Answer:
There were 12 people at the party
Answer:
Step-by-step explanation:
Other answers have already shown that there are n=12 people at the party, either using combinatorial choose notation
(n2)=n!2!(n−2)!=66
or by counting handshakes person by person, noting that each successive person has one fewer unique handshake than the prior (as the previously counted people are disregarded), and then using the sum-of-consecutive-integers formula to get
(n−1)+(n−2)+...+2+1=∑n−1k=1k=(n−1)n2=66
and solving for n .
Here I will provide another method of arriving at n(n−1)2=66.
Instead of keeping track of unique handshakes from the start, note that each person shakes hands with n−1 other people. As there are n people at the party, this gives us n(n−1) handshakes. However, notice that we counted each handshake twice; for example, if Alice and Bob shook hands, we counted that once for Alice, and then again for Bob. To account for the double-counting, we can divide by 2, which gives us the previously mentioned formula of n(n−1)2.
As a side note, if we did not previously know the sum formula, we could use this as a combinatorial proof to show that it works. Also, if we account for repeated counting by dividing by k! , the number of permutations of k objects, a similar method can be used to derive the chosen formula (nk)=n!k!(n−k)!.
Find the average speed of a car that is travelling 45 km in 5 hours. *
4 points
6 km/h
8 km/h
9 km/h
20 km/h
Answer:
8km/h
Step-by-step explanation:
Given:
Distance ,d = 45 kmTime taken, t = 5 hoursTo be calculated:
Calculate the average speed of a car ?
Formula used :
Average speed = Distance/Time
Solution:
We know that,
Average speed = Distance/Time
☆ Substituting the values in the above formula, we get
Average speed = 45 km / 5 h
= 9 km/h
Thus, the average speed of a car is 9 km/h .
262.5=10.5x+24x
How can I solve this?
Answer:
x=7.608696
Step-by-step explanation:
Simplify both sides of the equation.
262.5=10.5x+24x
262.5=(10.5x+24x)(Combine Like Terms)
262.5=34.5x
262.5=34.5x
Step 2: Flip the equation.
34.5x=262.5
Step 3: Divide both sides by 34.5.
34.5x
34.5
=
262.5
34.5
x=7.608696
How do I do this? I'm really confused. I'm probably gonna post another question soon as well
Step-by-step explanation:
The number of students who jog and have one sibling who jogs is 416.
The total number of students who have one sibling who jogs is 1823 + 416 = 2239.
So the probability that a student jogs if they have one sibling who jogs is 416/2239 = 0.186.
The number of students who jog and have two siblings who jog is 400.
The total number of students who have two siblings who jog is 1380 + 400 = 1780.
So the probability that a student jogs if they have two siblings who jog is 400/1780 = 0.225.
Therefore, a student is more likely to jog if they have two siblings who jog than one sibling who jogs.
What is the measure of ∠S?
Answer:
30
Step-by-step explanation:
These two triangles are similar, thus they have equal angle measures.
Answer:
30
Step-by-step explanation:
all the interior angles in the triangle adds up to 180
85 + 65=150
180-150=30
solve. Eight less than 7 times a number is 6. Find the number.
The word "less than" switches the order around.
So instead of 8 - 7n = 6, our equation is 7n - 8 = 6.
Solving from here, we add 8 to both sides to get 7n = 14.
Now divide both sides by 7 to get n = 2.
Answer:
The number is 2
Step-by-step explanation:
The fastest way to solve this it to retrace the steps. So.....
(7)(x)-8=6
6+8=14
14/7=2
Thus, 2 is your answer.
what attributes of a solid figure should you identify to classify it as a polyhedron HELP ME ASAP PLEASE!!!!!!
Answer:
If all the sides of the solid are flat, then it is said to be a polyhedron
Step-by-step explanation:
Given: a polyhedron
To find: attributes of a solid figure to classify it as a polyhedron
Solution:
A polyhedron is a three-dimensional figure with flat faces as polygons. It has straight edges and sharp vertices. It is made by joining polygons together.
If all the sides of the solid are flat, then it is said to be a polyhedron but if the solid has at least one curved side, then it is not a polyhedron.
Find the
measure
of X
[tex]x+50+x=180\\2x+50=180\\2x=180-50\\2x=130\\x=65[/tex]
What is the mode of the following numbers?
4,9,6, 3, 4,2
Answer:
4
Step-by-step explanation:
Whichever number appears the most in the list of numbers which in this is 4
What is the slope of the situation?
Answer: 4.2
Step-by-step explanation:
Everytime the x goes up 1, the height goes up 4.2
Answer:
The slope is 4.2 cm per week
Step-by-step explanation:
Take the difference in time and divide by the difference in time
m = (y2-y1)/(x2-x1)
= (20.4-16.2)/(2-1)
=4.2/1
The slope is 4.2 cm per week
A group of 80 students in a college are surveyed. They are asked which of Spanish or French they are studying. a) complete the Venn Diagram. b) How many students study ONLY French c) How many students study Spanish?
Answer:
a) Find attached the completed Venn diagram (2nd diagram)
b) 25
c) 46
A related Question found at brainly (ID 16765143):
A group of 80 students in a college are surveyed. They are asked which of Spanish or French they are studying. 71 of the students surveyed studies at least one of the two languages.
a) Complete the Venn diagram.
b) How many students study only french?
c) How many students study Spanish?
Step-by-step explanation:
Find attached the Venn diagram (1st diagram)
a) Total number of students in college = 80
Since 71 out of the 80 students surveyed studies at least one of the two languages, the number of students that studied neither French nor Spanish = 80-71 = 9
From the venn diagram:
Number of students that study Spanish = 14
Number of students that study French = 25
We need to determine if the values are for Spanish only and French only respectively or for at least Spanish and French respectively.
Estimated value for the middle term = 80-(14+25+9) = 32
From the above calculation, the number of students that study both Spanish and French is 32 and it is more than each set value. This implies the value given in the Venn diagram is for Spanish only and French only respectively.
Let number of students that study both Spanish and French = x
Spanish only = 14
French only = 25
the number of students that studied neither French nor Spanish = 9
Total:
14 + 25 + x + 9 = 80
48 + x = 80
x = Number of students that study both Spanish and French = 32
b) French only = 25
c) Number of students that study Spanish = students that study at least Spanish
= 14+x = 14+32
Number of students that study Spanish = 46
Find the surface area of the cylinder. Use 3.14 for pi and round your answer to the nearest tenth.
A.282.6 ft
B.439.6 ft
C.394.1 ft
D.553.4 ft
Answer:
B.
Step-by-step explanation:
[tex]2\pi *5*9+2\pi* 5^2[/tex]
[tex]2*3.14*5*9+2*3.14*25=439.6[/tex]
Brin was making a bird house for the chickadees. How much birdseed will it take to fill the birdhouse? 80 cm3 240 cm3 320 cm3 400 cm3
Answer:
320cm³ (option C)
Step-by-step explanation:
The complete image of the question can be found in:
https://brainly.com/question/16820683
Volume of bird house = volume of a cuboid + volume of a triangular prism
Volume of a cuboid = length × breadth × height
= 8cm × 5cm × 6cm = 240cm³
Volume of triangular prism = ½ base ×height ×length
= ½ × 8×4×5 = 80cm³
Volume of bird house = 240+80
Volume of bird house = 320cm³
Amount of birdseed that will it take to fill the birdhouse = Volume of bird house = 320cm³
Simplify to create an equivalent expression (2j+1)9-7j
Answer:
Simplifying
(2j + 1) * 9 + -7j = 0
Reorder the terms:
(1 + 2j) * 9 + -7j = 0
Reorder the terms for easier multiplication:
9(1 + 2j) + -7j = 0
(1 * 9 + 2j * 9) + -7j = 0
(9 + 18j) + -7j = 0
Combine like terms: 18j + -7j = 11j
9 + 11j = 0
Solving
9 + 11j = 0
Solving for variable 'j'.
Move all terms containing j to the left, all other terms to the right.
Add '-9' to each side of the equation.
9 + -9 + 11j = 0 + -9
Combine like terms: 9 + -9 = 0
0 + 11j = 0 + -9
11j = 0 + -9
Combine like terms: 0 + -9 = -9
11j = -9
Divide each side by '11'.
j = -0.8181818182
Simplifying
j = -0.8181818182
Answer:
11j + 9
Step-by-step explanation:
(2j + 1)9 - 7j
or
9(2j + 1) - 7j
18j + 9 - 7j
18j - 7j + 9
11j + 9
What is the solution to this equation?
–5(s – 30) = –10
A. s = –4
B. s = 8
C. s = 28
D. s = 32
Answer:
s = 32
Step-by-step explanation:
–5(s – 30) = –10
Divide each side by -5
–5/ -5(s – 30) = –10/-5
s - 30 = 2
Add 30 to each side
s-30+30 = 2+30
s = 32
Answer:
D. s=32
Step-by-step explanation:
To solve the equation, we want to find out what s is. In order to do this, we have to get s by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.
–5(s – 30) = –10
s-30 is being multiplied by -5. The opposite of multiplication is division. Divide both sides by -5.
–5(s – 30)/-5= –10/-5
s-30=-10/-5
s-30=2
30 is being subtracted from s. The opposite of subtraction is addition. Add 30 to both sides.
s-30+30=2+30
s=2+30
s=32
Let's check our solution. Substitute 32 in for s in the original equation. If our solution is correct, the left side of the equation should match the right side.
–5(s – 30) = –10
-5(32-30)=-10
-5(2)= -10
-10=-10
The statement above is true, so we know that s is equal to 32, and D is the correct answer.
how do I solve this?
Step-by-step explanation:
(i) Use law of cosine:
c² = a² + b² − 2ab cos C
c² = (√3 − 1)² + (√3 + 1)² − 2(√3 − 1)(√3 + 1) cos 60°
c² = 3 − 2√3 + 1 + 3 + 2√3 + 1 − 2(3 − 1) (½)
c² = 6
c = √6
(ii) Use law of sines:
a / sin A = c / sin C
(√3 − 1) / sin A = √6 / (½√3)
(√3 − 1) / sin A = 2√2
½ (√3 − 1) = √2 sin A
½ (√6 − √2) = 2 sin A
¼ (√6 − √2) = sin A
Use a calculator:
A = 15°
(iii) Use SAS area:
A = ½ ab sin C
A = ½ (√3 − 1) (√3 + 1) sin 60°
A = ½ (3 − 1) (½√3)
A = ½√3
Which of the following looks the most like a straight angle?
A. The letter I
B. The letter T
C. The letter X
D. The letter O
The letter I
hope it helps
Answer:
The letter l
Answer A is correct
hope this helps
brainliest appreciated
good luck! have a nice day!
The linear question y=-2x+4 is represented on the graph below
(2,0)
(0,4)
(0,-1)
(4,-4)
At a baseball game, 70% of people attending were supporting the home team, while 30% were supporting the visiting team. If 350 people attending the game supported the home team, what was the total number of people attending the game?
Answer:500 people
Step-by-step explanation:
70% = 0.70
.70x = 350
x = 350/.70
x = 500
Two cars leave the same parking lot, with one heading north and the other heading east. After several minutes, the eastbound car has traveled 12 kilometers. If the two cars are now a straight-line distance of 15 kilometers apart, how far has the northbound car traveled?
Answer 3 kilometers
15 kilometers total minus 12 kilometers of the east bound car leaves only 3 kilometers for the northbound car to travel.
Glen Davis is shooting free throws. Making or missing free throws doesn't change the probability that he will make his next one, and he makes his free throws 74%
Answer:
0.00456
Step-by-step explanation:
Given: Percentage of free throws = 74%
Required: What is the probability of Glen Davis making none of his next 4 free throw attempts?
Since, there is a free throw 74% of the time, thus, the time he misses = 26% of the time.
To miss four in a row, it is requires to miss the first throw, the second throw, the third throw and also the fourth throw.
Thus, the probabilities of Gien missing will be multiplied.
By using the probability formula -
P ( MMMM) = 26/100 × 26/100 × 26/100 × 26/100
= 456976/ 100000000
= 0.00456
Therefore, the probability that he will have next 4 free attempts is 0.00456.
Can someone plz help?
Answer:
x = 12 in ; Type in 12 in the box
Step-by-step explanation:
If we were to apply triangle formula ; 1/2 * base * height, we would see that length of height ⇒ 10 inches, and length of base ⇒ x inches,
Given an Area of 60 square inches let us substitute into the formula 1/2 * base * height and solve for x;
Area of Triangle = 1/2 * base * height,
60 in^2 = 1/2 * x in * 10 in ⇒ take 1/2 * 10,
60 in^2 = 5 in * x in ⇒ divide either side by 5 in,
12 in = x in ⇒ divide either side by inches,
x = 12 inches,
Solution; x = 12 in
A candy jar contains flavored jelly beans. There are 7 orange, 9 cherry, 3 lemon, 15 licorice, and 6 blueberry. Find the probability of choosing two cherry jelly beans in a row (the first jelly bean is not replaced). PLEASE HELP!!!
Answer: 0.046
Step-by-step explanation:
From the question,
orange jelly beans= 7
Cherry jelly beans =9
Lemon jelly beans = 3
Licorice jelly beans = 15
Blueberry jelly beans = 6
Total jelly beans = 40
The probability of choosing the first cherry jelly beans will be = 9/40
After the first one is chosen, there'll be 8 cherry jelly beans and total of 39 left. The probability of choosing the second one will be = 8/39
The probability of choosing two cherry jelly beans in a row will be:
= 9/40 × 8/39
= 72/1560
= 0.046
Solve for b. ab + c = d b = b = a + b =
Answer:
b. ab + c = d b = a + c/d b = a/(c - d) b = (d - c)/a
Step-by-step explanation:
The highest and lowest scores on a test taken by 80 students are within 19 points of the average of the exam. The average for this exam was 72. Set up an equation to solve for the highest and lowest scores. Show your original equation and the process used to find the highest and lowest exam score.
Answer:
The highest score is 91 and the lowest score is 53
Step-by-step explanation:
The highest and lowest scores on a test taken by 80 students are within 19 points of the average of the exam. The average is 72.
1. The method used to solve this question, is the use of absolute values.
2. Let x be the value that we can use to represent the lowest and highest scores. The equation using absolute values is given as:
| x - 72 | = 19.
Therefore:
x - 72 = 19 (highest score) or
- (x - 72) = 19 (lowest score)
3. We have to find the value of x for which it is the highest or lowest score.
The highest score is given as:
x - 72 = 19
x = 19 + 72
x = 91
For lowest score:
-(x - 72) = 19
-x + 72 = 19
x = 72 - 19
x = 53
The highest score is 91 and the lowest score is 53
QUESTION 3 of 10: You have a $112,000 adjustable rate mortgage that was 8% per year. You were just notified that next year it is going up to
13%. What is the annual dollar difference between the old and newly adjusted interest rates if your balance stayed the same at $112,000?
a) $1,120
b) $1,253
c) $5,600
d) $8,960
Based on the information given, the annual dollar difference will be C. $5600.
Based on the information given, the annual dollar difference will be calculated as follows:
= (13% × $112000) - (8% × $112000)
= (0.13 × $112000) - (0.08 × $112000)
= $14560 - $8960
= $5600
In conclusion, the correct option is $5600.
Learn more about percentages on:
https://brainly.com/question/14323743
Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!!!!
A. subtract the bottom equation from the top equation
Step-by-step explanation:
The elimination method for solving systems of linear equations uses the addition property of equality. You can add the same value to each side of an equation. So if you have a system: x – 6 = −6 and x + y = 8, you can add x + y to the left side of the first equation and add 8 to the right side of the equation.
// have a great day //
Help?Find the product.
(a - b)(a – 7b)
Answer:
all work shown and pictured
Given the point A(-3, 5), find the image after performing the following two transformations First: Translation (x, y) -> (x, y - 4) Reflection: in the y - axis. PLEASE HELP.
Answer:
A' (3,1)
Step-by-step explanation:
You start with (-3,5)
Translation Down 4: (-3,1), just subtract 4 from the y-coordinate
Reflection over the y-axis: (3,1), multiply -1 to the x-coordinate
Which statement best explains why this expression is equal to 9.4?
Answer:
Where is the answers, they might help.
Answer:
Any number multiplied by 0 is 0
Step-by-step explanation:
imagine math answer.
which of the following is a geometric sequence?
The key thing to look for to determine whether a sequence is geometric is to see whether the ratio between consecutive terms - the number I would multiply one term by to get the next - is constant.
By inspection, we see that the fourth answer choice satisfies that, as [tex]\frac{81}{27}=\frac{27}{9}=\frac{9}{3}=\frac{3}{1}=3.[/tex] Why not the first? We have [tex]2=\frac{12}{6}\ne\frac{6}{2}=3.[/tex]
The third choice is not a geometric sequence, but rather an arithmetic sequence, where the difference between consecutive terms is constant. Just to make sure that it isn't geometric, we compute [tex]\frac{14}{9}\ne\frac{9}{4}.[/tex]
The second sequence is not geometric (although it does eventually converge to 1, but not its corresponding series), as [tex]\frac{4}{3}=\frac{2/3}{1/2}\ne\frac{3/4}{2/3}=\frac{9}{8}.[/tex]
Answer:
its D
Step-by-step explanation:
