End Of The Year Exam

An airplane travels at a constant speed of 320 miles per hour. How far, in miles, will the airplane travel in 15 minutes?

Explanation:
To find the distance traveled, use the formula:

Distance = Speed × Time

The speed is given as 320 miles per hour. The time is 15 minutes. First, convert 15 minutes to hours:

15 minutes = 15/60 = 0.25 hours

Now, multiply the speed by the time:

Distance = 320 miles/hour × 0.25 hours = 80 miles

So, the airplane will travel 80 miles in 15 minutes.

• 21.33 miles

• 80 miles

• 4,800 miles

• 800 miles

Answer explanation

To find the distance traveled in 15 minutes, convert 15 minutes to hours: 15/60 = 0.25 hours. Then, multiply the speed by time: 320 mph * 0.25 hours = 80 miles. Thus, the airplane travels 80 miles.

Tags

CCSS.6.RP.A.3D

Ryan is building a tree house. It will take 85¼ hours to complete. He can work on the tree house 15½ hours each week. To the nearest tenth, how many weeks will it take Ryan to complete the tree house?

Explanation:
First, convert the mixed numbers to improper fractions or decimals:
85¼ = 85 + 1/4 = 85.25 hours
15½ = 15 + 1/2 = 15.5 hours per week

To find the number of weeks, divide the total hours by the hours per week:
85.25 ÷ 15.5 ≈ 5.5 weeks

So, it will take Ryan about 5.5 weeks to complete the tree house.

• 54.8

• 15.3

• 5.5

• 3.5

Answer explanation

To find the number of weeks, divide the total hours (85.25) by the hours per week (15.5). This gives 85.25 ÷ 15.5 = 5.5 weeks. Thus, it will take Ryan approximately 5.5 weeks to complete the tree house.

Tags

CCSS.7.EE.B.3

What is the value of x when ¹/₃ x = 9 ¹/₃?

Explanation:
To solve for x, we need to isolate x on one side of the equation.

Given: ¹/₃ x = 9 ¹/₃

This means x divided by 3 equals 9 1/3.

Step 1: Convert 9 1/3 to an improper fraction.
9 1/3 = (9 × 3 + 1)/3 = 28/3

Step 2: Set up the equation:
x / 3 = 28/3

Step 3: Multiply both sides by 3 to solve for x:
x = 28/3 × 3 = 28

So, the value of x is 28.

• 28

• 3⅓

• 27

• 2¾

Answer explanation

To solve \( \frac{1}{3} x = 9 \frac{1}{3} \), convert \( 9 \frac{1}{3} \) to an improper fraction: \( 9 \frac{1}{3} = \frac{28}{3} \). Multiply both sides by 3: \( x = 28 \). Thus, the value of x is 28.

Tags

CCSS.6.EE.B.7

Jenny has finished 12 of the 20 lessons in her piano book. Liam has finished the same percent of lessons from his piano book. His book contains 30 lessons. How many lessons has Liam finished?

Explanation:
First, find the percent of lessons Jenny has finished:
Jenny: 12 out of 20 lessons.
Percent = (12/20) × 100 = 60%.
Liam has finished 60% of his 30-lesson book.
Number of lessons = 60% of 30 = (60/100) × 30 = 18.
So, Liam has finished 18 lessons.

• 13

• 2.5

• 12

• 18

Answer explanation

Jenny has completed 12 out of 20 lessons, which is 60%. Liam's book has 30 lessons, so he has finished 60% of 30, which is 0.6 * 30 = 18 lessons. Therefore, the correct answer is 18.

Tags

CCSS.6.RP.A.3C

Sam is using the expression ^m/_8n in class. What is the value of the expression when m = 4 and n =¹/₂ ?

Explanation:
Let's substitute the given values into the expression:
m = 4, n = 1/2

The expression is m/(8n).

Substitute the values:
= 4 / (8 × 1/2)
= 4 / (8 × 0.5)
= 4 / 4
= 1

So, the value of the expression is 1.

• 1

• 16

• 32

• 28

Answer explanation

Substituting m = 4 and n = 1/2 into the expression m/(8n) gives 4/(8*(1/2)) = 4/(8/2) = 4/4 = 1. Thus, the value of the expression is 1.

Tags

CCSS.6.EE.A.2C

There are 4 trucks for every 5 cars in a parking lot. How many trucks and cars could be in the parking lot?

Explanation:
Let the number of trucks be 4x and the number of cars be 5x, where x is a positive integer. The total number of trucks and cars must be in the ratio 4:5.
Now, check each option:

• Option A: 64 trucks and 80 cars. 64/80 = 4/5, so this matches the ratio.
• Option B: 72 trucks and 73 cars. 72/73 is not 4/5.
• Option C: 84 trucks and 100 cars. 84/100 = 21/25, not 4/5.
• Option D: 96 trucks and 110 cars. 96/110 = 48/55, not 4/5.

So, the correct answer is 64 trucks and 80 cars.

• 64 trucks and 80 cars

• 72 trucks and 73 cars

• 84 trucks and 100 cars

• 96 trucks and 110 cars

Answer explanation

The ratio of trucks to cars is 4:5. For every 4 trucks, there are 5 cars. The correct choice, 64 trucks and 80 cars, maintains this ratio (64/80 = 4/5). Other options do not fit the ratio.

Jamal scored 62, 75, 76, and 90 on four tests. What does he need to score on the fifth test in order to have a mean of exactly 80?

Explanation:
To find the score Jamal needs on the fifth test, let the unknown score be x.
The mean of five tests should be 80, so:
(62 + 75 + 76 + 90 + x) / 5 = 80
Adding the known scores: 62 + 75 + 76 + 90 = 303
So, (303 + x) / 5 = 80
Multiply both sides by 5: 303 + x = 400
Subtract 303 from both sides: x = 400 - 303 = 97
Therefore, Jamal needs to score 97 on the fifth test to have a mean of exactly 80.

• 80

• 100

• 93

• 97

Answer explanation

To find the score needed on the fifth test for a mean of 80, calculate the total score required: 80 * 5 = 400. The current total is 62 + 75 + 76 + 90 = 303. Thus, Jamal needs 400 - 303 = 97 on the fifth test.

Tags

CCSS.6.SP.B.5C

Seventy-five 6th-grade students chose to watch a movie on the last day of school. This is 25% of the 6th-grade class. How many total students are in the 6th grade?

Explanation:
Let the total number of 6th-grade students be x.
25% of x equals 75 students.
So, 0.25 × x = 75
To find x, divide both sides by 0.25:
x = 75 ÷ 0.25 = 300
Therefore, there are 300 students in the 6th grade.

• 100

• 200

• 300

• 400

Answer explanation

If 75 students represent 25% of the class, to find the total, divide 75 by 0.25. This gives 75 / 0.25 = 300. Therefore, there are 300 students in the 6th grade.

Tags

CCSS.6.RP.A.3C

This table shows the number of minutes Carol and Anna walked each day for 5 days. Which statement is true?

Detailed Explanation:
Let's calculate the mean and median for both Carol and Anna.

Carol's data: 60, 30, 20, 70, 45
Sorted: 20, 30, 45, 60, 70
Mean = (60+30+20+70+45)/5 = 225/5 = 45
Median = 45 (middle value)

Anna's data: 45, 35, 60, 65, 30
Sorted: 30, 35, 45, 60, 65
Mean = (45+35+60+65+30)/5 = 235/5 = 47
Median = 45 (middle value)

Now, let's check each statement:
1. Carol’s mean for the number of minutes she walked is equal to her median. True (Both are 45)
2. Carol’s mean is greater than Anna’s mean. False (45 < 47)
3. Anna’s median is greater than her mean. False (45 < 47)
4. Anna’s mean is equal to Carol’s mean. False (47 ≠ 45)

Correct answer: Carol’s mean for the number of minutes she walked is equal to her median.

• Carol’s mean for the number of minutes she walked is equal to her median.

• Carol’s mean for the number of minutes she walked is greater than Anna’s mean.

• Anna’s median for the number of minutes she walked is greater than her mean.

• Anna’s mean for the number of minutes she walked is equal to Carol’s mean.

Answer explanation

Carol's mean equals her median because her walking times are symmetrically distributed. This means the average and the middle value of her walking minutes are the same, confirming the first statement as true.

Tags

CCSS.6.SP.B.5C

• 15

• 20

• 25

• 30