This situation exemplifies the distributive property, where the number outside the parentheses impacts all the terms within through multiplication. Therefore, the resulting action here is:
<span>The 4 should be multiplied by each term found inside the parentheses.
</span>
Answer: 26.3 mm
Step-by-step explanation:
The two-standard deviations rule for outliers states that any value lying outside two standard deviations from the average is considered an outlier.
Given that the Mean is 23.5 millimeters (mm) and the standard deviation is 1.4 mm
The maximum thickness that should be reviewed = mean + 2 (standard deviation)
= 23.5 + 2(1.4)
= 23.5 + 2.8
= 26.3 mm
therefore, the maximum thickness warranting machine configuration review by the statistician = 26.3 mm.
In certain cases, a function necessitates multiple formulas to achieve the desired outcome. An example is the absolute value function \displaystyle f\left(x\right)=|x|f(x)=∣x∣. This function applies to all real numbers and yields results that are non-negative, defining absolute value as the magnitude or modulus of a real number regardless of its sign. It indicates the distance from zero on the number line, requiring all outputs to be zero or greater.
<pwhen inputting="" a="" non-negative="" value="" the="" output="" remains="" unchanged:="">
\displaystyle f\left(x\right)=x\text{ if }x\ge 0f(x)=x if x≥0
<pwhen inputting="" a="" negative="" value="" the="" output="" is="" inverse:="">
\displaystyle f\left(x\right)=-x\text{ if }x<0f(x)=−x if x<0
Due to the need for two distinct operations, the absolute value function qualifies as a piecewise function: a function defined by several formulas for different sections of its domain.
Piecewise functions help describe scenarios where rules or relationships alter as the input crosses specific "boundaries." Business contexts often demonstrate this, such as when the cost per unit of an item decreases past a certain order quantity. The concept of tax brackets also illustrates piecewise functions. For instance, in a basic tax system where earnings up to $10,000 face a 10% tax, additional income incurs a 20% tax rate. Thus, the total tax on an income S would be 0.1S when \displaystyle {S}\leS≤ $10,000 and 1000 + 0.2 (S – $10,000) when S > $10,000.
</pwhen></pwhen>
Answer:
128/15 minutes or 8.5 minutes
Step-by-step explanation:
Utilizing the unitary method,
The duration to paint 5/8 of the wall is 16 minutes.
Consequently, the time to paint the entire wall is calculated as 16 × 8/5.
Thus, the time required to paint 1/3 of the wall amounts to 16 × 8/5 × 1/3.
Answer:
1.0 gram (rounded from.98)
Step-by-step explanation:
This is an exponential equation represented as 
, where a denotes the initial quantity and b represents the rate of decay (or growth). The initial amount a is straightforward, being 430, but for b, ensure it's expressed in decimal form. To convert the percentage (like 27.4%) to decimal, simply move the decimal point two places to the left, yielding.274.
Next, with the equation 
, we can apply the value of x as 19.
Also, be aware that if different units are involved, like if t represented a decay over 19 hours, those would need to be converted as well. I'm here to help if you require further clarification.
