A rectangular park has an area of 1.36×108 ft2

Question

. 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.

Answer 1

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.

Answer 2

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

Answer 3

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}.

Answer 4

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

Answer 5

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.

Answer 6

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

Answer 7

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}.

Answer 8

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

Answer 9

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}.