Compute each matrix sum or product if it is defined. If an expression is undefined. Explain why. Let A = (3 4 0 -4 -1 4), B = (8
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The answer is: " $0.67 / metre " ;
or, write as: " [ dollar] per metre."
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<u>Step-by-step explanation</u>:
This is a unit rate problem:
Find the cost in dollars per [single unit—in this case: "metre(s)", "<em>m</em>" ;
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; Solve for the "?" <u>amount of dollars</u>.
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Method 1) "Cross-factor multiply" :
<u>Note</u>: <u>Given</u><u>:</u> " " ;
then: ⟷ " " ;
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So: " \frac{200 dollars}{300m} = \frac{? dollars}{1m} " ;
then: ⟷ " (200*1) = (300* ?) ;
→ " (200) = (300 * ?)" ;
↔ " (300 * ?) = 200 " ;
Let "x" refer to the "?" ; the "<u>unknown value</u>" (<u>in dollars</u>);
for which we are trying to solve.
⇒ " 300x = 200 " ; Solve for "x" ;
→ Divide each side of the equation by: "300" ;
to isolate "x" on the "left-hand side" of the equation; & to solve for "x" ;
⇒ 300x/ 300 = 200/300 ;
To get: " x = dollars" ;
= $0.666666666... ;
round to: $0.67 .
{since: " 1 dollar = $1.00 = 100 cents" ;
and since: "\frac{2}{3} " ;
= ["2 ÷ 3" = 0.666666...." ] ;
⇒ round to: "0.67 " ;
and write as:
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⇒ $0.67 / metre ; or, write as:
" [ dollar] per metre."
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Method 2) <u>Note</u>:
\frac{200 dollars}{300m} = \frac{? dollars}{1m} ;
⇔ = "
" ;
{<u>Note</u>: "[200÷300]" can be simplified by "canceling out" the two (2) zeros in both the numerator and the denominator.}.
= " \frac{2 dollars}{3m} ";
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= i.e. " " or;
; or: <u>$0.67 / metre</u> .
⇒ {since: " of 1 dollar" = " \frac{2}{3} dollars of 100 cents" ;
⇒ {since: "1 dollar = 100 cents"} ;
⇒ {and: " " = 0.6666666666666... " } ;
→ round to: "0.67 " ; and thus: $0.67 / metre.
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Note that using either of these 2 (two) methods result in the same answer.
Hope this is helpful! Best wishes to you within your academic pursuits!
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Answer:
<em>It will take 9 years for the population to double</em>
Step-by-step explanation:
<u>Exponential Growth </u>
The natural growth of some magnitudes can be modeled by the equation:
Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.
The population of a city grows at a rate of r=8% = 0.08 per year. We are required to find when (t) the population will double, or P=2Po.
Substituting in the equation:
Simplifying:
Taking logarithms:
Applying the exponent property of logs:
Solving for t:
Calculating:
It will take 9 years for the population to double