I run a book club with $n$ people, not including myself. Every day, for $365$ days, I invite four members in the club to review a book. What is the smallest positive integer $n$ so that I can avoid ever having the exact same group of four members over all $365$ days?
Answers
Answer: 12
Step-by-step explanation:
If we have n people and we want to do groups of 4, the total number of different combinations is:
\(c = \frac{n!}{(n - 4)!4!}\)
and we want find the smallest n such c > 365.
let's do it by brute force:
if n = 5, we have:
\(c = \frac{5!}{1!*4!} = 5\)
if n = 6
\(c = \frac{6!}{2!*4!} = \frac{6*5}{2} = 15\)
if n = 7
\(c = \frac{71}{3!*4!} = \frac{7*6*5}{3*2} = 35\)
if n = 8
\(c = \frac{8!}{(4!*4!} = \frac{8*7*6*5}{4*3*2} = 70\)
if n = 9
\(c = \frac{9!}{5!*4!} = \frac{9*8*7*6*5}{5*4*3*2} = 126\)
if n = 10
\(c = \frac{10!}{6!*4!} = \frac{10*9*8*7}{4*3*2} = 210\)
So you can see the patern here.
So we have the previous number multiplied by n and divided by n - 4
if n = 11
C = 210*11/(11- 4) = 330
if n = 12
C = 330*12/(12 - 4) = 495
Then the minimum number of members such we have more than 365 combinations is 12 members
Related Questions
0.0008012 in standard form
Answers
Answer:
Step-by-step explanation:
8.012 x 10^-4
Answer:
8.012×10^-4
Step-by-step explanation:
..............
A computer chooses a number at random from a list of 6 different positive, single-digit numbers. The probabilities of different events are shown below in the table below. Use this information to find the 6 numbers the computer is choosing from.
Answers
The 6 numbers for the given probabilities can be:
(2, 4, 5, 6, 7, 8)
How to find the numbers?There are 6 numbers, we know that:
probability of any event = (outcomes that meet the event)/6
Then, if:
probability of an even number = 2/3 = 4/6
This means that there are 4 even numbers.
if:
P Number chosen is less than 5 = 1/3 = 2/6
There are 2 numbers less than 6.
And there is a 50% of gettting a prime, so there are two primes.
Then the 6 numbers could be:
(2, 4, 5, 6, 7, 8)
There are 4 even numbers {2, 4, 6, 8}Two primes {2, 7}Two smaller than 5 { 2, 4}Learn more about probability at.
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The phone company Splint has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 380 minutes, the monthly cost will be $173. If the customer uses 570 minutes, the monthly cost will be $249.
A) Find an equation in the form
y
=
m
x
+
b
,
where
x
is the number of monthly minutes used and
y
is the total monthly cost of the Splint plan.
Answer:
y
=
B) Use your equation to find the total monthly cost if 942 minutes are used.
Answer: If 942 minutes are used, the total cost will be
dollars.
Answers
The solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.
What is an equation?The similar symbol (=) is used in arithmetic equations to signify equality between two statements. It is shown that it is possible to compare various numerical factors by applying mathematical algorithms, which have served as expressions of reality. For instance, the equal sign divides the number 12 or even the solution y + 6 = 12 into two separate variables many characters are on either side of this symbol can be calculated. Conflicting meanings for symbols are quite prevalent.
Part A:
Given:
customer uses 380 minutes, the monthly cost will be $173.customer uses 570 minutes, the monthly cost will be $249.To find an equation,
Where x is number of monthly minutes.
and y is total monthly of splint plan.
So, equation is:
\(\rightarrow \text{y} =\text{mx} +\text{b}\)
For the first case:
\(\rightarrow\bold{173 = 380x + b}\)
Second case:
\(\rightarrow\bold{249= 570x + b}\)
Solve for x:
\(\rightarrow{173 - 380\text{x}=249- 570\text{x}\)
\(\rightarrow{-207=-321\)
\(\rightarrow \text{x} =\dfrac{321}{207}\)
\(\rightarrow \text{x} =\dfrac{107}{69}\)
\(\rightarrow \text{x} \thickapprox1.55\)
For value of b
\(\rightarrow 173 = 380(1.55) + \text{b}\)
\(\rightarrow 173 - 589 = \text{b}\)
\(\rightarrow -416 = \text{b}\)
Part B:
\(\rightarrow \text{y} = 942(1.55) - 416\)
\(\rightarrow \text{y} = 1460.1 - 416\)
\(\rightarrow \text{y} \thickapprox1044\)
Therefore, the solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.
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The average horse requires 0.0333 Megacalories (Mcal) each day for every kilogram (kg) it weighs. If your horse weights 678 kg, and the food you are buying provides 810 kcal per pound of food, how many pounds of food do you need each day for your horse?
Use the following facts:
1000 kcal = 1 Mcal
1 pound food = 810 kcal
0.0333 Mcal = 1 kg horse
Round to the nearest whole number.
Answers
On solving the provided question, we can say that Therefore, you would need multiply approximately 27.84 pounds of food each day for your horse.
what is multiplyOne of the four mathematical operations, along with arithmetic, subtraction, and division, is multiplication. Mathematically, adding subgroups of identical size repeatedly is referred to as multiplication. The multiplication formula is multiplicand multiplier yields product. To be more precise, multiplicand: Initial number (factor). Number two as a divider (factor). The outcome is known as the result after dividing the multiplicand as well as the multiplier. Adding numbers involves making several additions. as in 5 x 4 Equals 5 x 5 x 5 x 5 = 20. 5 times by 4 is what I did. This is why the process of multiplying is sometimes called "doubling."
First, we need to convert the weight of the horse from kilograms to pounds, so:
678 kg x 2.20462 lbs/kg = 1495.69 lbs
Next, we need to calculate how many Mcal the horse needs per day:
0.0333 Mcal/kg x 678 kg = 22.58 Mcal/day
Then, we can convert the Mcal to kcal:
22.58 Mcal/day x 1000 kcal/Mcal = 22,580 kcal/day
Finally, we can divide the total daily kcal needed by the kcal per pound of food to find the total pounds of food needed:
22,580 kcal/day ÷ 810 kcal/lb = 27.84 lbs/day
Therefore, you would need approximately 27.84 pounds of food each day for your horse.
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Solve the linear equation 7x+4^2=12x-8
Answers
Answer:
x = 24/5
Step-by-step explanation:
A chocolate company selects 30 random packages to check their weight. They find 3 packages have an incorrect weight. How many packages out of 3,000 should the company predict have incorrect weights?
Answers
Answer:
300 packages
Step-by-step explanation:
Solve the system using the addition method. Write your answer as an ordered pair. If there is no solution,write NS for your answer.4x - y = 202x + y = 22
Answers
Given
4x - y = 20
2x + y = 22
Using the addition method, align like variables and constant, then, add them together
4x - y = 20
+ 2x + y = 22
6x + 0y = 42
6x = 42
Divide both sides by 6, to get rid of the coefficient on the left side
6x/6 = 42/6
x = 7
Now that we have x = 7, substitute it to any of the two given equations, in this case we will use 2x + y = 22 (note: using 4x - y = 20 works just as well)
2x + y = 22
2(7) + y = 22
14 + y = 22
y = 22 - 14
y = 8
Therefore, the solution to the system is (7,8).
This figure was created with three different rectangles. Find the total area in square centimeters.
Answers
The total area for the figure is given as follows:
288 cm².
How to obtain the area of a rectangle?The area of a rectangle is given by the multiplication of the width and the length of the triangle, as follows:
A = lw.
The dimensions of each rectangle are given as follows:
8 cm and 9 cm.9 cm and 12 cm.9 cm and 12 cm.Hence the total area is given as follows:
A = 8 x 9 + 2 x 9 x 12
A = 288 cm².
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Pls can someone help me
Answers
Answer:
I'm sorry but the question is not clear enough for me to understand the question asked snap the entire question
Consider functions fand gUsing a table of values, what is the approximate solution to the equation f(I) = g(I| to the nearest quarter of a unit?
Answers
Given:
Two functions f(x) and g(x) are given.
\(\begin{gathered} f(x)=\frac{x-1}{x^2+x-1} \\ g(x)=3^x-2 \end{gathered}\)Required:
Find the approximate solution to the equation f(x)=g(x) to the nearest quarter of the unit.
Explanation:
(a) substitute x= 0.50in f(x) and g(x).
\(\begin{gathered} f(x)=\frac{0.5-1}{(0.5)^2+0.5-1} \\ f(x)=\frac{-0.5}{-0.25} \\ f(x)=2 \end{gathered}\)\(\begin{gathered} g(x)=3^{0.5}-2 \\ g(x)=-0.268 \end{gathered}\)(b) substitute x=-1.75 in f(x) and g(x).
\(\begin{gathered} f(x)=\frac{-1.75-1}{(-1.75)^2-1.75-1} \\ f(x)=\frac{-2.75}{0.38125} \\ f(x)=-7.2 \end{gathered}\)\(\begin{gathered} g(x)=3^{-1.75}-2 \\ g(x)=-1.854 \end{gathered}\)(c) substitute x= 0.75 in f(x) and g(x).
\(\begin{gathered} f(x)=\frac{0.75-1}{(0.75)^2+0.75-1} \\ f(x)=\frac{-0.25}{0.3125} \\ f(x)=-0.8 \end{gathered}\)\(\begin{gathered} g(x)=3^{0.75}-2 \\ g(x)=2.795 \end{gathered}\)(d) substitute x= -2.25 in f(x) and g(x).
\(\begin{gathered} f(x)=\frac{-2.25-1}{(-2.25)^2-2.25-1} \\ f(x)=\frac{-3.25}{1.8125} \\ f(x)=-1.793 \end{gathered}\)\(\begin{gathered} g(x)=3^{-2.25}-2 \\ g(x)=-1.916 \end{gathered}\)we can observe that at x = -2.25 the functions f(x) and g(x) has the approximate values.
Final Answ
Tell the measure of the angles In degrees 1/4
Answers
Answer:
so 1/4 of a circle is 90 degrees 1/4 is equal to 90 over 360 C it's 90 parts of 360. so here we go with this one. this angle is 20 degrees remember that's 90 alright the square one and this little part would be 20 degrees each angle appears wider as the Rays get longer.
Step-by-step explanation:
Let me know if this help's you lol :)
PLEASE HELP
Suppose that the functions fand g are defined for all real numbers x as follows.
f(x) = 5x
g(x)=4x-4
Write the expressions for (g.f)(x) and (g-f)(x) and evaluate (g+f)(2).
(g•f)(x) =
(g-f)(x) =
(g+r) (2)=
Answers
= 20x^2 - 16
(g - f)(x) = (4x - 4) - (5x)
= (-1x) - 4
= -x -4
(g + f)(2) = (4(2) - 4) + (5(2))
= 4 + 10
= 14
25 POINTS PLS HELP SOME1!!
Answers
The transformation from the graph of f(x) = x to the graph of g(x) = (1/9)·x -2, is a rotation and a translation. The correct option is therefore;
The transformation are a rotation and a translation
What is a translation transformation?A translation transformation is a transformation in which there is a displacement of all points on the preimage figure in a specified direction.
The transformation from f(x) = x to f(x) = (1/9)·x - 2, includes a slope reduction by a factor of (1/9), or rotating the graph of f(x) = x in the clockwise direction, and a translation of 2 units downwards, such that the y-intercept changes from 0 in the parent function, f(x) = x to -2 in the specified function f(x) = (1/9)·x - 2, therefore, the translation includes a rotation clockwise and a translation downwards by two units
The correct option is the second option; The transformation are a rotation and a translation
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What is spread of data on a dot plot?
Answers
Answer:
The spread is the range of the data. :)
HEEELLLLPPP!
Whoever answers right will get brainliest!!!!!!!!!
Answers
Answer:
\(y =\frac{x}{4}\)
Step-by-step explanation:
Pre-SolvingWe are given several functions, and we want to figure out which one is linear.
A linear function has both of its variables (x and y) with a power of 1. Variables with other powers do not mean that the function is linear.
SolvingLet's go through the list.
Starting with \(y=\frac{3}{x} -7\), we can see that x is in the denominator. If this is the case, it means that the power of x is -1.
Even though y has a power of 1, this is NOT linear, because x has a power of -1.
Now, with y=√x-2, this is also not linear. This is because √x = \(x^\frac{1}{2}\), even though y has a power of 1.
For x² - 1 = y, we can clearly see that x has a power of 2, while y has a power of 1. This means that the function is not linear.
This leaves us with \(y = \frac{x}{4}\). x is in a fraction, however it is not in the denominator. This means that the power of x in this function is 1. We can also see that the power of y in this function is 1.
This means that \(y=\frac{x}{4}\) is linear.
Solve for x leave your answer in simplest radical form
Answers
Answer:
X=11 trust me on my mom
The marked price of a bicycle is Rs 2000. If the shopkeeper allows some discount and a customer
bought it for Rs 1921 including 13% VAT, how much amount was given as the discount?
Answers
Answer:
Discount amount = $328.73
Step-by-step explanation:
Below is the calculation for the discount amount:
The marked price of bicycle = 2000
Purchase price = Rs 1921
VAT = 13%
First find the purchase price excluding VAT = 1921 - (13% of 1921) = 1671.27
Discount amount = 2000 - 1671.27
Discount amount = $328.73
HELP PLS ASAPPP!!!
algebra problem; solving linear inequalities !!! :)
Answers
Answer: x = -3/2
Step-by-step explanation:
The difference of 9 and half of a number
Answers
Answer:
Subtract 9, then divide by 2
If x equals the affected number, the expression would be: \(\frac{x-9}{2} \)
Step-by-step explanation:
Difference means subtraction
Half a number means to divide by two, or multiply by \(\frac{1}{2} \)
An office building worth $1 million when completed in 2010 is being depreciated linearly over 50 years. What was the book value of the building in 2014? What will it be in 2022? (Assume the scrap value is $0.)
Answers
Answer:
To calculate the book value of the building, we need to calculate the annual depreciation amount and multiply it by the number of years elapsed since the building was completed.
The annual depreciation amount is calculated as: $1 million / 50 years = $20,000
In 2014, the book value of the building was: $1 million - ($20,000 * (2014 - 2010)) = $1 million - ($20,000 * 4) = $960,000
In 2022, the book value of the building will be: $1 million - ($20,000 * (2022 - 2010)) = $1 million - ($20,000 * 12) = $680,000
Answer quick please
Answers
Answer:
18
Step-by-step explanation:
3 3/8 becomes 27/8.
27/8 x 16/3=18
You have to flip 3/16 since you are dividing.
Answer:18
Step-by-step explanation:
3 3/8 devided by 3/16=18
2mn – 5z + 7
PLEASE HELP!!
Answers
Answer:
it's already simplified
what do you want me to do? tell me what kind of equation it is?
it's a linear trinomial
Step-by-step explanation:
an item is regularly priced at 29. Joe bought it at a discount of 45% off the regular price.
Answers
Answer:
$13.05
Step-by-step explanation:
The prize will be $13.05 after the discount.
29x45%=13.05
OR
29x0.45=13.05
HELP PLEASEE
11. a) find two integers with a sum of -1 and a difference of +5.
Answers
Answer:
-3 and 2
Step-by-step explanation:
Anyone know wat 792 divided by 5 is?
Answers
Answer:
158.4 i think
Step-by-step explanation:
5. The value of 25sqare -24sqare
Answers
Answer:
49
Step-by-step explanation:
25²-24²
625-576
=49
use calculator lah dehh
A cup of coffee costs $4 and a cup of tea costs $3.50. If ray has $40 and has bought 6 cups of coffee, find the maximum of tea he can buy.
Answers
Answer:
Coffee= $4
Tea= 3.50
6x4=$24
so with this in mind you must take 24 and divide it by the price of tea
24/3.50 is 6.8 so they max cups of tea he can buy is 6.
Hope this helps. :)
Step-by-step explanation:
The maximum number of cups he can buy will be 7.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that a cup of coffee costs $4 and a cup of tea costs $3.50. If ray has $40 and has bought 6 cups of coffee.
6x4=$24
Divide 24 by 3.50 to get the number of cups.
24/3.50= 6.8
Therefore, the maximum number of cups he can buy will be 7.
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The measure of an exterior angle of a triangle is equal to which of the following measures?
Answers
Measures of sum of the two opposite angles.
A model rocket is launched with an initial upward velocity of 195 ft/S the Rockets height H (in feet) after T seconds is given by the following. H= 195T -16 T^2 find all values for t for which the Rockets height is 87 feet. Round your answer to the nearest hundredth
Answers
The height, H (in ft), is related to time, T (in seconds), by the next equation:
\(H=-16T^2+195T\)Substituting with H = 85 ft we get:
\(\begin{gathered} 85=-16T^2+195T \\ 0=-16T^2+195T-85 \end{gathered}\)Applying the quadratic formula:
\(\begin{gathered} T_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ T_{1,2}=\frac{-195\pm\sqrt[]{195^2-4\cdot(-16)\cdot(-85)}}{2\cdot(-16)} \\ T_{1,2}=\frac{-195\pm\sqrt[]{32585}}{-32} \\ T_1\approx\frac{-195+180.5}{-32}\approx0.45\text{ seconds} \\ T_2\approx\frac{-195-180.5}{-32}\approx11.73\text{ seconds} \end{gathered}\)
An intravenous solution needs 2 liters (L) of glucose to be mixed with 7 units of blood. How much glucose (in liters) is needed for 30 units of blood
Answers
8.57 liters glucose (in liters) is needed for 30 units of blood.
What is Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
For 7 units of blood = 2 l of glucose needed.
Foe 1 units of blood, glucose needed = 2/7
For, 30 units of blood , glucose needed = 8.57 liters
Hence, 8.57 liters glucose (in liters) is needed for 30 units of blood.
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