Geometry
Which set of number may represent the lengths of the sides of a triangle?
A) 2, 5, 9
B) 6, 6, 7
C) 6, 4, 2
D) 7, 8, 1
B) 6, 6, 7
Triangle Inequality Theorem: The sum of the two shorter sides must be greater than the longest side.
6+6>7
What is 0.095 as a percent?
Move the decimal two places to the right.
0.095=9.5%
Answer: 9.5%
What is the formula for constant of proportionality?
k=
k=y/x
Write an equation for the following statement.
The product of a number and 8 is one more than 72.
Answer: 8n+1=72
Find the mean, median, mode and range of the 5 numbers below.
1, 2, 3, 4, 5
Mean=
Median=
Mode=
Range=
1, 2, 3, 4, 5
Mean=aka average=sum/n
15/5=3
Mean=3
Median=middle number
Median=3
Mode=most frequent number
No mode - there are no numbers that repeat
Range=Max-Min
Range=5-1=4
Answer: Mean=3, Median=3, Mode= No mode, Range=4
In triangle ABC, m<A=520 and m<B=680. Find the measure of the third angle.
52+68=120
180-120=60
Answer: 600
12 is what percent of 48?
Hint: is/of
12/48
Reduce the fraction.
12/48=1/4
1/4=25%
Answer: 25%
Yesterday Paige drove 22 1/2 miles and used 1 1/4 gallons of gas. What is her unit rate for miles per gallon?
Hint: Per gallon means that x must be the number of gallons.
miles/gallons.... 22.5/1.25=18
Answer: 18 miles per gallon
Evaluate.
5+(-3)2*4
Use order of operations, PEMDAS, to evaluate.
5+(-3)2*4
5+9*4
5+36
41
Answer: 41
You are choosing an outfit to wear for Activity night. You have the following choices: three pairs of pants, four shirts, and two belts. Find the total number of possible outfits consisting of one pair of pants, one shirt, and one belt.
3 pants*4 shirts*2 belts=24 outfits
Answer: 24 possible outfits
Find the circumference of a circle with a diameter of 25 meters. Use the pi key for pi). Round to the nearest tenths.
The diameter, d, is 25 m.
c=pi*d
c=pi*25
c=78.5398...
Answer: 78.5 m
18 is 60% of what number?
Hint: is over of ....
is/of
18/x=60/100
Cross multiply.
60x=1800
Divide by 60.
x=30... This means that 18/30=60%
Answer: 30
Valerie is 30 inches tall and casts a shadow that is 12 inches long. At the same time, her teddy bear casts a shadow that is eight inches long. How tall is the teddy bear?
Hint: Draw a picture of two similar triangles.
30/12=x/8
Cross multiply.
12x=240.
x=20
Answer: 20 inches
The sum of three consecutive integers is 54. Find all three numbers.
Set up a let statement, write an equation, then solve your equation.
Let:
x= small number
x+1=middle number
x+2=large number
Sum of numbers=54
3x+3=54
3x=51
x=17.... The smallest integer is 17.
Answer: 17, 18, 19
Find the mean, median and mode for the data set below.
1, 21, 3, 12, 2, 7, 11, 2
Mean=
Median=
Mode=
Mean... Add the numbers in the list. Divide the sum by the number of numbers in the list.
sum=59
There are 8 numbers in the list. Divide 59 by 8.
59/8=7.375
Mean=3.75
Median...The median is the number in the middle.
List the numbers from least to greatest.
1, 2, 2, 3, 7, 11, 12, 21
Median s between 3 and 7. 3+7=10 and 10/2=5
Median=5
Mode... Think most. The mode is the most frequent number or numbers to repeat itself in a list. If no numbers repeat, then there is no mode. If there is a tie for the most repeats, then there is more than one mode.
The mode is 2 because that is the number that we have the most of.
Answer: Mean=7.375, Median=5, Mode=2
Draw a picture.
<A and <B are complementary. m<A=4x+5 and m<B=5x+4.
Solve for x.
Complementary means that the angle sum is 900.
4x+5+5x+4=90
9x+9=90
9x=81
x=9
Answer: x=9
The price of a cell phone rose from $90 to $125. Find the percent of increase. Round your answer to the nearest 100th.
Hint: change/og
90---->125
+35
35/90=0.388888...=38.8888...%
Round to the nearest 100ths place.
Answer: 38.89% increase
Find the actual length of a train if a model train that uses a scale of 7 inches to 90 feet is 35 inches long.
Write a proportion. Start with the scale.
inches over feet... 7/90=35/x
Cross multiply.
7x=3,150
x=450
Answer: 450 feet
Solve for n then graph your solution.
2.25n+0.75n+4<25
2.25n+0.75n+4<25
Add like terms first.
3n+4<25
3n<21
n<7
Answer: n<7
The graph should be a number line. Only the solutions are shaded. All number less than 7 are shaded on the number line.
7 is circled but is not shaded because 7 is not less than 7. The number less than 7 (on the left) are shaded.
What is the probability of rolling a 3 on a standard die and getting a tails when tossing a coin?
Answer: 1/12
Find the radius of the circle with area of 50.24 square centimeters, using 3.14 for pi.
A=pi*r2
50.24=3.14*r2
Divide by 3.14...
16=r2
4=r
Answer: The radius is 4 cm.
Jessica bought shoes that regularly sells for $48. They are on sale at a 25% discount and the sales tax is 8%. Find...
A) Discount=
B) Sale price=
C) Tax=
D) Final price=
A) Discount=(25%)(48)
Discount=$12
B) Sale price=48-12
Sale price=$36
C) Tax=(8%)(36)
Tax=$2.88
D) Final price=36+2.88
Final price=$38.88
A 4-pack of bottled Starbucks Frappuccinos cost $7.80. Calculate the unit price per bottle, then calculate how much it would cost if you wanted to buy 6 bottles.
Unit price= $/quantity
$7.80/4 bottles=$1.95/bottle
1.95*6=11.70
Answer: Unit price=$1.95 per bottle and 6 bottles cost $11.70.
You have $30 and you are buying one movie ticket and some candy. If admission to the movie theater is $12 per person and each box of candy costs $3.50, how many boxes of candy can you purchase?
Set up a let statement, write an equation, then solve your equation.
Let x=# of boxes of candy
3.50x+12=30
3.50x=18
x=5.142...
You cannot buy a portion of a box. You can buy 5 boxes.
Answer: 5 boxes
A bag contains 15 marbles. There are 5 orange, 4 yellow, and 6 red in a bag. Once a marble is drawn, it is not replaced. Find the probability in simplest form of selecting an orange marble on your first draw and then a red marble on the second draw.
Compound probability...Find the probability of each event and then multiply.
P(O, R)=5/15*6/14
I reduced the fractions before I multiplied.
=1/3*3/7=1/1*1/7=1/7
Answer: 1/7