at one of george washington's parties, each man shook hands with everyone except his spouse, and no handshakes took place between women. if 1313 married couples attended, how many handshakes were there among these 2626 people?
The total number of handshakes was 234.
The first man shook hands with 12 other men.The second man shakes hands with 11 other men, as he had already shaken hands with the first man.Like-wise, the last man does not need to shake hands again as every man has already shaken hands with him in their respective turns.The number of handshakes among men is 0 + 1 + 2 + … + 12.The sum of "n" natural numbers = (n)(n+1)/2The number of handshakes among men is 12(13)/2.The number of handshakes among men is 78.Each man shakes hands with every woman except his spouse.Each man shakes hands with 12 other women.The number of handshakes between men and women is 13*12.The number of handshakes between men and women is 156.The total number of handshakes is 78 + 156.The total number of handshakes is 234.To learn more about natural numbers, visit :
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I need to graph y=−2.5, please help!?!
Answer:
Step-by-step explanation:
plz help i will report if your not trying to answer
Answer:
c
Step-by-step explanation:
It might be wrong but I think its right
Answer:
36
2^2 = 4
9^0 = 1
Samantha puts $800.00 into an account to use for school expenses. The account earns 11% interest, compounded annually. How much will be in the account after 10 years? Round your answer to the nearest cent.
Answer:
$2271.54
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Compounded Interest Formula: [tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
A is final amountP is principle amountr is raten is compoundt is time in yearsStep-by-step explanation:
Step 1: Define
P = 800.00
r = 0.11
n = 1
t = 10
Step 2: Find A
Substitute [Formula]: [tex]A=800(1+\frac{0.11}{1} )^{1(10)}[/tex]Divide/Multiply: [tex]A=800(1+0.11 )^{10}[/tex]Add: [tex]A=800(1.11 )^{10}[/tex]Exponents: [tex]A=800(2.83942)[/tex]Multiply: [tex]A=2271.54[/tex]a small college had 2570 students in 1994 and 2734 students in 1996. if the enrollment follows a linear growth pattern, how many students should the college have in 2004 ?
Answer: The final answer is 3390.
Step-by-step explanation:
Before answering the question, you have to understand that a linear growth pattern is a straight-line pattern (not exponential growth).
-From 1994 to 1996 are 2 [years]
-In 2 [years], there is a growth of 2734-2570 = 164 [students]
-With a linear growth, we can take the above [number of students] (164) divided by 2 [years] to get a [growth rate] of 82 [students per year]
⇒ [tex]\frac{164}{2} =82[/tex] [[tex]\frac{number of students}{years}[/tex] or number of students per year or growth rate]
-From 1996 to 2004, there are 8 [years]
-Therefore:
8 [years] × 82 [students per years] = 656 [students] => increased in students
-We add 656 [students] increased to 2734 [students] in 1996 = 3390 [students] in 2004
The final answer is 3390.
Hope this help. :D
What is 2x-47+(4-1)?
Answer:
x = 280/17 = 16.471
Step-by-step explanation:
At Acme Inc., there are 3 more than twice as many salespeople as inventors. If the whole company has 27 employees,
how many inventors are there?
Answer:
There are 8 inventors.
Step-by-step explanation:
Let 's' be the salespersonLet 'i' be the inventorsGiven that there are 3 more than twice as many salespeople as inventors.
i.e s = 3+2iAlso given that the whole company has 27 employees.
i.e.
s + i = 27
substituting s = 3+2i
3 + 2i + i= 27
3 + 3i = 27
3i = 27 - 3
3i = 24
divide both sides by 3
i = 8
Thus, there are 8 inventors.VERIFICATION
As the total number of employees is 27.
so the salespeople will be:
s = 3+2i
= 3 + 2(8)
= 3 + 16
= 19
Thus, the total employees are verified as:
s + i = 27
19 + 8 = 27
27 = 27
HELP ASAPPP!!!! Please dude
Answer:
A
Step-by-step explanation:
That's the only one that makes sense
Answer:
It's either A or C
Step-by-step explanation:
Find the length of the third side to the nearest tenth.
3
9
Answer:
8.5
Step-by-step explanation:
X^2 = 9^2 - 3^2
x^2 = 81 - 9
x^2 = 72
x = √72
x = 8.485
What are the solutions of the quadratic equation?
3x? - 23x + 40 = 0
4 ÷ (-6) =
please write the answer as a fraction
Answer:
[tex] \frac{ - 2}{3} [/tex]
Step-by-step explanation:
if it is right mark me brainliest
If CM=15, Find DC and DM
image ????? please attach image and try again
Lee won 30 tickets at the carnival. He then gave each of his friends 2 tickets. He has 4 tickets left. How many friends does Lee have?
Answer: 30-4=x 4+x=30 x=26
Step-by-step explanation: So he has 30 tickets and he gives 2 to each of his friends which means that lee has 26 friends with 4 tickets left over.
Help pls and thank you!!
Answer:
it's 8x
hope i could help :)
In order to prove △ABC ≅ △DBC by SAS, what additional information must be given?
Two triangles are congruent if two pairs of corresponding angles and included sides are congruent.
What is the triangle?Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.
In order to prove △ABC ≅ △DBC by SAS. Then the additional information must be given will be
SAS: Two triangles are congruent if two pairs of corresponding sides and included angles are congruent.
More about the triangle link is given below.
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Could anybody help me with this i will cashapp u $5 if its right
Answer:
a. Correct
b. Incorrect
c. Correct
d. Incorrect
e. Incorrect
Step-by-step explanation:
b. Incorrect because negative hours do not make sense
d. 80 is achieved only with more than 3.89 hours of study, so 3.5 is not enough
e. No, the score is the dependent, it comes out of the formula.
To manufacture scooters, the manufacturer has a fixed cost of 34,400$$ plus a variable cost of n $$ per scooter. Find 100$$, the number of scooters that need to be produced so that the average cost per scooter is 180$$.
Answer:
The number of scooters that need to be produced so that the average cost per scooter is $180 is 430 scooters.
Step-by-step explanation:
Note: This question is not properly structured/written. The question is therefore rewritten properly before answering the question as follows:
To manufacture scooters, the manufacturer has a fixed cost of $34,400 plus a variable cost of $100 per scooter. Find n, the number of scooters, that need to be produced so that the average cost per scooter is $180.
The explanation of the answer is now provided as follows:
The number of scooters can be calculated as follows:
Variable cost per scooter = $100
n = number of scooter = ?
Total variable cost = Variable cost per scooter * n = $100 * n = $100n
Total cost = Fixed cost + Total variable cost = $34,400 + $100n
Average cost per scooter = Total cost / n = $180 ................ (1)
Substituting the value for Total cost into equation (1) and solve for n, we have:
($34,400 + $100n) / n = $180
$34,400 + $100n = $180n
$34,400 = $180n - $100n
$34,400 = $80n
n = $34,400 / $80
n = 430
Therefore, the number of scooters that need to be produced so that the average cost per scooter is $180 is 430 scooters.
The endpoints of CD are (-2,-4) and D (6,2). What are the coordinates of the midpoint of CD?
The midpoint of the line segment CD whose coordinates (-2,-4) and D (6,2) will be (2, -1).
What is the mid-point of the line segment?Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).
Then the coordinate of the mid-point of the line segment is given as,
(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]
The endpoint of the segment CD is given as C(-2, -4) and D(6, 2). Then the mid-point of the line segment CD will be
(x, y) = [(-2 + 6) / 2, (-4 + 2) / 2]
(x, y) = (4/2, -2/2)
(x, y) = (2, -1)
The midpoint of the line segment CD whose coordinates (-2,-4) and D (6,2) will be (2, -1).
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find the 24th term of the arithmetic
sequence whose common difference is d=4
and whose first term is a1=1
what is the answer?
Answer:93
Step-by-step explanation:
Do all numbers have a prime factorization
Answer:
It depends on the numbers
Step-by-step explanation:
Give some examples
Find the ratio of the speed of a cycle 15km per hour to the speed of scooter 30km per hour
Step-by-step explanation:
15:30
Divide by 5
3:6
1:2
Answer:
3:4
Step-by-step explanation:
speed of cycle=15 km pers
speed of scooter=30 km per s
Now,
Ratio of speed= distance travelled ÷time taken
= (15+30)÷60 (1 hour=60 min)
= 45÷60
= 3÷4
= 3:4
:: The answer is 3:4.
Between 7 and 8 o'clock, there were 56 vehicles in the zoo parking lot. There were 3 times as many vans as cars.
How many vans and how many cars were counted?
Answer:
14 cars, 42 vans
Step-by-step explanation:
can divide the total by 4, since the number of cars is just 3x the number of vans
x+3x=56
4x=56
56/4
14 cars times 3 plus the original 14
There are 14 cars times 3 plus the original 14.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given Between 7 and 8 o'clock, there were 56 vehicles in the zoo parking lot. There were 3 times as many vans as cars.
Then it can divide the total by 4, since the number of cars is just 3x the number of vans.
x+3x=56
4x=56
56/4
Therefore, there are 14 cars times 3 plus the original 14.
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Line r is parallel to line t. Find m<5.
Answer:
B. 135
Step-by-step explanation:
According to corresponding angles answer is b
135 is congruent to angle 1 and angle 1 is congruent to angle 5
so if angle 1 is 135 then angle 5 is 135
Brainliest please
Hope this helps
Answer:
d.
Step-by-step explanation:
straight angle = 180 degress
135+45=180
Can you help me I have no idea how to do this
Answer:
[tex](f + g)(x) = 7 - 6x[/tex] --- (1)
[tex](f - g)(x) = 6x - 1[/tex] -- (2)
[tex](f . g)(x) =4(5^x)[/tex] ---- (3)
[tex](f / g)(x) = \frac{4}{5^x}[/tex] ----- (4)
[tex](f + g)(x) = -7x-7[/tex] --- (5)
[tex](f - g)(x) = 9x+ 9[/tex] --- (6)
[tex](f . g)(x) = (-8)(x+1)^2[/tex] --- (7)
[tex](f / g)(x) = -\frac{1}{8}[/tex] ----- (8)
[tex]F(t) = \frac{9}{5}t^2 + 32[/tex] ---- (9)
[tex]T(t) = (t - 2)^2 - 4[/tex] --- (10)
Step-by-step explanation:
Given
[tex]f(x) = 3[/tex]
[tex]g(x) = 4 - 6x[/tex]
Solving (1): (f + g)(x)
[tex](f + g)(x) = f(x) + g(x)[/tex]
So, we have:
[tex](f + g)(x) = 3 + 4 - 6x[/tex]
[tex](f + g)(x) = 7 - 6x[/tex]
Solving (2): (f - g)(x)
[tex](f - g)(x) =f(x) - g(x)[/tex]
So, we have:
[tex](f - g)(x) =3 - (4 - 6x)[/tex]
[tex](f - g)(x) =3 - 4 + 6x[/tex]
[tex](f - g)(x) =-1 + 6x[/tex]
[tex](f - g)(x) = 6x - 1[/tex]
Given
[tex]f(x) = 4[/tex]
[tex]g(x) = 5^x[/tex]
Solving (3): (f . g)(x)
[tex](f . g)(x) =f(x) * g(x)[/tex]
So, we have:
[tex](f . g)(x) =4 * 5^x[/tex]
[tex](f . g)(x) =4(5^x)[/tex]
Solving (4): (f / g)(x)
[tex](f / g)(x) = \frac{f(x)}{g(x)}[/tex]
So, we have:
[tex](f / g)(x) = \frac{4}{5^x}[/tex]
Given
f(x) = x + 1
g(x) = -8 - 8x
Solving (5): (f + g)(x)
[tex](f + g)(x) = f(x) + g(x)[/tex]
So, we have:
[tex](f + g)(x) = x + 1 -8-8x[/tex]
Collect Like Terms
[tex](f + g)(x) = x -8x+ 1 -8[/tex]
[tex](f + g)(x) = -7x-7[/tex]
Solving (6): (f - g)(x)
[tex](f - g)(x) = f(x) - g(x)[/tex]
So, we have:
[tex](f - g)(x) = x + 1 -( -8-8x)[/tex]
[tex](f - g)(x) = x + 1 +8+8x[/tex]
Collect Like Terms
[tex](f - g)(x) = x +8x+ 1 +8[/tex]
[tex](f - g)(x) = 9x+ 9[/tex]
Solving (7): (f . g)(x)
[tex](f . g)(x) = f(x) . g(x)[/tex]
So, we have:
[tex](f . g)(x) = (x+1) . (-8 - 8x)[/tex]
Factorize
[tex](f . g)(x) = (x+1) .(-8) (1 + x)[/tex]
Rewrite as:
[tex](f . g)(x) = (x+1) .(-8) (x+1)[/tex]
[tex](f . g)(x) = (-8)(x+1) (x+1)[/tex]
[tex](f . g)(x) = (-8)(x+1)^2[/tex]
Solving (8): (f / g)(x)
[tex](f / g)(x) = \frac{f(x)}{g(x)}[/tex]
So, we have:
[tex](f / g)(x) = \frac{(x+1)}{(-8-8x)}[/tex]
Factorize
[tex](f / g)(x) = \frac{(x+1)}{-8(1+x)}[/tex]
[tex](f / g)(x) = \frac{1}{-8}[/tex]
[tex](f / g)(x) = -\frac{1}{8}[/tex]
Solving (9):
From the question, we have that:
[tex]F(c) = \frac{9}{5}c + 32[/tex]
[tex]C(t) = t^2[/tex]
Required
Determine function F in terms of c
The implication of this question is to solve for [tex]F(c(t))[/tex]
If [tex]F(c) = \frac{9}{5}c + 32[/tex] and [tex]C(t) = t^2[/tex],
Then
[tex]F(c(t)) = \frac{9}{5}*t^2 + 32[/tex]
[tex]F(c(t)) = \frac{9}{5}t^2 + 32[/tex]
This can be rewritten as:
[tex]F(t) = \frac{9}{5}t^2 + 32[/tex]
Solving (10):
[tex]T(h) = h^2 - 4[/tex]
[tex]h(t) = t - 2[/tex]
Required
Find [tex]T(h(t))[/tex]
If [tex]T(h) = h^2 - 4[/tex] and [tex]h(t) = t - 2[/tex], then
[tex]T(h(t)) = (t - 2)^2 - 4[/tex]
This is gotten by substituting t -2 for h
The solution can be rewritten as:
[tex]T(t) = (t - 2)^2 - 4[/tex]
2. (05.02 LC) Which equation does the graph below represent? (5 polnts) 8 2 .2 O y = 2x Y = 2 x y = 2 + x
Answer:
b
Step-by-step explanation:
7x + 2y + x + 10y=180
Which function has only one x-intercept at (-6, 0)?
O fx) =x(x -6)
O fx) = (x-6)(x -6)
O f() = (x+ 6)(x - 6)
O f)= (x+ 6)(x + 6)
Please help
Answer: O f)= (x+ 6)(x + 6)
Hope this helps :)
I NEED HELP AND FAST PLEASE!!! I’m not sure if I chose the right answer or not!!
Answer:
d
Step-by-step explanation:
the graph increases then goes horizontal
Answer:
D
Step-by-step explanation:
D is the choice you have to make. The culprit is the word quickly. You can't tell if the speed is increasing quickly or not.
The correct part of d is that the bicycle stays at a constant rate until the end of the timing of the graph.
Select the correct answer.
A parabola has an x-intercept of -1, a y-intercept of -3, and a minimum of -4 at x = 1.
Which graph matches this description? ( in the screenshots)
Step-by-step explanation:
answer A should be correct
Mrs. Farnam is getting new carpet in her class! Her classroom is 12 meters long and 22 meters wide. How many square meters of carpet does she need?
Answer:
264 square meters
Step-by-step explanation: