Calculations I
What is the lowest natural number with exactly 9 factors?
36
8!
40320
Cheese argues that since there are an infinite amount of odd numbers, and an infinite amount of even numbers, the amount of numbers in general must be represented as greater than infinity. What, if anything, is wrong with Cheese's argument?
Arithmetic operations do not apply to infinity. Therefore, the amount of odd numbers, even numbers, and numbers in general are all equal to infinity.
If you scored 72% on an exam and answered 21 questions wrong, how many questions were on the test?
75 questions
Which whole number has the most whole-number factors?
0
(Infinity is not a whole number because it is not a real number)
2x2+4x+2=6x-4x
No solution.
Simplify:
(x2/y)/(y2/x)÷(y/y3x)
x4/y (x,y≠0)
If one team were to answer every single question correctly in this game of jeopardy, then how many points would they have, assuming their first question was for 200 points, and the leading team only earns half the point amount?
3850 points
Write ((((100%)%)%)%)% in scientific notation.
((((100%)%)%)%)% = 100 x 0.015
= 1.0 x 0.014
= 1.0 x (10-2)4
= 1.0 x 10-8
What is the maximum axes of symmetry a rectangle can have?
4
What is the prime factorization of 23456?
25 x 733
Find values for x and y:
x + y = x ⋅ y = xy = yx
x=y=2
If Sam is balding at a rate if 5 hairs every day, how many weeks will it take for him to lose all his hair if he starts with 12285 strands of hair?
351 weeks.
A circle whose area is 144π has an inscribed angle of 10o. What is the area enclosed by the inscribed arc and the corresponding central angle?
The central angle is always double the inscribed angle, so it is 20o. The area of this sector can be found by multiplying the total area by 20o/360o.
144π x 20/360 = 8π units2
What number under 1000, when expressed in Roman numerals, is the largest number that contains exactly two "I"s?
CMXCVII or 997
-1x4=4x-1
Please answer in exact value.
Assume x≠0
-1x4=4x-1
-1x5=4
x5=-4
x= -5√4
What values of x exist for:
a) 1/(|x|-x)
b) (-|x|)^(1/2)
a) x<0
b) x=0
If Jesse has 10 chromosomes, a potato has x chromosomes, a fly has y chromosomes, and the product of their chromosome counts is 400, what is the chromosome count of the potato and fly that will result in the lowest sum of total chromosomes?
5 and 8
The probability of selecting a word in Language I is 1 out of f(n), where f(n)=5/2+5|n-4|/n, and n represents the amount of letters in the word. Find:
a) The probability of selecting a one-letter word
b) Which length of word is most common
a) 2/255
b) 4 letter words are most common
What are skew lines?
Lines on different planes that do not intersect. They can not be parallel.
What is √29 to the nearest tenth?
5.4
What is the largest five-digit perfect square?
99856
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=k2/2
k2/2 = πr2
r2=k2/(2π)
r=k/√(2π) or r=k√(2π)/(2π)
The probability of selecting a word in Language II is 1 out of f(n), where f(n)=1/4+k|n-5|/n, n represents the amount of letters in the word, and k represents a constant. If words in this language range from 1 to 3 letters long, then what is the value of k, to the nearest natural number? A calculator can be used for this question.
k≈2
Since probabilities add up to 1, that means k can be approximated by substituting k into
1/f(1) + 1/f(2) + 1/f(3)
and taking the value that produces the sum that is closest to 1.
What is the formula for the surface area of a sphere?
A=4πr2