Question
Which of the following answers gives the best estimate for x given the following equation?
−2x+902=1,518
(1 point)
Responses
300
300
−600
negative 600
600
600
−300
−2x+902=1,518
(1 point)
Responses
300
300
−600
negative 600
600
600
−300
Answers
GPT-4o mini
To solve the equation \(-2x + 902 = 1,518\), we first need to isolate \(x\).
1. Start by subtracting 902 from both sides:
\[
-2x = 1,518 - 902
\]
\[
-2x = 616
\]
2. Now, divide both sides by -2 to solve for \(x\):
\[
x = \frac{616}{-2}
\]
\[
x = -308
\]
Given the options, the best estimate for \(x\) from the provided answers is:
-300
So the correct response is **−300**.
1. Start by subtracting 902 from both sides:
\[
-2x = 1,518 - 902
\]
\[
-2x = 616
\]
2. Now, divide both sides by -2 to solve for \(x\):
\[
x = \frac{616}{-2}
\]
\[
x = -308
\]
Given the options, the best estimate for \(x\) from the provided answers is:
-300
So the correct response is **−300**.
🧋 is life
There are three petri dishes in a laboratory. The first one contains 22,340 cells, the second contains 43,560 cells, and the last dish contains 36,612 cells. Approximately how many cells are there in total?(1 point)
Responses
150,000
150,000
100,000
100,000
1,000,000
1,000,000
10,000
Responses
150,000
150,000
100,000
100,000
1,000,000
1,000,000
10,000
GPT-4o mini
To estimate the total number of cells in the three petri dishes, we can add the number of cells in each dish:
1. First dish: 22,340 cells
2. Second dish: 43,560 cells
3. Third dish: 36,612 cells
Adding these together:
\[
22,340 + 43,560 + 36,612
\]
Calculating step-by-step:
1. \(22,340 + 43,560 = 65,900\)
2. \(65,900 + 36,612 = 102,512\)
So, the total number of cells is approximately \(102,512\).
Among the provided options, the closest estimate is **100,000**.
1. First dish: 22,340 cells
2. Second dish: 43,560 cells
3. Third dish: 36,612 cells
Adding these together:
\[
22,340 + 43,560 + 36,612
\]
Calculating step-by-step:
1. \(22,340 + 43,560 = 65,900\)
2. \(65,900 + 36,612 = 102,512\)
So, the total number of cells is approximately \(102,512\).
Among the provided options, the closest estimate is **100,000**.
🧋 is life
Which of the following answers gives the best estimate for x given the following equation?
x50−94=189
(1 point)
Responses
1,500
1,500
150,000
150,000
150
150
15,000
x50−94=189
(1 point)
Responses
1,500
1,500
150,000
150,000
150
150
15,000
GPT-4o mini
To solve the equation \( x50 - 94 = 189 \), we first simplify and isolate \( x \).
1. Add 94 to both sides of the equation:
\[
x50 = 189 + 94
\]
\[
x50 = 283
\]
2. Now, divide both sides by 50 to solve for \( x \):
\[
x = \frac{283}{50}
\]
\[
x \approx 5.66
\]
Since we are looking for the best estimate for \( x \), none of the given answers (1,500; 150,000; 150; 15,000) match the calculated result of approximately 5.66 closely. However, if we consider only reasonable scales, **150** might be the best estimate.
Therefore, the best estimate for \( x \) from the provided options is **150**.
1. Add 94 to both sides of the equation:
\[
x50 = 189 + 94
\]
\[
x50 = 283
\]
2. Now, divide both sides by 50 to solve for \( x \):
\[
x = \frac{283}{50}
\]
\[
x \approx 5.66
\]
Since we are looking for the best estimate for \( x \), none of the given answers (1,500; 150,000; 150; 15,000) match the calculated result of approximately 5.66 closely. However, if we consider only reasonable scales, **150** might be the best estimate.
Therefore, the best estimate for \( x \) from the provided options is **150**.
🧋 is life
Which of the following answers gives the best estimate for x given the following equation?
x/50−94=189
(1 point)
Responses
1,500
1,500
150,000
150,000
150
150
15,000
x/50−94=189
(1 point)
Responses
1,500
1,500
150,000
150,000
150
150
15,000
GPT-4o mini
To solve the equation
\[
\frac{x}{50} - 94 = 189,
\]
we will follow these steps:
1. **Add 94 to both sides**:
\[
\frac{x}{50} = 189 + 94
\]
\[
\frac{x}{50} = 283
\]
2. **Multiply both sides by 50** to isolate \(x\):
\[
x = 283 \times 50
\]
\[
x = 14150
\]
Now, we approximate the value of \(x\). The result \(14150\) is closest to **15,000**.
So the best estimate for \(x\) from the provided options is **15,000**.
\[
\frac{x}{50} - 94 = 189,
\]
we will follow these steps:
1. **Add 94 to both sides**:
\[
\frac{x}{50} = 189 + 94
\]
\[
\frac{x}{50} = 283
\]
2. **Multiply both sides by 50** to isolate \(x\):
\[
x = 283 \times 50
\]
\[
x = 14150
\]
Now, we approximate the value of \(x\). The result \(14150\) is closest to **15,000**.
So the best estimate for \(x\) from the provided options is **15,000**.
🧋 is life
A local taqueria sold 11,321 carne asada tacos, 13,132 chicken tacos, and 8,982 carnitas tacos last year. If each taco was sold for $3.89, which value best estimates their total earnings from tacos?(1 point)
Responses
$130,000
$130,000
$90,000
$90,000
$160,000
$160,000
$33,000
Responses
$130,000
$130,000
$90,000
$90,000
$160,000
$160,000
$33,000
GPT-4o mini
To estimate the total earnings from the tacos, we first need to find the total number of tacos sold and then multiply it by the price per taco.
### Step 1: Calculate the total number of tacos sold
- Carne asada tacos: 11,321
- Chicken tacos: 13,132
- Carnitas tacos: 8,982
Total tacos sold:
\[
Total = 11,321 + 13,132 + 8,982
\]
Calculating this:
\[
Total = 11,321 + 13,132 = 24,453
\]
\[
Total = 24,453 + 8,982 = 33,435
\]
### Step 2: Calculate the total earnings
Now, multiply the total number of tacos by the price per taco, which is $3.89:
\[
Total\ Earnings = 33,435 \times 3.89
\]
To estimate, we can round $3.89 to approximately $4 for simplicity:
\[
Total\ Earnings \approx 33,435 \times 4 = 133,740
\]
### Conclusion
The calculated estimate is approximately $133,740, which is closest to **$130,000** among the provided options.
Therefore, the best estimate for their total earnings from tacos is **$130,000**.
### Step 1: Calculate the total number of tacos sold
- Carne asada tacos: 11,321
- Chicken tacos: 13,132
- Carnitas tacos: 8,982
Total tacos sold:
\[
Total = 11,321 + 13,132 + 8,982
\]
Calculating this:
\[
Total = 11,321 + 13,132 = 24,453
\]
\[
Total = 24,453 + 8,982 = 33,435
\]
### Step 2: Calculate the total earnings
Now, multiply the total number of tacos by the price per taco, which is $3.89:
\[
Total\ Earnings = 33,435 \times 3.89
\]
To estimate, we can round $3.89 to approximately $4 for simplicity:
\[
Total\ Earnings \approx 33,435 \times 4 = 133,740
\]
### Conclusion
The calculated estimate is approximately $133,740, which is closest to **$130,000** among the provided options.
Therefore, the best estimate for their total earnings from tacos is **$130,000**.
🧋 is life
Which of the following answers gives the best estimate for x given the following equation?
21x+1,998=2,243
(1 point)
Responses
10
10
1
1
100
100
1,000
21x+1,998=2,243
(1 point)
Responses
10
10
1
1
100
100
1,000
GPT-4o mini
To solve the equation
\[
21x + 1,998 = 2,243,
\]
we will isolate \(x\):
1. **Subtract 1,998 from both sides**:
\[
21x = 2,243 - 1,998
\]
\[
21x = 245
\]
2. **Divide both sides by 21** to solve for \(x\):
\[
x = \frac{245}{21}
\]
Now, calculating \( \frac{245}{21} \):
- Dividing gives us:
- \(21\) goes into \(245\) \(11.666...\) times.
We can estimate:
\[
x \approx 11.67
\]
To find the best estimate, among the provided options (10, 1, 100, or 1,000), the closest estimate is **10**.
Thus, the best estimate for \(x\) is **10**.
\[
21x + 1,998 = 2,243,
\]
we will isolate \(x\):
1. **Subtract 1,998 from both sides**:
\[
21x = 2,243 - 1,998
\]
\[
21x = 245
\]
2. **Divide both sides by 21** to solve for \(x\):
\[
x = \frac{245}{21}
\]
Now, calculating \( \frac{245}{21} \):
- Dividing gives us:
- \(21\) goes into \(245\) \(11.666...\) times.
We can estimate:
\[
x \approx 11.67
\]
To find the best estimate, among the provided options (10, 1, 100, or 1,000), the closest estimate is **10**.
Thus, the best estimate for \(x\) is **10**.