Exponent Properties
This is the same as aman.
If a & b = 2a + b2, than this is the value of 4 and 6.
What is 44?
4 & 6 = 2(4) +62 = 8+36 = 44
This is the sum of the digits of the product 11 x 111 x 11,111.
What is 30?
11 x 111 x 11,111
=11,111 x (100+10+1) x (10+1)
=(1,111,100 + 111,110 + 11,111) x (10+1)
=11,111,000 + 1,111,100 + 1,111,100 + 111,110 + 111,110 + 11,111
=1x30 + 0X9 = 30
This is the number must be added to 4884 to equal the product of 48 and 84.
What is -852?
48x84 = 4032
4884 + x = 4032
x= -852
This is the difference of squares:
a2-b2=
What is (a+b)(a-b)?
This is the same as (am)n.
What is amn?
If each Mathlete solves, on average, 30 problems in 40 minutes, this is many problems will 12 Mathletes solve in an hour.
What is 540 problems?
Each Mathlete solves, on average, 30 problems in 40 minutes. So 12 Mathletes will solve 12x30=360 problems in 40 minutes. 360 problems divided by 40, is 9 problems per minute. So in 60 minutes, they complete 9x60 = 540 problems.
Let n represent a mystery three-digit number whos digits have a sum of 15. If the hundreds digit is a perfect square number, this is the possible values for n.
What are 20 values?
The three positive perfect squares in this range are 1, 4, 9. We are looking for 3-digit numbers that have a sum of 15. If 1 is in the hundred's digit, the 5 possible values are 159, 168, 177, 186, and 195. When the hundred's digit is 4, there are 8 possibilities: 429, 438, 447, 456, 465, 474, 483 and 492. When the hundred's digit is 9, there are 7 possible values: 906, 915, 924, 933, 942, 951, and 960.
Therefore, 5 + 8 +7 = 20.
A school bus driver runs three morning routes to take kids to school and two routes in the late afternoon to take kids back home. If the routes average 46 miles, this is how many miles the driver will cover in three 5-day weeks and one 4-day a week.
What is 4370 miles?
The bus driver drives 46 x 5 = 230 miles per day. Together, three 5-day weeks and one 4-day week equals 3(5) +4 = 19 days. That's a total of 230 x 19 = 4370 miles.
This is the midpoint of line AB if
A=(x1,y1) and B=(x2,y2)
What is
((x1+x2)/2),((y1+y2)/2)
This is the same as (ab)m.
What is ambm?
Nena invented a new and unusual unit of distance known as the luftballoon, defined to be exactly 640 inches. If there are 5280 feet in a mile, this is how many luftballoons are in mile.
What is 99 luftballoons in a mile?
5280*12 = 63360
inches in a mile so there are
63360/640 = 99
luftballoons in a mile.
Pablo walked around a 400 meter track at his school 3 times each day of May, June, July, and August. This is how many kilometers in total did he walk during those months. (Express your answer as a decimal to the nearest hundredth).
What is 147.6 km?
Pablo walked 400 x 3 = 1200 meters each day. There are a total of 31 + 30 +31 + 31 = 123 days in months May-August. So, Pablo walked
1200*123 = 147600
meters, which is
147000/1000 = 147.6 km.
A fair, standard six-sided dice is rolled twice. This is the probability that the sum of the numbers rolled is divisible by 5, expressed in as a common fraction.
What is 7/36?
When rolling a pair of dice, there are only two possible sums that are divisible by 5 which are 5 and 10. There are 4 outcomes that yield a sum of 5: (1,4) (2,3) (3,2) (4,1). There are 3 ways to roll a sum of 10: (6,4) (5,5) (4,6). Since there a 6x6=36 total outcomes, the fraction would be 7/36.
This is the formula for distance between two given points:
A (x1, y1) and B (x2, y2)
What is
d=sqrt((x2-x1)^2+(y2-y1)^2
This is the same as am/an?
Two part answer hint: A cannot equal this number....
What is am-n when a does not equal 0?
A middle school band sold raffle tickets to raise money. Tickets sold for $5 each, and the net profit from ticket sales was $900. If the only expense was the $150 prize, this is how many raffle tickets were sold.
What is 210 raffle tickets?
If the net profit was $900, then 900+150=$1050 the total amount made from raffle tickets. Then, since they are $5 a ticket, we need 1050/5=210 raffle tickets.
This is how many different arrangements of the letters in the word ALGEBRA have no two consonants next to each other.
What is 72 arrangements?
Since ALGEBRA has 7 letters, 4 consonants (c) and 3 vowels (v), the only arrangements that have no two adjacent consonants have the form CVCVCVC. There are 4! = 4x3x2x1 = 24 arrangements. There are 2 As for the vowels, so there are only 3 arrangements in this format. Therefore, 24x3 = 72.
This is the distance between the points (-1,15) and (8,-3), expressed as an answer to the nearest whole number.
What is about 20 units?
The distance formula is
sqrt [(-1-8)^2+(15-(-3))^2]
sqrt ((-9)^2+22]
9 sqrt (5)
= 9x2.2 = 19.8 which is approximately 20 units.
This is the formula for slope between two given points:
A (x1, y1) and B (x2, y2)
What is
(y2-y1)/(x2-x1)
This is the same as am/n.
What is
rootn(a^m) = (rootn(a))^m
If 2 yats are equal to 3 yots, 4 yits are equal to 7 yuts, and 2 yuts are equal to 5 yots, this is how many yats are equal to 12 yits.
What is 35 yats?
12 yits = 12yits ((7yuts)/(4yits))((5yots)/(2yuts))((2yats)/(3yots))=((12*7*5*2)/(4*2*3))yats=35 yats
A rectangle has an area of 392 in2, and its length is twice its width. This is the perimeter of this rectangle.
What is 84 inches?
Cut the rectangle in half so we have two squares. The area of the square is 196 in2. and the side length is the
sqrt 196 = 14.
The width of the rectangle is 14 and the length is 28. So the perimeter equals 2(14+28) = 84 inches.
This is the value of 1-2+4-5+7-8+...+97-98+100.
What is 67?
Notice the expression is the sum of 33 differences, each equal to -1 and 100. So, 1-2+4-5+7-8+...+97-98+100 = -1x33+100 = 67
This theorem helps the mathematician solve for the side lengths if the triangle is a right triangle.
(Extra 50 points if you can also give the formula)
What is the Pythagorean Theorem?
AND a2+b2=c2?