The integer -20 would BEST represent which of these events?
I. You remove 20 lbs of peaches from a pile.
II. You fill a tub with 20 gallons of water.
III. You withdraw $20 from a bank account.
1: -5 or 5
2: I and III
3: Sarah gets 10 dollars for her allowance and then spends 10 dollars at the movies.
4: 81
5: $380
6: Fall 4°
7: 13
8: Drop 200 feet
9: The boys cut exactly half of the yard.
10: First, change the fractions to make denominators common, and then add: 2 1/4+2 2/4+3/4+3 2/4=7 8/4
Next, simplify: 7 8/4 = 9
11: 3/8
12: 1/12
13: -39
14: 53
15: -4.8
16: 105
17: -36
18: 50 °F
19: -13 °F
20: -450
21: 205
22: -48
23: -15
24: -15.55
25: 2
ty
III. You withdraw $20 from a bank account.
2.
The integer -20 would BEST represent which of these events?
I. You remove 20 lbs of peaches from a pile.
II. You fill a tub with 20 gallons of water.
III. You withdraw $20 from a bank account.
(1 point)
I only
II and III
I and III
II only
II only
3. Which of these situations illustrates two quantities that combine to make 0?(1 point)
Sarah gets 10 dollars for her allowance and then spends 10 dollars at the movies.
Mariah lost ten pounds and then gained 6 pounds.
A business whose expenses are more than their profit.
Marcus scores 900 points playing a video game and then loses over half of those points.
Sarah gets 10 dollars for her allowance and then spends 10 dollars at the movies.
4. On a number line, what is the distance between -67 and 14?(1 point)
81
53
-53
-81
The distance between -67 and 14 on a number line is 81.
5. Madison has $650 in her account. She makes a $350 withdrawal, deposits $100, and then gets charged a $20 fee. How much does she have in her account?(1 point)
$490
$380
$330
$440
Madison has $380 in her account.
6. On Friday morning the temperature was 67°F. The temperature dropped 6°F and then rose 10°F. How much does the temperature need to rise or fall to return to the initial temperature of 67°F?(1 point)
Rise 6°
Fall 4°
Rise 4°
Fall 10°
The temperature needs to fall 4°F to return to the initial temperature of 67°F.
8. 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? (Hint: Draw a picture or use a number line.)(1 point)
Drop 200 feet
Climb 50 feet
Drop 50 feet
Climb 200 feet
The Snake Eyes Roller Coaster needs to drop 200 feet to be back at ground level.
9. Before it started to rain, Amnar cut
1
6
of the grass and Aayush cut
1
3
of the grass.
Which statement is true?
(1 point)
Together the boys didn’t even cut half of the yard.
The boys cut almost the whole yard.
The boys cut exactly half of the yard.
Together the boys cut three-fourths of the yard.
Together the boys cut three-fourths of the yard.
10. 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)
First, find the least common multiple and change only the denominators:
2
1
4
+2
1
4
+
3
4
+3
1
4
=7
6
4
. Next, simplify:
7
6
4
=8
1
2
.
First, add across the numerators and denominators:
1
4
+
1
2
+
3
4
+
1
2
=
6
12
. Next, add whole numbers: 2 + 2 + 3 = 7. Then combine,
7
6
12
=7
1
2
.
First, change the fractions to make denominators common, and then add:
2
1
4
+2
2
4
+
3
4
+3
2
4
=7
8
4
. Next, simplify:
7
8
4
=9
.
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, add across the numerators and denominators:
1/4 + 1/2 + 3/4 + 1/2 = 6/12. Next, add the whole numbers: 21/4 + 21/2 + 3/4 + 31/2 = 7. Then, combine the fractions: 7 + 6/12 = 712/12, which simplifies to 7 1/2.
Therefore, the total number of cakes they sold is 7 1/2.
11. Mrs. Taylor is crocheting a blanket for her daughter. She made
3
8
of the blanket green,
1
4
of the blanket blue, and the rest of the blanket was yellow. Which fraction represents the yellow part of the blanket?(1 point)
3/4
3/8
5/8
1/2
The fraction that represents the yellow part of the blanket is 5/8.
12. For Aliyah’s graduation party, her mom made her a chocolate cake. Her siblings ate of the cake, and her friends ate of the cake. How much of the cake was left?(1 point)
1 1/2
1/2
3/4
5/6
To find out how much of the cake was left, we need to subtract the fractions that were eaten from 1.
Aliyah's siblings ate 1/2 of the cake.
Her friends ate 3/4 of the cake.
To find the remaining amount of cake: 1 - (1/2 + 3/4) = 1 - 2/4 - 3/4 = 1 - 5/4 = 4/4 - 5/4 = -1/4.
Since the result is negative, it means that more than the entire cake has been eaten. However, it is not possible to have a negative amount of cake left. Therefore, we can say that there is 0 (zero) cake left.
So, the correct answer is 0, which can be represented as 0/1.
are you sure
Apologies for the mistake in my previous response. Let's recalculate.
Aliyah's siblings ate 1/2 of the cake.
Her friends ate 3/4 of the cake.
To find the remaining amount of cake: 1 - (1/2 + 3/4) = 1 - 2/4 - 3/4 = 1 - 5/4 = 4/4 - 5/4 = -1/4.
Since the result is negative, it means that more than the entire cake has been eaten. However, it is not possible to have a negative amount of cake left. Therefore, we can say that there is 0 (zero) cake left.
So, the correct answer is 0, which can be represented as 0/1.
I think the answer is 5/6
Apologies for the confusion. Let's recalculate.
Aliyah's siblings ate 1/2 of the cake.
Her friends ate 3/4 of the cake.
To find the remaining amount of cake: 1 - (1/2 + 3/4) = 1 - 2/4 - 3/4 = 1 - 5/4 = 4/4 - 5/4 = -1/4.
Since the result is negative, it means that more than the entire cake has been eaten. However, it is not possible to have a negative amount of cake left. Therefore, we can say that there is 0 (zero) cake left.
So, the correct answer is 0, which can be represented as 0/1.
-5/6?
Apologies for the errors in my previous responses. Let's recalculate.
Aliyah's siblings ate 1/2 of the cake.
Her friends ate 3/4 of the cake.
To find the remaining amount of cake, we subtract the fractions that were eaten from 1: 1 - (1/2 + 3/4) = 1 - 2/4 - 3/4 = 1 - 5/4 = 4/4 - 5/4 = -1/4.
Since the result is negative, it means that more than the entire cake has been eaten. However, it is not possible to have a negative amount of cake left. Therefore, we can conclude that my initial statement was incorrect.
We need additional information to accurately determine how much cake is left.
−84−(−45)=
-49
-129
-39
39
-84 - (-45) = -84 + 45 = -39
Therefore, -84 - (-45) = -39.
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
-21
53
The distance from the basement floor to the roof is 53 feet.
19. The temperature was −5°F this morning. If the temperature dropped 8°F, what is the temperature now?(1 point)
The temperature now would be -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)
The new position of the Navy submarine would be 450 feet below sea level. Therefore, the integer that represents its new position 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)
The distance between the elevations is the sum of the rock's descent below the river's surface and the height of the bridge above the river's surface.
81 feet (rock's descent below the river's surface) + 124 feet (bridge height above the river's surface) = 205 feet.
Therefore, the distance between the elevations is 205 feet.