Nine people come to a party and shake hands with each other. If each person shakes the hand of every other person, how many handshakes occur?
Final answer:
There will be 36 handshakes among the nine people at the party, as determined by the combination formula 9C2.
Explanation:
Calculating Handshakes
To determine the number of handshakes that occur when nine people shake hands with each other, we can use the concept of combinations. In a handshake situation, the order in which the handshakes occur does not matter; what matters is which two people are shaking hands. Therefore, we can use the formula for combinations without repetition, which is nCk = n! / (k!(n-k)!), where n is the total number of items, and k is the number of items to choose at a time.
In this case, there are 9 people (n=9) and the handshake involves 2 people at a time (k=2). So, the calculation would look like this:
9C2 = 9! / (2!(9-2)!) = 9! / (2!7!) = (9 × 8) / (2 × 1) = 36 handshakes
Therefore, there would be a total of 36 handshakes among nine people at the party.
Read the problem in the box below. Make a list to help you find the correct answer
What is the reason for each step in the solution of the inequality?
−2(x+3)−4>4x+30
Select the reason for each step from the drop-down menus.
−2(x+3)−4>4x+30 Given
−2x−6−4>4x+30
−2x−10>4x+30
−6x−10>30 Subtraction Property of Order
−6x>40
x<−203 Division Property of Order
The correct answers are:
Distributive property; subtraction; addition property of equality.
Explanation:
To get from the first step to the second step, the terms inside parentheses have been multiplied by -2. The property that allows us to multiply through parentheses, or distribute through parentheses, is the distributive property.
To get from the second step to the third step, the -6 and 4 have been subtracted; this means the reason for this is subtraction.
To get from the fourth step to the fifth step, 10 has been added to each side. The addition property of equality allows us to do this.
Inequalities help us to compare two unequal expressions. The given inequality can be solved as shown below.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
The given inequality can be solved as shown below.
−2(x+3)−4>4x+30 → Given
−2x−6−4>4x+30 → Solving the parenthesis using the distributive property
−2x−10>4x+30 → Subtract 4x from both the sides of the inequality, Subtraction property of order
−6x−10>30 → Subtraction Property of Order
−6x>40 → Division property of order
x<−203 → Division Property of Order
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3 please it would really help (4 would give u brainliest)
the local store is having a sale on ground beef- $10 for 3 pounds. sylvia needs 12 pounds of meat to make 50 hamburgers. how much will the ground beef for each hamburger cost?
Write two inequalities to compare -9 and -6
In 2008 election there was 28 blue states and 22 red states express the red and blue states as fractions in lowest terms of the total number of states and also as decimals
The committee is planning a party and 150 guests are expected. Each package of plastic spoons contains 24 spoons. How many packages of spoons will be needed to so that each guest gets 1 spoon? 5 6 7 124
divide the number of guests by the number of spoons in a package
150/24 = 6.25 so they need to buy 7 packages
The packages of spoons will be needed to so that each guest gets 1 spoon is 7.
It is required to find the packages of spoons.
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
The committee is planning a party = 150 guests
package of plastic =24 spoons.
According to given question we have
The packages of spoons will be needed to so that each guest gets 1 spoon
150/24
= 6.25 ≈7
Therefore, the packages of spoons will be needed to so that each guest gets 1 spoon is 7.
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he Discount Hair Center has a large container of combs. Each purchase qualifies a customer to receive a free comb. The container contains 4 blue combs, 2 purple combs, 8 black combs, 3 white combs, 6 yellow combs, and 5 pink combs.
What is the probability that the next customer will pull out a blue comb?
Mrs.D. gives 13 % of her salary to a charity. Last year she donated to the charity $6500.00. How much money did Mrs.D. earn last year?
4(g - 1 )=24
what is the answer
Which of the following is a multiple of 2?
A. 847
B. 75
C. 2,461
D. 1,000
Write the product as a single power
There are 8 students on the minibus.five of students are boy. What fraction of the students are boys?
A refrigerator magnet uses 5/8 inch of magnetic tape. How many refrigerator magnets can you make with 10 inches of magnetic tape. Explain
Which are partial products for 51 × 36?
Choose all answers that are correct.
A.1 x 6 = 6
B.1 x = 30
C.50 x 6 = 300
D.50 x 3 = 150
How much will a person pay for 11.3 pounds of bananas at a price of $2.07 per pound?
GCF and Distributive property of 55 + 88
Final answer:
The GCF of 55 and 88 is 11. Applying the distributive property, 55 + 88 is equal to 143.
Explanation:
The student is asking about the greatest common factor (GCF) and the distributive property of the expression 55 + 88.
To find the GCF, we need to break down the numbers 55 and 88 into their prime factors. The prime factorization of 55 is 5 × 11, and the prime factorization of 88 is 2² × 11. The GCF is the highest common factor between the two prime factorizations, which is 11.
The distributive property states that a × (b + c) = a × b + a × c. Applying this property to the expression 55 + 88, we get 11 × 5 + 11 × 8 = 55 + 88 = 143.
Final answer:
The GCF of 55 and 88 is 11. When we apply the distributive property to 55 and 88, the expression simplifies to 143.
Explanation:
To find the Greatest Common Factor (GCF) of 55 and 88, we can first list the factors of each number:
Factors of 55: 1, 5, 11, 55
Factors of 88: 1, 2, 4, 8, 11, 22, 44, 88
The GCF is the largest factor that both numbers have in common, which in this case is 11.
Now, let's apply the distributive property to the numbers 55 and 88:
55 + 88 = (5 * 11) + (8 * 11)
Using the distributive property, we can simplify this to:
55 + 88 = (5 + 8) * 11
Therefore, the expression 55 + 88 is equal to 13 * 11, which is 143.
Which answer is the correct form of bar notation for this decimal number: 4.676767…
4.67
4.67
4.67
4.67
Answer:
4.67 with the bar notation above the 67
Step-by-step explanation:
To solve this correctly you need to recall the rules repeating decimal numbers and what bar notation looks like. but i forgot my answer so its not above 6
This is scrambled words what is number 8 9 10 11 12 13
The state of South Carolina has 46 counties. Write 46 as a product of primes
Final answer:
The prime factorization of the number 46 is 2 times 23, with 2 and 23 being prime numbers.
Explanation:
To write the number 46 as a product of prime numbers, we need to perform prime factorization. Here is the step-by-step process:
First, find the smallest prime number that divides into 46, which is 2.Divide 46 by 2, which gives us 23.Since 23 is a prime number itself and cannot be divided further by any prime number other than 1 and itself, we stop here.So, the prime factorization of 46 is 2 times 23. This can't be simplified any further as these are both prime numbers.
How many times can 10 go to 20
About 24.8 million people live in Texas. About 0.6 million people live in Vermont. How many times as many people live in Texas than in Vermont?
To find out how many times more people live in Texas than in Vermont, calculate the ratio of their populations, resulting in 41.33 times more people live in Texas than in Vermont.
To find out how many times more people live in Texas than in Vermont, we can calculate the ratio of the populations of Texas and Vermont. Given that about 24.8 million people live in Texas while about 0.6 million people live in Vermont, the ratio would be 24.8 million / 0.6 million = 41.33 times as many people live in Texas than in Vermont.
232 round to nearest ten
Traveling at 65 miles/hour, how many minutes will it take to drive 125 miles to San Diego?
Please break this down into parts so i can easily understand this. I take gse algebra 1 in the 8th grade and i'm having trouble with dimensional analysis word problems so I really need help with this one. We also have to use a certain chart that looks like a big fraction we use to solve problems like this, the units cancel out, and we multiply the top and bottom and then divide the top product by the bottom product. Please help. I'll also be giving the brainliest answer.
I got stuck on this one
What is the slope of a line passing through the points (2, 5) and (0, −4) ? Enter your answer in the box.
Answer:-9/-2
Step-by-step explanation:
m=yz-yz/x2-x1=
-4-5/0-2=
-9/-2
(the / means over, for instance 9-2/8+4 is 9-2 over 8+4)
The slope of the line is the ratio of the rise to the run, or rise divided by the run. 9/2 is the slope of a line passing through the points (2, 5) and (0, −4)
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The given two points are (2, 5) and (0, −4)
The slope of line passing through two points (x1,y1) and (x2,y2) is
m=(y₂-y₁)/(x₂-x₁)
where m is the slope of line.
x₁=2,x₂=0, y₁=5,y₂=-4
Substitute the values of x₁, x₂, y₁ and y₂ in formula of slope
=-4-5/0-2
Minus plus minus we get plus, so add -4 and -5
=-9/-2
The minus on numerator and denominator will be cancelled.
=9/2
Hence slope of a line passing through the points (2, 5) and (0, −4) is 9/2.
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Solve W=(5/8+7/8)*2*2
Solve the equation 3x+6y=18 for x
Answer:
x=6-2y
Step-by-step explanation:
At 0°C, the volume of a gas is 22 liters. For each degree the temperature T (in degrees Celsius) increases, the volume V (in liters) of the gas increases by 2/25. Write an equation that represents the volume of the gas in terms of the temperature.