I need help ### Sandbox Volume and Grain Count CalculationThe dimensions of Roy and Roger’s sandbox are $ t^2 $ meters by $ t^5 $ meters. One cubic meter of the sandbox contains $ 3t^{21} $ grains of sand. Which of the following expressions represent the amount of grains of sand in the sandbox?#### Options:1. $ 27t^{10-7}t^{21} $2. $ 9t^7t^{21} $3. $ t^{10-7}t^{21} $4. $ 3t^7t^{21} $ **(Selected)**#### Explanation:To determine the correct expression, consider the following steps:1. Calculate the volume of the sandbox: - Volume = $ t^2 \times t^5 $ - Simplified, this is $ t^{2+5} = t^7 $ cubic meters.2. Calculate the grains of sand in the sandbox: - Given that 1 cubic meter contains $ 3t^{21} $ grains, the total grains in $ t^7 $ cubic meters is: \[ \text{Total Grains} = t^7 \times 3t^{21} = 3t^{7+21} = 3t^{28} \]Therefore, the correct expression representing the amount of grains of sand in the sandbox is $ 3t^{28} $, matching the choice labeled under option 4: $ 3t^7t^{21} $.

dimensions of the Roy and Roger's sandbox : length = t2 width = t5 height = v2…

The dimensions of Roy and Roger's sandbox are t² meters by t5 meters. One cubic meter of the sandbox contains 3821 grains of sand. Which of the following expressions represent the amount of grains of sand in the sandbox? O 27t ¹07,21 ○ 9t7²,21 O t¹0², 21 31² ²²1

The dimensions of Roy and Roger's sandbox are t² meters by t5 meters. One cubic meter of the sandbox contains 3821 grains of sand. Which of the following expressions represent the amount of grains of sand in the sandbox? O 27t ¹07,21 ○ 9t7²,21 O t¹0², 21 31² ²²1

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.

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I need help

### Sandbox Volume and Grain Count Calculation

The dimensions of Roy and Roger’s sandbox are $ t^2 $ meters by $ t^5 $ meters. One cubic meter of the sandbox contains $ 3t^{21} $ grains of sand. Which of the following expressions represent the amount of grains of sand in the sandbox?

#### Options:

1. $ 27t^{10-7}t^{21} $
2. $ 9t^7t^{21} $
3. $ t^{10-7}t^{21} $
4. $ 3t^7t^{21} $ **(Selected)**

#### Explanation:

To determine the correct expression, consider the following steps:

1. Calculate the volume of the sandbox:
- Volume = $ t^2 \times t^5 $
- Simplified, this is $ t^{2+5} = t^7 $ cubic meters.

2. Calculate the grains of sand in the sandbox:
- Given that 1 cubic meter contains $ 3t^{21} $ grains, the total grains in $ t^7 $ cubic meters is:
\[ \text{Total Grains} = t^7 \times 3t^{21} = 3t^{7+21} = 3t^{28} \]

Therefore, the correct expression representing the amount of grains of sand in the sandbox is $ 3t^{28} $, matching the choice labeled under option 4: $ 3t^7t^{21} $.

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