There would be a total of 28 handshakes between the 3 latecomers and the initial group of 5 members.
To calculate the number of combinations, we use the formula:
C(n, r) = n! / (r!(n-r)!)
where "n" represents the total number of items (in this case, people), and "r" represents the number of items to be chosen (in this case, 2 for a handshake).
Let's apply this formula to our scenario. We have 3 latecomers and 5 initial members. We want to select 2 people to form a handshake. Plugging these values into the combination formula, we get:
C(8, 2) = 8! / (2!(8-2)!)
= 8! / (2!6!)
To simplify the calculation, let's break down the factorial terms:
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
2! = 2 * 1
6! = 6 * 5 * 4 * 3 * 2 * 1
Now we can substitute these factorial terms back into the combination formula:
C(8, 2) = (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / [(2 * 1) * (6 * 5 * 4 * 3 * 2 * 1)]
Simplifying further:
C(8, 2) = (8 * 7) / (2 * 1)
= 56 / 2
= 28
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race borrows $135,000 at a yearly simple interest rate of 4.5%. How much less would she pay if she pays the loan off in 15 years rather than in 30 years?
Answer:
$226,125
Step-by-step explanation:
the annual percentage rate is $6,075 (135,000×.045)
multiply $6,075 for 15 years = $91,125
add $135,000 (amount borrowed) and $91,125 (amount of interest) = $226,125
She would pay $91,125 less if she pays the loan off in 15 years rather than in 30 years.
What is Simple interest?To calculate simple interest, multiply the loan principal by the interest rate, then by the loan's period. Borrowers can get a rough estimate of the cost of borrowing by calculating simple interest. Simple interest loans are frequently used for auto loans and short-term personal loans.
As per the given data:
Money borrowed by race = $135,000
Simple interest rate = 4.5%
Principal amount (P) = $135,000
Interest paid = [tex]\frac{P \times R \times T}{100}[/tex] {T is time in years}
Interest paid when loan in paid in 15 years:
= [tex]\frac{135000 \times 4.5 \times 15}{100}[/tex] = $91,125
Interest paid when loan in paid in 30 years:
= [tex]\frac{135000 \times 4.5 \times 30}{100}[/tex] = $182,250
Amount she pays less = $182,250 - $91,125 = $91,125
Hence, she would pay $91,125 less if she pays the loan off in 15 years rather than in 30 years.
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Krysta is looking for a job cutting hair. One option is self-employment at The Richmond Salon, where she would pay $474 per month to rent a station and keep all of her earnings. Another option is to work at a franchise, where she would just have to pay the salon $6 for every haircut. If she performed a certain number of haircuts every month, the amount paid to either salon would be the same. How many haircuts would that be? How much would Krysta pay?
Answer:
79 haircuts and $474
Step-by-step explanation:
The computation is shown below:
Given that
she would have to pay $474 per month
And $6 for every haircut
So, the number of haircuts would be
= $474 ÷ $6
= 79 haircuts
The amount that she have to pay is $474
4 minutes 53 seconds to seconds
Answer:
It's 293 seconds
Step-by-step explanation:
Answer:
293 seconds
Step-by-step explanation:
There are 60 seconds in a minute so 4x60=?
you know 4x6=24 so just take away the zero then add it back so it would be 240 then you just add 53 so, 240+53= 293 seconds and that's the answer.
Pencils come in packages of 10 . Erasers come in package of 12 . Phillip wants to purchase the smallest number of pencils and erasers so that he will have exactly 1 eraser per pencil . How many packages of pencils and erasers should Phillip buy ?
Answer: 60
Step-by-step explanation:
From the question, we are informed that pencils come in packages of 10 while erasers come in package of 12 .
We are further told that Phillip wants to purchase the smallest number of pencils and erasers so that he will have exactly 1 eraser per pencil, this simply means that we have to calculate the lowest common multiple for 10 and 12.
Multiples of 10 = 10, 20, 30, 40, 50, 60,
Multiples of 12 = 12, 24, 36, 48, 60, 72
Therefore, the packages of pencils and erasers that Phillip should buy will be 60
PLEASE HELP! I WILL GIVE BRAINLIEST!!
One side of a rectangle is 9 inches longer than another side. If the longer sides of this rectangle decreases by 5 inches and the shorter sides increases by 3 inches, the area of the new rectangle equals the area of the original rectangle. Find the dimensions of the original rectangle
Answer: The original rectangle was 15 inches by 6 inches
=============================================================
Explanation:
L = original lengthW = original widthLet's make the length longer than the width, so L = W+9 since we're told that one side is 9 inches longer than another.
The area of this rectangle is
Area = length*width
A = L*W
Through substitution, we can replace L with W+9
A = (W+9)W
A = W^2 + 9W
We'll come back to this later.
--------------
Now let's decrease the longer side L by 5 inches to get L-5. At the same time, we'll increase the shorter side W by 3 to get W+3.
The new rectangle is (L-5) inches by (W+3) inches which leads to the area of...
A = (length)*(width)
A = (L-5)*(W+3)
A = (W+9-5)*(W+3) .... L replaced with W+9
A = (W+4)(W+3)
A = W^2 + 3W + 4W + 12 .... FOIL rule
A = W^2 + 7W + 12
--------------
We found these two area expressions
W^2 + 9WW^2 + 7W + 12We're told that the two areas (of the original and new rectangle) are equal to one another. Set them equal to each other and solve for W
W^2 + 9W = W^2 + 7W + 12
9W = 7W + 12 ............ subtracted W^2 from both sides
9W-7W = 12
2W = 12
W = 12/2
W = 6
The original width is 6 inches
L = W+9 = 6+9 = 15
The original length is 15 inches
The original area is L*W = 15*6 = 90 square inches
The new rectangle has side lengths of (L-5) = (15-5) = 10 inches and (W+3) = (6+3) = 9 inches. Then note how the area of this new rectangle is 10*9 = 90 square inches to match the other area. This helps confirm we have the correct answer.
Answer:
15 by 6
sorry i dont know how to do it
It would be very appreciated mister
The numbers 1 to 5 are placed in a hat. What is the probability that you will pick the number 1 pm
4, and without replacing the number in the hat, select the number 3? Write your answer as a
simplified fraction. *
And can you please explain what does
SAS-AA-ASA-SSS mean
Answer:
sas means side angle side
aa means angle angle
asa means angle side angle
sss means side side side
hope it helps you
please mark me as brainlist
what device is used to indicate passage of time?
Answer:
Qué unidades se utilizan? El instrumento que utilizamos para medir el tiempo es el reloj. La unidad que utilizaremos como referencia será el día. Con respecto al día, hay unidades de tiempo menores y mayores que el día.
Step-by-step explanation:
Which whole numbers does the square root of 69 falls in between?
Can someone help me?
2b²+17b+21
Thanks
Answer:
(2b+3) (b+7)
Step-by-step explanation:
2b²+17b+21
2b²+14b+3b+21
2b(b+7) + 3(b+7)
(2b+3) (b+7)
Answer:
roots are -3 and -14
Step-by-step explanation:
Calculate for Area. 5 cm
Answer: 25 cm
Step-by-step explanation:
f(x) = 4/9x + 7
linear or nonlinear?
Answer:
linear. :)
Step-by-step explanation:
Answer:
It depends on what you meant. See below.
Step-by-step explanation:
What you wrote means this:
[tex] f(x) = \dfrac{4}{9}x + 7 [/tex]
This is linear.
If you meant this
[tex] f(x) = \dfrac{4}{9x} + 7 [/tex]
or this
[tex] f(x) = \dfrac{4}{9x + 7} [/tex]
then it's non-linear.
An x in the denominator makes a function non-linear.
if f(x) = 5x-20 find f(y+2)
Answer:
f(y + 2) = 5y - 10
Step-by-step explanation:
To evaluate f(y + 2), substitute x = y + 2 into f(x), that is
f(y + 2) = 5(y + 2) - 20
= 5y + 10 - 20
= 5y - 10
identify error GIVEN, bracelets - php200 necklaces php300 sales at least 3600 sells at most 50 pieces of bracelets and necklaces correct the errors
A student received a coupon for 17% off the total purchase price at a clothing store. Let c be the
original price of the purchase. Use the expression below for the new price of the purchase. Write an
equivalent expression by combining like terms.
When you buy a new car it is a depreciating asset. Which means the moment you purchase your car it begins losing value. If you
tried to sell it back to the dealership they would pay you less than you bought it for. The depreciation of a car is around 15% per
year. Complete the graphic organizer below for a car worth $20,000
I can't see the graph but I'll try anyway
Answer:
x y
0 $20,000
1 $18,000
2 $16,200
3 $14,580
4 $13,122
5 $11,809.80
Drag and drop the correct value next to its equivalent expression. Numbers may be used once or not at all.
Answer:
[tex]5(32) = 5(30 + 2)[/tex]
Step-by-step explanation:
Given (omitted from the question)
Expression: 5(32) = ( + )
Numbers: 12, 30, 500, 10, 2, 5
Required
Write an equivalent expression
Express 32 as 30 + 2.
So, we have:
[tex]5(32) = 5(30 + 2)[/tex]
Answer:
I think you meant to add a picture?-
Step-by-step explanation:
I just noticed how late I am lol
answer pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
2: the relation of coefficient of is multiple of 2y
Which expression is equivalent to
(fg) (5)?
F(5)* g(5)
F(5)+g(5)
5f(5)
5g(5)
Answer:
they F (5) g (5)
Step-by-step explanation:
(fg)=(f.g)
and then this is the first doing (fg)(X)= f(x) [g(x)]
x=5
f(5).g(X)
and they final result is
they top of answer
happy answering
The the composition of f and g denoted by the expression (fg)(5) is equivalent to f(g(5))
What is composition of functions?The composition of two functions f and g is an operation where two functions f and g generates a new function h such that h(x)=f(g(x)).
First we find the value of g(x). If g(x)=y then f(g(x))=f(y).
The value of composition (fg)(x) is equal to f(g(x)).
Thus the value of (fg)(5) is f(g(5)) .
If g(5)=c , some c.
Then (fg)(5)=f(g(5))=f(c)
Hence the value of the composition of f and g of 5 is f(g(5)).
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Car dealers sometimes use the rule of thumb that a car loses about 30% of its value each year. 1. Suppose you bought a new car in December 2010 for $15,000. 2. Develop a general formula for the value of the car t years after its purchase. HELP
Answer: [tex]A=15000(1.30)^t[/tex]
Step-by-step explanation:
Formula to find the price of an item after t years after withe a depreciation rate of r% is [tex]A=P(1-\dfrac{r}{100})^t[/tex], where P = Initial value of item.
Given: P = $15,000, r= 30%
Then, the value of car after t years will be :
[tex]A= 15000(1+\dfrac{30}{100})^t\\\\\Rightarrow\ A=15000(1+0.30)^t\\\\\Rightarrow\ A=15000(1.30)^t[/tex]
The required general formula for the value of the car t years after its purchase:
[tex]A=15000(1.30)^t[/tex]
math work pls help :)
the the answer is SAS
side angle side
Pls help ASAP!! Plss
Answer:
c>72
Step-by-step explanation:
−12+c>60
Step 1: Simplify both sides of the inequality.
c−12>60
Step 2: Add 12 to both sides.
c−12+12>60+12
c>72
"A HARFİ ile ilgili atasözleri ve anlamları
Answer:
al sana atasözleri ile igili atasözleri ve anlamları
What is the solution to the equation? 12 = |X| - 3 X= -36 or 36 X= -9 or 9 X = -4 or 4 X = -15 or 15
Answer:
x = -15 or 15
Step-by-step explanation:
We can simplify |x| - 3 = 15 to |x| = 15 because we can add 3 on both sides due to -3 being outside of the absolute value bars. Next, we can say that x is either 15 or -15 because of the absolute value (|15| is equal to 15 and |-15| is also equal to 15).
Point R divides in the ratio 1 : 3. If the x-coordinate of R is -1 and the x-coordinate of P is -3, what is the x-coordinate of Q?
A. -1/3
B. 3
C. 5
D. 6
E. -9
Answer:
C. 5
Step-by-step explanation:
plato
Answer:
C. 5
Hope this helps!
Step-by-step explanation:
someone please help, i’m stuck on this question
Answer:
Step-by-step explanation:
f(-1)=-(-1)²+(-1)
=-1-1
= -2
Answer:
that's the answer for you..
help please I really need it
Answer:
If x is 6, y is 9
Step-by-step explanation:
In your equation, substitute 6 in for each x. This would be (6) + 3y = 4(6) + y.
This ends up being 6 + 3y = 24 + y.
After that, you can subtract y from both sides to get 6 + 2y = 24.
Then you can subtract 6 from both sides to get 2y = 18.
Finally, divide both sides by 2 to get y = 9.
7. The ratio of the weight of cement to the weight of sand in a concrete mixture is 1:3.
Complete the table to show the different weights of cement or sand in the concrete mixture.
Find the GCF ( 50 points!)
Answer:
B
Step-by-step explanation:
Becaus it just is
Answer:yea he right...btw why u cheatin-..on a unit test
Step-by-step explanation: