

The range is 0 ≤ h(t) ≤ 590.90122.

_____

Alternate interpretation of the question

The function h(t) is defined for all values of t, so that could be considered the domain.

The function h(t) only gives values less than its vertex value, so the range could be considered to extend from negative infinity to that maximum.

Answer:

11

Step-by-step explanation:

Answer:

nickels- 5, quarters- 11

Step-by-step explanation:

nickel= 5 p,  quarter= 25 p

5x+25(x+6)= 300

30x+150=300

30x=150

x=150/30

x=5 nickels

x+6= 11 quarters

Answer:

b

Step-by-step explanation:

externally consistent ideas are the ideas that are consistent with other well-confirmed hypothesis.

Fruitfulness of a hypothesis can be measured from the fact it it suggests something other than what it was originally suppose to explain.

Answer:

Hello!

I believe this is what you are looking for:

x=3

33=27

32=9

S=Surface area

V=Volume

L=Length

R=Radius

I hope this helped.  If not, please let me know.  I will try my best again. :)

Step-by-step explanation:

The right answer is (1/2 , 5)

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

Answer:

7mph

Step-by-step explanation:

Given

Time Taken to go upstream Tup = 35 min

Time Taken to go downstream Tdown=21 min.

Let the absolute speed (i.e speed relative to the stationary riverbed) be :

Vup : going upstream

Vdown: going downstream.

We know that the distance traveled upstream = distance traveled downstream, hence we can equate both distances, i.e. :

Distance Traveled Upstream = Distance Traveled Downstream

Vup · Tup = Vdown · Tdown   (substituting the values for time above)

35Vup = 21Vdown

Vup = (21/35) Vdown ------------(eq 1)

We are also given that the motorboat can travel at V = 28 mph relative to the water.

Since going upstream, we are going AGAINST the current, relative to the riverbed, we expect to be travelling slower. In fact, the absolute difference between the speed relative to the water (i.e V = 28 mph) and the speed relative to the seabed (i.e Vup), is equal to the speed of the current.

The same can be said for going downstream WITH the current, that the absolute difference between V = 28mph and Vdown is also equal to the speed of the current.

Hence we can equate the two:

28 - Vup = Vdown - 28

Vup + Vdown = 2(28)

Vup + Vdown = 56 ---------------------(eq 2)

If we solve the system of equations (eq 1) and (eq2), we will get

Vup = 21 mph and Vdown = 35 mph

(sanity check tells us that this makes sense because we expect to be going slower upstream because we are going against the current)

Hence current speed

= 28-Vup

= 28 - 21

= 7 mph. (answer)

Sanity Check:

Current speed can also be written:

= Vdown-28

= 35 - 28

= 7 mph (same as what we found above, so this checks out)

The speed of the current motorboat = 7 mph

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Speed of boat in still water = 28 mph

Let the speed of stream = w

Here, The upstream time is 35 min = 35/60 h = 7/12 h

downstream time is 21 min = 21/60 h = 7/20 hours

Since, The distance (d = vt) traveled either way is the same, but at different speeds and times.

Hence, Set upstream and downstream distances (vt) equal and solve for w as;

⇒ (28 - w)(7/12) = (28 + w)(7/20)

⇒ 20 (28 - w) = 12 (28 + w)

⇒ 5(28 - w) = 3(28 + w)

⇒ 140 - 5w = 84 + 3w

⇒ 140 - 84 = 5w + 3w

⇒ 56 = 8w

⇒ w = 7

Thus, The speed of the current = 7 mph

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Answer:

Air resistance

Step-by-step explanation:

Air resistance is a type of friction that occurs when air pushes against a moving object causing it to negatively accelerate

Answer:

Air resistance

Step-by-step explanation:

Air resistance is a type of friction that occurs when air pushes against a moving object causing it to negatively accelerate.

Answer:

“It is a binomial with a degree of 3”

Step-by-step explanation:

Since it has just two different coefficients, it would be considered “binomial” for that reason. As you can notice, the highest degree is 3. So match those up and the correct answer would be the second choice “It is a binomial with a degree of 3”

Answer:

B

Step-by-step explanation:

Answer:

C. 41,800

Step-by-step explanation:

Multiply 0.44 by 95,000.

0.44 x 95,000 = 41,800

Answer: Choice C

Step-by-step explanation:

Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true.

3/10≠3/5*1/4

so event A and B are not independent.

Answer:

41-60 => 5

Step-by-step explanation:

41-50 => 2

51-60 => 3

So 2+3 =5

Answer:

5

Step-by-step explanation:

Add up the number of children between 41 and 60

41-50: 2

51-60: 3

------------

total 5

Answer:

Solve for  

w

by simplifying both sides of the equation, then isolating the variable.

Exact Form:

w

=

49

2

Decimal Form:

w

=

24.5

Mixed Number Form:

w

=

24

Answer:

24

Step-by-step explanation:

Answer:

Thus; the slope is positive

Step-by-step explanation:

Given that :

the sample size = 20

for the slope; the degree of freedom df = n - 2

= 20 -2

= 18

Using ∝ = 0.05

From t -table , one tailed, at df =18)

[tex]t_{\alpha , df}}= t_{0.05, df = 18} = 1.734[/tex]

Thus the t- critical for the right tailed test is 1.734. This simply refers to the fact that the critical region is test statistics.

Incorporating the Excel Formula [ T.INV (1 - 0.05).18) = 1.734063607

≅ 1.734

Answer:

  -7

Step-by-step explanation:

To find the differences in a sequence, subtract the term before:

  -15 -(-8) = -7

  -22 -(-15) = -7

These differences are the same, so constitute the "common" difference.

The common difference of the sequence is -7.

Answer:

Step-by-step explanation:

This is  the method I am familiar with.

I Hope It helps :)

[tex]METHOD- 1 : Elimination\\6x - 2y=10------(1)\\2x+3y =51------(2)\\Multiply -eq-(1)- by -the-coefficient-of-x-in-equation (2)\\Multiply-eq-(2) -by -the-coefficient-of-x-in-equation (1)\\6x - 2y=10------(1) *2\\2x+3y =51------(2)*6\\\\12x-4y=20 ------(3)\\12x+18y=306 ------(4)\\Subtract -eq- (4)- from- eq -(3)\\-22y =-286\\\frac{-22y}{-22} =\frac{-286}{-22} \\y =13\\[/tex]

[tex]Substitute- 13- for y -in-equation -(1)-or-(2)\\6x - 2y=10------(1)\\6x -2(13)=10\\6x -26=10\\6x =10+26\\6x =36\\\frac{6x}{6} =\frac{36}{6} \\x =6[/tex]

Answer:

Correct answers is

Step-by-step explanation:

1. 3

2. B

3. 6

4. (6,13)

Answer:

Step-by-step explanation:

Null hypothesis: u = 10

Alternative hypothesis: u =/ 10

Using the formula: t = (x - u) / (s /√n)

Where x = 12, u = 10, s = 5 and n = 25

t= (12-10) / (5/√25)

t = (2)/(5/5)

t = 2/1= 2

t = 2.0

At a 0.01 level of significance with a degree of freedom of 24, the p-value is 0.0569, which is greater than 0.01 we will fail to reject the null and conclude that parents do not read more than the average number of books to their children

Answer: 0.97

Step-by-step explanation:

Formula : For events A and B

P(A or B) = P(A) + P(B) - P(A and B)

Given : The probability of teenager owning a game system is .72.

i.e. P(game system) =0.72

The probability of teenager owning a cell phone is .93.

i.e. P(cell phone) = 0.93

The probability of a teenager owning both gaming system and cell phone is .68

i.e. P( game system and cell phone) = 0.68

Now , the probability of a teenager owning a gaming system or a cell phone is given by :_

P(game system or cell phone) = P(game system) +P(cell phone)- P( game system and cell phone)

= 0.72+0.93-0.68

= 0.97

Hence, the probability of a teenager owning a gaming system or a cell phone is 0.97.

Answer:

A) 15

B) 0.9

Step-by-step explanation:

Use the correct order of operations.

A) 40 − 5 ÷ 1/5 =

= 40 − 5 * 5

= 40 - 25

= 15

B) (4.8 − 1.8 ÷ 6) ÷ 5 =

= (4.8 − 0.3) ÷ 5

= 4.5 ÷ 5

= 0.9

Answer:

  (-2, 1)

Step-by-step explanation:

For a relation consisting of (x, y) pairs to be a function, all of the x-values must be unique. In the given relation, points (-2, -3) and (-2, 1) have the same x-value. Removing either point will make the relation a function.

Of these, the only one listed among answer choices is (-2, 1).

Answer:

-2 , 1

Step-by-step explanation:

good luck love

Answer:

Categorical data includes

b. How did you pay for the vehicle? (Cash, Lease, or Finance)

c. How likely would you be to recommend this vehicle to a friend? (Definitely Not, Probably Not, Probably Will, and Definitely Will)

e. What is your overall rating of your new vehicle? A 1 to 10 point scale, ranging from I for unacceptable to 10 for truly exceptional, was used.

Quantitative data includes

a. What price did you pay for the vehicle?

d. What is the current mileage?

Step-by-step explanation:

Categorical data refers to the kind of data in which the variables are grouped based on a particular quality, ticking a particular box or satisfying some specific requirements.

It uses one or more qualitative property/properties to assign variables into a limited, usually fixed groups or categories. Note that the qualitative property might be a grouped data of numerical values. As long as there are easily separable and recognizable groups, it is categorical data.

This is also called qualitative data.

Quantitative data is a data that is strictly about numerical values. A dataset that consists of numerical values of the members of the dataset. Deals almost exclusively with numbers, usually ungrouped.

So, examining the given datasets one at a time

a. What price did you pay for the vehicle?

The answer to this question is a numerical value and for various customers, it builds up a dataset of strictly numerical values. Hence, this resulting data is a quantitative data.

b. How did you pay for the vehicle? (Cash, Lease, or Finance)

The answers to this question can only take 3 forms; Cash, Lease or Finance, indicating that all the variables in the dataset can only take on limited, fixed number of groups/categories. Hence, this dataset is a categorical data.

c. How likely would you be to recommend this vehicle to a friend? (Definitely Not, Probably Not, Probably Will, and Definitely Will)

The answers to this question too can take on 4 limited, fixed categories or groups, Hence, it's easy to see that this dataset is also categorical data.

d. What is the current mileage?

The answer to this question is a numerical value. Various answers from numerous persons would lead to a data of numbers. Hence, this is a quantitative data.

e. What is your overall rating of your new vehicle? A 1 to 10 point scale, ranging from I for unacceptable to 10 for truly exceptional, was used.

Limited, fixed categories or groups (10 groups) are also available for this data, hence, it is easily a categorical data.

Hope this Helps!!!

Answer:  nice and funnyyyyy y=4

Step-by-step explanation:

Question:

It is known that 20% of products on a production line are defective. Products are inspected until first defective is encountered. a) What is the probability that the experimenter must inspect six products to find a defective product?

Answer:

P(x = 6) = 0.0655

P(x = 6) = 6.55%

Step-by-step explanation:

It is given that 20% of products on a production line are defective.

p = 0.20

Then

q = 1 - p = 1 - 0.20 = 0.80

Which means that 80% of products on the production line are not defective.

We want to find out the probability that the experimenter must inspect six products to find a defective product.

Let x is the number of inspections to get a defective product.

P(x = 6) = ?

If out of 6 inspections 1 is defective then it means 5 are not defective

so the probability is

P(x = 6) = p¹ × q⁵

P(x = 6) = 0.20¹ × 0.80⁵

P(x = 6) = 0.20 × 0.32768

P(x = 6) = 0.0655

P(x = 6) = 6.55%

Therefore, there is 6.55% chance that the experimenter finds a defetive product in 6 inspections.

Answer:

Step-by-step explanation:

1. The angle facing the given arcs is half their sum, so is (180 +116)/2 = 148°. Angle 1 is the supplement of this, ...

  angle 1 = 180° -148° = 32°

__

2. Short arc WY is the supplement of 70°, Long arc WVY is the difference of that and 360°:

  arc WVY = 360° -(180° -70°) = 180°+70°

  arc WVY = 250° . . . . . matches choice C

__

3. Call the point of intersection of the secants X. The rule for secants is ...

  (XA)(XC) = (XB)(XD)

So, the length XC is ...

  XC = (XB)(XD)/(XA) = 2.4

and ...

  AC = XA +XC = 3.2 +2.4 = 5.6 . . . . . matches choice D

__

4. As in problem 3, the product of lengths from the point of secant intersection to the points of circle intersection is the same for both secants.

  (NQ)(NR) = (NP)(NS)

Substituting segment sums where necessary, we have ...

  NQ(NQ +QR) = NP(NP +PS)

Solving for PS, we have ...

  PS = NQ(NQ +QR)/NP - NP . . . . . matches choice A

Answer:

The answer is No Solution

Answer:

No solution

Step-by-step explanation:

There is no solution to this question.

Since the x is an absolute number, the answer cannot be -4. It would have to equal 4

So if that x was a -4 it would equal 4 since it is in absolute value brackets

Answer: 4 / 663

Step-by-step explanation:

There are 4 queens in a deck of 52 cards.

Probability = 4/52 = 1/13

There are 4 sevens

Probability = 4/51

Total probability = 1/13 x 4/51 = 4 / 663

The probability of drawing a queen first and a seven-second is 3/613.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

There are 4 queens in a standard deck, and once one queen is drawn, there are 51 cards left, including 3 sevens.

So, the probability of drawing a queen first is 4/52 or 1/13, and the probability of drawing a seven-second is 3/51.

By the multiplication rule of probability, multiply the probabilities of each event occurring:

P(Queen and Seven) = P(Queen) × P(Seven after Queen)

P(Queen and Seven) = (1/13) × (3/51)

P(Queen and Seven) = 3/613

Thus, the probability of drawing a queen first and a seven-second is 3/613.

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