14. In the Manchester Building, the elevation of the basement floor is -16 ft. The elevation of the roof is 37 feet. What is the distance from the basement floor to the roof? (Hint: Draw a picture or a number line.)(1 point)
53
-21
-53
21
To find the distance from the basement floor to the roof, we need to subtract the elevation of the basement floor (-16 ft) from the elevation of the roof (37 ft).
37 ft - (-16 ft) = 37 ft + 16 ft = 53 ft
So, the distance from the basement floor to the roof is 53 feet.
Therefore, the correct answer is 53.
11. Mrs. Taylor is crocheting a blanket for her daughter. She made of the blanket green, of the blanket blue, and the rest of the blanket was yellow. Which fraction represents the yellow part of the blanket?(1 point)
5
8
1
2
3
4
3
8
The fraction that represents the yellow part of the blanket is 3/8.
12. For Aliyah’s graduation party, her mom made her a chocolate cake. Her siblings ate
1
4
of the cake, and her friends ate of the cake. How much of the cake was left?(1 point)
3
4
1
12
5
6
1
2
To find out how much of the cake was left, we need to subtract the fraction of the cake that was eaten from 1 (whole cake).
Her siblings ate 1/4 of the cake, and her friends ate 5/6 of the cake.
1 - (1/4 + 5/6)
To add these fractions, we need a common denominator. The common denominator for 4 and 6 is 12.
1 - (3/12 + 10/12)
1 - (13/12)
Since the numerator is greater than the denominator, we can simplify this to a mixed number.
1 - (1 + 1/12)
1 - 1/12
12/12 - 1/12
11/12
So, 11/12 of the cake was left.
Therefore, the correct answer is 11/12.
18. What is the change in temperature between −20°F and 30°F?(1 point)
-50 °F
50 °F
-10 °F
10 °F
To find the change in temperature, we need to subtract the initial temperature from the final temperature.
Final temperature: 30°F
Initial temperature: -20°F
30°F - (-20°F) = 30°F + 20°F = 50°F
So, the change in temperature between -20°F and 30°F is 50°F.
Therefore, the correct answer is 50 °F.
19. The temperature was −5°F this morning. If the temperature dropped 8°F, what is the temperature now?(1 point)
13 °F
-3 °F
-13 °F
3 °F
To find the current temperature, we need to subtract the decrease in temperature from the initial temperature.
Initial temperature: -5°F
Decrease in temperature: 8°F
-5°F - 8°F = -13°F
So, the temperature now is -13°F.
Therefore, the correct answer is -13 °F.
20. A Navy submarine is 650 feet below sea level. If it ascends 200 feet, which integer represents its new position?(1 point)
450
-450
-850
850
To find the new position of the submarine, we need to add the change in position to its initial position.
Initial position: -650 feet
Change in position: +200 feet
-650 feet + 200 feet = -450 feet
So, the new position of the submarine is -450 feet.
Therefore, the correct answer is -450.
21. John threw a rock into a lake from a bridge 124 feet above the river's surface. The rock sinks 81 feet below the river’s surface. What is the distance between the elevations? (Hint: Draw a picture or use a number line.)(1 point)
-43 feet
-205 feet
205 feet
43 feet
To find the distance between the elevations, we need to subtract the depth of the rock below the river's surface from the height of the bridge above the river's surface.
Height of the bridge: 124 feet
Depth of the rock: 81 feet
124 feet - 81 feet = 43 feet
So, the distance between the elevations is 43 feet.
Therefore, the correct answer is 43.
For Aliyah’s graduation party, her mom made her a chocolate cake. Her siblings ate 1/4
of the cake, and her friends ate 2/3
of the cake. How much of the cake was left?
To find out how much of the cake was left, we need to subtract the fractions of the cake that were eaten from 1 (whole cake).
Aliyah's siblings ate 1/4 of the cake, and her friends ate 2/3 of the cake.
1 - (1/4 + 2/3)
We need to find a common denominator to add these fractions. The common denominator for 4 and 3 is 12.
1 - (3/12 + 8/12)
1 - (11/12)
Since the numerator is greater than the denominator, we can simplify this to a mixed number.
1 - (1 + 11/12)
1 - 1/12
12/12 - 1/12
11/12
So, 11/12 of the cake was left.
Therefore, the correct answer is 11/12.
wrong
I apologize for the mistake in my previous response. Let's calculate it correctly this time.
Aliyah's siblings ate 1/4 of the cake, and her friends ate 2/3 of the cake.
To find out how much of the cake was left, we need to subtract the sum of these fractions from 1 (whole cake).
1 - (1/4 + 2/3)
We need to find a common denominator to add these fractions. The common denominator for 4 and 3 is 12.
1 - (3/12 + 8/12)
1 - (11/12)
To subtract the fractions, we need the same denominator.
1 - (11/12) = 1/1 - 11/12
Now, let's find a common denominator for 1/1 and 11/12, which is 12.
12/12 - 11/12 = 1/12
So, 1/12 of the cake was left.
Therefore, the correct answer is 1/12.
The Sweet Surprise Bake Shop sold slices of cake at the arts festival last weekend. Each cake was cut into eight slices. They sold 2 1/4
chocolate cakes, 2 1/2
red velvet cakes, 3/4
of a carrot cake and 3 1/2
sugar cream cakes.
Which statement tells the total number of cakes they sold and explains how the total can be calculated?
(1 point)
Responses
First, change the numerators to 3 to make them common, and then add: 2 3/4+2 3/2+3/4+3 3/4=7 12/14
. Next, simplify: 7 12/14=7 6/7
.
First, change the numerators to 3 to make them common, and then add: 2 and 3 fourths plus 2 and 3 halves plus 3 fourths plus 3 and 3 fourths is equal to 7 and 12 over 14. Next, simplify: 7 and 12 over 14 is equal to 7 and 6 sevenths .
First, change the fractions to make denominators common, and then add: 214+224+34+324=784
. Next, simplify: 784=9
.
First, change the fractions to make denominators common, and then add: 2 and 1 fourth plus 2 and 2 fourths plus 3 fourths plus 3 and 2 fourths is equal to 7 and 8 fourths . Next, simplify: 7 and 8 fourths is equal to 9 .
First, find the least common multiple and change only the denominators: 214+214+34+314=764
. Next, simplify: 764=812
.
First, find the least common multiple and change only the denominators: 2 and 1 fourth plus 2 and 1 fourth plus 3 fourths plus 3 and 1 fourth is equal to 7 and 6 fourths . Next, simplify: 7 and 6 fourths is equal to 8 and 1 half .
First, add across the numerators and denominators: 14+12+34+12=612
. Next, add whole numbers: 2 + 2 + 3 = 7. Then combine, 7612=712
.
First, add across the numerators and denominators: 1 fourth plus 1 half plus 3 fourths plus 1 half is equal to 6 over 12 . Next, add whole numbers: 2 + 2 + 3 = 7. Then combine, 7 and 6 over 12 is equal to 7 and 1 half .
Question 7
The correct statement that tells the total number of cakes sold and explains how to calculate it is:
First, add across the numerators and denominators: 2 1/4 + 2 1/2 + 3/4 + 3 1/2 = 7 12/14. Next, simplify: 7 12/14 = 7 6/7.
Therefore, the total number of cakes sold is 7 and 6/7.
John threw a rock into a lake from a bridge 124 feet above the river's surface. The rock sinks 81 feet below the river’s surface. What is the distance between the elevations? (Hint: Draw a picture or use a number line.)(1 point)
Responses
-43 feet
205 feet
-205 feet
43 feet
To find the distance between the elevations, we need to subtract the depth of the rock below the river's surface from the height of the bridge above the river's surface.
Height of the bridge: 124 feet
Depth of the rock: 81 feet
124 feet - 81 feet = 43 feet
So, the distance between the elevations is 43 feet.
Therefore, the correct answer is 43 feet.
On a number line, what is the distance between -67 and 14?
To find the distance between -67 and 14 on a number line, we can subtract the smaller number from the larger number, regardless of their signs.
14 - (-67) = 14 + 67 = 81
So, the distance between -67 and 14 on a number line is 81.
Therefore, the correct answer is 81.
The Snake Eyes Roller Coaster climbs 125 feet from ground level then drops 60 feet before climbing another 135 feet. How far does the coaster need to drop or climb to be back at ground level?
To find the distance the coaster needs to drop or climb to be back at ground level, we need to add up the distances of the climbs and drops and then take the absolute value to ignore the signs.
Climb: 125 feet
Drop: 60 feet
Climb: 135 feet
Total distance: 125 + (-60) + 135 = 200 feet
However, since we want to find the distance from ground level, we need to take the absolute value of the total distance:
|200| = 200
Therefore, the coaster needs to drop or climb 200 feet to be back at ground level.
In the Manchester Building, the elevation of the basement floor is -16 ft. The elevation of the roof is 37 feet. What is the distance from the basement floor to the roof
To find the distance from the basement floor to the roof, we need to subtract the elevation of the basement floor (-16 ft) from the elevation of the roof (37 feet).
37 ft - (-16 ft) = 37 ft + 16 ft = 53 ft
So, the distance from the basement floor to the roof is 53 feet.
What is the change in temperature between −20°F and 30°F?(1 point)
Responses
To find the change in temperature, we need to subtract the initial temperature from the final temperature.
Final temperature: 30°F
Initial temperature: -20°F
30°F - (-20°F) = 30°F + 20°F = 50°F
So, the change in temperature between -20°F and 30°F is 50°F.
Therefore, the correct answer is 50°F.
A Navy submarine is 650 feet below sea level. If it ascends 200 feet, which integer represents its new position?
To find the new position of the submarine, we need to add the change in position to its initial position.
Initial position: -650 feet
Change in position: +200 feet
-650 feet + 200 feet = -450 feet
So, the new position of the submarine is -450 feet.
Therefore, the correct integer that represents its new position is -450.
John threw a rock into a lake from a bridge 124 feet above the river's surface. The rock sinks 81 feet below the river’s surface. What is the distance between the elevations?
To find the distance between the elevations, we need to add the height of the bridge above the river's surface to the depth of the rock below the river's surface.
Height of the bridge: 124 feet
Depth of the rock: 81 feet
124 feet + 81 feet = 205 feet
So, the distance between the elevations is 205 feet.
Therefore, the correct answer is 205 feet.