What are the dimensions of the smaller rectangle

Reference no: EM133104490

Question 1: James is painting a wooden slat fence he had installed around his backyard. The fence has a total of 180 wooden slats. Suppose James is able to paint 2 slats every 5 minutes. His friend Gabe offers to help him. Together, they finish painting the fence in 3 hours 20 minutes. At what rate did Gabe paint the fence?

a. 0.4 slats per minute
b. 0.5 slats per minute
c. 0.9 slats per minute
d. 1.1 slats per minute

Question 2: In order to create cotton-candy pink paint, the ratio of red paint to white paint must be 7 to 4. In this scenario, which of the following is NOT a correct interpretation of 4/7 ?
a. For every 4 gallons of white paint, there are 7 gallons of red paint in the mixture.
b. The number of gallons of white paint per one gallon of red paint.
c. The constant of proportionality that describes the relationship of white paint to red paint.
d. The slope of the line that represents the relationship of red paint to white paint, with red paint on the horizontal axis and white paint on the vertical axis.

Question 3: Which of the following does NOT represent a proportional relationship?

a. a and b in this equation: a/3b = 1/5
b. Total cost and total number of pizzas ordered if you pay $8 for each pizza.

Number of peanuts in mixture	Number of almonds in mixture
5	10
10	15
15	20
20	25

Question 4: A landscaper wants to install a border around a small rectangular lap pool. The pool measures 12 feet 8 inches long by 8 feet 6 inches wide. He wants the border to be 1 foot wide, as shown in the diagram below:

In order to make the border, the landscaper decides to crush recycled tile and then lay the pieces down in a mosaic. If each tile will cover 4.2/3 square feet, how many tiles will the landscaper need to complete the border? Keep in mind that the landscaper can ONLY buy whole tiles (i.e., he cannot purchase a fraction of a tile).

a. 5
b. 10
c. 24
d. 33

Question 5: The normal price of certain 50-inch LED television set at Buy Big is $799. After Thanksgiving, Buy Big offers the same television set for $615.

i. To the nearest percent, what is the percent decrease in the price of the television set from before Thanksgiving to after Thanksgiving?
ii. If Buy Big decreases the price of the television set by the same rate after Christmas, what will the new sale price be?

a. i. 23% decrease ii. $431.00

b. i. 23% decrease ii. $473.55

c. i. 77% decrease ii. $431.00

d. i. 77% decrease ii. $473.55

Question 6: Maria and Anna are about to run a half-marathon. Maria is able to run 1.6 times faster than Anna. A half-marathon is 13.1 miles long. Which of the following statements is NOT accurate?

a. If Maria can complete the half-marathon in 2 hours, it will take Anna 3.2 hours to finish the half-marathon.
b. If Maria completes the half-marathon in 2.5 hours, then Anna's rate will be 3.28 miles per hour.
c. If Maria's rate is m and t equals time, then the relationship between distance and time for Anna's performance in the half55-marathon can be written as 13.1 = 1.6 × ????
d. If Maria runs the marathon at a rate of 4.2 miles per hour, then it will take Anna almost 2
hours to complete the half-marathon.

Question 7: Consider the tape diagrams below, then answer the question that follows:

Which of the following problems could best be represented by the model above?

a. You placed $4,200 in an investment account. After five years, the total amount in the account appreciated by 25%. At this point, you decided to withdraw one-third of the money in the account to move to a new investment. How much money was left in the account?
b. You placed $5,250 in an investment account. After five years, the total amount in the account depreciated by 20%. It then depreciated by one-third. How much money was left in the account?
c. A furniture dealer buys a sofa from his distributor for $4,200. However, he marks this price up by 20% when he sells it to you. You eventually sell the sofa for a third of what you paid for it. How much did you sell the sofa for?
d. A furniture dealer sold you a sofa for 20% off of $5,250. If you eventually sell the sofa for one-third less than what you paid for it, for how much money did you sell the sofa?

Question 8: In the figure below, the two rectangles are similar:

If the area of the smaller rectangle is 24 in2, and the area of the larger rectangle is 96 in2, what are the dimensions of the smaller rectangle?

a. 4 inches x 6 inches
b. 8 inches x 3 inches
c. 8 inches x 4 inches
d. 12 inches x 2 inches

Question 9: There are 550 students enrolled in Happy Day School. 46% of the students enrolled in Happy Day School are boys. 36% of the students enrolled in Happy Day School are in seventh grade. 50% of seventh graders are boys. What percent of the total number of boys enrolled in Happy Day School are in seventh grade?

a. 18%
b. 36%
c. 39.13%
d. 45.54%

Question 10: A cranberry-pomegranate juice mixture calls for 3 cups of cranberry juice for every 4 cups of pomegranate juice. Tamara has a pitcher that contains 14 cups of this cranberry-pomegranate juice. However, she wants the juice to have a higher volume of pomegranate juice. She adds enough pomegranate juice to change the ratio to 1 cup of cranberry juice for every 2 cups of pomegranate juice. How much pomegranate juice did she add?

a. 2 cups
b. 4 cups
c. 6 cups
d. 12 cups

Reference no: EM133104490

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