Arithmetic and Algebra I
x2 - 2(4 - x) = (x + 2)x - 8
All real numbers satisfy this equation.
What is 5000403.02 in expanded notation?
(5×1000000) + (4×100) + (3×1) + (2×0.02)
first to stand up wins 100 points
good job
Kassia has 80 cookies. Each cookie contains 23 grams of sugar.
If the average lethal dose of sugar is 2 kg, what is the maximum amount of her cookies Kassia can eat without dying?
80 cookies
1 gram = 1000 kg
23x < 2000
x < 86.96
Which property is this?
(a)(1) = a
Identity Property of Multiplication
Find the least common multiple for the first 10 natural numbers.
2520
What is 1/7 as a repeating decimal?
0. 142857 142857 142857...
Jorge claims that the area of a sphere is given by (4/3)πr3, where r is the semi-diameter of the sphere.
Find every flaw in Jorge's statement.
The formula, (4/3)πr3, gives the volume of a sphere, not the area.
"Semi-diameter" is synonymous with radius. This is not an error.
(remainder from Jeopardy IV)
Sam is balding at a rate if 5 hairs per day.
How many weeks will it take for him to go completely bald if he starts with 12285 follicles of hair?
351 weeks
In what situation would the two sets of alternate interior angles be congruent?
When the transversal intercepts the parallel lines at a 90o angle, both sets of alternate interior angles are the same.
Given the following:
(a+1)2 = a2 + 2a + 1
33332 = 11108889
Find 33342, without the use of a calculator.
33342 = 11108889 + 6666 + 1
= 11115556
12 + 3{72 - [2 - (20/5) - 3(1 - 5)]2 - (2)(10)} + 1
-200
Edgar is cleaning a 10-metre long extension cable. He must scrub the entire length of the cable, which is completely covered in duct tape residue.
If the cable has a diameter of 1 cm, what is the total area that must be scrubbed?
A Lateral = 2πrh
= 2 π (1/200) (10)
= π/10 m2 or 1000π cm2
Andrew roll a fair die 5 times in succession and records his results: (6, 6, 6, 6, 6)
Tristan rolls the same die 5 more times and records his results: (1, 3, 1, 4, 6)
Which result is more likely to occur? Explain.
Both are equally likely to occur.
Rolling any number on a fair die has the same probability. Each roll is an independent event.
The greek symbol used to represent a ratio of a circle's circumference to its radius. It is equal to 2π.
Tau (τ)
(remainder from Jeopardy IV)
What is the prime factorization of 23456?
25 × 733
Evaluate the sum of the following series:
(2+3) + (2×3) + (23) + (32)
Tetration is repeated exponentiation:
32 = 22² = 16
5 + 6 + 8 + 16 = 35
(remainder from Jeopardy IV)
Jesse has 10 chromosomes;
a potato has N chromosomes;
and a fly has M chromosomes.
If the product of their chromosome counts is 400, what are the chromosome counts of the potato and fly that will result in the lowest sum of total chromosomes?
5 and 8, respectively
(remainder from Jeopardy IV)
A circle and a square have the same area. If the diagonal in the square is k meters long, what is the radius of the circle in terms of k?
A = 1/2 k2
1/2 k2 = πr2
r2 = 1/2π k2
r = k/√(2π) or r = k√(2π)/2π
What is the divisibility rule for 16?
Hint: consider the divisibility rule for 4 and 8.
For a number to be divisible by 4, the last 2 digits must be divisible by 4. The same can be stated for 8 with the last 3 digits.
Following this pattern, it can be concluded that any number whose last 4 digits are divisible by 16 will be divisible. This can be proven by the fact that 10000 is divisible by 16, and any multiple of 10000 added to a multiple of 16 will therefore be divisible.
(remainder from Jeopardy IV)
What is √29 to the nearest tenth?
5.4
Given the following:
4!! = 8
6!! = 48
7!! = 105
Evaluate 9!!
To evaluate n!!, multiply n by all of its preceding natural numbers that have the same parity as n.
9!! = 9×7×5×3×1 = 945
There are 100 people in the room. If 99% of the room is left-handed, how many left-handed people must leave for the room to be 98% left-handed?
Let x represent the amount of people leaving.
99-x/100-x = 98/100
99 - x = 98 - 98/100 x
1 = 2/100 x
x = 50
You may use a calculator for this question.
What is the probability of being born on leap day?
(Reminder: according to the Gregorian Calendar, Leap years include years that are divisible by 4, EXCEPT years that are divisible by 100 but not 400)
Ex. Years 1632 and 2000 are leap years, while 1800 and 1002 are not.
It can be determined that over 400 consecutive years, there will be exactly 97 leap years.
303 normal years × 365 = 110595 days
97 leap years × 366 = 35502 days
Since leap day occurs once every leap year, the probability is 97/110595+35502
= 97/146097 or 0.0664% chance
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