Proportional Sides
Proportional Sides - Related Videos
01:20
Sample Proportion and Population Proportion
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2023
Collecting samples or responses from an entire population takes significant time and effort, so a researcher collects responses from only a sample of that population. Suppose a study needs to collect information about a specific mobile application. After sample collection, the researcher analyzes the data and discovers that most individuals in the sample use that specific mobile application. The sample proportion measures the number of individuals in a sample who either use or don't use the...
01:24
Testing a Claim about Population Proportion
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2023
A complete procedure for testing a claim about a population proportion is provided here. There are two methods of testing a claim about a population proportion: (1) Using the sample proportion from the data where a binomial distribution is approximated to the normal distribution and (2) Using the binomial probabilities calculated from the data. The first method uses normal distribution as an approximation to the binomial distribution. The requirements are as follows: sample size is large...
01:09
Pharmacodynamic Models: Additive and Proportional Drug Effect Model
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2026
Drug response models describe how pharmacological agents interact with biological systems to produce measurable effects. Baseline responses are inherent physiological activities without a drug significantly influencing the observed pharmacological outcomes. Depending on the drug response model employed, these baseline responses may combine with the drug's effect in either an additive or proportional manner.Additive Drug Response ModelIn the additive model, the drug effect is independent of the...
09:01
Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
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Cited by 5 •
2017
We propose a method to extend the corresponding frequency by using a pre-emphasis technique. This method compensates for the gain reduction of a galvanometer mirror in sine-wave path tracking using proportional-integral-differential control.
02:54
Trends in Lattice Energy: Ion Size and Charge
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2020
An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process: Conventions Here, the convention is used where the ionic...
FAQs
The scale factor tells how a known length changes when moving to its corresponding length in another figure. Multiply by that factor to enlarge or reduce the measurement; reversing the comparison requires the reciprocal factor. Keeping the direction consistent prevents assigning the larger figure’s relationship to the smaller figure.
Correspondence determines which lengths should be compared. A side in one figure must match the side occupying the same geometric position in the other, while equal corresponding angles support that pairing in similar figures. If lengths are paired incorrectly, the ratios may not share one scale factor, producing an unreliable unknown measurement.
Equivalent ratios offer two compatible ways to solve for an unknown side: preserve the ratio relationship or cross-multiply to isolate the missing value. After solving, substitute the result back into both ratio positions and verify that the comparisons agree. This check helps detect arithmetic errors and confirms that the selected sides were corresponding.
In a scale drawing or map, proportional sides connect a represented distance with an actual dimension. A known scale factor lets you convert between the two, provided the same relationship is applied consistently throughout the drawing. The resulting calculation can estimate an otherwise unavailable length while preserving the intended geometric proportions.
Similar triangles make indirect measurement possible when a length cannot be measured directly. Measure a known side and its corresponding side, then use the established ratio to calculate the unknown triangle length. Equal corresponding angles identify the similarity relationship, so the calculated result is tied to the geometry rather than to a simple visual estimate.
Use the relationship when the figures or triangles are treated as similar and the compared lengths correspond. A shared ratio is not justified merely because two shapes contain sides; without the similarity relationship, multiplying by one scale factor can misrepresent the unknown dimension. Establishing similarity first makes the resulting measurement meaningful.