One lucky day, you meet a leprechaun who promises to give you fantastic wealth, but hands you only a penny before disappearing. You head home and place the
penny under your pillow. The next morning, to your surprise, you find two pennies under your pillow. The following morning, you find four pennies, and the morning after
that, eight pennies.
Suppose that you could keep making a single stack of the pennies. After how many days would the stack be long enough to reach a star that is about 3x10¹3 km
away? (Assume that 1 penny = 1.5 mm)

Answers

Answer 1

The number of  days would the stack be long enough to reach a star that is about 3 × 10¹³ km away is 64 days

How to find the number of days the penny would stack?

Since from the question, we see that the number of pennies double with each day. It forms a geoemetric progression with

first term a = L and common ratio , r = 2.

Since the number of pennies after n days equals N = 2ⁿ

Let

L = length of 1 penny = 1.5 mm = 1.5 × 10⁻³ m

So, after n days, the length of the stack of pennies is the geoemetric progression D = 2ⁿ × L

Number of days pennies would stack to reach star

Making n subject of the formula, we have

n = ㏒(D/L)/㏒2

Since D = the distance of the star = 3 × 10¹³ km = 3 × 10¹⁶ m, and L = length of 1 penny = 1.5 mm = 1.5 × 10⁻³ m

Substituting the values of the variables into the equation, we have

n = ㏒(D/L)/㏒2

n = ㏒(3 × 10¹⁶ m/1.5 × 10⁻³ m)/㏒2

n = ㏒(3/1.5 × 10¹⁹)/㏒2

n = ㏒(2 × 10¹⁹)/㏒2

n = ㏒2 + ㏒10¹⁹/㏒2

n = (19㏒10 + ㏒2)/㏒2

n = (19 + 0.3010)/0.3010

n = 19.3010/0.3010

n = 64.1

n ≅ 64 days

So, the number of  days would the stack be long enough to reach a star that is about 3 × 10¹³ km away is 64 days

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Related Questions

Select all numbers that are a solution of the inequality.
Every month a salesperson adds 7 new accounts. The algebraic expression that represents the number of new accounts that he will add in m months is _____.

Answers

The algebraic expression that represents the number of new accounts that he will add in m months is x ≥ 7m.

What is inequality?

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Every month, a salesperson adds 7 new accounts.

Let m be the number of the month and x be the number of the accounts.

Then the inequality equation will be

x ≥ 7m

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what can this be classified as?

Answers

Answer:

D. None of the Above

Step-by-step explanation:

They don't relate whatsoever

como faltar a la escuela​

Answers

Answer:

Como faltar a la escuela. Por favor, ¿cuál es el significado?

write and solve a proportion to complete the statement. Round to the nearest hundredth if necessary.
1. 6km ≈ ?mi
2. 2.5 L≈ ?gal
3. 90lb ≈ ?kg
pls help

Answers

Answer:

Step-by-step explanation:

Convert kilometer to miles:

1 km = 0.62 mi

So, to convert 6 km to mi, multiply 6 by 0.62.

6km = 6* 0.62

        = 3.72 mi

Convert liter to gallon:

1 L = 0.26 gal

To convert 2.5 L to gallon, multiply 2.5 by 0.26.

2.5 L = 2.5 * 0.26

         = 0.65 gal

Convert pound to kilogram:

1 lb = 0.45 Kg

To convert 90 lb to Kg, multiply 90 by 0.45.

90 lb = 90 *0.45

        = 40.5 Kg

which greek mathematician wrote the most definitive text on geometry, one that is still referred torday.

Answers

Answer:

Pythagoras

Step-by-step explanation:

please mark me as brainlest

I think the answer is Euclid.

A main area of mathematics is called Euclidean Geometry.

City A and City B had two different temperatures on a particular day. On that day, four times the temperature of City A was 8° C more than 3 times the temperature of City B. The temperature of City A minus twice the temperature of City B was −3° C. What was the temperature of City A and City B on that day?

A) City A was 5: C. and City B was 4° C.
B) City À was 3° C, and City B was -1° C
C)City A was 8° C. and City 3 was -3° C.
D)City À was 5° C, and City 3 was -5° C. ​

Answers

Answer:

A) City A was 5°C and City B was 4°C

Step-by-step explanation:

let temperature of City A be x and City B be y

According to the conditions of the question

4x = 8 + 3y (first temperature)

x - 2y = -3 (second temperature)

x = -3 + 2y

4(x) = (-3 + 2y)×4

4x = -12 + 8y

But it's already given that 4x = 8 + 3y

So,

8 + 3y = -12 + 8y

8 + 12 = 8y - 3y

20 = 5y

y = 20/5

y = 4

That means City B temperature was 4°C

So Option A

If you want you can find x to find City A temperature

Can you please mark Brainliest

If b = 5, then the exact value of a is?

Answers

Answer:

5sqrt3

Step-by-step explanation:

You can use trigonometry to figure out the answer

TOA is tan(any angle) = opposite/adjacent

Tan(30) = 5/x

tan(30) = sqrt3/3

x = tan inverse (30) multiplied by 5

x = 5sqrt3

Determine the measure of the indicated angle!

Answers

The measure of the angle PUT is 13 degrees and the measure of the angle PQR = 21 degrees

What is an angle?

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

We have triangles shown in the picture.

In the first triangle SUT:

PU is bisecting the angle SUT:

The measure of angle PUT:

Angle PUT = Half of Angle SUT

= 26/2

= 13 degrees

In the triangle SQR:

Angle SQP = Angle PQR

Angle SQP  = 21 degrees

Angle PQR = 21 degrees

Thus, the measure of the angle PUT is 13 degrees and the measure of the angle PQR = 21 degrees

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Suppose we want to choose 6 letters without replacement from 10 distnict letters. how many ways can this be done if the order of the choices is relavant

Answers

The number of ways this can be done is 151200 if they choose 6 letters without replacement from 10 distinct letters.

What are permutation and combination?

A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.

We have:

Suppose we want to choose 6 letters without replacement from 10 distinct letters.

Number of letters = 10

Number of letters need to select = 6

Order is important.

A number of ways:

C(10, 6) = 10!/(10-6)!

= 10!/(4)!

= 151200

Thus, the number of ways this can be done is 151200 if they choose 6 letters without replacement from 10 distinct letters.

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Given f(x) and g(x) = k⋅f(x), use the graph to determine the value of k. 3 1/3 -1/3 −3

Answers

This is about interpretation of graphs.

Option C is correct.

From the graph, we can see the 2 lines representing function f(x) and function g(x).

Now for us to find the value of x in g(x) = k⋅f(x), we need get a mutual x-coordinate where we can easily read their respective y-coordinate values.

We see that the best point for that is where x = -3.

For f(x), when x = -3, y = 1

For g(x), when x = -3, y = -3

we can rewrite them as;

x = -3, f(-3) = 1 and x = -3, g(-3) = -3

Let us plug in the relevant values into g(x) = k⋅f(x) to get;

-3 = k(1)

Thus; k = -1/3

Which classification describes the following system of equations?
12x+5y-3z= 36
x-2y+4z=3
9x-10y+5z = 27

Answers

A consistent and independent system of equations describes the given system of equations.

The consistent and independent system of equations are given below.

12x+5y-3z= 36x-2y+4z=39x-10y+5z = 27

What is a consistent independent equation?

A consistent equation is a system of linear equations that is consistently unbiased when it has precisely one solution. While this is the case, the graphs of the lines within the system move at exactly one point. In inconsistent, a system of linear equations is inconsistent if it has no solutions.

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Each child ticket for a ride costs $3, while each adult ticket costs $5. if the ride collected a total of $115, and 33 tickets were sold, how many of each type of ticket were sold

Answers

There were 8 of the $5 and 25 $3

I give you 12 points if you help me ;) it’s math

Answers

Answer:

y=23.6

Step-by-step explanation:

20+0.45×8

20+3.6

23.6

translate the following to and expression 5 times the difference of a number and 12

Answers

Answer:

5(a-12)

Step-by-step explanation:

5(a-12)

Please help me! I need help. Please help me, I need help, please help me!

Answers

Answer:

17x

Step-by-step explanation:

3x+4+4x+4+3x-4+3x-4+4x

Collect liketerms

What is the sum of the arithmetic sequence 3, 9, 15..., if there are 24 terms? (5 points)

Answers

There's a fixed difference of 6 between terms (9 - 3 = 6, 15 - 9 = 6, and so on). The first term of the sequence is 3, so the [tex]n[/tex]-th term is

[tex]3 + 6(n-1) = 6n - 3[/tex]

If there are 24 terms in the sum, then the last term is 6×23 - 3 = 135.

Let [tex]S[/tex] be the sum,

[tex]S = 3 + 9 + 15 + \cdots + 123 + 129 + 135[/tex]

Reverse the order of terms:

[tex]S = 135 + 129 + 123 + \cdots + 15 + 9 + 3[/tex]

If we add up the terms in the same positions, we get twice [tex]S[/tex] on the left side, while on the right side we observe that each pair of terms will sum to 138.

[tex]S + S = (3 + 135) + (9 + 129) + (15 + 123) + \cdots + (135 + 3)[/tex]

[tex]2S = 138 + 138 + 138 + \cdots + 138[/tex]

and since there are 24 terms in the sum, the right side is the sum of 24 copies of 138. In other words,

[tex]2S = 24 \times 138[/tex]

and solving for [tex]S[/tex] gives

[tex]S = \dfrac{24\times138}2 = \boxed{1656}[/tex]

Click for the picture of the question it’s a multiple choice, I don’t even know where to begin

Answers

Answer:

b - read explanation if you are confused for future problems

Step-by-step explanation:

Inverse variation is when x*y = k whereas direct variation (may come up in future problems) is when y = x*k

Remember that k is always a set value while x and y are values that can change

In this case y*x = k so k = 18 (since y is 9 when x is 2)

So when  x = 8

8y = 18

y = 18/8 = 9/4

Answer is b! Not quite sure how to explain it tho

A trader bought 30 baskets of pawpaw and 100 baskets of mangoes for 2450. she sold the pawpaw at a profit of 40% and the mangoes at a profit of 30%. if her profit on the entire transaction was 855, find the cost price of a basket of pawpaw and the selling price of 100 baskets of mangoes.

Answers

The cost price of pawpaw is 40 and the cost if the basket of mangoes is 1250.

How to calculate the price?

Based on the information given, the equations to solve the question will be:

30p + 100m = 2450 .... i

1.3 × 40p - 30 p + 1.3 × 100m = 855 ..... ii

30p + 100m = 2450

12p + 30m = 855

Solving simultaneously, the price of pawpaw is 40 and the price of mango is 12.5.

Therefore, the cost of 100 basket of mangoes will be:

= 12.5 × 100

= 1250

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solve 3(10)^x = 30,000

Answers

Answer: x = 4

Step-by-step explanation:

We will need to use logs here...

First divide each side by 3

[tex]3(10)^x=30000[/tex]

[tex]10^x=10000[/tex]

Then take the log of each side

Keep in mind that [tex]log_{10} (10)[/tex] gets canceled out to leave x

[tex]log_{10} (10^x)=log(10000)[/tex]

Finally, log(10000) = 4 because [tex]10^4=10000[/tex]

[tex]x = 4[/tex]

Try to get x isolated on one side.
Divide by 3 on both sides.
(10)^x = 10,000
Count how many zeroes there are in the number 10,000. There are 4 zeroes, therefore 10 was raised to the 4th power to get to 10,000.
That means “x” is 4. Hope this helps :)

If the divisor is a decimal then you must multiply by a power of 10 to make it a whole number. Why is it important to multiply the dividend and the divisor by the same power of 10?

Answers

It is important to multiply the dividend and the divisor by the same power of 10 to remove the decimal point.

Division of whole numbers

When the numerator and denominator of improper fractions are in whole number form, it makes the division a lot easier.

For example;

what is the simplest form of 0.1/0.2?

To obtain the simplest form of the above function, we multiple the numerator and denominator by 10.

= (0.1 x 10)/(10 x 0.2)

= 1/2

Note: introducing factor of 10 to both numerator and denominator has not changed the function.

Thus, it is important to multiply the dividend and the divisor by the same power of 10 to remove the decimal point.

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How much weight does the women in the video lose in a year? 80 pounds 90 pounds 50 pounds 20 pounds

Answers

Medical practitioners recommend losing around 365 pounds or 730 pounds per year.

What is an equation?

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

Medical practitioners recommend losing around 1–2 pounds (0.5–0.9 kg) per week.

Hence for a year:

Amount of weight loss = (1 * 365) or (2 * 365)

Medical practitioners recommend losing around 365 pounds or 730 pounds per year.

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m<1 = (3x + 4)º
m<2 = (3x + 4)º
m<3 = 29°
m<4 = 34°
m<5 = 25°

Answers

Answer: x = 44

Step-by-step explanation:

The exterior angles of a polygon add to 360 degrees so:

(3x+4)+(3x+4)+29+34+25=360 [forming equation]6x+96=360 [combine like terms]6x=264 [subtract 96 from both sides]x = 44 [divide both sides by 6]

Find the value of y.

Answers

Answer:

its 0

Step-by-step explanation:

you just gotta do the math correctly to get the answer. x & y are both values with different meanings. but in this case it's 0

what does a equal if 2÷a=(5/2)÷(5/4)

Answers

Question:

2÷a=(5/2)÷(5/4)

Answer:

a = 1

the roots of x+1/x=3 are: (x not equal to 0)​

Answers

Answer:

x^2-2x-3

Step-by-step explanation:

(x+1)(x-3)

x(x-3)+1(x-3)

Multiply both sides by x
x^2 + 1 = 3x
x^2 - 3x + 1 = 0
Completing the square
x^2 - 3x + (1.5)^2 - 1.25 = 0
(x - 1.5)^2 = 1.25
x - 1.5 = +- sr(1.25)
x = 1.5 +- sr(1.25)
x = 2.61803… or 0.381966…

You could use the quadratic formula x = (-b +- sr(b^2 - 4ac)) / 2a where ax^2 + bx + c = 0

Solve for x in the diagram below.

Answers

Answer:

x = 34

Step-by-step explanation:

A straight line is 180 degrees

We can sum angles to form a straight line

x+12 + 100 +x = 180

Combine like terms

2x+112 = 180

2x+112-112 = 180-112

2x = 68

Divide each side by 2

2x/2 = 68/2

x = 34

answer:

=x+12+100+x =180

=x+x+12+100=180

=2x+112=180

=2x=180-112

=2x=68

=2/2x=68/2

=x=34

there are 2 quarters 1 nickle and 2 dimes in a pocket what is the probility of choosing a coin not returning it too the pocket and then choosing another of greater value

Answers

The first coin chosen can be either a dime or nickel as the second coin must be of greater value.
P(dime followed by quarter) = 2/5 x 2/4 = 4/20 = 1/5
P(nickel followed by quarter or dime) = 1/5 x 4/4 = 1/5

P(second coin has higher value) = 1/5 + 1/5 = 2/5

Given a b and m/1 = 42°
What is m/6?
Enter your answer in the box.

Answers

Answer:0.166666667 metros

Step-by-step explanation:
espero te ayude

what are the true statements

Answers

D and C are true statements

HEEEEEEELPPP AND QUICKKKKK PLEASE OMGOMGOMGGMOGMGOMGOMGOMGOGMOMGOMGOMGOGMOGMOMGOMGOMOGOG

Answers

Answer:

C (The third answer). The square root of terms separated by addition and subtraction cannot be calculated individually.

Step-by-step explanation:

This problem can be thought similarly to: (x-2)²

A common mistake would to make the x squared and the -2 squared like x²+4, however, the problem should be solved like (x-2)(x-2) which equals to: x² - 4x + 4

In this question, if you square root an expression like ±√(b²-4ac), you cannot just take the square root of b² unless it was (b²)(-4ac).

The terms can only be divided individually if they are either multiplied or divided, but cannot if they are added or subtracted.

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_____ is not considered a challenge when designing applications for multicore systems. A) Deciding which activities can be run in parallel B) Ensuring there is a sufficient number of cores C) Determining if data can be separated so that it is accessed on separate cores D) Identifying data dependencies between tasks. Drivers pay a toll to pass over a busy bridge, and there are many toll booths that collect money. The city manager counted the total number of cars waiting to pay their tolls at 15-minute intervals during two different days, once on a weekday and once on a weekend. The histograms below show the results.2 histograms. A histogram titled weekday traffic has number of cars in line on the x-axis, and frequency on the y-axis. 0 to 10, 4; 10 to 20, 13; 20 to 30, 19; 30 to 40, 8; 40 to 50, 5; 50 to 60, 1. A histogram titled weekend traffic has number of cars in line on the x-axis, and frequency on the y-axis. 0 to 10, 12; 10 to 20, 20; 20 to 30, 14; 30 to 40, 3; 40 to 50, 1.Using the histograms, which of the following is the correct comparison of the distributions?The 1020 interval contains the most observations on both days.The two distributions for number of cars in line are both skewed right.The median number of cars for both distributions lies in the 2030 interval.There were more than 40 cars in line more often on the weekend than the weekday. In macroeconomics, the connection from inputs to outputs for the entire economy is called _______________. Who made the light switch what statement can you use to divide a script into multiple batches? What type of relationship is expressed below?5x = 2x 9O equationO functionO inequality if i poured green solution into another test tube and added some copper pieces to the solution will a displacment action occur What is a spring tide? When and why does it occur? Read the excerpt from Malala Yousafzai's speech atthe United NationsThe terrorists are misusing the name of Islam andPashtun society for their own personal benefits.Pakistan is a peace-loving democratic country.Pashtuns want education for their daughters and sons.And Islam is a religion of peace, humanity andbrotherhood. Islam says that it is not only each child'sright to get education, rather it is their duty andresponsibility.Mark this and returnHow could Yousafzai improve the effectiveness of herargument?O by explaining why education is important for youngpeopleO by giving examples of other countries that valueeducationO by describing ways that terrorists' actions andbeliefs conflict with Islam and Pashtun societyO by providing examples of how Islam and Pashtunsociety support education for girls Determine whether the given graph is a function or not. a town B is 12km from another town A on a bearing of 47degree and another C is 8km from town B on a bearing of 124degree.how far is town A from town C?what is the bearing of A from C please help! i suck at these lol Rewrite the sentences using the underlided adjectives as adverbsHINT- identify the noun which the adjective is describing. change it to its verb form and replace the existing verba) you have done a nice work ( use nicely) ------ b) she gave a graceful performance ------------ c) the teacher gave a patient explaination ----------d) the coach extended a fair treatment to all players -----e) despite the slow walk, the tortoise won the race ------- Write an article on "child labour". Which group constituted the backbone of the american labor force throughout the nineteenth century? can someone help meeee "There's Don and Eva," Mrs. Hutchinson yelled. "Make them take their chance!""Daughters draw with their husbands' families, Tessie," Mr. Summers said gently. "You know that as well as anyone else.""It wasn't fair," Tessie said."I guess not, Joe," Bill Hutchinson said regretfully. "My daughter draws with her husband's family, that's only fair. And I've got no other family except the kids."The Lottery,Shirley JacksonWhat kind of tone should be used to express how Tessie Hutchinson feels when she says, It wasnt fair?puzzledforgivingunderstandingdistressed Sleep deprivation ________ the production of body fat by ________ levels of the stress hormone cortisol a water tank is empty. Anil needs to fill the tank with 2400 litres of eater Explain the process of sporulation with the help of example.