A large container holds 8 gallons of water. It begins leaking at a constant rate. After 16 minutes, the container has 7 gallons
1 answer:
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First find the slope.
We know these two points are in the line: (0,8) and (6,5)
The slope is -1/2. The y-intercept can be found when x = 0. And we know that the point (0,8) is on the line and x = 0, therefore the y-intercept is 8.
Plugging this into the slope-intercept form which is
y = mx + b, where m is the slope and b is the y-intercept, we get:
y = (-1/2)x + 8
We know these two points are in the line: (0,8) and (6,5)
The slope is -1/2. The y-intercept can be found when x = 0. And we know that the point (0,8) is on the line and x = 0, therefore the y-intercept is 8.
Plugging this into the slope-intercept form which is
y = mx + b, where m is the slope and b is the y-intercept, we get:
y = (-1/2)x + 8
The correct answers are:
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1) " 0.8 = 80 % " .
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2) " = 62. 5 % " .
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3) " 0.01 = 1 % " .
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Explanation:
To solve:
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Write the numbers: " 0.8 " ; " 5/8 " ; <u><em>and</em></u>: " 0.01 " ; as "percentages" .
To write a "number" as a "percentage" :
- You take the "number" ;
- Multiply that "number" by "100" ; <em><u>AND</u></em>:
- add a "percent symbol";
→ that is: " % " ;
→ to denote the "percentage" ; or, "parts per hundred" .
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Let us start with the number: " 0.8 " .
→ " 0.8 " * 100 = ?
→ Take the decimal point, and move it 2 decimal spaces to the right; since we are "multiplying" by "100" (which has "2 zeros") ;
→ 0.8 * 100 = ? ; If we move the decimal space "one space" forward, we have: "8" . If we move the decimal space yet "one more space forward" ;
→ "8." to: " 80 " .
→ Then we add the "percent symbol":
→ " 80 " ; to: " 80 % "
Answer: " 0.8 = 80 % " .
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Other method:
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→ Note that "percentage" means: "parts per hundred" :
→ Given: " 0.8 " ; Convert to a "percentage" :
→ " 0.8 = " ;
→ " " ;
→ Find the "?" value.
→ To do so; look at the "denominators" :
→ " 10 * (what) = 100 " ?
→ Divide each side by "10" ;
→ " [10 * what ] / 10 = 100 / 10 " ;
→ to get:
→ " [what] " = "10" .
→ So; " " ;
→ If "{10 * 10 = 100}" ; then, "{8 * 10 = 80}" .
→ So; " {?} " = " 80 " .
→ So; " " ;
→ As such: " 0.8 " = " () " ;
= " 80 " parts per hundred ;
= " 80 % " .
Answer: " 0.8 " = 80 % " .
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Now, let convert: "()" ; into a percentage.
→ Multiply by "100" ;
→ "()" * 100 ;
→ "() * (
)" ;
→ "()" ;
→ "()" ;
= " { 500 ÷ 8 } " ;
= " 62. 5 " ;
→ Now, add the "percent symbol" ;
→ " 62. 5 " ; → 62. 5 % " .
Answer: " = 62. 5 % " .
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Now, let us finish with our last "given value":
Convert: " 0.01 " ; to a "percentage" :
→ " 0.01 " * 100 = ?
→ Take the decimal point, and move it 2 decimal spaces to the right; since we are "multiplying" by "100" (which has "2 zeros") ;
→ 0.01 * 100 = ? ; If we move the decimal space "2 spaces forward" , we have: " 1 " .
As such:
→ " 0.01 " to: " 1 " .
→ Then we add the "percent symbol":
→ " 1 " ; to: " 1 % " .
Answer: " 0.01 = 1 % " .
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Hope this answer is of help to you.
Best wishes!
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