Linear Equations and Inequalities
Here is a linear equation in two variables:
2x+4y-31=123
Solve the equation for x.
x=77-2y
Function P gives the perimeter of an equilateral triangle of side length s. It is represented by the equation P(s)=3s.
What does P(s)=60 mean in this situation?
The perimeter of an equilateral triangle of side length s is 60.
A sea turtle population p is modeled by the equation p=400(5/4)^y where y is the number of years since the population was first measured.
How many turtles are in the population when it is first measured? Where do you see this in the equation?
400, this is the coefficient of the expression (5/4)^y and the value of p when y=0.
The data set represents the number of errors on a typing test.
5, 6, 8, 8, 9, 9, 10, 10, 10, 12
What is the median? Interpret this value in the situation.
9 errors. Half of the people had 9 errors or more and half had 9 errors or fewer.
A copy machine can print 480 copies every 4 minutes.
How many copies can it print in 10 minutes?
1,200 copies, because the rate is 120 copies per minute, and 120 x 10 = 1,200
Tyler goes to the store. His budget is $125. Write an inequality representing x, the amount in dollars Tyler can spend at the store.
x is less than or equal to 125
x<=125
W gives the weight of a puppy, in pounds, as a function of its age, t, in months.
Describe the meaning of W(6)>W(4)
The puppy weighed more when it was 6 months old than when it was 4 months old.
A sea turtle population p is modeled by the equation p=400(5/4)^y where y is the number of years since the population was first measured.
Is the population increasing or decreasing? How can you tell from the equation?
The population is increasing. Since 5/4>1, this means that the population increases by 1/4 each year.
Select all the statistical questions.
A: What is the typical amount of rainfall for the month of June in the Galapagos Islands?
B: How much did it rain yesterday at the Mexico City International Airport?
C: Why do you like to listen to music?
D: How many songs does the class usually listen to each day?
E: How many songs did you listen to today?
F: What is the capital of Canada?
G: How long does it typically take for 2nd graders to walk a lap around the track?
A, D, and G
Andre lives 1.6 km from school. What is 50% of 1.6 km?
0.8 km
The entrepreneurship club is ordering potted plants for all 36 of its sponsors. One store charges $8.50 for each plant plus a delivery fee of $20. The equation 320=x+7.50(36) represents the cost of ordering potted plants at a second store.
What does the x represent in this situation?
The delivery fee at the second store
A small bus charges $3.50 per person for a ride from the train station to a concert. The bus will run if at least 3 people take it, and it cannot fit more than 10 people.
Function B gives the amount of money that the bus operator earns when n people ride the bus.
Identify all numbers that make sense as inputs and outputs for this function.
The inputs are whole numbers between 3 and 10.
The outputs are all multiples of $3.50 between $10.50 and $35.
The value of a home in 2015 was $400,000. Its value has been doubling each decade.
If v is the value of the home, in dollars, write an equation for v in terms of d, the number of decades since 2015.
v=400,000x2^d
For which distribution shape is it usually appropriate to use the median when summarizing the data?
A: bell-shaped
B: skewed
C: symmetric
D: uniform
B: Skewed
Two planes travel at a constant speed. Plane A travels 2,800 miles in 5 hours. Plane B travels 3,885 miles in 7 hours. Which plane is faster? Explain your reasoning.
Plane A is faster. Plane A travels 2800/5=560 or 560 miles per hour. Plane B travels 3885/7=555, or 555 miles per hour. Plane A travels a farther distance in one hour.
The environmental science club is printing T-shirts for its 15 members. The printing company charges a certain amount for each shirt plus a setup fee of $20.
If the T-shirt order costs a total of $162.50, how much does the company charge for each shirt?
$9.50
The population of a city grew from 23,000 in 2010 to 25,000 in 2015.
What was the average rate of change during this time interval?
400 people per year
A fish population, p, can be represented by the equation p=800x(1/2)^t where t is time in years since the beginning of 2015.
What was the fish population at the beginning of 2012?
6,400
A student has these scores on their assignments. The teacher is considering dropping a lowest score. What effect does eliminating the lowest value, 0, from the data set have on the mean and median?
0, 40, 60, 70, 75, 80, 85, 95, 95, 100
The mean increases from 70 to approximately 77.78. The median increases from 77.5 to 80.
A kangaroo hops 2 kilometers in 3 minutes. At this rate:
Jada has p pennies and n nickels that add up to more than 40 cents. She has fewer than 20 coins altogether.
Write a system of inequalities that represents how many pennies and nickels that Jada could have.
0.01p+0.05n>0.40
p+n<20
The number of years, y, is a function of the number of months, m. The number of months, m, is also a function of the number of years, y.
1. m=12y and y=m/12
2.
The population of a city in 2010 is 50,000, and it grows by 5% each year after.
Write a function f which models the population of the city years after 2010.
f(t)=50,000(1.05)^t
What is the five-number summary (Minimum, Q1, Median, Q3, Maximum) for the data 2, 2, 4, 4, 5, 5, 6, 7, 9, 15?
When the maximum, 15, is removed from the data set, what is the five-number summary?
At a hardware store, a tool set normally costs $80. During a sale this week, the tool set costs $12 less than usual. What percentage of the usual price is the savings?
15%, because 12/80=3/20=15/100.