Add 7.3×107+1.8×107. Which is the correct sum?(1 point)

Question

Responses

9.1×1014
9.1 times 10 superscript 14 baseline

9.1+107
9.1 plus 10 superscript 7 baseline

8.1×107
8.1 times 10 superscript 7 baseline

9.1×107

Answer 1

To add \(7.3 \times 10^7\) and \(1.8 \times 10^7\), you can combine the coefficients since they have the same exponent:

\[ (7.3 + 1.8) \times 10^7 = 9.1 \times 10^7 \]

Thus, the correct sum is:

9.1×10^7 (9.1 times 10 superscript 7 baseline)

Answer 2

The population of a city is given as 3.45×106 . A nearby city has a population of 1.3×105 . What is the sum of the populations of the two cities in scientific notation?(1 point)
Responses

4.75×105
4.75 times 10 superscript 5 baseline

4.75×1011
4.75 times 10 superscript 11 baseline

3.58×106
3.58 times 10 superscript 6 baseline

35.8+105
35.8 plus 10 superscript 5 baseline

Answer 3

To find the sum of the populations \(3.45 \times 10^6\) and \(1.3 \times 10^5\), you first need to express both numbers with the same exponent. We can convert \(1.3 \times 10^5\) to an equivalent expression in terms of \(10^6\):

\[ 1.3 \times 10^5 = 0.13 \times 10^6 \]

Now, we can add the two populations:

\[ 3.45 \times 10^6 + 0.13 \times 10^6 = (3.45 + 0.13) \times 10^6 = 3.58 \times 10^6 \]

Thus, the sum of the populations of the two cities in scientific notation is:

3.58×10^6 (3.58 times 10 superscript 6 baseline)

Answer 4

An empty dump truck weighs about 2.8×105 pounds. How much does it weigh if 15,300 pounds of trash is added? The answer should be in scientific notation.(1 point)
Responses

29,530 pounds
29,530 pounds

2.953×105 pounds
2.953 times 10 superscript 5 baseline pounds

15,302.8 pounds
15,302.8 pounds

4.33×105 pounds
4.33 times 10 superscript 5 baseline pounds

Answer 5

To find the total weight of the dump truck after adding 15,300 pounds of trash, start with the weight of the empty dump truck, which is given as \(2.8 \times 10^5\) pounds.

First, convert 15,300 to scientific notation. \(15,300\) can be expressed as:

\[ 15,300 = 1.53 \times 10^4 \]

Next, we need to add these two numbers. However, since they are in different powers of ten, we should convert \(2.8 \times 10^5\) to an equivalent expression using the same exponent as \(1.53 \times 10^4\):

\[ 2.8 \times 10^5 = 28.0 \times 10^4 \]

Now you can add them together:

\[ 28.0 \times 10^4 + 1.53 \times 10^4 = (28.0 + 1.53) \times 10^4 = 29.53 \times 10^4 \]

Finally, convert this back to scientific notation:

\[ 29.53 \times 10^4 = 2.953 \times 10^5 \text{ pounds} \]

Thus, the total weight of the dump truck after adding the trash is:

2.953×10^5 pounds (2.953 times 10 superscript 5 baseline pounds)

Answer 6

The half-life of uranium-235 is 700,000,000 years. The half-life of uranium-238 is 4.463×1011 years longer. What is the half-life of uranium-238? The answer should be in decimal form.(1 point)
Responses

447,000,000,000
447,000,000,000

4.4637×1011
4.4637 times 10 superscript 11 baseline

516,300,000,000
516,300,000,000

11,463,000,000

Answer 7

To find the half-life of uranium-238, you start with the half-life of uranium-235, which is given as \(700,000,000\) years, and you know that the half-life of uranium-238 is \(4.463 \times 10^{11}\) years longer than that.

First, convert \(4.463 \times 10^{11}\) to decimal form:

\[ 4.463 \times 10^{11} = 446,300,000,000 \text{ years} \]

Now, add this to the half-life of uranium-235:

\[ 700,000,000 + 446,300,000,000 = 447,000,000,000 \text{ years} \]

Therefore, the half-life of uranium-238 is:

447,000,000,000 years.

Answer 8

A mobile phone holds 1.28×1011 bytes of storage. You can also pay more money to get an additional 384,000,000,000 bytes. How much storage would your phone have if you buy the additional bytes? The answer should be in scientific notation.(1 point)
Responses

385,280,000,000
385,280,000,000

512×109
512 times 10 superscript 9 baseline

385.28×1011
385.28 times 10 superscript 11 baseline

5.12×1011

Answer 9

To determine the total storage capacity of the mobile phone after adding the additional bytes, you can start by converting everything to scientific notation.

The original storage of the mobile phone is given as:

\[ 1.28 \times 10^{11} \text{ bytes} \]

The additional storage you can purchase is:

\[ 384,000,000,000 \text{ bytes} = 3.84 \times 10^{11} \text{ bytes} \]

Now, add these two quantities together:

\[ 1.28 \times 10^{11} + 3.84 \times 10^{11} = (1.28 + 3.84) \times 10^{11} = 5.12 \times 10^{11} \text{ bytes} \]

Thus, the total storage of the phone after buying the additional bytes is:

5.12×10^11 (5.12 times 10 superscript 11 baseline)

Answer 10

are you that all the answers are right

Answer 11

Let's review each of the previous calculations to confirm their accuracy:

1. Sum of populations:

   • We added \(3.45 \times 10^6\) (for City A) and \(1.3 \times 10^5\) (for City B).
   • Converted \(1.3 \times 10^5\) to \(0.13 \times 10^6\) to have a common exponent.
   • The correct sum was calculated as \(3.58 \times 10^6\).

2. Total weight of the dump truck:

   • We started with \(2.8 \times 10^5\) pounds and added \(15,300\) (converted to \(1.53 \times 10^4\)).
   • Converted \(2.8 \times 10^5\) to \(28.0 \times 10^4\) for common exponent.
   • The final total was \(2.953 \times 10^5\) pounds.

3. Half-life of uranium-238:

   • Started with a half-life of uranium-235 at \(700,000,000\) years.
   • Added \(4.463 \times 10^{11}\) years to that value, which was confirmed as \(446,300,000,000\) years when calculated.
   • The resulting half-life was correctly stated as \(447,000,000,000\) years.

4. Total storage capacity after purchasing additional bytes:

   • Phone storage was \(1.28 \times 10^{11}\) bytes and additional bytes were \(384,000,000,000\) or \(3.84 \times 10^{11}\) bytes.
   • Adding these gave \(5.12 \times 10^{11}\) bytes.

Based on the calculations provided, all answers given are correct. If you have specific concerns about any of the calculations or need further clarification, please let me know!