Asked by Hummingbird 7th
Evaluate: - 5/6 + (-1/3)
Responses
A −
− 7/6
B −
− 3/6
C
3/6
D
7/3
Responses
A −
− 7/6
B −
− 3/6
C
3/6
D
7/3
Answers
Answered by
Hummingbird 7th
Evaluate this expression.
(−98.2) − (−16.8)
Responses
A −115−115
B −81.4−81.4
C 81.481.4
D 115
(−98.2) − (−16.8)
Responses
A −115−115
B −81.4−81.4
C 81.481.4
D 115
Answered by
Hummingbird 7th
Last Friday, the temperature at 9:00AM was 17.2°F. By midnight, the temperature had decreased by 19.5 degrees. What was the temperature at midnight?
Responses
A 36.7°F36.7°F
B 2.3°F2.3°F
C –36.7°F–36.7°F
D –2.3°F
Responses
A 36.7°F36.7°F
B 2.3°F2.3°F
C –36.7°F–36.7°F
D –2.3°F
Answered by
Hummingbird 7th
Anna is evaluating some rational expressions. Which THREE are correct?
Responses
A 152 − 200 = −48152 − 200 = −48
B −25 + (−25) = 0−25 + (−25) = 0
C 89 − (−17) = 10689 − (−17) = 106
D 134 − (−16) = 118134 − (−16) = 118
E −39 − (−28) = −11
Responses
A 152 − 200 = −48152 − 200 = −48
B −25 + (−25) = 0−25 + (−25) = 0
C 89 − (−17) = 10689 − (−17) = 106
D 134 − (−16) = 118134 − (−16) = 118
E −39 − (−28) = −11
Answered by
Hummingbird 7th
What is the vertical distance between a diver that is submerged at a depth of
7 1/2
feet below the surface of the water and a parasailor that is in the air
52 1/4
feet above the surface of the water?
feet
7 1/2
feet below the surface of the water and a parasailor that is in the air
52 1/4
feet above the surface of the water?
feet
Answered by
GPT-4o mini
To evaluate \(-\frac{5}{6} + \left(-\frac{1}{3}\right)\), we first need to make the denominators the same.
The fraction \(-\frac{1}{3}\) can be converted to a fraction with a denominator of 6:
\[
-\frac{1}{3} = -\frac{2}{6}
\]
Now we can rewrite the original expression:
\[
-\frac{5}{6} + \left(-\frac{2}{6}\right) = -\frac{5}{6} - \frac{2}{6}
\]
Next, we add the fractions:
\[
-\frac{5 + 2}{6} = -\frac{7}{6}
\]
Thus, the final result is:
\[
-\frac{7}{6}
\]
Looking at the provided responses, the correct answer is:
**A** \(-\frac{7}{6}\)
The fraction \(-\frac{1}{3}\) can be converted to a fraction with a denominator of 6:
\[
-\frac{1}{3} = -\frac{2}{6}
\]
Now we can rewrite the original expression:
\[
-\frac{5}{6} + \left(-\frac{2}{6}\right) = -\frac{5}{6} - \frac{2}{6}
\]
Next, we add the fractions:
\[
-\frac{5 + 2}{6} = -\frac{7}{6}
\]
Thus, the final result is:
\[
-\frac{7}{6}
\]
Looking at the provided responses, the correct answer is:
**A** \(-\frac{7}{6}\)
Answered by
GPT-4o mini
To evaluate the expression \((-98.2) - (-16.8)\), we can simplify it by converting the subtraction of a negative number into addition:
\[
-98.2 - (-16.8) = -98.2 + 16.8
\]
Now, we perform the addition:
\[
-98.2 + 16.8 = -81.4
\]
Thus, the result is:
\[
-81.4
\]
Looking at the provided responses, the correct answer is:
**B** \(-81.4\)
\[
-98.2 - (-16.8) = -98.2 + 16.8
\]
Now, we perform the addition:
\[
-98.2 + 16.8 = -81.4
\]
Thus, the result is:
\[
-81.4
\]
Looking at the provided responses, the correct answer is:
**B** \(-81.4\)
Answered by
GPT-4o mini
To find the temperature at midnight, we need to subtract the decrease in temperature from the temperature at 9:00 AM.
The initial temperature at 9:00 AM is 17.2°F, and the temperature decreased by 19.5 degrees. Thus, we calculate:
\[
\text{Temperature at midnight} = 17.2°F - 19.5°F
\]
Now, performing the subtraction:
\[
17.2 - 19.5 = -2.3°F
\]
Therefore, the temperature at midnight is:
\[
-2.3°F
\]
Looking at the provided responses, the correct answer is:
**D** \(-2.3°F\)
The initial temperature at 9:00 AM is 17.2°F, and the temperature decreased by 19.5 degrees. Thus, we calculate:
\[
\text{Temperature at midnight} = 17.2°F - 19.5°F
\]
Now, performing the subtraction:
\[
17.2 - 19.5 = -2.3°F
\]
Therefore, the temperature at midnight is:
\[
-2.3°F
\]
Looking at the provided responses, the correct answer is:
**D** \(-2.3°F\)
Answered by
GPT-4o mini
Let's evaluate each of the options to determine which three are correct.
**A:** \(152 - 200\)
Calculating:
\[
152 - 200 = -48
\]
This is correct: **A** is true.
---
**B:** \(-25 + (-25)\)
Calculating:
\[
-25 + (-25) = -50
\]
This is incorrect: **B** is false.
---
**C:** \(89 - (-17)\)
Calculating:
\[
89 - (-17) = 89 + 17 = 106
\]
This is correct: **C** is true.
---
**D:** \(134 - (-16)\)
Calculating:
\[
134 - (-16) = 134 + 16 = 150
\]
This is incorrect: **D** is false.
---
**E:** \(-39 - (-28)\)
Calculating:
\[
-39 - (-28) = -39 + 28 = -11
\]
This is correct: **E** is true.
---
The correct evaluations are: **A, C,** and **E.**
**A:** \(152 - 200\)
Calculating:
\[
152 - 200 = -48
\]
This is correct: **A** is true.
---
**B:** \(-25 + (-25)\)
Calculating:
\[
-25 + (-25) = -50
\]
This is incorrect: **B** is false.
---
**C:** \(89 - (-17)\)
Calculating:
\[
89 - (-17) = 89 + 17 = 106
\]
This is correct: **C** is true.
---
**D:** \(134 - (-16)\)
Calculating:
\[
134 - (-16) = 134 + 16 = 150
\]
This is incorrect: **D** is false.
---
**E:** \(-39 - (-28)\)
Calculating:
\[
-39 - (-28) = -39 + 28 = -11
\]
This is correct: **E** is true.
---
The correct evaluations are: **A, C,** and **E.**
Answered by
GPT-4o mini
To find the vertical distance between the diver submerged at a depth of \( 7 \frac{1}{2} \) feet below the surface and the parasailor who is \( 52 \frac{1}{4} \) feet above the surface, we can follow these steps:
1. **Convert the mixed numbers to improper fractions** or decimals for easier calculation:
- Convert \( 7 \frac{1}{2} \):
\[
7 \frac{1}{2} = 7 + \frac{1}{2} = \frac{14}{2} + \frac{1}{2} = \frac{15}{2} \text{ feet}
\]
- Convert \( 52 \frac{1}{4} \):
\[
52 \frac{1}{4} = 52 + \frac{1}{4} = \frac{208}{4} + \frac{1}{4} = \frac{209}{4} \text{ feet}
\]
2. **Calculate the total vertical distance**. Since the diver is below the water surface and the parasailor is above, the total distance can be calculated as the sum of the two depths:
\[
\text{Vertical Distance} = \text{above} + \text{below} = \frac{209}{4} + \frac{15}{2}
\]
3. **Get a common denominator** to combine the fractions. The least common denominator of 4 and 2 is 4.
- Convert \( \frac{15}{2} \) to a fraction with a denominator of 4:
\[
\frac{15}{2} = \frac{15 \times 2}{2 \times 2} = \frac{30}{4}
\]
4. **Now, add the two fractions**:
\[
\frac{209}{4} + \frac{30}{4} = \frac{239}{4}
\]
5. **Convert the result back to a mixed number**:
\[
\frac{239}{4} = 59 \frac{3}{4}
\]
So, the vertical distance between the diver and the parasailor is \( 59 \frac{3}{4} \) feet.
1. **Convert the mixed numbers to improper fractions** or decimals for easier calculation:
- Convert \( 7 \frac{1}{2} \):
\[
7 \frac{1}{2} = 7 + \frac{1}{2} = \frac{14}{2} + \frac{1}{2} = \frac{15}{2} \text{ feet}
\]
- Convert \( 52 \frac{1}{4} \):
\[
52 \frac{1}{4} = 52 + \frac{1}{4} = \frac{208}{4} + \frac{1}{4} = \frac{209}{4} \text{ feet}
\]
2. **Calculate the total vertical distance**. Since the diver is below the water surface and the parasailor is above, the total distance can be calculated as the sum of the two depths:
\[
\text{Vertical Distance} = \text{above} + \text{below} = \frac{209}{4} + \frac{15}{2}
\]
3. **Get a common denominator** to combine the fractions. The least common denominator of 4 and 2 is 4.
- Convert \( \frac{15}{2} \) to a fraction with a denominator of 4:
\[
\frac{15}{2} = \frac{15 \times 2}{2 \times 2} = \frac{30}{4}
\]
4. **Now, add the two fractions**:
\[
\frac{209}{4} + \frac{30}{4} = \frac{239}{4}
\]
5. **Convert the result back to a mixed number**:
\[
\frac{239}{4} = 59 \frac{3}{4}
\]
So, the vertical distance between the diver and the parasailor is \( 59 \frac{3}{4} \) feet.
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