Thinking Proportionally
In a survey that James conducted of the students in his school, he determined that 3 out of 8 students chose basketball as their favorite sport.
How many students choose basketball as their favorite sport if James surveys 240 students?
90 Students
-19 + _____ = -48
-29
use the distributive property to rewrite each expression in its equivalent form.
-2x(3y+9)
-6xy-18x
What is the probability of flipping a coin and landing on heads
1/2
determine if it is possible to form a triangle using the set of segments with the given measurements. explain your reasoning.
7 in., 8.7 in., 15.4 in.
Yes. It is possible to from a triangle because 7 + 8.7 = 15.7, and 15.7 is greater than 15.4.
36 3/4 gallons of water come out of a hose in 15 minutes. Write the ratio in fractional form and determine the water rate in gallons per hour.
147 gallons per hour
-28.47 - (-33.4)
4.93
rewrite each expression by factoring out the greatest common factor.
-3p^2-4p
-p(3p+4)
Greg is the lead scorer on his school’s hockey team. He scores a goal 3 out of every
4 attempts. Design a simulation to determine the probability Greg will score a goal on his next attempt.
Sample answer: using two coins, assign heads to represent a goal made and tails to represent a goal missed. Flip both coins. if at least one heads comes up, that represents a goal scored by Greg.
You and your friend each construct triangles with the angle measures 15°, 125°, and 40°.Will both triangles have the same size and shape? explain your reasoning.
The triangles will both have the same shape because there is only one way to construct a triangle with the given angles. However, the triangles could have different sizes because you can make the side lengths longer or shorter even if the angles are the same.
Calculate the area of a circle who's diameter is 13 inches
6.5 inches
5/9 x -3/8
-5/24
Solve 3x-5<14 and graph your solution
x<-3
Alexandra is designing a children’s wooden chair. She wants the height of the chairs to best fit younger students. She decides to use the mean height of students in elementary school as a guide. rather than using the heights of all the students in the school, she decides to take a sample of students.
Suppose Alexandra decides to use 15 third graders as the sample. Is this sample a random sample? explain your reasoning.
The sample is not random because the students in other grades have no chance of being selected.
The measure of ∠QRS is 64°. ray RT bisects ∠QRS. What are the measures of ∠QRT and ∠TRS? explain your reasoning.
The measure of ∠QRT is 32° and the measure of ∠TRS is 32°. When a ray bisects an angle, it divides the angle in half and creates two congruent angles.
Karen buys a sweatshirt for $30. The sales tax in her state is 7%. What is the total amount Karen will pay for the sweatshirt, including sales tax?
$32.10
-34.932 ÷ 4.1
-8.52
Delaney’s internet provider charges $14.95 per month plus $5.75 for each gigabyte of data she stores in the cloud.
Write an equation to model the cost per month for this situation.
C= 5.75t + 14.95
Jim has a collection of 40 blocks. each block has a different size, shape, and color. each block has a unique number between 01 and 40 printed on one side. He wants to select 3 pieces at random.
How might Jim randomly choose 3 blocks?
Use a random number table, use a calculator, place the numbers on slips of paper and randomlychoose 3 slips of paper.
The measure of ∠UVW is 23°. What is the measure of an angle supplementary to ∠UVW? What is the measure of an angle complementary to ∠UVW?
The measure of an angle supplementary to ∠UVW is 157°. The measure of an angle complementary to ∠UVW is 67°.
A restaurant bill is $56.39. Estimate a 20% tip.
$11.40
-3/4 x (-2/7) x 4/3
2/7
An airplane is descending from 35,600 feet at a rate of 3200 feet per minute.
Write an equation to represent the airplane’s altitude.
A=35,600 - 3200t
Decide if each of the following sample is a random samples. Explain why or why not.
The principal asks every 20th student from the school roster do they bring their lunch from home or buy lunch in the cafeteria.
Yes. This is a random sample of the entire school population.
Explain why triangles constructed from the same three angles are not necessarily congruent.
Given only the three angles, it is possible to adjust the side lengths such that an infinite number of different triangles can be constructed.