To ensure Lionel does not exceed the maximum weight of the elevator, we need to subtract his weight from the maximum weight capacity of the elevator to find out how much weight is available for the boxes of books.
Maximum elevator weight: 2,000 pounds
Lionel's weight: 170 pounds
Weight available for boxes = Maximum elevator weight - Lionel's weight
Weight available for boxes = 2,000 pounds - 170 pounds
Weight available for boxes = 1,830 pounds
There are 10 equal boxes of books to be loaded. To find out the maximum weight each box can be, divide the total available weight by the number of boxes:
Weight per box = Weight available for boxes / Number of boxes
Weight per box = 1,830 pounds / 10
Weight per box = 183 pounds
Each box can weigh up to 183 pounds without exceeding the elevator's weight limit.
Lionel is loading boxes of books into an elevator to move to the 35th floor of an office building. There are 10 boxes of books, and Lionel wants to make sure he is not exceeding the maximum weight of the elevator, which is 2,000 pounds. Lionel weighs 170 pounds. If each box of books weighs the same amount, how much can each box weigh?
19 answers
Kris currently has $190 and plans to earn more money each of the 8 weekends this summer. She wants at least $1,625 by the end of the summer. Write and solve an inequality for the amount of money Kris needs to earn each weekend. Which answer choice best interprets the solution in the context of the problem? (1 point)
• Kris needs to earn $13.13 each hour to meet her goal.
Kris needs to earn at least $179.38 each weekend to meet her goal.
• Kris needs $179.38 more to meet her goal.
• Kris needs to earn $105 more to meet her goal.
• Kris needs to earn $13.13 each hour to meet her goal.
Kris needs to earn at least $179.38 each weekend to meet her goal.
• Kris needs $179.38 more to meet her goal.
• Kris needs to earn $105 more to meet her goal.
To write an inequality for the amount of money Kris needs to earn each weekend, we need to denote her current savings and the amount she needs to reach. Let's denote the amount she needs to earn each weekend as x.
Kris's current savings: $190
Kris's goal: $1,625
Number of weekends: 8
The amount Kris earns over the 8 weekends, plus her current savings, should be at least equal to her goal:
Current savings + 8 * (Amount earned each weekend) ≥ Goal
190 + 8x ≥ 1,625
Now let's solve for x:
8x ≥ 1,625 - 190
8x ≥ 1,435
Dividing both sides by 8 to find x:
x ≥ 1,435 / 8
x ≥ 179.375
This means Kris needs to earn at least $179.375 each weekend to meet her goal. Given that we generally do not deal with fractional cents when it comes to money, we round up to the nearest cent.
Therefore, Kris needs to earn at least $179.38 each weekend to meet her goal. The answer choice that best interprets the solution is:
• Kris needs to earn at least $179.38 each weekend to meet her goal.
Kris's current savings: $190
Kris's goal: $1,625
Number of weekends: 8
The amount Kris earns over the 8 weekends, plus her current savings, should be at least equal to her goal:
Current savings + 8 * (Amount earned each weekend) ≥ Goal
190 + 8x ≥ 1,625
Now let's solve for x:
8x ≥ 1,625 - 190
8x ≥ 1,435
Dividing both sides by 8 to find x:
x ≥ 1,435 / 8
x ≥ 179.375
This means Kris needs to earn at least $179.375 each weekend to meet her goal. Given that we generally do not deal with fractional cents when it comes to money, we round up to the nearest cent.
Therefore, Kris needs to earn at least $179.38 each weekend to meet her goal. The answer choice that best interprets the solution is:
• Kris needs to earn at least $179.38 each weekend to meet her goal.
Jada has challenged herself to do at least 100 full push-ups this week. On Sunday, she does 30 push-ups. Her arms are sore, so she decides to do fewer push-ups on the remaining days of the week. She wants to do the same number of push-ups each day for the rest of the week. Write and solve an inequality for the number of push-ups Jada needs to do each day for the rest of the week to meet her goal of 100 push-ups. Which answer choice best interprets the solution in the context of the problem?
(1 point)
• Jada needs to do push-ups for at least 12 more days to meet her goal.
• Jada needs to do at least 14 push-ups each day for the rest of the week to meet her goal.
• Jada needs to do at least 12 push-ups each day for the rest of the week to meet her goal.
• Jada needs to do at least 10 push-ups each day for the rest of the week to meet her goal.
(1 point)
• Jada needs to do push-ups for at least 12 more days to meet her goal.
• Jada needs to do at least 14 push-ups each day for the rest of the week to meet her goal.
• Jada needs to do at least 12 push-ups each day for the rest of the week to meet her goal.
• Jada needs to do at least 10 push-ups each day for the rest of the week to meet her goal.
To solve the inequality for the number of push-ups Jada needs to do each day for the rest of the week to meet her challenge, let's start by identifying the total number of push-ups left to reach her goal and the number of days she has to complete them.
Jada's weekly goal: 100 push-ups
Push-ups done on Sunday: 30 push-ups
Remaining push-ups needed to reach her goal = Goal - Push-ups already done
Remaining push-ups needed = 100 - 30
Remaining push-ups needed = 70 push-ups
Jada has the rest of the week to complete these push-ups. Since she did 30 on Sunday, she has 6 days left (Monday through Saturday).
Let's denote y as the number of push-ups Jada plans to do each day for the remaining 6 days.
6y ≥ 70
Now, divide both sides by 6 to find y:
y ≥ 70 / 6
y ≥ 11.666...
Since Jada can't do a fraction of a push-up, she needs to round up to the nearest whole number to meet her goal.
Therefore, Jada needs to do at least 12 push-ups each day for the rest of the week to meet her goal. The answer choice that best interprets the solution is:
• Jada needs to do at least 12 push-ups each day for the rest of the week to meet her goal.
Jada's weekly goal: 100 push-ups
Push-ups done on Sunday: 30 push-ups
Remaining push-ups needed to reach her goal = Goal - Push-ups already done
Remaining push-ups needed = 100 - 30
Remaining push-ups needed = 70 push-ups
Jada has the rest of the week to complete these push-ups. Since she did 30 on Sunday, she has 6 days left (Monday through Saturday).
Let's denote y as the number of push-ups Jada plans to do each day for the remaining 6 days.
6y ≥ 70
Now, divide both sides by 6 to find y:
y ≥ 70 / 6
y ≥ 11.666...
Since Jada can't do a fraction of a push-up, she needs to round up to the nearest whole number to meet her goal.
Therefore, Jada needs to do at least 12 push-ups each day for the rest of the week to meet her goal. The answer choice that best interprets the solution is:
• Jada needs to do at least 12 push-ups each day for the rest of the week to meet her goal.
Teddy is solving the following problem: James earns $400 a week plus $5 in tips for each customer he serves. He is hoping to earn more than $1,000 this week. How many customers would he have to serve to meet his goal? Describe the solutions. Teddy writes the inequality 5x + 400 > 1, 000, where x is the number of customers James serves. Teddy solves the inequality and finds that ∞ > 120. How should Teddy interpret this solution in the context of the problem? (1 point)
• James needs to earn more than $120 each day this week to meet his goal.
James needs to serve more than 120 customers this week to meet his goal.
• James needs to serve at least 120 customers this week to meet his goal.
• James needs to earn at least $120 each day this week to meet his goal.
• James needs to earn more than $120 each day this week to meet his goal.
James needs to serve more than 120 customers this week to meet his goal.
• James needs to serve at least 120 customers this week to meet his goal.
• James needs to earn at least $120 each day this week to meet his goal.
Teddy's inequality 5x + 400 > 1,000 represents the situation well, where x is the number of customers James serves. To solve this inequality:
5x + 400 > 1,000
First, we need to isolate x:
5x > 1,000 - 400
5x > 600
Next, divide by 5 to find x:
x > 600 / 5
x > 120
The inequality "x > 120" means James needs to serve more than 120 customers this week to meet his goal. It does not mean that there's an infinite number of solutions greater than 120; it simply means James needs to serve any number of customers greater than 120 to earn more than $1,000.
Teddy should interpret the solution as:
• James needs to serve more than 120 customers this week to meet his goal.
This interpretation best fits the solution Teddy found. James serving 120 customers, when multiplied by $5 per customer, would give James exactly $600 in tips, plus his $400 base pay, equalling $1,000. But since he wants to earn more than $1,000, he needs to serve more than 120 customers.
5x + 400 > 1,000
First, we need to isolate x:
5x > 1,000 - 400
5x > 600
Next, divide by 5 to find x:
x > 600 / 5
x > 120
The inequality "x > 120" means James needs to serve more than 120 customers this week to meet his goal. It does not mean that there's an infinite number of solutions greater than 120; it simply means James needs to serve any number of customers greater than 120 to earn more than $1,000.
Teddy should interpret the solution as:
• James needs to serve more than 120 customers this week to meet his goal.
This interpretation best fits the solution Teddy found. James serving 120 customers, when multiplied by $5 per customer, would give James exactly $600 in tips, plus his $400 base pay, equalling $1,000. But since he wants to earn more than $1,000, he needs to serve more than 120 customers.
Which expression does this number line represent?
4
-in
(1 point)
© 4-3
0 -3 + (-4)
0 3 + (-7)
0 -3-4
4
-in
(1 point)
© 4-3
0 -3 + (-4)
0 3 + (-7)
0 -3-4
It seems that there may have been a formatting issue or an error in the way the question has been asked as it appears incompletely presented. It looks like you are trying to describe a number line and asking which arithmetic expression it represents.
From what I can see, there are some numbers and addition/subtraction signs provided, but without additional information like the positioning of these numbers on the number line, it's difficult to give a definitive answer. If you could provide the way the numbers are arranged or any specific points marked on the number line, I can give you the correct expression.
In a number line, positive numbers are usually to the right of 0, and negative numbers are to the left. Addition would move you to the right, and subtraction would move you to the left. If you meant to present a sequence of movements on the number line that started at 4 and then involved moving left (subtracting) 3, then right (adding negative numbers exacerbates the move left), the expression would reflect those movements.
For instance:
- If you start at 4 and then move left 3, that would be expressed as "4 - 3"
- If you further move left 4 more, that can be expressed as "4 - 3 - 4" or "4 + (-3) + (-4)"
- If you start at 4, move left 3 and then left 7 more, it would be "4 - 3 - 7" or "4 + (-3) + (-7)"
Without the proper number line representation or clarification of the numbers' arrangement, it's challenging to determine which expression is correct. If you can provide a more detailed description or the arrangement of the number line, I would be able to help you accurately.
From what I can see, there are some numbers and addition/subtraction signs provided, but without additional information like the positioning of these numbers on the number line, it's difficult to give a definitive answer. If you could provide the way the numbers are arranged or any specific points marked on the number line, I can give you the correct expression.
In a number line, positive numbers are usually to the right of 0, and negative numbers are to the left. Addition would move you to the right, and subtraction would move you to the left. If you meant to present a sequence of movements on the number line that started at 4 and then involved moving left (subtracting) 3, then right (adding negative numbers exacerbates the move left), the expression would reflect those movements.
For instance:
- If you start at 4 and then move left 3, that would be expressed as "4 - 3"
- If you further move left 4 more, that can be expressed as "4 - 3 - 4" or "4 + (-3) + (-4)"
- If you start at 4, move left 3 and then left 7 more, it would be "4 - 3 - 7" or "4 + (-3) + (-7)"
Without the proper number line representation or clarification of the numbers' arrangement, it's challenging to determine which expression is correct. If you can provide a more detailed description or the arrangement of the number line, I would be able to help you accurately.
Sarah was writing a report about the weather in Fairbanks, Alaska. Sarah included this information about the weather in Fairbanks in her report.
• Average Summer Temperature: 64°F
• Average Winter Temperature: -10°F
What was the difference between the average summer temperature and the average winter temperature in °F?
(1 point)
• 27°F
• 39°F
© 54°F
~ 74°F
• Average Summer Temperature: 64°F
• Average Winter Temperature: -10°F
What was the difference between the average summer temperature and the average winter temperature in °F?
(1 point)
• 27°F
• 39°F
© 54°F
~ 74°F
To find the difference between the average summer temperature and the average winter temperature in Fairbanks, Alaska, we simply subtract the winter temperature from the summer temperature. Since we're looking for the difference, we'll ignore the signs and focus on the absolute difference.
Average Summer Temperature: 64°F
Average Winter Temperature: -10°F
Difference = Average Summer Temperature - (Average Winter Temperature)
Since the winter temperature is negative, subtracting a negative is the same as adding a positive:
Difference = 64°F - (-10°F)
Difference = 64°F + 10°F
Difference = 74°F
The difference between the average summer temperature and the average winter temperature in Fairbanks is 74°F.
The correct answer is:
~ 74°F
Average Summer Temperature: 64°F
Average Winter Temperature: -10°F
Difference = Average Summer Temperature - (Average Winter Temperature)
Since the winter temperature is negative, subtracting a negative is the same as adding a positive:
Difference = 64°F - (-10°F)
Difference = 64°F + 10°F
Difference = 74°F
The difference between the average summer temperature and the average winter temperature in Fairbanks is 74°F.
The correct answer is:
~ 74°F
McKenna and Benjamin are competing in a diving competition. McKenna's dive ended -50 m from the starting platform. Benjamin's dive ended -25 m from the starting platform. How many times farther was the end of
McKenna's dive than the end of Benjamin's dive? (1 point)
• 1,250
• 500
• 125
2
McKenna's dive than the end of Benjamin's dive? (1 point)
• 1,250
• 500
• 125
2
To determine how many times farther McKenna's dive was than Benjamin's dive, we can divide the depth of McKenna's dive by the depth of Benjamin's dive.
McKenna's dive depth: -50m
Benjamin's dive depth: -25m
Since we are comparing distances, we will consider the absolute values of these depths because distance is a scalar quantity and is always positive.
The ratio of McKenna's dive to Benjamin's is thus:
Absolute depth of McKenna's dive / Absolute depth of Benjamin's dive
= 50m / 25m
= 2
This means that McKenna's dive was 2 times farther than Benjamin's dive. The answer is 2.
McKenna's dive depth: -50m
Benjamin's dive depth: -25m
Since we are comparing distances, we will consider the absolute values of these depths because distance is a scalar quantity and is always positive.
The ratio of McKenna's dive to Benjamin's is thus:
Absolute depth of McKenna's dive / Absolute depth of Benjamin's dive
= 50m / 25m
= 2
This means that McKenna's dive was 2 times farther than Benjamin's dive. The answer is 2.
If the temperature dropped by 36 degrees over 6 hours, how much did the temperature change per hour?
(1 point)
O -6°F
9 -7°F
О -42°F
0 -64°F
(1 point)
O -6°F
9 -7°F
О -42°F
0 -64°F
To find out how much the temperature changed per hour, divide the total temperature change by the number of hours:
Total temperature change: -36 degrees
Number of hours: 6 hours
Change per hour = Total temperature change / Number of hours
Change per hour = -36 degrees / 6 hours
Change per hour = -6 degrees per hour
The temperature changed by -6 degrees per hour.
The correct answer is:
O -6°F
Total temperature change: -36 degrees
Number of hours: 6 hours
Change per hour = Total temperature change / Number of hours
Change per hour = -36 degrees / 6 hours
Change per hour = -6 degrees per hour
The temperature changed by -6 degrees per hour.
The correct answer is:
O -6°F
On a given morning, the temperature was 52°F. The temperature dropped 7°F and then rose 11°F. How much does the temperature need to rise or fall to return to the initial temperature of 52°F? (1 point)
• Fall 4°F
• Rise 3°F
• Fall 7°F
• Rise 11°F
• Fall 4°F
• Rise 3°F
• Fall 7°F
• Rise 11°F
Let's track the changes in the temperature to find out what needs to happen to return to the initial temperature of 52°F.
The initial temperature was 52°F.
Then the temperature dropped 7°F:
52°F - 7°F = 45°F
Next, it rose 11°F:
45°F + 11°F = 56°F
Now the temperature is at 56°F. To find out how much the temperature needs to change to return to the initial temperature of 52°F, we compare the current temperature to the initial temperature:
56°F (current temperature) - 52°F (initial temperature) = 4°F
Since the result is positive, this means the temperature needs to fall by 4°F to return to the initial temperature of 52°F.
The correct answer is:
• Fall 4°F
The initial temperature was 52°F.
Then the temperature dropped 7°F:
52°F - 7°F = 45°F
Next, it rose 11°F:
45°F + 11°F = 56°F
Now the temperature is at 56°F. To find out how much the temperature needs to change to return to the initial temperature of 52°F, we compare the current temperature to the initial temperature:
56°F (current temperature) - 52°F (initial temperature) = 4°F
Since the result is positive, this means the temperature needs to fall by 4°F to return to the initial temperature of 52°F.
The correct answer is:
• Fall 4°F
Determine which of these illustrates two quantities that combine to make 0. (1 point)
• The football player gains 8 yards and then a penalty causes the team to move back 5 yards.
• Madisyn spent $5 on a movie ticket and then spent $5 on popcorn.
• Lauryn deposited $20 in her bank account and then used her debit card for $20 on gas.
• Madalyn gets ten dollars for her allowance and then spends eight dollars at the store.
• The football player gains 8 yards and then a penalty causes the team to move back 5 yards.
• Madisyn spent $5 on a movie ticket and then spent $5 on popcorn.
• Lauryn deposited $20 in her bank account and then used her debit card for $20 on gas.
• Madalyn gets ten dollars for her allowance and then spends eight dollars at the store.
To find two quantities that combine to make 0, we need to look for a situation where the amount gained is equal to the amount lost, so the net effect is zero.
• The football player gains 8 yards and then a penalty causes the team to move back 5 yards. This does not combine to make 0 because 8 - 5 = 3.
• Madisyn spent $5 on a movie ticket and then spent $5 on popcorn. This results in spending $10 in total, not a combination that equals 0.
• Lauryn deposited $20 in her bank account and then used her debit card for $20 on gas. This does combine to make 0 because +$20 - $20 = 0. This means the money deposited has been canceled out by the money spent on gas.
• Madalyn gets ten dollars for her allowance and then spends eight dollars at the store. This does not combine to make 0 because +$10 - $8 = $2.
The correct answer that illustrates two quantities combining to make 0 is:
• Lauryn deposited $20 in her bank account and then used her debit card for $20 on gas.
• The football player gains 8 yards and then a penalty causes the team to move back 5 yards. This does not combine to make 0 because 8 - 5 = 3.
• Madisyn spent $5 on a movie ticket and then spent $5 on popcorn. This results in spending $10 in total, not a combination that equals 0.
• Lauryn deposited $20 in her bank account and then used her debit card for $20 on gas. This does combine to make 0 because +$20 - $20 = 0. This means the money deposited has been canceled out by the money spent on gas.
• Madalyn gets ten dollars for her allowance and then spends eight dollars at the store. This does not combine to make 0 because +$10 - $8 = $2.
The correct answer that illustrates two quantities combining to make 0 is:
• Lauryn deposited $20 in her bank account and then used her debit card for $20 on gas.
1 answer