Jeopardy G7 6/24'

Algebra

100

4^4+5^4=

4^4=4*4*4*4=256

5^4=5*5*5*5=625

256+625=881

200

Simplify:

5^0-2abs(-3-5)+2^-1

1-2abs(-8)+1/2

1-2(8)+1/2

1-16+0.5

-14.5

300

Solve for x: 

 2(x+5)-3(x-1)=8x-5

2(x+5)-3(x-1)=8x-5

2x+10-3x+3=8x-5

-x+13=8x-5

18=9x

x=2

400

(2x-6)/x-(x-1)/x=6

(2x-6)/x-(x-1)/x=6

(2x-6)/x-(x-1)/x=6

(2x-6-x+1)/x=6

(x-5)/x=6

x-5=6x

-5=5x

x=-1

500

Draw the number line that would be the solution to this inequality:

-3(x+2)-10<2

-3(x+2)-10<2

-3x-6-10<2

-3x-16<2

-3x<18

x> -6

Geometry

100

The formula for the surface area of a sphere is  4pir^2 . What is the surface area for a sphere with a diameter of 10 cm? Leave your answer in terms of  pi 

d = 10 cm, r = 5 cm 

4pi(5)^2=4pi(25)=100pi

200

Lines m and n are parallel lines. Find the measure of angle x.

x = 48

300

The time on a clock similar to the one below is 2 pm. 2.5 hours later, it is 4:30 pm. How many degrees does the hour hand rotate from 2 pm to 4:30 pm?

360 degrees / 12 hours = 30 degrees per hour

2.5 hours x 30 = 75 degrees

400

Trapezoid (ABCD) is graphed on the coordinate plane and has the 4 vertices (corners). What is the area of the trapezoid?

Point A (-4,2) 

Point B (-2,5)

Point C (3,5)

Point D (3,2)

Area trapezoid = 

1/2(b1+b2)(h)

1/2(7+5)(3)=1/2(12)(3)

18

500

Luffy's mouth is in the shape of a semisphere and has a radius of 6 inches. The formula for the volume of a sphere  4/3pir^3 . Luffy is attempting the fluffy bunny challenge and stuffing marshmallows into his mouth. Assuming each marshmallow has a volume of 20 in³ when compressed, how many marshmallows can Luffy fit in his mouth? Use 3.14 for  pi . 

ANS: 22

Area of sphere =

4/3(3.14)(6^3)=904.32 

Area of semisphere

904.32/2=452.16

452.16/20=22.6

Ratios and Proportions

100

The ratio of girls:boys at a school is 3:2. If there are 81 girls at the school, how many students are there?

3/2=81/b

81/3=27

b=2*27=54

students = 81 + 54 = 135

200

Magnus is creating a juice cocktail using pineapple, orange and apple juice. The amount of pineapple is 4 times the amount of orange juice. The amount of apple juice is  1/3 the amount of orange juice. What is the ratio of apple juice to pineapple juice?

P:O = 4:1 = 12:3

A:O = 1:3 

Ratio of A:P = 1:12

300

The points W, X, Y and Z are on a number line. The ratio of WX: XY:YZ is 2:2:5. What is the length of WZ?

2 + 2 + 5 = 9 parts

WX = 12 units which is equivalent to 2 parts 

1 part is half of 12 = 6 units

9 parts = 9 * 6 = 54 units

400

DOUBLE JEOPARDY - wager your points up to 1000 points

Circle A has a radius that is 2.5 times the radius of Circle B. If Circle B has an area of 40 inches², what is the area of circle A?

500

In a candy jar, there are 42 pieces of candy of which 15 are chocolate. After Julius eats some of the chocolates,  1/4 of the candy are chocolates. How many chocolates did Julius eat?

(15-x)/(42-x)=1/4

4(15-x)=1(42-x)

60-4x=42-x

18=3x

x=6

Statistics and Probability

100

What is the interquartile range for the data set:

9, 0, 1, 5, 6, 7, 10, 12, 1, 10, 10

Rearrange in numerical order first

0, 1, 1, 5, 6, 7, 9, 10, 10, 10, 12

11 values --> median 6th value --> 7

Q1 = median of 1, 1, 1, 5, 6 = 1

Q3 = median of 9, 10, 10, 10, 12 = 10

IQR = Q3 - Q1 = 9 

200

The Box plot below displays the results of a chemistry test. The number of students who took the test was 32. How many students received a score of at least 70? 

75% of students received a 70 or higher = 0.75 x 32

= 24

300

x is a real, integer such that  7<sqrtx<11 , what is the largest possible value for x?

7<sqrtx<11

sqrt49<sqrtx<sqrt121

Since x is an integer, largest possible x = 120

400

The Box plot below displays the results of a chemistry test. The number of students who took the test was 32. What is the mean test score? 

Cannot be determined. We don't know the exact values of the test scores or the sum, so we cannot calculate the mean

500

Draw the number line that would be the solution to this inequality

-3(x-1)+6<10

 -3x+3+6<10 

 -3x+9<10 

 -3x<1 

 x> -1/3 

Miscellaneous

100

If the price of a pair of shoes increases from $80 to $400, what is the percent change?

(400-80)/80*100=320/80*100=400%

200

What is the largest possible integer solution for x in the inequality:   x + 2 < -3.1

x+2<-3.1

x<-5.1

So x must be less than -5.1 and the largest possible integer solution would be -6

ANS: -6

300

 sqrt240  is immediately between which 2 integers?

12² = 144

13² = 169

14² =196

15² = 225

16² = 256

ANS: Between 15 and 16

400

If M = x/y and N = a/b then what is 

(2M)/N

(2M)/N=(2x/y)/(a/b)=(2x)/y*b/a=(2xb)/(ay)

500

What is the inequality that represents the number line below?

Filled in circle at -3 and less than -3 

x < -3 

Open circle at 6 and more than 6

x > 6

x < -3 OR x > 6

Extra Hard (500 points each)

100

The figure below is part of a circle with a slice cut out. What is the perimeter of the figure below?

Circumference = 

2pir

Perimeter = 

(240)/360*2pi(12)+ 2(12)

(2/3)(2pi)(12)+24

16pi+24

200

What is the value of k in the equation:

(x-k)^2=4x^2-6x+9/4

(2x-k)(2x-k)=4x^2-2xk-2xk+k^2

4x^2-4xk+k^2=4x^2-6x+9/4

k^2=9/4

k=3/2

300

Solve for x in the equation:

1-2/x=x/(x+5)

1-2/x=x/(x+5)

(1-2/x=x/(x+5))(x)(x+5)

x^2+5x-2(x+5)=x^2

x^2+5x-2x-10=x^2

3x-10=0

x=10/3

400

Solve for a and b in given the following equations:

3^a*3^b=9 and 2^a/2^b=64

3^a*3^b=9 and 2^a/2^b=64

3^(a+b)=3^2 and 2^(a-b)=2^6

a+b=2 and a-b=6

a=4 and b = -2

500

If the letters in the word Mississippi are rearranged, how many different combinations are possible?

If order matters then combinations = 11!

With 2 i's, divide by 2

With 4 s's, 24 combinations that are really 1 

With 4 i's, 24 combinations that are really 1

Total combinations = 

(11!)/(24*24*2)

ANS: 34,650