A piece of copy paper has a thickness of approximately 4 × 10^-3 in, and a human hair has a thickness of approximately 1 × 10^-3 in. Which of the following is true?

Question

A piece of copy paper has a thickness of approximately 4 × 10^-3 in, and a human hair has a thickness of approximately 1 × 10^-3 in. Which of the following is true?

A.
A human hair is approximately four times thicker than a piece of copy paper.

B.
A piece of copy paper is approximately forty times thicker than a human hair.

C.
A human hair is approximately forty times thicker than a piece of copy paper.

D.
A piece of copy paper is approximately four times thicker than a human hair

👇

11 answers
(click or scroll down)

👇

Answer 1

Bot GPT 4-o mini answered
4 days ago

Let's compare the thicknesses of the two items given:

- Thickness of a piece of copy paper: \(4 \times 10^{-3}\) inches
- Thickness of a human hair: \(1 \times 10^{-3}\) inches

To determine how many times thicker one is than the other, we can divide the thickness of the piece of copy paper by the thickness of the human hair:

\[
\frac{4 \times 10^{-3}}{1 \times 10^{-3}} = \frac{4}{1} = 4
\]

This means that a piece of copy paper is approximately 4 times thicker than a human hair.

Thus, the correct answer is:

**D. A piece of copy paper is approximately four times thicker than a human hair.**

Answer 2

UnicornSparkles answered
4 days ago

According to the 2008 U.S. census, California had a population of approximately 4 × 10^7 people and Florida had a population of approximately 2 × 10^7 people. Which of the following is true?

A.
The population of Florida was approximately two times the population of California.

B.
The population of Florida was approximately twenty times the population of California.

C.
The population of California was approximately two times the population of Florida.

D.
The population of California was approximately twenty times the population of Florida

Answer 3

Bot GPT 4-o mini answered
4 days ago

Let's compare the populations given:

- Population of California: \(4 \times 10^{7}\) people
- Population of Florida: \(2 \times 10^{7}\) people

To determine how many times larger the population of California is compared to the population of Florida, we can divide the population of California by the population of Florida:

\[
\frac{4 \times 10^{7}}{2 \times 10^{7}} = \frac{4}{2} = 2
\]

This means that the population of California is approximately 2 times larger than the population of Florida.

Thus, the correct answer is:

**C. The population of California was approximately two times the population of Florida.**

Answer 4

UnicornSparkles answered
4 days ago

The equatorial radius of Mars is 3,394 km. Which of the following would be a reasonable estimate for the equatorial radius of Mars?

A.
3 × 10^3 km
B.
3 × 10^-4 km
C.
3 × 10^-3 km
D.
3 × 10^4 km

Answer 5

Bot GPT 4-o mini answered
4 days ago

The equatorial radius of Mars is given as 3,394 km. We want to estimate this quantity in scientific notation:

- The number 3,394 can be expressed in scientific notation as \(3.394 \times 10^3\) km.

Among the options provided, we want to find a reasonable estimate. The most straightforward approach is to round 3,394 to the nearest significant figure which is 3,000 or \(3 \times 10^3\).

Looking at the options:

A. \(3 \times 10^3\) km
B. \(3 \times 10^{-4}\) km
C. \(3 \times 10^{-3}\) km
D. \(3 \times 10^4\) km

The only reasonable estimate for the equatorial radius of Mars is:

**A. \(3 \times 10^3\) km**

Answer 6

UnicornSparkles answered
4 days ago

The equatorial radius of Earth is approximately 6 × 10^3 km, while the equatorial radius of Saturn is approximately 6 × 10^4 km. Which of the following is true?

A.
The equatorial radius of Saturn is approximately ten times that of Earth.

B.
The equatorial radius of Earth is approximately ten times that of Saturn.

C.
The equatorial radius of Saturn is approximately one hundred times that of Earth.

D.
The equatorial radius of Earth is approximately one hundred times that of Saturn

Answer 7

Bot GPT 4-o mini answered
4 days ago

Given the equatorial radii:

- The equatorial radius of Earth: \(6 \times 10^3\) km
- The equatorial radius of Saturn: \(6 \times 10^4\) km

To compare the two, we can express the relationship between them:

1. To find how many times the radius of Saturn is compared to the radius of Earth, we can divide Saturn's radius by Earth's radius:

\[
\frac{6 \times 10^4}{6 \times 10^3} = \frac{6}{6} \times \frac{10^4}{10^3} = 1 \times 10^{4-3} = 1 \times 10^1 = 10
\]

This means that the equatorial radius of Saturn is approximately 10 times that of Earth.

Now let's examine the options:

A. The equatorial radius of Saturn is approximately ten times that of Earth.
B. The equatorial radius of Earth is approximately ten times that of Saturn.
C. The equatorial radius of Saturn is approximately one hundred times that of Earth.
D. The equatorial radius of Earth is approximately one hundred times that of Saturn.

The correct statement is:

**A. The equatorial radius of Saturn is approximately ten times that of Earth.**

Answer 8

UnicornSparkles answered
4 days ago

Which of the following numbers written in scientific notation is the least?

A.
-6 × 10^-8
B.
-8 × 10^-8
C.
-5 × 10^-7
D.
-2 × 10^-7

Answer 9

Bot GPT 4-o mini answered
4 days ago

To determine which number is the least, we can compare the values one by one.

1. **Option A:** \(-6 \times 10^{-8}\)
\[
= -0.00000006
\]

2. **Option B:** \(-8 \times 10^{-8}\)
\[
= -0.00000008
\]

3. **Option C:** \(-5 \times 10^{-7}\)
\[
= -0.0000005
\]

4. **Option D:** \(-2 \times 10^{-7}\)
\[
= -0.0000002
\]

Now we can compare these values:

- \(-0.00000008\) (Option B) is the smallest (least) because it is more negative than the others.
- \(-0.00000006\) (Option A) is greater than \(-0.00000008\).
- \(-0.0000005\) (Option C) is greater than \(-0.00000008\).
- \(-0.0000002\) (Option D) is also greater than \(-0.00000008\).

Thus, the least of these numbers is:

**B. \(-8 \times 10^{-8}\)**.

Answer 10

UnicornSparkles answered
4 days ago

The distance from the Earth to the Sun is approximately 90,000,000 miles, which can be written as 9 × 10a miles, where a = ___

The distance from Jupiter to the Sun is approximately 500,000,000 miles, which can be written as 5 × 10b miles, where b = ___
Rounded to the nearest tenth, Jupiter is about___times further from the Sun than the Earth is from the Sun.

Answer 11

Bot GPT 4-o mini answered
4 days ago

Let's break down the problem step by step.

### Finding \(a\)
The distance from Earth to the Sun is approximately 90,000,000 miles. To express this in scientific notation:

\[
90,000,000 = 9 \times 10^7 \text{ miles}
\]

So, \(a = 7\).

### Finding \(b\)
The distance from Jupiter to the Sun is approximately 500,000,000 miles. To express this in scientific notation:

\[
500,000,000 = 5 \times 10^8 \text{ miles}
\]

So, \(b = 8\).

### Calculating how many times Jupiter is further from the Sun than Earth
To find out how many times further Jupiter is from the Sun than Earth:

1. Distance from Earth to Sun: \(90,000,000\) miles or \(9 \times 10^7\) miles.
2. Distance from Jupiter to Sun: \(500,000,000\) miles or \(5 \times 10^8\) miles.

Now, divide the distance from Jupiter by the distance from Earth:

\[
\text{Ratio} = \frac{500,000,000}{90,000,000} = \frac{5 \times 10^8}{9 \times 10^7} = \frac{5}{9} \times \frac{10^8}{10^7} = \frac{5}{9} \times 10^{1} = \frac{5}{9} \times 10
\]

Calculating \(\frac{5}{9} \times 10\):

\[
\frac{5}{9} \approx 0.555 \quad \Rightarrow \quad 0.555 \times 10 \approx 5.555
\]

Rounded to the nearest tenth:

\[
5.555 \approx 5.6
\]

### Final Answers
- \(a = 7\)
- \(b = 8\)
- Jupiter is about **5.6 times** further from the Sun than the Earth is from the Sun.