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.
This has really gotten confuzzing for me. SOS
let number of hours = x
1st equation is 15.54+0.11x
2nd equation is 16.14-0.09x
now calulate x so the 2 equations are equal:
15.54+0.11x=16.04-0.09x
mutiply evrything by 100 to get rid of the decimal points andmake the calculations a little easier
1554+11x=1604-9x
add 9 x to both sides:
1554+20x=1604
subtract 1554 from both sides:
20x=50
divide 50 by 20 for x
x=50/20 = 2.5
x = 2.5
so they were the same after 2.5 hours
what is y=-3x+4 and y=3x-2
by using transitive property
Deniz tried to subtract two polynomials. Her work is shown below.
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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X Y
-2 5
-1 3
0 1
1 -1
2 -3
Find the explicit formula and the type of function
Help me asap!!
To the nearest percent, what is the probability of rolling a 4 on the number cube?
What is .04 as a mixed number
A refrigerator magnet uses 5/8 inch of magnetic tape. How many refrigerator magnets can you make with 10 inches of magnetic tape. Explain
This is scrambled words what is number 8 9 10 11 12 13
7x-4d use x = 8 and d = have (simplify algebraic exression)
Write the product as a single power
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?
4.625 as a fraction in simplest form
4.625 as a fraction in the simplest form can be written as 37/8.
Given is a decimal number 4.625.
Here the decimal point is 3 units to the left.
So any decimal number can be written as a fraction with powers of 10 as the denominator.
Here since the decimal point is 3 units to the left divide by 1000.
So,
4.625 = 4625 / 1000
Both 4625 and 1000 are multiples of 25.
So this can be written as :
4625 / 1000 = 4625 ÷ 25/ 1000 ÷ 25
= 185 / 40
= 37/8
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If Susan subtracts 11 from one-fourth of her number she gets 11
Final answer:
Susan's number is found by solving the equation x/4 - 11 = 11, which after isolating the variable and multiplying both sides by 4 yields the answer x = 88.
Explanation:
If Susan subtracts 11 from one-fourth of her number, she gets 11. To solve this problem, we set up an equation where x represents Susan's number. The one-fourth of her number would be x/4, and subtracting 11 from one-fourth of her number yields: x/4 - 11 = 11.
To find x, we first isolate the variable on one side by adding 11 to both sides of the equation, so we have x/4 = 22. Next, we multiply both sides by 4 to solve for x: x = 22 * 4. Therefore, Susan's number is 88.
When a number x is multiplied by 6, the result is 3/8 . What is the value of x? Drag and drop the correct number into the box so that the equation is true.
A rectangle has a perimeter of 16 inches.
What dimensions (length, width) could be the dimensions of the sides?
A. (8, 0)
B. (2, 12)
C. (6, 2)
D. (13, 3)
E. (3, 10)
option C: (6, 2).
The student has asked for the possible dimensions of a rectangle given that its perimeter is 16 inches. To find the dimensions that are correct, we need to remember that the perimeter of a rectangle is calculated by the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. We must check each pair of dimensions provided and see if they satisfy this equation when the perimeter is 16 inches.
A. (8, 0) - This would give us a perimeter of 2(8) + 2(0) = 16 inches, which is correct, but it is not a possible dimension for a rectangle, as having a side of length 0 inches does not make a rectangle.B. (2, 12) - The perimeter here would be 2(2) + 2(12) = 28 inches, which is not equal to 16 inches.C. (6, 2) - Checking this option, we get 2(6) + 2(2) = 12 + 4 = 16 inches. This one is correct and is a possible dimension for a rectangle.D. (13, 3) - The perimeter in this case would be 2(13) + 2(3) = 26 + 6 = 32 inches, clearly more than 16 inches.E. (3, 10) - This would give us a perimeter of 2(3) + 2(10) = 6 + 20 = 26 inches, which also does not equal the 16-inch perimeter required.Therefore, the only possible dimensions for the rectangle given the choices provided and where both dimensions are greater than zero is option C: (6, 2).
When is the sum to two negative mixed numbers an integer?
3 pizzas for $ 16.50 what is the unit rate for one pizza
Is this a funtion? Explain.
3(x+1)^(4/3)=48
how do i solve this?
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
In the diagram to the right three lines intersect at n.The measure of < GNF is 60, and the measure of < MNL is 47. What is the measure of < HNK?
Measure of ∠HNK is equals to 73°.
What are linear pair angles?
" Linear angles are formed when the sum of pairs of adjacent angles is equals to 180°."
According to the question,
Measure of ∠GNF = 60°
Measure of ∠MNL = 47°
As per the linear pair angles definition ,
∠GNF, ∠FNM, ∠MNL forms linear pair angles .
Therefore,
∠GNF + ∠FNM + ∠MNL = 180°
Substitute the given values we get,
60° + ∠FNM + 47° = 180°
⇒ ∠FNM = 180° - 107
= 73°
As given three lines intersect at 'N'
∠FNM and ∠HNK are vertically opposite angles and are congruent.
Therefore,
Measure of ∠HNK = 73°
Hence, measure of ∠HNK is equals to 73°.
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Manuela has two boxes. The larger of the two boxes has dimensions of 15cm by 25cm by 29 cm. The smaller of the two boxes is a cube with sides that are 10 cm long. If she were to put the smaller box inside the larger, what would be the remaining volume of the larger box?
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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84, 99, 88, 82, 95, 85
Myra's test scores are shown. She has one more test for the semester. What is the minimum score that she can make on her last test and have an average greater than 90?
Note: All scores are whole numbers and scores are not rounded
a. 95
b.96
c.97
d.98
Answer:
Option: d is the correct answer.
d. 98
Step-by-step explanation:
The scores of Myra's test are as follows:
84, 99, 88, 82, 95, 85
Let 'x' be the minimum score that is obtained by Myra in the last test so that the average is greater than 90 marks.
i.e.
[tex]\dfrac{84+99+88+82+95+85+x}{7}>90\\\\\\i.e.\\\\\\\dfrac{533+x}{7}>90\\\\\\i.e.\\\\\\533+x=90\times 7\\\\\\533+x>630\\\\\\x>630-533\\\\\\x>97[/tex]
Hence, the minimum score has to be 98.
( Since, the scores are in whole number )
Find the equation of the line (3,-2) and parralel to the line containing the points (-2,4) and (-4,-2).
Earth diameter is 12,756 kilometers.How many meters is this?
A rectangular pool is 30 1/3 feet long and 12 1/2 feet wide what is the area of the pool
A recipe for apple cake needs 10 mL of baking powder, 70 mL of butter, 190 mL of sugar and 420 mL of flour. This is enough to make a cake for 8 people. How much of each ingredient would be needed to make a cake for 20 people?
20/8 = 2.5
multiply all the ingredients by 2.5
10 ml * 2.5 = 25 ml of baking powder
70 *2.5 = 175 ml of butter
190 * 2.5 = 475 ml of sugar
420 * 2.5 = 1050 ml of flour