Answer:
Step-by-step explanation:
This problem can be solved using a technique called the Pigeonhole Principle. The Pigeonhole Principle states that if n+1 or more objects are placed into n pigeonholes, then at least one pigeonhole will contain two or more objects.
In this problem, we have 1600 delegates divided into 16000 committees of 80 persons each. We can think of each delegate as an object and each committee as a pigeonhole. Since 1600 delegates are placed into 16000 pigeonholes, we know that by the Pigeonhole Principle, at least one pigeonhole will contain two or more delegates.
In other words, there must be at least one committee that has at least two delegates in common with another committee. We can prove that there will be at least four common members by assuming the worse scenario where each committee is formed by different people, and noting that there are more delegates than the number of committees, so it's impossible that all committees have different members, and therefore there will be at least four common members.
Therefore, it is possible to find two committees having at least four common members.
The wood you are using for the floor costs 3.50 per square foot. how much will it cost to buy the material assuming you can buy a piece exactly the right size
On solving the provided question, we can say that by equation it cost to buy the material assuming you can buy a piece exactly the right size = $350.
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
the floor costs = 3.50 per square foot
assuming we can buy a piece exactly the right size = x
then cost =
x * 3.50
let x be 100
cost = $350
To know more about equation visit:
https://brainly.com/question/649785
#SPJ4
←
▲
of 1
Suppose that a new employee starts working at $7.54 per hour
and receives a 3% raise each year. After time t, in years, his
hourly wage is given by the equation y = $7.54(1.03). Find the
amount of time after which he will be earning $10.00 per hour.
www
After what amount of time will the employee be earning $10.00
per hour?
years (Round to the nearest tenth of a year as needed.)
Qu
The amount of time after which the employee will be earning $10 is 9 years.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 8 is an equation.
We have,
The raise per year = 3%
The amount received per hour = $7.54
The equation for the hourly wage after t years.
y = 7.54 x [tex]1.03^t[/tex]
Now,
For t = 9,
y = 7.54 x [tex]1.03^9[/tex]
y = 7.54 x 1.326
y = $10
Thus,
After 9 years the hourly earning is $10.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ1
as a part of a customer loyalty program, a restaurant's computer chooses orders at random to receive a free appetizer. each order has a 111 in 181818 chance of receiving a free appetizer. (each order is limited to one free appetizer.) let xxx be the number of orders the restaurant fills in a day until they give away the first appetizer. assume that each order getting the appetizer is independent. find the probability that the restaurant first gives away an appetizer on the 6^{\text{th}}6 th 6, start superscript, start text, t, h, end text, end superscript order of the day.
The probability of the 6th order being the order with the free appetizer is 0.0417 (approx).
The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not. In general, probability has many wonderful uses in games, in business to make forecasts based on likelihood, and in this emerging branch of artificial intelligence.
The probability of getting a free appetizer is 1/18.
The probability of not getting a free appetizer is 17/18.
If the restaurant gives away an appetizer on the 6th order, then there must have been 5 orders before the 6th one that had no free appetizer, followed by the one with the free appetizer.
[tex]P (X = 6) = P(N N N N N F)[/tex]
= 17/18 x 17/18 x 17/18 x 17/18 x 17/18 x 1/18
[tex]= \frac{17^4}{18^5}[/tex] ≈ 0.0417
Thus, the probability of the 6th order being the order with the free appetizer is 0.0417 (approx).
To learn more about probability, visit the link:
brainly.com/question/30034780
#SPJ4
the size of a television screen is given by the length of diagonal of the screen. What size is a tv screen the is 21.6 inches wide and 16.2 inches high
The size of a television screen that is 21.6 inches wide and 16.2 inches high is approximately 27 inches (measured diagonally).
What is the Pythagorean theorem?
It's a relation in Euclidean geometry among the three sides of a right triangle. In it, the square of the hypotenuse is equal to the sum of the squares of the other 2 sides.
The size of a television screen can be found by using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the length of the diagonal of the screen is the hypotenuse, the width is 21.6 inches, and the height is 16.2 inches. We can use the theorem to find the length of the diagonal:
diagonal²= width² + height²
diagonal² = 21.6² + 16.2²
diagonal² = 467.76 + 262.44
diagonal² = 730.2
diagonal = √730.2
diagonal ≈ 27 inches
Hence, the size of a television screen that is 21.6 inches wide and 16.2 inches high is approximately 27 inches (measured diagonally).
To learn more about the Pythagorean theorem visit,
https://brainly.com/question/21332040
#SPJ1
3x² + 2 × 3x × 5 - 5²
Qui pourait m'expliquer svp ?
Answer:
Step-by-step explanation:
3x² + 2 * 3x * 5 - 5²
= 3x^2 +2 * 3x * 5 - 25 ( then do 2*3x*5 = 30x)
=3x^2+30x-25
The measure of angle JKL is 145°.
The measure of angle MKL is 60°.
The measure of angle JKM is x°.
Find the value of x.
X=
0
X
5
Xº
K
145°
M
60°
D
Otis wants to borrow 10000 to buy a used car. he examined his budget and decided that he can afford a payment of $200 a month. if his bank offers him a rate of 7.5%, how long should he borrow the money so he can afford his monthly payment?
Answer: Otis should borrow the money for 60 months (5 years) so he can afford his monthly payment of $200.
Step-by-step explanation: To calculate the duration of the loan, we can use the formula:
Duration (in months) = Loan amount / Monthly payment
In this case, the loan amount is $10,000, and the monthly payment is $200. So by substituting the values, we get:
Duration (in months) = 10000 / 200 = 50
The duration of the loan is 50 months, however, the bank offers him a rate of 7.5%.
To calculate the total interest, we can use the formula:
Total Interest = Loan amount * Interest Rate * Duration (in months) / 12
The total interest is = 100007.5/10050/12 = 3750
So the Otis will have to pay an additional $3750 in interest over the course of the loan.
So, the total amount he will have to pay is 10000+3750 = 13750
And the time duration to pay this amount is 60 months ( 5 years)
Note: As per the information provided, the interest rate is not annual, it is monthly. So, it is not necessary to divide it by 12 in the interest formula. The equation should be Total Interest = Loan amount * Interest Rate * Duration (in months)
the length of each side of a square is 3 inches more than the length of each side of a smaller square. the sum of the areas of the squares is 149 inches squared. find the length of the side of the smaller square.
The length of the side of the smaller square is 7 inches.
Let x be the length of the side of the smaller square.
The length of each side of a square is 3 inches more than the length of each side of a smaller square. Thus the length of the side of the larger square is
(x + 3) inches.
The area of the smaller square is
x^2 square inches.
The area of the larger square is
(x + 3)^2 square inches.
We can set up the equation:
x^2 + (x + 3)^2 = 149
Expanding and simplifying the equation gives:
x^2 + x^2 + 6x + 9 = 149
Combining like terms:
2x^2 + 6x - 140 = 0
Using the quadratic formula, we can solve for x:
x = (-b ± √(b^2 - 4ac)) / 2a
x = (-6 ± √(6^2 - 4 * 2 * (-140))) / 2 * 2
x = (-6 ± √(36 + 1120)) / 4
x = (-6 ± √(1156)) / 4
x = (-6 ± √(596)) / 4
x = (-6 ± 34) / 4
x = -10 or x = 7
The side length of the smaller square can't be negative, so x = 7 inches.
To know more on quadratic formula
https://brainly.com/question/11540485
#SPJ4
the dominican republic has 10.7 million people and a national population growth rate of 1.5 percent. paraguay has 6.8 million people and a national population growth rate of 1.5 percent. in how many years will each country double in size?
The population of each country will become double in 47 years.
Given that,
The population of the Dominican republic is, n = 10.7 million.
The growth rate of the Dominican republic is, p = 1.5 %.
The population of Paraguay is, n' = 6.0 million.
The growth rate of Paraguay is p' = 1.5 %.
The doubling time of population growth depends on the rate of population growth.
Here,
n is the final population and n0 is the initial population and doubling the value in the future, n= 2*n0.
Solving this, we get:
t= ln (2*n0/n0)/(1.5/100) = 47 years.
Thus, we can conclude the population of each country will become double in 47 years.
To learn more about the population model visit: brainly.com/question/22852351
#SPJ4
2. Togetherness Are good grades in high school associated with family togetherness? A random sample of 142 high school students was asked how many meals per week their families ate together. Their responses produced a mean of 3.78 meals per week, with a standard deviation of 2.2. Researchers then matched these responses against the students' grade point aver- ages (GPAs). The scatterplot appeared to be reasonably linear, so they created a line of regression. No apparent pattern emerged in the residuals plot. The equation of the line was GPA = 2.73 + 0.11 Meals. a) Interpret the y-intercept in this context. b) Interpret the slope in this context. c) What was the mean GPA for these students? d) If a student in this study had a negative residual, what did that mean? e) Upon hearing of this study, a counselor recommended that parents who want to improve the grades their children get should get the family to eat together more often. Do you agree with this interpretation? Explain.
As per the given standard deviation, the y intercept of the equation is 2.78 and the slope of the equation is 0.11 and the mean of the equation is 24.08
The term standard deviation in math is known as a quantity expressing by how much the members of a group differ from the mean value for the group
Here we have random sample of 142 high school students was asked how many meals per week their families ate together. And their responses produced a mean of 3.78 meals per week, with a standard deviation of 2.2.
And the equation of the line was written as,
=> GPA = 2.73 + 0.11 Meals.
Here let us consider that x meals and y refers the GPA.
Then the equation is rewritten as,
=> y = 0.11x + 2.73
While we compare this one with the standard form of the equation, then we get
the value of the slope as 0.11 and the intercept as 2.73
Then the value of the mean is calculated as,
=> 144/ (3.78 + 2.2)
=.> 24.08
To know more about standard deviation here.
https://brainly.com/question/16555520
#SPJ4
1.2m divided by 40 cm
Answer:3
Step-by-step explanation:
Answer: the answer is 3
Step-by-step explanation:I did the dividing on paper and the answer is 3
an equilateral triangle has a side measure of 10 in. what is the measure of each of the angles of the triangle? question 1 options: 10 degrees 60 degrees 30 degrees 18 degrees
On solving the provided question, we can say that since an equilateral triangle so, each angle will be 60
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
since an equilateral triangle has a side measure of 10 in.
and it is a equilateral triangle
so, all sides will be 10
so, each angle will be 60
To know more about triangle visit:
https://brainly.com/question/2773823
#SPJ4
Convert 46.1031 to 4 significant figures
Converting 46.1031 to 4 significant figures, we have 46.10.
Rounding off to 4 significant figure.Rounding off numbers implies reducing the number of digits in a given number to a preferred length. The two modes are significant figures, or decimal places.
Decimal places requires reducing the numbers of digits in a given number to a required number but considering the position of the decimal point. In significant figures, the length of the given number is reduced to a required number by not considering the position of the decimal.
In the given question, we are to convert 46.1031 to 4 significant figures.
This can be done by counting four digits, and rounding off the digits after.
So that we have;
46.1031 = 46.10 (4 sf)
Learn more about significant figures of numbers at https://brainly.com/question/24491627
#SPJ1
The conversation of 46.1031 to 4 significant figures would be = 46.10
What is a four significant figures?A four significant figures are those figures that shows that all zeros to the right of the last significant zero after the decimal point.
From the given figure such as 46.1031, to convert to four significant figures, 46.10
Learn more about significant figures here:
https://brainly.com/question/24491627
#SPJ1
do you need to multiply everything on one side of an equation if you are only multiplying a fractionating that's adding
Yes, we can multiply everything on one side of an equation if you are only multiplying a fractionating that's adding.
Multiplicative Property:
The multiplicative nature of the equation dictates that both sides of the equation can be multiplied or divided by the same nonzero fraction or Gebraic Equation without changing the solution.
if a, b, and c are any three fractions
if a = b and c ≠ 0
1. a × c = b × c
2. a ÷ c = b ÷ c
Multiplicative property for Fraction:
When multiplying two fractions, the numerator and denominator are multiplied separately. The first numerator is multiplied by his second numerator, and the first denominator is multiplied by his second denominator. Finally, reduce the fraction to its lowest term. A fraction has the smallest form if 1 is the only common divisor between the numerator and denominator.
Properties of Multiplying Fractions
1. Multiplying a non-zero fraction by 1 yields the exact fraction
Example: 38 × 1 = 38
2. Multiplying 0 by a non-zero fraction yields zero.
Example: 38 × 1 = 38
3. The product of a fraction and its reciprocal is always 1.
Example: 25×52 = 2×55×2 =1010 =1
(the reciprocal of 25 is 52)
Learn more about Equation:
https://brainly.com/question/29538993
#SPJ4
if a bar of soap cost $2,49 in 2003 how much did a bar of soap cost in 2005
Therefore , the solution of the given problem of unitary method comes out to be the cost of soap after 2005 is $ 2.6145.
A unitary method is precisely what?To finish a work using the unitary strategy, multiply the quantity with two after determining the size of a small slice. The unit variable technique, to put it simply, works to isolate a coded object from a specific group or sets of sets. For instance, 40 pens would cost 400 pounds (expression $1.01) = Rs. There is a chance that one nation will have complete control over the technique used to do this. Almost all living things have a unique trait..
Here,
Given :
=> Cost of soap $2.49 in 2003
=> Cost of soap in 2005
=> 2.49 + 5/100 * 2.49
=> 2.49 + 0.1245
=> 2.6145
Therefore , the solution of the given problem of unitary method comes out to be the cost of soap after 2005 is $ 2.6145.
To know more about unitary method visit:
https://brainly.com/question/28276953
#SPJ1
A group of researchers investigated the effect of media usage (whether or not subjects watch television or use the Internet) in the bedroom on ""Tiredness"" during the day (measured on a 50 point scale a. Identify each of the variables, state whether the variables are quantitative or categorical, and identify each variable as either explanatory or response variables. nterviewed b. To collect these data, the researchers randomly selected homes to visit and i the adult member of the household whose birthday was nearest. Is this an experiment or an observational study? Briefly explain.
a. Media usage is categorical and Tiredness is quantitative. The effect of media is the explanatory variable and Tiredness is the response variable.
b. Yes, this is an observational study.
What is an Observational Study?In fields including epidemiology, social sciences, psychology, and statistics, observational studies draw conclusions from a sample of the population when the independent variable is not under the researcher's control due to ethical issues or practical constraints.In a normal observational study, participants are assigned to either the treated group or the control group, and the researcher observes how the therapy may influence them.This does not occur in experiments such as randomized controlled trials when each subject is randomly assigned to either a treated group or a control group. Observational studies by their very nature provide difficulties for inferential analysis due to the absence of an assignment process.This research was done via observation. The researchers are not modifying or controlling any variables; instead, they are watching and assessing the correlation between media use and fatigue. By visiting randomly chosen households and interviewing the adult household member with the closest birthday, they are gathering data.
To know more about Observational Study visit:
https://brainly.com/question/15938198
#SPJ4
jerry is trying to figure out how much pizza remains after his party last night. he finds six whole pizzas, as well as 5/8 of another pizza. if he finds one more slice in the fridge (1/8 of a whole pizza), then how many pizzas does jerry have?
On solving the provided question we can say that by equation we have
remain = x+y = 5/8 + 1/8 = 6/8 3/4
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
six whole pizzas, as well as = 5/8 of another pizza
another one = 1/8 of a whole pizza
Remain -by forming equation
let x = 5/8 of another pizza
and y = 1/8 of a whole pizza
remain = x+y = 5/8 + 1/8 = 6/8 3/4
To know more about equation visit:
https://brainly.com/question/649785
#SPJ4
Which of the following is a valid base for an exponential function?
A. f(x)=1x
B. f(x)=0.8x+1
C. f(x)=(3.14)3x
D. f(x)=(7/3)x
E. f(x)=42x
F. f(x)=−(2)x
G. f(x)=(−2)x
H. f(x)=x4
The following are the valid bases for an exponential function:
C. f(x)=(3.14)3xD. f(x)=(7/3)xE. f(x)=42xF. f(x)=−(2)xG. f(x)=(−2)xAn exponential function has the form f(x) = ab^x, where a and b are constants, and b is greater than 0 but not equal to 1. In this case, C, D, E, F, and G all have the correct form of an exponential function.
Options A, B and H are incorrect because:
A is not a valid base for an exponential function because the base is not a constant but the variable x.B is not a valid base for an exponential function because it is a linear function, not an exponential function.H is not a valid base for an exponential function because the base is x, which is a variable, not a constant.
The options C, D, E, F, and G are valid exponential functions because they have the correct form of f(x) = ab^x, where a and b are constants, and b is greater than 0 but not equal to 1.
C. f(x) = (3.14)^3x, where the base is (3.14)^3, which is a constant, and the exponent is x, which is a variable.D. f(x) = (7/3)x, where the base is (7/3), which is a constant, and the exponent is x, which is a variable.E. f(x) = 42x, where the base is 42, which is a constant, and the exponent is x, which is a variable.F. f(x) = -(2)x, where the base is -(2), which is a constant, and the exponent is x, which is a variable.G. f(x) = (-2)x, where the base is (-2), which is a constant, and the exponent is x, which is a variable.The base can be negative or fractional, but as long as it's a constant, it's still a valid exponential function.
Learn more about exponential function here: brainly.com/question/2456547
#SPJ4
which of the changes would keep then hanger in balance? select all that apply
the answer is just D
