Elise has budgeted $800 in her checking account to spend during the summer for entertainment. She would like to have at least $200 available at the end of summer. If Elise withdraws $50 per week, which inequality could she use to determine the greatest number of weekly withdrawals (w) she can make without exceeding her budget?
Let's start by defining the variables:
- w = number of weekly withdrawals
- c = amount of money in Elise's checking account
Each week, Elise withdraws $50, so the amount of money in her checking account after w weeks is:
c = $800 - $50w
Elise would like to have at least $200 available at the end of summer, so the amount of money left in her checking account after w weeks needs to be greater than or equal to $200:
c ≥ $200
Substituting the value of c from the first equation, we have:
$800 - $50w ≥ $200
Simplifying the inequality, we get:
- $50w ≥ $200 - $800
- $50w ≥ -$600
Multiplying both sides by -1 and flipping the inequality sign:
$50w ≤ $600
Therefore, the inequality that Elise can use to determine the greatest number of weekly withdrawals (w) she can make without exceeding her budget is: w ≤ $600 / $50.
Elise has budgeted $800 in her checking account to spend during the summer for entertainment. She would like to have at least $200 available at the end of summer. If Elise withdraws $50 per week, which inequality could she use to determine the greatest number of weekly withdrawals (w) she can make without exceeding her budget?
Responses
A 200 + 50w > 800200 + 50w > 800
B 800 − 50w ≥ 200800 − 50w ≥ 200
C 800 + 50w ≥ 200800 + 50w ≥ 200
D 800 − 50w > 200
Let's analyze the options provided one by one:
Option A: 200 + 50w > 800
This inequality states that the total amount Elise spends throughout the summer, represented by 200 + 50w, is greater than her initial budget of $800. However, Elise wants to make sure she does not exceed her budget. Therefore, this option does not accurately represent the situation.
Option B: 800 − 50w ≥ 200
This inequality states that the amount of money remaining in Elise's account after w withdrawals, represented by 800 - 50w, is greater than or equal to $200. This accurately represents the situation as Elise wants to ensure she has at least $200 remaining at the end of the summer.
Option C: 800 + 50w ≥ 200
This inequality states that the amount of money in Elise's account after w withdrawals, represented by 800 + 50w, is greater than or equal to $200. This does not accurately represent the situation as it implies that Elise has more than $800 in her account.
Option D: 800 − 50w > 200
This inequality states that the amount of money remaining in Elise's account after w withdrawals, represented by 800 - 50w, is strictly greater than $200. This does not accurately represent the situation as Elise wants to ensure she has at least $200 remaining, not necessarily more.
Therefore, the correct answer is option B: 800 − 50w ≥ 200.
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05:10
Question
Find the area of the gray shaded region in the figure.
Responses
A 120 ft2
120 ft 2
B 130 ft2
130 ft 2
C 720 ft2
720 ft 2
D 1140 ft2
1140 ft 2
Unfortunately, I am unable to see the figure or the gray shaded region mentioned in the question. Could you please provide a more detailed description or upload an image of the figure?
the grey figure is 50ft by 30 ft by 24 ft
To find the area of the gray shaded region, we need to determine the surface area of the figure.
The figure is a rectangular prism with dimensions:
Length = 50 ft
Width = 30 ft
Height = 24 ft
The surface area of a rectangular prism can be calculated using the formula:
Surface Area = 2lw + 2lh + 2wh
Substituting the given dimensions into the formula:
Surface Area = 2(50)(30) + 2(50)(24) + 2(30)(24)
Surface Area = 3000 + 2400 + 1440
Surface Area = 6840 ft^2
Therefore, the area of the gray shaded region in the figure is 6840 ft^2.
Answer: The correct option is C) 720 ft^2.
Some of the dimensions of a rectangular pyramid are shown in the diagram. The prism is not drawn to scale. The height of the rectangular pyramid is 17 meters.
What is the volume of the pyramid in cubic meters
Responses
A 112 m³112 m³
B 1,904 m³1,904 m³
C 8,553 m³8,553 m³
D 170 m³
To find the volume of a rectangular pyramid, we use the formula:
Volume = (1/3) * base area * height
From the diagram, it is mentioned that the height of the rectangular pyramid is 17 meters. However, we are not given the dimensions of the base (length, width).
Therefore, without the information about the dimensions of the base, we cannot determine the volume of the pyramid. The correct response cannot be determined based on the information provided.
Please provide the dimensions of the base of the pyramid to calculate the volume accurately.