Math....You're Done
Draw two triangles with side lengths 9 units and 5 units and an included angle of 115°. Are the triangles the same?
Teacher checks both triangles. Angle of 115° must be inside of the side lengths 9 units and 5 units.
The triangles are the same.
No Calculator! The temperature in a town is 31.9°F during the day and −7.2°F at night. Find the difference in the temperatures.
The difference in temperature is 39.1°F.
Craig likes to collect records. Last year he had 10 records in his collection. Now he has 15 records. What is the percent increase of his collection?
The percent increase of his collection is 50%.
No Calculator! A parachutist descends 40 feet in 4 seconds. Express the rate of the parachutist's change in height as a unit rate.
The unit rate of the parachutist's change in height is −10 feet per second.
The school athletic department is thinking about including tennis lessons in the physical education curriculum. They are thinking about using the methods described below to find out if students like this idea. Identify the sampling method for each description. Does each description produce a representative sample?
A. Survey students at the tennis courts.
B. Survey students whose names were picked out of a hat.
C. Survey every third student entering the school.
B. Simple Random Sample, Representative
C. Systematic Sample, Representative
You bike 14.4 miles in 1.8 hours at a steady rate. What equation represents the proportional relationship between the x hours you bike and the distance y in miles that you travel?
The equation y = 8x represents the distance y in miles you bike in x hours.
A music store bought a CD set at a cost of $20. When the store sold the CD set, the percent markup was 30%. Find the selling price. Round to the nearest dollar as needed.
The selling price was $26.
Describe what the horizontal cross section of a rectangular prism looks like.
The horizontal cross section is a rectangle.
About 50% of people say they like dogs. Design a simulation to estimate the probability that the next three people like dogs. Determine the experimental probability using the simulation.
(5,8,4) (5,3,3) (5,4,2) (1,3,3) (1,3,1) (8,4,4) (7,3,7) (4,4,7)(9,6,2) (4,5,7) (2,5,1) (3,6,9) (4,5,2) (1,3,8) (6,2,5) (6,7,9)(1,2,4) (0,1,0) (4,1,9) (5,3,2)
Simulation Model:
Like Dogs: 0 to 4 Don't Like Dogs: 5 to 9
The experimental probability that the next three people like dogs is 20%.
At noon, a tank contained 8 in. of water. After several hours, it contained 6 in. of water. What is the percent decrease of water in the tank?
The percent decrease of water in the tank is 25%.
A class is flipping a coin to see what the probability of getting heads is. The class flips a coin 41 times and heads comes up 10 times and tails comes up 31 times. What is the experimental probability of getting heads? What is the theoretical probability of getting heads?
The experimental probability of getting heads is 10/41.
The theoretical probability of getting heads is 1/2.
Solve the inequality. Then graph the solutions on a number line.
−4 < −2(2x−6)
The solution is x < 4.
The graph is an open dot on 4 with an arrow to the left.
Suppose you deposit $600 in a bank account with a simple interest rate of 3.3%. You want to keep your deposit in the bank long enough to earn at least $150 in interest. How long should you keep your deposit in the bank? Round up to the nearest year.
To earn at least $150 interest, you should keep your deposit in the bank for 8 year(s).
A tunnel for an amusement park ride has the shape of a regular hexagonal prism. The apothem (distance from one side of the hexagon to the middle) is 7 m. The height of the prism is 21 m. To the nearest cubic meter, what is the volume of the regular hexagonal prism? Round to the nearest whole number as needed.
The volume of the regular hexagonal prism is about 3,572 m^3.
At a graduation dinner, an equal number of guests was seated at each of 6 large tables, and 7 late-arriving guests were seated at a smaller table. There were 67 guests in all. If n represents the number of people seated at each of the large tables, what equation could you use to find the value of n?
The equation is 6n + 7 = 67.
Find the value of x when 6 − 4x = 7x − 9x + 12.
The value of x is -3.
A circular plate has circumference 16.3 inches. What is the area of this plate? Use 3.14 for pi. Round the final answer to the nearest whole number as needed. Round all intermediate values to the nearest thousandth as needed.
The area of this plate is about 21 square inches.
4 1 2 3 9 7
You can make 25,200 passwords.
You can make 3,600 passwords that begin with Z.
In the diagram, m∠1=92°, m∠2=(x+59)°, and m∠3=(y−45)°. Find the values of x and y.
m∠1 and m∠2 are supplementary angles
m∠1 and m∠3 are vertical angles
x = 29
y = 137
No Calculator! In her garden Pam plants the seed 2-3/4 in. below the ground. After one month the tomato plant has grown a total of 12-1/2 in. How many inches is the plant above the ground?
The tomato plant is 9-3/4 in. above the ground.
Squares DEFG and D'E'F'G' are similar. Side DE is 5 units and side D'E' is 20 units. Identify the scale factor for this dilation.
The scale factor is 4.
A company has two manufacturing plants with daily production levels of 7x+19 items and 5x−2 items, respectively. The first plant produces how many more items daily than the second plant?
The first plant produces 2x+21 more items daily than the second plant.
No Calculator! What is the value of −5/4x + 30 when x = −68?
The value is 115.
Mark and Michelle Morrison are celebrating their 15th anniversary by having a reception at a local reception hall. They have budgeted $4,500 for their reception. The reception hall charges a $50 cleanup fee plus $34 per person. Write an inequality that you can use to find the greatest number of people that they can invite and still stay within their budget. Then solve and graph the inequality.
The inequality 34n + 50 less than or equal to 4,500 models the situation.
The inequality n less than or equal to 130 represents the solutions.
The graph is a closed dot on 130 with an arrow to the left.
The selling price of an item is $385. After 6 months of not selling, it is marked down by 20%. After another 6 months of not selling, it is further marked down by 10%. Find the sale price after both markdowns. Round to the nearest dollar as needed.
The sale price after both markdowns is $277.