2 last questions:
1.) You toss 5 dimes. What is the probability that at least two dimes land on tails?
2.) King Francis decided to divide up his kingdom among his sons. He gave his first son one-eight of the villages he ruled over and one more village. The king gave his second son one-ieth of the remaining villages and two more villages. He continued like this, until he gave his seventh and youngest son one-eight of the remaining villages and and seven more villages. After that, all the villages in the kingdom had been passed on to his children. How many total villages are there in the kingdom?
Answers
Problem 1
Answer: 26/32-----------------------
Work Shown:
There are is 1 way to get 0 tails (aka 5 heads)
There are 5 ways to flip the coins so that exactly one coin shows tails and the rest are heads.
We have 1+5 = 6 ways of getting at most 1 tail. The phrasing "at most 1" means "1 is the largest number we can get".
There are 2^5 = 32 ways to flip five coins, so there are 32-6 = 26 ways of getting at least two tails. Note the events "getting at most 1 tail" and "getting at least 2 tails" are complementary events. One or the other must happen.
The probability of getting two or more tails is therefore 26/32.
========================================================
Problem 2
Answer: 56 total villages-----------------------
Work Shown:
We'll work our way backwards starting with the last (7th) son
x = number of villages left before the 7th son gets his share
x/8 + 7 = number of villages the 7th son gets
x - (x/8+7) = 7x/8 - 7 = number of villages left after the 7th son gets his share
This amount should be 0, so,
7x/8 - 7 = 0
7x/8 = 7
7x = 7*8
7x = 56
x = 56/7
x = 8
There are 8 villages left before the 7th son gets his share; this means he gets x/8+7 = 8/8+7 = 1+7 = 8 villages. Or you can note that if there are 8 villages left, and he's the last in line, then he gets the remaining 8.
Plugging x = 8 into 7x/8 - 7 leads to 0.
----------
y = amount of villages left before the 6th son gets his share
y/8 + 6 = amount of villages the 6th son gets
y - (y/8+6) = 7y/8 - 6 = amount of villages left after 6th son gets his share
We match up the x = 8 found earlier with this new expression and we solve for y. This is because x represents the number of villages leftover after the 6th son gets his share. After the 6th son gets his share, that leftover x is then handled for the 7th son as discussed above.
7y/8 - 6 = x
7y/8 - 6 = 8
7y/8 = 14
7y = 14*8
7y = 112
y = 112/7
y = 16
There are 16 villages leftover before the 6th son gets his share.
This means the 6th son gets y/8 + 6 = 16/8 + 6 = 2+6 = 8 villages.
----------
z = amount of villages left before the 5th son gets his share
z/8 + 5 = amount of villages the 5th son gets
z - (z/8+5) = 7z/8 - 5 = amount of villages left after 5th son gets his share
You can probably spot the pattern by now. We'll follow the same idea as before. Set 7z/8-5 equal to the 16 villages and we get
7z/8-5 = y
7z/8-5 = 16
7z/8 = 16+5
7z/8 = 21
7z = 21*8
7z = 168
z = 168/7
z = 24
There are 24 villages before the 5th son gets his share.
He gets z/8 + 5 = 24/8 + 5 = 3 + 5 = 8 villages.
------------
I'll do one more iteration
w = amount of villages left before the 4th son gets his share
w/8 + 4 = amount of villages the 4th son gets
w - (w/8+4) = 7w/8 - 4 = amount of villages left after 4th son gets his share
Set that equal to the previous value 24 and solve for w
7w/8-4 = z
7w/8-4 = 24
7w/8 = 24+4
7w/8 = 28
7w = 28*8
7w = 224
w = 224/7
w = 32
There are 32 villages before the 4th son gets his share.
He gets w/8 + 4 = 32/8 + 4 = 4 + 4 = 8 villages.
------------
The rest of the steps to find the other village counts will follow this template. You should find that each son gets 8 villages. There are 7 sons, so that means there are 7*8 = 56 villages total.
------------
It makes sense that the answer is some multiple of 8 because when taking 1/8 of the value leads to an integer. In other words, (1/8)*x is an integer.
Furthermore, it also makes sense that each son gets a multiple of 8 villages because if let's say the first son gets 9 villages (some non-multiple of 8), then 56-9 = 47 is not a multiple of 8. Plugging that into x/8+2 for the second son will lead to some non-integer result. So it's a bit nice that everything is a multiple of 8.
A stronger verification is shown in the table below. The table keeps track of how many leftover villages there are for any given son, whether its before or after they get their share. At the top we start with 56 and then slowly make our way down to 0 villages.
Related Questions
If I have 50 envelopes I put equal amounts of money in each one how much will I have at the end of 50 days
Answers
Answer:
At the end of 50 days , Amount of money = $2500x
where x is the value that added every day.
Step-by-step explanation:
Let daily amount added in 1 envelope = $x
As, we have 50 envelope,
so, daily added amount in 50 envelope = $ 50x
⇒ Each day , we add money = $ 50 x
After 50 day, it becomes $50×50x = $2500x
For example -
If we add $ 1 every day in each envelope
then ,
Total amount added in 50 envelope each day = $50×1 = $ 50
Then,
After 50 days,
Total amount = $ 50×50 = $2500
∴ we get
At the end of 50 day, total amount we have = $2500
PLEASE HURRY!!!
Fill in the blanks to complete the equation that describes the diagram.
Answers
Answer:
-5
-3 + -5 = -8
A middle school football player, Bo, is just learning how to kick field goals. Currently, he only makes 1/3 of his kicks. A die is being used to simulate the result of Bo's kicks where the numbers 1 or 2 represent a made field goal the numbers 3, 4, 5, or 6 represent a missed field goal. Use the following 20 trials of rolling a fair die to answer the question.
Based on the outcomes given, what is the estimate of the probability that Bo does not make any field goals? Write your answer as a fraction
Answers
Answer:
The correct answer is 75%.
Step-by-step explanation:
If you count all the misses in each trial as one whole miss, then you will have 15 total misses which would then leave to 5 makes. Then you divided 15 by 20 which would give you a perfect 75% of him missing the field goal. So basically, your answer is 75%.
Can someone tell me the answer plss
Answers
Answer:
the sum of 4m+1(4m-1)+3
Step-by-step explanation:
Please help me with my algebra homework.
Solve log x = 3
a. x=3
b. x=30
c. x=1,000
d.x=10,000
Answers
Answer:
c. x=1,000
Step-by-step explanation:
log x = 3
Imagine that it's log10 x = 3
So, x = 10^3 (10 to the third power)
x = 10 * 10 * 10
x = 1,000
What is the product of (3x + 1)(3x – 4)?
Step by step.
Answers
Answer:
9x^2-9x-3
Step-by-step explanation:
3x*3x=9x^2
3x*-4=-12x
1*3x=3x
1*-4=-3
9x^2-12x+3x-3
9x^2-9x-3
Answer:
9x^2 - 9x - 4
Step-by-step explanation:
(3x + 1)(3x – 4)
Here you can use the FOIL method (FOIL stands for: First, Outer, Inner and Last)
First you multiply 3x by 3x since these are the First inside both binomials.
3x * 3x = 9x^2
Then you multiply 3x by -4 since these are the Outer inside both binomials.
3x * -4 = -12x
Then you multiply 1 by 3x since these are the Inner inside both binomials.
1 * 3x = 3x
Then you multiply 1 by -4 since these are the Outer inside both binomials.
1 * -4 = -4
And finally add everything together:
9x^2 + (-12x) + 3x + (-4)
Since adding a negative number is the same as subtracting it:
9x^2 - 12x + 3x - 4
We can now simplify this a little by adding all the x's together:
9x^2 - (12x + 3x) - 4 =
9x^2 - 9x - 4
Hope I could help you understand!
If you still wonder anything, don't hesitate to ask in the comments below!
Have a wonderful day! (●'◡'●)
If f(x) = x^3 + 8x² + 11x-20 and x+5 is a factor of f(x), then find all of the zeros of f(x) algebraically
Answers
Answer:
The zeros are (-5,-4,-1)
Step-by-step explanation:
Since we have a linear factor, we can use the method of long division to get the other factors
What this mean is that we simply divide the polynomial by the linear expression
we have this division result as;
By dividing, we have the other factor as ;
x^2 + 3x - 4
so we simply factorize this
x^2 -x + 4x - 4
x(x-1) + 4(x-1)
(x + 4)(x-1)
So the complete factors are;
(x + 5)(x + 4)(x-1)
To get the zeros, we simply equate each of the terms to zero
and we have our answer as;
-5 , -4 , 1
Calcule o saldo de salário, o funcionário foi admitido em 10 de janeiro como mensalista, salário R$ 1400,00?
Answers
Responda:
$ 980
Explicação passo a passo:
Dado que:
Salário mensal = $ 1400
Data de emprego = 10 de janeiro
Usando o sistema de mês de 30 dias:
Taxa diária =. $ 1400/30 = $ 46.66666
Dias não trabalhados = janeiro - 9 de janeiro = 9 dias
Subtraia o salário de 9 dias do total:
Salário total - (9 * taxa diária)
$ 1400 - (9 * $ 46,66666)
$ 1400 - $ 420
= $ 980
Portanto, o saldo do salário é de $ 980
Is x = 5 the solution to 2x - 3 = 6
(show me why! Or maybe why not)
Answers
Answer:
no
Step-by-step explanation:
2 times x or 5 which is 10
then subtract ten by 3
which is 7 not 6
(Brainliest?)
Welcome!
PLEASE HELP PLEASEEE!!!
Answers
Answer:
C to A, C to D, C to B, 3cm and 4 cm
Answer:
C to A, C to D, C to B, 3cm and 4 cm
Step-by-step explanation:
12ft 5ft what is the length of the hypotenuse
Answers
Square root of 169= 13
The answer is 13ft
Use the Distributive Property to rewrite each expression.
-7 (5 - n)
Answers
-35 - 7n
What is most likely the line of best fit for this scatter plot? (5 points)
А
20
18
16
14
12
10
3
6
9 10 12 14
Line A
Line B
O
Line C
Line D
Answers
Answer:
Line C
Step-by-step explanation:
The scatter plot follows line C the most.
Hope this helps! :)
PLEASE HURRY. WORTH 50 POINTS + BRAINLIEST IF CORRECT ANSWER
The local business will donate $5.00 for every 10 tickets sold. Let x represent tickets sold, and y represent dollars donated. Student A claims that the equation is y = 2x. Student B claims that the equation is y = 1
2
x. Explain who is correct.
Answers
Answer:
sorry
Step-by-step explanation:
what is the value of y in 2/3y-6=6
Answers
Answer:
18
Step-by-step explanation:
2/3y-6=6
Combine 2/3 and y
2y/3-6=6
Move all terms not containing y to the right side of the equation :
2y/3=12
Multiply both sides of the equation by 3/2
3/2*2y/3=3/2*12
Simplify both sides
y=18
laura has 160 pounds of green beans at her vegetable stand. she sells 10 pounds of green beans every hour, what is the percent decrease in green beans after 3 hours?
Answers
Answer:
18.75%
Step-by-step explanation:
Green beans = 160 pounds
Amount sold in 1 hour = 10 pounds
Amount sold in 3 hours = 3x10= 30 pounds
Decrease in 3 hours = 30 pounds
% decrease = (30/160) x 100
=300/16
=75/4
=18.75%
What is the rate of change of the line through (9, 8) and (0, -10)?
Answers
Answer:
-18/9 when u simply it’s 2
Step-by-step explanation:
What is the equation of the line that includes the points (1,6) and (2,8)?
Answers
Answer: y = 2x + 4
Step-by-step explanation:
y = mx + b
(1,6) and (2,8)
Finding Slope:
(8 - 6) / (2 - 1)
=> 2/ 1 or 2
y = 2x + b
Finding "B":
y = 2x + b
=> 6 = 2(1) + b
=> 6 = 2 + b
=> b = 4
so y = 2x + 4
I need help what’s the answer ?
Answers
Answer:
4
Step-by-step explanation:
you can subtract them because they in the same family
Lines a and b are parallel. Line c is perpendicular to both line a and line b. Which statement about a,b and c is NOT true?
Answers
Answer:
You haven’t given statements
Step-by-step explanation:
ahhhh if someone can please help!!
Answers
Answer and Step-by-step explanation:
The y-intercept is (0, 3)
The value 3 is in the y place.
#teamtrees #WAP (Water And Plant)
The ratio of a model car to a regular car is 1:16. The model is 6.25 inches long. What is the length of the actual car in feet and inches? what if the ratio of the model car was 2:35, then what would be the actual length of the car?
Answers
Answer:
Step-by-step explanation:
model car 1 : regular car 16
model 6.25 inches : actual car 6.25*16 = 100 inches
1foot = 12 inches
100/12 = 8 feet and 4 inches
model car 2 : regular car 35
model 6.25 inches : actual car 6.25*35/2 = 109. 375 inches
Por favor, ayudenme en estos terminos semejantes.
43mx3 + 7mx3 - 17mx3
2a3 - 3 a2b + 4b2 + 6a3 - 5 b2 + 5a2b.
Answers
Answer:
33mx38a3+2a2b-1b2Step-by-step explanation:
because use dimas ruleonly like terms can be subtract and add5 x 143 = 5 x ( + + ) write 143 in expanded form.
Answers
Answer:
Step-by-step explanation:
143 = 100 + 4 0 + 3
5*(143) = 5 * (100 + 40 + 3)
= 5*100 + 5*40 +5*3
= 500 + 200 + 15
= 715
A bank randomly selects one of four free gifts to send to each new customer. Gifts include a calculator, a keychain, a notepad, and a pen. Design and use a simulation to find the experimental probability that the next two customers both receive calculators. Then use the simulation to find the experimental probability that neither of the next two customers receive calculators.
Answers
Answer:
Step-by-step explanation:
Both:
1/4 x 1/4
1/16
Neither:
3/4 x 3/4
9/16
If a baseball team's ratio of wins to losses is 3 to 4, what is the ratio of wins to games played? (There are no ties).
4 to 3
3 to 7
4 to 7
3 to 4
Answers
Answer:
Hey can we talk if you are there please
Answer:
3 to 4
Step-by-step explanation:
90% of what equals 81?? Please show how you got the answer!!
Answers
x = 81/0.9 = 90
the answer is 90
Answer:
90Step-by-step explanation:
First you want to divide 81 by 90%. You do this because 81 is the number you have and 90 is the percent you have.
81/90% = 90
Doing this will get you 90. This works for all percentages too.
Also you can check your answer by reversing this.
90 × 90% = 81
round 0.009 to the nearest hundredth
Answers
Answer:
0.01
Step-by-step explanation:
Rounded to the nearest hundredth 0.009 is 0.01.
The term "Rounding off" means the process of approximating a number to a specified degree of accuracy by replacing it with a neighboring value that is efficient to work with, and makes calculation easy or more meaningful in a given context. This involves reducing the number of significant digits or decimal places in a numerical value while retaining its overall magnitude.
To round off 0.009 to the nearest hundredth, 1 is added to the digit in second place after the decimal, i.e., 0, and the digit in the third place after the decimal, i,e, 9 is replaced by 0.
Thus, when rounded to the nearest 100th, 0.009 results as 0.01.
Learn more about Rounding off here:
https://brainly.com/question/13391706
#SPJ6
Which shows how to solve the equation -4/5 x = 80 for x in one step?
Answers
Answer:
Add the reciprocal or -4/5 which is +5/4 and then add it
Step-by-step explanation:
The point-slope form of the equation of the line that passes through (44, -3) and (12, 1) is y-1 = (x - 12). What is
the standard form of the equation for this line?
Answers
Answer:
-y+(x-12)=-1
Step-by-step explanation: