Denali, which is about 20,000 ft. above sea level, is the highest mountain in the United States. Mt. Everest, the highest mountain on earth, is about 9×103 ft. higher than Denali. About how high is Mt. Everest? The answer should be in scientific notation.(1 point)

Question

Responses

2.9×103 ft.
2.9 times 10 cubed ft.

2.9×104 ft.
2.9 times 10 superscript 4 baseline ft.

29,000 ft.
29,000 ft.

1.1×10^3 ft.

Answer 1

To calculate the height of Mt. Everest, we add the height of Denali (20,000 ft, or \(2 \times 10^4\) ft) to the additional height of Mt. Everest over Denali, which is given as about \(9 \times 10^3\) ft.

So, we perform the following addition:

\[ \text{Height of Mt. Everest} = \text{Height of Denali} + \text{Additional Height} \]

Converting Denali's height to scientific notation:

\[ 20,000 \text{ ft} = 2 \times 10^4 \text{ ft} \]

Adding the height of Denali and the additional height:

\[ 2 \times 10^4 + 9 \times 10^3 \]

First, we convert \(9 \times 10^3\) to have the same exponent as \(2 \times 10^4\):

\[ 9 \times 10^3 = 0.9 \times 10^4 \]

Now we can add them together:

\[ 2 \times 10^4 + 0.9 \times 10^4 = (2 + 0.9) \times 10^4 = 2.9 \times 10^4 \]

Therefore, the height of Mt. Everest is:

\[ \text{Height of Mt. Everest} \approx 2.9 \times 10^4 \text{ ft} \]

The correct answer is:

2.9×10^4 ft.