Lois needs at least 750 gigabytes of storage to take pictures and videos on her upcoming vacation. She checks and finds that she has 215 gigabytes available on her phone. She plans on buying additional memory cards to get the rest of the storage she needs. The cheapest memory cards she can find each hold 256 gigabytes
Let C represent the number of memory cards that Lois buys.
Which inequality describes this scenario?
A.215C+256≤750
B.215+256C≤750
C.215+256C≥750
D.215C +256≥750
2.Water freezes at 32°F /Write an inequality for all temperatures that water is NOT frozen.
A.x≤32
B.x>32
C.x<32
D.x≥32
3.Mrs. Simmons' math class is planning to going on a field trip. The school bus which is taking them can hold at most 44 people. Write an inequality to represent the number of students who can attend the field trip on the bus.
A. s<44
B. s>44
C.s≤44
D.s≥44
The speed limit sign on the expressway says that the speed limit is 70mph. Write an inequality that represents all speeds you can legally drive on the expressway.
A.x>70
B.x≥70
C.x<70
D.x≤70
Hazel is trying to solve this inequality. After she solves it, she shows it to you, and she asks you if she did it correctly. This is the work she completed:
3(t+1)−4t≥−5
Step 1: 3t +3−4t≥−5
Step 2: −t+3≥−5
Step 3: −t≥−8
Step 4: t≥8
Part A: In which step did Hazel make a mistake?
Part B: How would you explain to Hazel what her mistake was, so she won't make the mistake again on a future test?
pleassee help i don't want to fail
1. To determine the inequality that describes the scenario, we need to consider the amount of storage Lois needs and the available storage on her phone. Since Lois needs at least 750 gigabytes and has 215 gigabytes available on her phone, she will need to buy additional memory cards. Let's represent the number of memory cards Lois buys with C.
Since each memory card holds 256 gigabytes, the total storage she will have from the memory cards is 256C. Thus, the inequality would be:
215 + 256C ≥ 750
Therefore, the correct answer is option C: 215 + 256C ≥ 750.
2. The temperature at which water freezes is 32°F. To represent all temperatures at which water is NOT frozen, we need to have an inequality that excludes 32°F.
Since we want to represent all temperatures greater than 32°F, the correct inequality would be:
x > 32
Therefore, the correct answer is option B: x > 32.
3. The school bus has a maximum capacity of 44 people. To represent the number of students who can attend the field trip on the bus, we need to consider the maximum limit of 44.
Since the inequality represents the maximum number of students, it would be:
s ≤ 44
Therefore, the correct answer is option C: s ≤ 44.
4. The speed limit on the expressway is 70mph. To represent all speeds that are legal on the expressway, we need an inequality that allows speeds up to and including 70mph.
Therefore, the correct inequality would be:
x ≤ 70
Therefore, the correct answer is option D: x ≤ 70.
5. Part A: Hazel made a mistake in Step 2.
Part B: Hazel made the mistake when she subtracted 3 from both sides of the inequality. Instead of subtracting 3, she should have added 3 to both sides. This mistake changes the sign of the inequality.
To explain it to Hazel, you can say that she made an error in the sign when subtracting 3 from both sides. When subtracting a positive number, the inequality sign should remain the same. So the correct step 2 should be:
-3t + 3 ≥ -5
By correcting this mistake, the further steps and the final answer would be accurate.