Answer:
1. 200 per two years or 100/year, 2. 4%
Step-by-step explanation:
2700-2500=200 interest earned for two years or 100 per year
principle x interest rate =interest earned per year
2500 x interest rate =100
interest rate =100/2500
interest rate =.04 or 4%
4. There are 10 people in a room. If everyone high fives everyone else exactly once, how many hig flves took place in the room?
Answer:
45
Step-by-step explanation:
Let's do it for smaller numbers first.
0 people -> 0 high fives
1 people -> 0 high fives
2 people -> 1 high fives
3 people -> person 1 high fives 2 then 3
And person 2 high fives 3
->2+1= 3 high fives
4 people -> person 1 high fives 2,3, then 4
And person 2 high fives 3 then 4
And 3 high fives 4
->3+2+1=6
5 people -> person 1 high fives 2,3,4, then 5
And person 2 high fives 3,4, 5
And 3 high fives 4,5
And 4 high fives 5
-> 4+3+2+1=10
So for n people there would be (n-1)+(n-2)+....+3+2+1 high fives or (n-1)n/2 people.
Test:
3 people -> (3-1)3/2=(2)3/2=3
4 people -> (4-1)4/2=(3)4/2=6
5 people -> (5-1)5/2=(4)5/2=10
10 people-> (10-1)10/2=(9)10/2=90/2=45
or you could do 9+8+7+6+5+4+3+2+1 which also gives 45.
The other person has a great answer. Here's another approach.
Let's say we're selecting 2 people to fill slots A and B.
Slot A has 10 choices and slot B has 9 choices (since we can't pick the same person again to fill both slots simultaneously).
We have 10*9 = 90 ways to do this if order mattered.
However, we don't care about the order so we actually have 90/2 = 45 ways
---------------------------
Put another way: we can form a table that has 10 rows and 10 columns.
This table has 10*10 = 100 cells inside it.
Cross off the main diagonal that runs from the upper left corner to the bottom right corner. Any of these cells represent a certain person handshaking with themself, which we don't consider.
We cross of 10 items along this diagonal so we have 100-10 = 90 cells leftover.
Now consider that person A shaking with B can be notated as AB. This is identical to BA because the order doesn't matter. So we have twice as many handshakes counted.
That's why we divide by 2 to go from 90 to 90/2 = 45
-----------------------------
Another way to find the answer is to use the nCr combination formula with n = 10 and r = 2.
Yet another way to find the answer is look at Pascal's triangle. Find the row that has 1,10,45... in it at the start. These values correspond to r = 0, 1 and 2 respectively. We can see that 45 is when r = 2, which means we have 2 people shaking hands and there are 45 ways to have ten people shake hands.
So there are many approaches you can take with this problem.
In a game of chess, a player can either
win, draw or lose.
The probability that Vishi wins any
game of chess is 0.5
The probability that Vishi draws any
game of chess is 0.3
Vishi plays two games of chess.
Work out the probability that Vishi will
lose exactly one of the two games.
Pls answer fast
Answer:
3.4
Step-by-step explanation:
0.5x + 0.3=2
then I subtracted 0.3 from both sides which I got 1.7 then I divided by 0.5x and then I got 3.4
A and B can fill a cistern in 4 hours. A and C can fill
the same cistern in 5 hours. B can fill twice as fast as
C. Find how long C would take to fill the cistern.
Step by step explanation please.
Answer:
20 hours
Step-by-step explanation:
We can work easier if we think in terms of an hour
the first equation that we can write is
A + B = 1/4 (its meaning is that in an hour A and B fill 1/4 of the cistern)
the second equation we can write is
A + C = 1/5 (its meaning is that in an hour A and C fill 1/5 of the cistern)
the third equation that we can write is
B = 2C (its meaning is that in an hour B fill 2 times C the cistern)
now we can substitute the value of B in the first two equations
A + 2C = 1/4
A + C = 1/5
A = 1/5 - C
1/5 - C + 2C = 1/4
C = 1/4 -1/5
C = (5-4)/20
C = 1/20 (this means that in an hour C will fill 1/20 of the cistern, so it takes 20 hours to fill the entire cistern)
A = 1/5 - 1/20
A = (4-1)/20 = 3/20
B = 1/20 *2 = 1/10
A and B can fill a cistern in 4 hours. A and C can fill the same cistern in 5 hours and C would take to fill the cistern 20 hours
We can work easier if we think in terms of an hour
The first equation that we can write is
What is the first equation?A + B = 1/4 (its meaning is that in an hour A and B fill 1/4 of the cistern)
The second equation we can write is
A + C = 1/5 (its meaning is that in an hour A and C fill 1/5 of the cistern)
The third equation that we can write is
B = 2C (its meaning is that in an hour B fill 2 times C the cistern)
now we can substitute the value of B in the first two equations
A + 2C = 1/4
A + C = 1/5
A = 1/5 - C
1/5 - C + 2C = 1/4
C = 1/4 -1/5
C = (5-4)/20
C = 1/20 (this means that in an hour C will fill 1/20 of the cistern, so it takes 20 hours to fill the entire cistern)
A = 1/5 - 1/20
A = (4-1)/20 = 3/20
B = 1/20 *2 = 1/10
A and B can fill a cistern in 4 hours. A and C can fill the same cistern in 5 hours and C would take to fill the cistern 20 hours.
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If 3x - 4y = 15 and -2x + 3y = 10, then x - y = ?
Answer:
x - y = 25
Step-by-step explanation:
3x - 4y = 15
-2x + 3y = 10
Add the two equations together
3x - 4y = 15
-2x + 3y = 10
----------------------
x - y = 25
Answer:
[tex]{\Huge{\underline{\underline{\textbf{\textsf{Answer}}}}}}[/tex]
>> 3x - 4y = 15
>> -2x + 3y = 10
Add the two equations together
>> 3x - 4y = 15
>> -2x + 3y = 10
----------------------
Hence, x - y = 25
WILL GIVE BRANLIEST! pls help thank u sm!! :-) u are all amazing
Answer:
A.)
Step-by-step explanation:
A.)
Answer:
A :)
Step-by-step explanation:
A total of 937 people attended the play.
Admission was $2.00 for adults and $0.75
for students. The total ticket sales
amounted to $1,109. How many students
and adults attended the school play?
Answer:
612 adults & 361 students
Step-by-step explanation:
the volume of a cuboid is 480cm cube,it's breadth and height are 8cm are 6cm respectively find its length
the sum of a number and 12 is 31. Inches hat is the number?
Answer:
n+12=31
n=31-12
n=19
Step-by-step explanation:
Answer:
19
Step-by-step explanation:
Find the area of the square ABCD.
196 is your answer. 14*4 is 56. 14*10 is 140. 56+140 is 196.
The small one only counts for the first multiplication step. 4*4, is 16 so carry the one over and add it in by how much it’s worth when doing 4*1, is 4. 4+1 is 5.
Which line of best fit is the best choice for the data given below?
Answer:
B
Step-by-step explanation:
Points need to be above and below a line of best fit.
Find measurement of IJ please?
Answer:
I’m = 5
Step-by-step explanation:
It seems that both side IN and JK were similar which implies That the shape was divided by five, therefore DC - 25/5 =5
if it’s wrong then I’m sorry this was all i could think of
In triangle CAP if c=7, a=6 and cosP = -3/7, find p
MCR3U1 Culminating 2021.pdf
#7.
A colony of bacteria is introduced into a growth medium. Its initial population
size is 350 thousand. 12 hours later, the colony has grown to a size of
800 thousand. If its population size increases exponentially, determine:
(a)
the exponential growth model for the size of the population Alt), after
t hours.
(b)
the population size after (i) 8 hours and (ii) 24 hours.
(c)
the rate of increase in the population size as a %/hour
(d)
the doubling time of the bacteria population.
Answer:
(a) [tex]y = 350,000 \times (1 + 0.07132)^t[/tex]
(b) (i) The population after 8 hours is 607,325
(ii) The population after 24 hours is 1,828,643
(c) The rate of increase of the population as a percentage per hour is 7.132%
(d) The doubling time of the population is approximately, 10.06 hours
Step-by-step explanation:
(a) The initial population of the bacteria, y₁ = a = 350,000
The time the colony grows, t = 12 hours
The final population of bacteria in the colony, y₂ = 800,000
The exponential growth model, can be written as follows;
[tex]y = a \cdot (1 + r)^t[/tex]
Plugging in the values, we get;
[tex]800,000 = 350,000 \times (1 + r)^{12}[/tex]
Therefore;
(1 + r)¹² = 800,000/350,000 = 16/7
12·㏑(1 + r) = ㏑(16/7)
㏑(1 + r) = (㏑(16/7))/12
r = e^((㏑(16/7))/12) - 1 ≈ 0.07132
The model is therefore;
[tex]y = 350,000 \times (1 + 0.07132)^t[/tex]
(b) (i) The population after 8 hours is given as follows;
y = 350,000 × (1 + 0.07132)⁸ ≈ 607,325.82
By rounding down, we have;
The population after 8 hours, y = 607,325
(ii) The population after 24 hours is given as follows;
y = 350,000 × (1 + 0.07132)²⁴ ≈ 1,828,643.92571
By rounding down, we have;
The population after 24 hours, y = 1,828,643
(c) The rate of increase of the population as a percentage per hour = r × 100
∴ The rate of increase of the population as a percentage = 0.07132 × 100 = 7.132%
(d) The doubling time of the population is the time it takes the population to double, which is given as follows;
Initial population = y
Final population = 2·y
The doubling time of the population is therefore;
[tex]2 \cdot y = y \times (1 + 0.07132)^t[/tex]
Therefore, we have;
2·y/y =2 = [tex](1 + 0.07132)^t[/tex]
t = ln2/(ln(1 + 0.07132)) ≈ 10.06
The doubling time of the population is approximately, 10.06 hours.
can someone please help for brainlest
Answer:
3:1
Step-by-step explanation:
It’s three times the original
Factor the common factor out of each expression: 30+6k+18k^5
Can someone please help me with this? help would be very much appreciated!
Answer:
so sorry i dont know
:(eeeeeeeeeeee
eeeeeeeStep-by-step explanation:
Hello! please helpp
5x divide 7 = y
turn this into a word problem and solve for x and y.
Answer:
5x÷7=y
x=7y/5
Step-by-step explanation:
5x÷7=y
5x=7y
x=7y/5
Round the answer to the nearest hundredth
tan= opp/adjacent
tan= 9/3
tan^-1 (9/3) =72°
how do you do this?
Step-by-step explanation: 6 22 22 51
one orange box is 10 the other box looks like 15
the scale factor is 15/10 or 1.5
the smaller triangle blue box is a 4
multiply 4 by the scale factor 1.5
4 × 1.5 = 6
Kendra is saving to buy a new computer write an expression to represent them out of money she will have if she has a dollar saved and adds D dollar per week for the next 12 weeks
!!URGENT PLEASE HELP!!
A line segment has endpoints A(-6, 1) and B(0, 7). When AB is reflected in the y-axis, triangle ABA’ is formed. Graph ABA’ , you will see and you will be able to prove it is a right triangle. Name the parts of the right triangle, identify the two legs and the hypotenuse. And, Explain how you would prove ABA' is a right triangle?
Answer:
im not sure i need points though
Step-by-step explanation:
The proof is given below
What is right angle triangle?A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly called a rectangled triangle, is a triangle in which one angle is a right angle or two sides are perpendicular. A right angled triangle is a triangle with one of the angles as 90 degreesHow to solve this problem?The steps are as follow:
Reflection about y-axisp(x,y) = p'(-x,y)
A(-6,1) = A'(6,1)
The longest side is AA' is the hypotenuseThe right angle of right triangle is opposite the hypotenuseAB and A'B are the two legs of triangleAB is opposite side
A'B is adjacent side
Length of AA' is 12 unitsThe vertical distance y=6ΔABC = ΔA'BC (both right angle)[tex]A'B=AB=\sqrt{6^{2}+6^{2} }=8.5[/tex]Sin∅=8.5/2∅ = 45° (Angle between AB and AA')Hence we can prove that triangle is right angle triangle
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Find the volume of the irregular
figure.
Answer:
59 cm^3
Step-by-step explanation:
You can split the shape into two rectangular prisms.
3*3*1=9
10*5*1=50
9+50=59
helpppppppppppppppppppppppppp
Answer:
Option D.
Step-by-step explanation:
==>27
r = 3
9r
which means 9x3 = 27.
Avery goes out to lunch. The bill, before tax and tip, was $9.80. A sales tax of 6% was added on. Avery tipped 19% on the amount after the sales tax was added. What was the total cost of the meal, plus tax and tip? Round to the nearest cent.
Answer:
12.36
Step-by-step explanation:
price x sales tax rate =sales tax
9.80 x .06=sales tax
.59=sales tax
price + sales tax=price with sales tax included
9.80+.59=10.39
price with sales tax x tip percentage=tip amount
10.39 x .19=1.97
price with sales tax + tip = total amount
10.39+1.97=12.36
Question
Lila has $40 in a savings account that earns 10% interest, compounded annually.
To the nearest cent, how much interest will she earn in 2 years?
Answer:
$40.8
Step-by-step explanation:
Use the formula
n(1+percentage given/100)[tex]x^{of the given year}[/tex]
PS: the x means nothing just wanted to show you it is an indices
40(1+10/100)^2
40x1.01^2=$40.80
A local chess tournament gives medals for first, second, and third place. There are five students from Midland High, three students from Leasburg High, and six students from Cassville High competing in the tournament.
Which statements are true? Check all that apply.
Order matters in this scenario.
There are 2,184 ways to select a first-place, second-place, and third-place winner.
The probability that all three winners are from Midland High is 0.0275.
The probability that all three winners are from Leasburg High is 0.0046.
The probability that all three winners are from Cassville High is 0.0549
Answer:
There are 2,184 ways to select a first-place, second-place, and third-place winner.
The probability that all three winners are from Midland High is 0.0275.
The probability that all three winners are from Cassville High is 0.0549
Step-by-step explanation:
Since a local chess tournament gives medals for first, second, and third place, and there are five students from Midland High, three students from Leasburg High, and six students from Cassville High competing in the tournament, to determine which of the following statements are true, the following calculations must be performed:
A) There are 2,184 ways to select a first-place, second-place, and third-place winner.
5 + 3 + 6 = 14
14 x 13 x 12 = X
182 x 12 = X
2.184 = X
B) The probability that all three winners are from Midland High is 0.0275.
5/14 x 4/13 x 3/12 = X
0.02747 = X
C) The probability that all three winners are from Leasburg High is 0.0046.
3/14 x 2/13 x 1/12 = X
0.00274 = X
D) The probability that all three winners are from Cassville High is 0.0549
6/14 x 5/13 x 4/12 = X
0.0549 = X
Answer:
A, B, C, E
Step-by-step explanation:
Edg 2021
Branliest?
helppp plzzzz i need this asap!!!!!! i need the domain and range
Using the diagram below, which of the following parts of the triangles are
congruent?
Answer:
C.
Step-by-step explanation:
ACE is a straight line that connects to line AB and line DE.
AB & ED have same gradient which mean that it is parallel.
The parts of triangles which are congruent is ∠A ≅ ∠E which is option (C)
What is congruent triangle?In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the otherCongruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal. We can tell whether two triangles are congruent without testing all the sides and all the angles of the two triangles.How to solve this problem?The steps are as follow:
As ACE is a straight line which connects to line AB and DEAlso the line AB and ED are parallel because their gradient are sameSo from above mention two reasons we can say that their is congruence between angle A and angle ESo the parts of triangles which are congruent is ∠A ≅ ∠E which is option (C)
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Can somebody pls help
Answer:
A, c, d
Step-by-step explanation:
Answer:
C & D
Step-by-step explanation:
In order to find the perimeter, we would need to add all the sides. w+L+w+L would be adding the lengths and the widths. Simplifying this, we would get 2w, because there are 2 sides that are the same width, and 2 sides that are 2 lengths.
w+L+w+L or w+w+L+L or 2w+2L
Hope this helps!
--Applepi101
An umbrella in the same picture is 5cm long. What is the actual length of the umbrella
Answer:
Not possible to answer from the given information
Step-by-step explanation:
Without the picture this cannot be answered
