GEOMETRY
How many colors are there in a rainbow?
Seven
If x^-2 = 64, what is the value of x^(1/3) + x^0?
Hint= a^-b=1/(a)^b
x^-2 = 64, 1/(x)^2=64, x^2=1/64
Take the square root on both sides,
x=1/8
x^(1/3) + x^0= (1/8)^(1/3) + x^0
(1/2)+1
=3/2
If 1/3 of a number is 4 less than 1/2 of the number, the number is
Let x represent the unknown number. Since 1/3 of x is 4 less than 1/2 of x, x/3 = x/2 - 4. So, 2x = 3x - 24, giving x = 24.
what's the largest organ in the human body?
Skin
What is cynophobia?
A fear of dogs
How many stars are in our solar system?
Just one — the sun!
Let the function f be defined by f(x) = 3x-1 and let the function g be defined by g(x) = x^2. If m is a positive number such that f(7) = g(m) + g(2), what is the value of m?
f(7)=3(7)-1= 20, g(2)=(2)^2=4
f(7) = g(m) + g(2), 20=g(m) +4
g(m)=20-4=16, g(m)=g(x)
g(m)=m^2, 16=m^2 =>Take the square root on both sides,
m=4
Susan weighs p pounds. If Susan gains 17 pounds, she will weigh as much as Carol, who weighs 8 pounds less than Judy. If Judy weighs x pounds, then Susan's weight, p, in terms of x is
s=p, c=s+17<=>c=p+17, c=j-8<=>c=x-8
c=p+17, c=x-8
p+17=x-8, solving for p,
p=x-8-17
p=x-25
Who's the greatest rapper of all time?
Kendrick Lamar & J Cole (it's a tie)!
The cost of admission to an event is $5.00 plus one half of its price. How much does the event cost?
$10.00 Because $5 + 0.5($10) = $10.
What is the name of Simba‘s father?
25ft pole/10ft shadow=xft pole/25ft shadow
cross multiply
25ft pole * 25 ft shadow= xft pole * 10ft shadow
x= (25ft pole * 25 ft shadow)/10ft shadow
62.5 feet. Proportional reasoning with similar triangles.
A culture of 5000 bacteria triples every 15 minutes. What is the size of the bacteria population after 2 hours have elapsed? (Calculator needed.)
Hint: y=a*(b)^x
Where: y=Bacteria population, x= Time
a= Initial amount of Bacteria, b= Multiplier (rate of growth)
y=a*(b)^x Note: There are 8 fifteen minute intervals in 2 hours. Therefore, x=8
y=5000(3)^8
y=32,805,000 Bacteria
How many countries are there in Africa?
54
Three fair coins are tossed at the same time. What is the probability that all three coins will come up heads OR all will come up tails?
Coin toss= 2 possibility (head or tail)
number of tosses=3
(1/2)^3+(1/2)^3=
1/8 (all heads) + 1/8 (all tails) = 2/8
1/4.
Generation Z makes up what percentage of the 2022 U.S. population?
A. 45% B.27% C. 12% D. 33%
What is the equation of the graph obtained by shifting the graph of y=x^2 horizontally to the left 4 units and vertically down 3 units?
Hint: y=(x-h)^2+/-k
where: h=horizontal shift, k=vertical shift
h=-4, k=-3
y=(x-(-4))^2 - 3
y = (x+4)^2 - 3
Jars A, B, and C each contain 8 marbles. What is the minimum number of marbles that must be transferred among the jars so that the ratio of the number of marbles in jar A to the number in jar B to the number in jar C is 1:2:3?
Since jars A, B, and C each contain 8 marbles, there are 24 marbles in the three jars. Let x, 2x, and 3x represent the new numbers of marbles in jars A, B, and C, respectively. Hence, x + 2x + 3x = 24 or 6x = 24, so x=4.
For the system of three equations: x-z=7, x+y=3, z-y=6, what is x?
x-z=7, x+y=3, z-y=6
x=z+7, x=3-y, z=y+6
z+7=3-y<=> y+6+7=3-y
2y=-10, y=-5
x=3-y, x=3-(-5)
x=8
What day is Star Wars Day?
May the 4th be with you:)
What is the number of sides of a polygon in which the sum of the degree measures of the interior angles is 4 times the sum of the degree measures of the exterior angles?
Hint: Sum of the degree measures of exterior angles is 360.
S = (n-2)180, where n=number of sides.
S = (n-2)180 = 4 x 360,
(n-2)= (4*360)/180
Solving for (n-2) = 8
n=10.
Which country has the most pyramids in the world?
Sudan
Fruit for a dessert costs $1.20 a pound. If 5 pounds of fruit are needed to make a dessert that serves 18 people, what is the cost of the fruit needed to make enough of the same dessert to serve 24 people?
If 5 pounds of fruit serve 18 people, then 5/18 pound serves one person, so 24 x 5/18 = 20/3 pounds. Since the fruit costs $1.20 a pound, the cost of the fruit needed to serve 24 people is 20/3 x $1.20 = $8.00.
x, y, 22, 14, 10... In this sequence, each term after the first term x is obtained by halving the term that comes before it and then adding 3 to that number. What is the value of x-y?
(y/2)+3=22
y/2=22-3, y/2=19
y=19*2, y=38
(x/2)+3=38, x/2=38-3, x=35*2, x=70
x=70, y=38.
x-y= 70-38=32.