How can you use proportional reasoning to solve problems involving percent

1 answer:

3 0

Example A, Step 1: Write a comparing the percent to the ratio of part to whole. ex- ?/25 = 28/100 *Notice that 25 is a factor of 100* Step 2: Find the multiplication factor. ex- ?*4 = 28 and 25*4 = 100 *Since 25*4 = 100, find what number times 4 equals 28* Step 3: Find the numerator. ex- 7/25 = 28/100 *Since 4*7 = 28, 28% of 25 = 7 Example B, Step 1: Write the percent as a fraction. ex-35% of 60 = 35/100 of 60 Step 2: Multiply. ex- 35/100 of 60 = 35/100x60=2100/100=21 *Simplify* Example C, Step 1: Write the percent as a decimal. ex- 5% = 5/100 = 0.05 Step 2: Multiply. ex- 180 * 0.05 = 9, 5% of 180 is 9.

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A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 45.0 and 55.

yuradex [85]

Given:

Uniform distribution of length of classes between 45.0 to 55.0 minutes.

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3 years ago

Can someone please help me factor this

Dmitry_Shevchenko [17]

Answer:

$\huge\boxed{\bf\:1}$

Step-by-step explanation:

$\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 } \times \frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }$

Take $\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 }$ & factorise it at first.

$\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 } \\= \frac{\left(x-3\right)\left(x-1\right)}{\left(x-4\right)\left(x-3\right)}\\= \frac{x-1}{x-4}$

Now factorise the next set : $\frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }$ .

$\frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }\\= \frac{\left(x-4\right)\left(x+6\right)}{\left(x-1\right)\left(x+6\right)}\\= \frac{x-4}{x-1}$

Now, multiply the two simplified results.

$\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 } \times \frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }\\= \frac{x-1}{x-4}\times \frac{x-4}{x-1} \\= \frac{\left(x-1\right)\left(x-4\right)}{\left(x-4\right)\left(x-1\right)} \\= \boxed{\bf\: 1}$