Answer:
[tex]\mathrm{26.\qua\:H\quad\:2 \dfrac{ 1 }{ 4 }\qua\:mi}[/tex]
[tex]\mathrm{27.\qua\:D\quad\: 9\dfrac{ 1 }{ 8 }\qua\:lb}[/tex]
[tex]\mathrm{28.\qua\:H\quad\:14.6}[/tex]
[tex]\mathrm{29.\qua\:C\quad\:25\%}[/tex]
[tex]\mathrm{30.\qua\:J\quad\:33.912\qua\ ft^{3} }[/tex]
Step-by-step explanation:
26.
[tex]\mathrm{\dfrac{ 3 }{ 4 }\:mile\:per\:one\:hour}[/tex]
[tex]\mathrm{To\:find\:how\:far\:Jet's\:cousin\:can\:walk\:in\:3\:hours\:,\:we\:multiply\:\dfrac{ 3 }{ 4 }\:by\:3}[/tex]
[tex]3 \times \dfrac{ 3 }{ 4 }[/tex]
[tex]\mathrm{Express\: 3 \times \left( \dfrac{ 3 }{ 4 } \right)\:as\:a\:singe\:fraction}[/tex]
[tex]\dfrac{ 3 \times 3 }{ 4 }[/tex]
[tex]\mathrm{Multiply\:3\:and\:3\:to\:get\:9}[/tex]
[tex]\dfrac{ 9 }{ 4 }[/tex]
[tex]\mathrm{Convert\:\dfrac{ 9 }{ 4 }\:to\:a\:mixed\:number}[/tex]
[tex]2 \dfrac{ 1 }{ 4 }[/tex]
[tex]\mathrm{So\:she\:can\:walk\:2 \dfrac{ 1 }{ 4 }\:miles\:in\:3\:hours}[/tex]
27.
[tex]\mathrm{Since\:we\:want\:to\:find\:how\:many\:pounds\:both\:pumpkins\:weigh\:together,\:we\:have\:to\:add.}[/tex]
[tex]5 \dfrac{ 3 }{ 4 } +3 \dfrac{ 3 }{ 8 }[/tex]
[tex]\mathrm{Turn\:both\:mixed\:fractions\:into\:improper\:fractions}[/tex]
[tex]\dfrac{ 23 }{ 4 } + \dfrac{ 27 }{ 8 }[/tex]
[tex]\mathrm{Least\:common\:multiple\:of\:4\:and\:8\:is\:8}[/tex]
[tex]\mathrm{Multiples\:of\:4}:\quad4,8,12,16,20[/tex]
[tex]\mathrm{Multiples\:of\:8}:\quad8,16,24,32,40[/tex]
[tex]\dfrac{ 23 }{ 4 } + \dfrac{ 27 }{ 8 }[/tex]
[tex]\mathrm{Convert\: \dfrac{ 23 }{ 4 } \:and\: \dfrac{ 27 }{ 8 } \:to\:fractions\:with\:denominator\:8}[/tex]
[tex]\dfrac{ 23 \times 2 }{ 4 \times 2 } + \dfrac{ 27 }{ 8 }[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]\dfrac{ 46 }{ 8 } + \dfrac{ 27 }{ 8 }[/tex]
[tex]\mathrm{Since\: \dfrac{ 46 }{ 8 }\:and\:\dfrac{ 27 }{ 8 }\:have\:the\:same\:denominators,\:add\:them\:by\:adding\:their\:numerators}[/tex]
[tex]\dfrac{ 46+27 }{ 8 }[/tex]
[tex]\mathrm{Add\:46\:and\:27\:to\:get\:73}[/tex]
[tex]\dfrac{ 73 }{ 8 }[/tex]
[tex]\mathrm{Convert\:\dfrac{ 73 }{ 8 }\:to\:a\:mixed\:number}[/tex]
[tex]9 \dfrac{ 1 }{ 8 }[/tex]
[tex]\mathrm{Both\:pumpkins\:weighed\:9 \dfrac{ 1 }{ 8 }\:pounds\:all\:together}[/tex]
28.
Since the question is asking us "How many more miles did Alyce travel than Jason", we have to subtract the miles Jason traveled from the miles Alyce traveled.
[tex]29.193-14.593[/tex]
[tex]\mathrm{Subtract\:14.593\:from\:29.193\:to\:get\:14.6}[/tex]
[tex]14.6[/tex]
[tex]\mathrm{Alyce\:traveled\:14.6\:more\:miles\:than\:Jason}[/tex]
29.
For this question, we must find "10 is what percent of 40"
The equation for this is:
[tex]\dfrac{ 10 }{ 40 } \times 100[/tex]
[tex]\mathrm{Simplify\: \dfrac{ 10 }{ 40 } \:to\: \dfrac{ 1 }{ 4 } }[/tex]
[tex]\dfrac{ 1 }{ 4 } \times 100[/tex]
[tex]\mathrm{Multiply\: \dfrac{ 1 }{ 4 }\:and\:100\:to\:get\: \dfrac{ 100 }{ 4 } }[/tex]
[tex]\dfrac{ 100 }{ 4 }[/tex]
[tex]\mathrm{Divide\:100\:by\:4\:to\:get\:25}[/tex]
[tex]25[/tex]
[tex]\mathrm{So\:she\:recieved\:a\:25\%\:off\:discount}[/tex]
To check if this is correct, you can do the following below:
What is 25 percent (%) off $40?
Use the formula and replace the given values:
Amount Saved = Original Price x Discount % / 100. So,
Amount Saved = 40 x 25 / 100
Amount Saved = 1000 / 100
Amount Saved = $10
In other words, a 25% discount for an item with original price of $40 is equal to $10
30.
Given that the calculated volume of the drum is 37.68 ft³ and it is 90% full, it implies that the current volume is calculated as:
[tex]\mathrm{Current\:compacity} = 90 \% \times 37.68[/tex]
[tex]\mathrm{Turn\:90\%\:into\:a\:decimal}[/tex]
[tex]\mathrm{Current\:compacity} = 0.9 \times 37.68[/tex]
[tex]\mathrm{Multiply\:0.9\:and\:37.68\:to\:get\:33.912}[/tex]
[tex]33.912[/tex]
[tex]\mathrm{The\:current\:compacity\:of\:the\:drum\:is\:33.912\:ft^{3} }[/tex]
