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GalinKa [24]
3 years ago
15

70% of Ms. Miller's class passed the test on the first try. Those who failed were able to retake and half of those students pass

ed on their second try. If there are 20 students in the class, what overall percentage passed the test?
Mathematics
1 answer:
MrRissso [65]3 years ago
5 0

Answer:

85%

Step-by-step explanation:

  1. Calculate how many students passed on their first try. 20 x 70% is 14, so 14 students passed on their first try.
  2. 6 students retook the test. Half of 6 is 3. Add 3 to the 14 students that passed earlier.
  3. Calculate the percent with the equation 17/20 = 0.85. 0.85 = 85%.
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What are the side lengths of the rectangle area 40 perimeter 26
shusha [124]
Recall the formula for finding the area of a rectangle:

           Area = Length × Width

Recall the formula for finding the perimeter of a rectangle:

         Perimeter = 2 ( Length + Width )

Given in your problem:
        Area = 40 sq. units
        Perimeter = 26 units

Required to solve for:
        Length (L) and width (W)

• First, substitute the given to the formula:

        Area = Length x Width
          40 = L × W      ⇒   equation number 1

       Perimeter = 2 ( Length + Width )
            26 = 2 ( L + W )     ⇒   equation number 2


• Simplifying equation number 2,
           13 = L + W

 • Rearranging the equation, 

         L = 13 - W   ⇒   equation 3

Substituting equation 3 from equation 1:

      ( equation 1 )               40 = (L)(W)
      ( equation 3 )                L = 13 - W
                                      40 = (13 - W) (W)
                                      40 = 13W - W² 
      ( regrouping )          W² - 13W + 40 = 0
      ( factoring )             (W - 8) (W - 5) = 0
                                     W - 8 = 0    ;     W - 5 = 0
                                        W = 8      ;        W = 5
   
Therefore, there are 2 possible values for the width of the rectangle. It can be 8 units or 5 units.

• Now to solve for the length of the rectangle, substitute the two values of width to equation 3.

      (equation 3)        L = 13 - W
                       for W = 8    ⇒   L = 13 - 8
                                                   L = 5 units
                   
                       for W = 5    ⇒  L = 13 - 5
                                                   L = 8 units

3 0
3 years ago
Rate of change of rational functions
densk [106]

Answer:

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Step-by-step explanation:

rate~of~change = \dfrac{f(x_2) - f(x1)}{x_2 - x_1}

rate~of~change = \dfrac{f(x_2) - f(x1)}{x_2 - x_1}

x_1 = 0       x_2 = 0.3

f(x) = \dfrac{-7x^3}{x^4 - 1}

f(x_1) = f(0) = \dfrac{-7(0)^3}{(0)^4 - 1}

f(x_1) = \dfrac{0}{-1} = 0

f(x_2) = f(0.3) = \dfrac{-7(0.3)^3}{(0.3)^4 - 1}

f(x_2) = \dfrac{-0.189}{-0.9919} = 0.190543

rate~of~change = \dfrac{0.190543 - 0}{0.3 - 0} = 0.635

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Nesterboy [21]

Answer:

y=0

Step-by-step explanation:

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