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Original Question
A rectangular park has an area of 1.36×10^8 ft^2 . The length of the park is 1.6×10^4 ft. Divide the area by the length to find...Asked by woosan♥
A rectangular park has an area of 1.36×108 ft2
. The length of the park is 1.6×104
ft. Divide the area by the length to find the width of the park.(1 point)
Responses
8.5×103
ft.
8.5 times 10 cubed ft.
8.5×102
ft.
8.5 times 10 squared ft.
8.5×104
ft.
8.5 times 10 superscript 4 baseline ft.
8.5×105
ft.
. The length of the park is 1.6×104
ft. Divide the area by the length to find the width of the park.(1 point)
Responses
8.5×103
ft.
8.5 times 10 cubed ft.
8.5×102
ft.
8.5 times 10 squared ft.
8.5×104
ft.
8.5 times 10 superscript 4 baseline ft.
8.5×105
ft.
Answers
Answered by
woosan♥
Divide 3.3×104
by 5.5×107
.(1 point)
Responses
6×10−5
6 times 10 to the negative 5 power
6×10−6
6 times 10 to the negative 6 power
6×10−4
6 times 10 to the negative 4 power
6×10−3
by 5.5×107
.(1 point)
Responses
6×10−5
6 times 10 to the negative 5 power
6×10−6
6 times 10 to the negative 6 power
6×10−4
6 times 10 to the negative 4 power
6×10−3
Answered by
woosan♥
A city lunch program for seniors received a grant of 1.925×106
dollars. Divide that figure by the cost of $2.75 per lunch to find out how many senior lunches the grant can provide. Write the answer in scientific notation.(1 point)
Responses
7×105
7 times 10 superscript 5 baseline
0.7×106
0.7 times 10 superscript 6 baseline
7×106
7 times 10 superscript 6 baseline
0.7×105
dollars. Divide that figure by the cost of $2.75 per lunch to find out how many senior lunches the grant can provide. Write the answer in scientific notation.(1 point)
Responses
7×105
7 times 10 superscript 5 baseline
0.7×106
0.7 times 10 superscript 6 baseline
7×106
7 times 10 superscript 6 baseline
0.7×105
Answered by
woosan♥
Solomon needs to distribute 10.5 gallons of perfume among 3.5×102
containers. How many gallons of perfume will be in each container? Write the answer in scientific notation.(1 point)
Responses
3×10−1
3 times 10 superscript negative 1 baseline
0.35×10−1
0.35 times 10 superscript negative 1 baseline
3×102
3 times 10 squared
3×10−2
containers. How many gallons of perfume will be in each container? Write the answer in scientific notation.(1 point)
Responses
3×10−1
3 times 10 superscript negative 1 baseline
0.35×10−1
0.35 times 10 superscript negative 1 baseline
3×102
3 times 10 squared
3×10−2
Answered by
woosan♥
A large pavilion is made of 2.967×105
bricks. There are 6.9 bricks per square foot. How many square feet is the pavilion? Write the answer in scientific notation.(1 point)
Responses
4.3×104
4.3 times 10 superscript 4 baseline
2.33×105
2.33 times 10 superscript 5 baseline
0.43×104
0.43 times 10 superscript 4 baseline
4.3×105
bricks. There are 6.9 bricks per square foot. How many square feet is the pavilion? Write the answer in scientific notation.(1 point)
Responses
4.3×104
4.3 times 10 superscript 4 baseline
2.33×105
2.33 times 10 superscript 5 baseline
0.43×104
0.43 times 10 superscript 4 baseline
4.3×105
Answered by
GPT-4o mini
To find the width of the park, we can use the formula for the area of a rectangle, which is:
\[
\text{Area} = \text{Length} \times \text{Width}
\]
We can rearrange this to find the width:
\[
\text{Width} = \frac{\text{Area}}{\text{Length}}
\]
Given the area is \(1.36 \times 10^8 \, \text{ft}^2\) and the length is \(1.6 \times 10^4 \, \text{ft}\):
\[
\text{Width} = \frac{1.36 \times 10^8}{1.6 \times 10^4}
\]
Now, let's divide the numerical coefficients and subtract the exponents:
1. **Divide the coefficients**:
\[
\frac{1.36}{1.6} = 0.85
\]
2. **Subtract the exponents**:
\[
10^{8 - 4} = 10^4
\]
Putting it all together:
\[
\text{Width} = 0.85 \times 10^4
\]
To express \(0.85\) in scientific notation:
\[
0.85 = 8.5 \times 10^{-1}
\]
So:
\[
\text{Width} = 8.5 \times 10^{-1} \times 10^4 = 8.5 \times 10^{3}
\]
Thus, the width of the park is:
\[
\text{Width} = 8.5 \times 10^3 \, \text{ft}
\]
The correct response is:
**8.5×10³ ft.**
\[
\text{Area} = \text{Length} \times \text{Width}
\]
We can rearrange this to find the width:
\[
\text{Width} = \frac{\text{Area}}{\text{Length}}
\]
Given the area is \(1.36 \times 10^8 \, \text{ft}^2\) and the length is \(1.6 \times 10^4 \, \text{ft}\):
\[
\text{Width} = \frac{1.36 \times 10^8}{1.6 \times 10^4}
\]
Now, let's divide the numerical coefficients and subtract the exponents:
1. **Divide the coefficients**:
\[
\frac{1.36}{1.6} = 0.85
\]
2. **Subtract the exponents**:
\[
10^{8 - 4} = 10^4
\]
Putting it all together:
\[
\text{Width} = 0.85 \times 10^4
\]
To express \(0.85\) in scientific notation:
\[
0.85 = 8.5 \times 10^{-1}
\]
So:
\[
\text{Width} = 8.5 \times 10^{-1} \times 10^4 = 8.5 \times 10^{3}
\]
Thus, the width of the park is:
\[
\text{Width} = 8.5 \times 10^3 \, \text{ft}
\]
The correct response is:
**8.5×10³ ft.**
Answered by
GPT-4o mini
To divide \(3.3 \times 10^4\) by \(5.5 \times 10^7\), we can use the following formula:
\[
\frac{a \times 10^m}{b \times 10^n} = \frac{a}{b} \times 10^{m-n}
\]
Here, \(a = 3.3\), \(b = 5.5\), \(m = 4\), and \(n = 7\).
1. **Divide the coefficients**:
\[
\frac{3.3}{5.5} = 0.6
\]
2. **Subtract the exponents**:
\[
10^{4 - 7} = 10^{-3}
\]
Putting it all together:
\[
\frac{3.3 \times 10^4}{5.5 \times 10^7} = 0.6 \times 10^{-3}
\]
To express \(0.6\) in scientific notation:
\[
0.6 = 6 \times 10^{-1}
\]
Thus:
\[
0.6 \times 10^{-3} = 6 \times 10^{-1} \times 10^{-3} = 6 \times 10^{-4}
\]
Therefore, the result of dividing \(3.3 \times 10^4\) by \(5.5 \times 10^7\) is:
**6×10^{-4}**.
\[
\frac{a \times 10^m}{b \times 10^n} = \frac{a}{b} \times 10^{m-n}
\]
Here, \(a = 3.3\), \(b = 5.5\), \(m = 4\), and \(n = 7\).
1. **Divide the coefficients**:
\[
\frac{3.3}{5.5} = 0.6
\]
2. **Subtract the exponents**:
\[
10^{4 - 7} = 10^{-3}
\]
Putting it all together:
\[
\frac{3.3 \times 10^4}{5.5 \times 10^7} = 0.6 \times 10^{-3}
\]
To express \(0.6\) in scientific notation:
\[
0.6 = 6 \times 10^{-1}
\]
Thus:
\[
0.6 \times 10^{-3} = 6 \times 10^{-1} \times 10^{-3} = 6 \times 10^{-4}
\]
Therefore, the result of dividing \(3.3 \times 10^4\) by \(5.5 \times 10^7\) is:
**6×10^{-4}**.
Answered by
GPT-4o mini
To find out how many senior lunches the grant can provide, we need to divide the total grant amount by the cost per lunch:
\[
\text{Number of lunches} = \frac{1.925 \times 10^6 \text{ dollars}}{2.75 \text{ dollars/lunch}}
\]
First, we can simplify the division by calculating the numerical coefficient:
1. **Divide the coefficients**:
\[
\frac{1.925}{2.75} \approx 0.7
\]
2. **Now, the remaining part is dividing the powers of ten**:
\[
10^6 \text{ (since we still have this from the grant amount)}
\]
Putting it all together:
\[
\text{Number of lunches} \approx 0.7 \times 10^6
\]
To express \(0.7\) in scientific notation:
\[
0.7 = 7 \times 10^{-1}
\]
So:
\[
0.7 \times 10^6 = 7 \times 10^{-1} \times 10^6 = 7 \times 10^{5}
\]
Thus, the number of senior lunches that the grant can provide is:
**7×10^5**.
\[
\text{Number of lunches} = \frac{1.925 \times 10^6 \text{ dollars}}{2.75 \text{ dollars/lunch}}
\]
First, we can simplify the division by calculating the numerical coefficient:
1. **Divide the coefficients**:
\[
\frac{1.925}{2.75} \approx 0.7
\]
2. **Now, the remaining part is dividing the powers of ten**:
\[
10^6 \text{ (since we still have this from the grant amount)}
\]
Putting it all together:
\[
\text{Number of lunches} \approx 0.7 \times 10^6
\]
To express \(0.7\) in scientific notation:
\[
0.7 = 7 \times 10^{-1}
\]
So:
\[
0.7 \times 10^6 = 7 \times 10^{-1} \times 10^6 = 7 \times 10^{5}
\]
Thus, the number of senior lunches that the grant can provide is:
**7×10^5**.
Answered by
GPT-4o mini
To find out how many gallons of perfume will be in each container, we need to divide the total amount of perfume by the number of containers:
\[
\text{Gallons per container} = \frac{10.5 \text{ gallons}}{3.5 \times 10^2 \text{ containers}}
\]
First, we can simplify the division:
1. **Calculate the division of the coefficients**:
\[
\frac{10.5}{3.5} = 3
\]
2. **Now, consider the exponent and write it with \(10^{-2}\)**:
Since \(10^2\) is in the denominator, we can write:
\[
\frac{1}{10^2} = 10^{-2}
\]
Thus, we have:
\[
\text{Gallons per container} = 3 \times 10^{-2}
\]
So, the number of gallons of perfume in each container is:
**3×10^{-2}**.
\[
\text{Gallons per container} = \frac{10.5 \text{ gallons}}{3.5 \times 10^2 \text{ containers}}
\]
First, we can simplify the division:
1. **Calculate the division of the coefficients**:
\[
\frac{10.5}{3.5} = 3
\]
2. **Now, consider the exponent and write it with \(10^{-2}\)**:
Since \(10^2\) is in the denominator, we can write:
\[
\frac{1}{10^2} = 10^{-2}
\]
Thus, we have:
\[
\text{Gallons per container} = 3 \times 10^{-2}
\]
So, the number of gallons of perfume in each container is:
**3×10^{-2}**.
Answered by
GPT-4o mini
To find out how many square feet the pavilion covers, we need to divide the total number of bricks by the number of bricks per square foot:
\[
\text{Square feet} = \frac{2.967 \times 10^5 \text{ bricks}}{6.9 \text{ bricks/sq ft}}
\]
First, calculate the division of the coefficients:
1. **Divide the coefficients**:
\[
\frac{2.967}{6.9} \approx 0.4300
\]
2. **Now, we divide the powers of ten**:
Since there is no exponent in the denominator, we have \(10^5\):
Putting it together:
\[
\text{Square feet} \approx 0.4300 \times 10^5
\]
To express \(0.4300\) in scientific notation:
\[
0.4300 = 4.3 \times 10^{-1}
\]
Thus:
\[
0.4300 \times 10^5 = 4.3 \times 10^{-1} \times 10^5 = 4.3 \times 10^{4}
\]
So, the area of the pavilion is:
**4.3×10^{4}**.
\[
\text{Square feet} = \frac{2.967 \times 10^5 \text{ bricks}}{6.9 \text{ bricks/sq ft}}
\]
First, calculate the division of the coefficients:
1. **Divide the coefficients**:
\[
\frac{2.967}{6.9} \approx 0.4300
\]
2. **Now, we divide the powers of ten**:
Since there is no exponent in the denominator, we have \(10^5\):
Putting it together:
\[
\text{Square feet} \approx 0.4300 \times 10^5
\]
To express \(0.4300\) in scientific notation:
\[
0.4300 = 4.3 \times 10^{-1}
\]
Thus:
\[
0.4300 \times 10^5 = 4.3 \times 10^{-1} \times 10^5 = 4.3 \times 10^{4}
\]
So, the area of the pavilion is:
**4.3×10^{4}**.