The actual length (L) of a rectangle is 27 centimeters. Use the scale drawing of the rectangle to find the actual width (W).
2 answers:
The proportion of length to width is 
.
The ratio remains consistent between both the scale representation and the actual dimensions.
I calculated the L/W for the scale and equated it with the L/W of the actual representation.
We can now derive the unknown width.
Performing cross-multiplication results in:
Now dividing by 2.4 and simplifying gives us:
I hope this helps!:)
The ratio remains consistent between both the scale representation and the actual dimensions.
I calculated the L/W for the scale and equated it with the L/W of the actual representation.
We can now derive the unknown width.
Performing cross-multiplication results in:
Now dividing by 2.4 and simplifying gives us:
I hope this helps!:)
Conclusion:
18 centimeters.
Detailed steps:
This problem can be solved using proportions. The given rectangle provides a ratio that is useful to derive the answer. This can be approached with the rule of three.
Next, we find :
Thus, as per the proportion, the actual width is determined to be 18 centimeters.
When employing proportions and ratios, it’s important to ensure correct alignment of dimensions; for instance, if width is placed in the numerator, it must also remain in that position in the corresponding ratio.
You might be interested in
To determine if there is evidence suggesting a change in average height, we can conduct a right-tailed test and formulate both null and alternative hypotheses.
H₀ (null hypothesis): μ = 162.5
H₁ (alternative hypothesis): μ > 162.5
With two samples to analyze, we can calculate the z-score using the formula provided below.
In this formula, Z symbolizes the z-score, Χ denotes the new sample mean, μ indicates the theoretical average, δ represents the standard deviation, and n signifies the sample size. Based on the gathered values,
Assuming a significance level of α = 0.05. With a z-score of 2.77, we can reference the z-table to ascertain the p-value. This yields P(Z > 2.77) =.0028. Since our p-value is below α, we reject the null hypothesis, indicating that the average height of female freshman students has indeed shifted.
H₀ (null hypothesis): μ = 162.5
H₁ (alternative hypothesis): μ > 162.5
With two samples to analyze, we can calculate the z-score using the formula provided below.
In this formula, Z symbolizes the z-score, Χ denotes the new sample mean, μ indicates the theoretical average, δ represents the standard deviation, and n signifies the sample size. Based on the gathered values,
Assuming a significance level of α = 0.05. With a z-score of 2.77, we can reference the z-table to ascertain the p-value. This yields P(Z > 2.77) =.0028. Since our p-value is below α, we reject the null hypothesis, indicating that the average height of female freshman students has indeed shifted.