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Nitella [24]
2 years ago
9

Multiply the binomials: (2c - d) (3c + d)

Mathematics
1 answer:
slega [8]2 years ago
3 0

Answer:

6c^2-cd-d^2

Step-by-step explanation:

How you get the answer is you use the process called FOIL. The F is front, so you multiply the 2c and the 3c to get 6c^2. The O is the outer, so you multiply the 2c and the d(because they are on the outer sides of the parenthesis) to get 2cd. The I is the inner, so you multiply the -d and the 3c(because they are on the inner sides of the parenthesis) to get -3cd. The L is the last, so you multiply d and -d to get -d^2. The 2cd and the -3cd are the same so you have to minus them to get -cd. So the answer is:

6c^2-cd-d^2.

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If ln(4x+y)=2x-3,then dy/dx=
Viktor [21]

\ln(4x+y)=2x-3

Differentiate both sides wrt x:

\dfrac{\mathrm d(\ln(4x+y))}{\mathrm dx}=\dfrac{\mathrm d(2x-3)}{\mathrm dx}

By the chain rule, we get

\dfrac1{4x+y}\dfrac{\mathrm d(4x+y)}{\mathrm dx}=2

\dfrac{4+\frac{\mathrm dy}{\mathrm dx}}{4x+y}=2

Solve for \frac{\mathrm dy}{\mathrm dx}:

4+\dfrac{\mathrm dy}{\mathrm dx}=8x+2y

\boxed{\dfrac{\mathrm dy}{\mathrm dx}=8x+2y-4}

4 0
2 years ago
Recent census data indicated that 14.2% of adults between the ages of 25 and 34 live with their parents. A random sample of 125
kicyunya [14]

Answer:

The  probability is  P(14 <  X  <  20 ) =  0.5354  

Step-by-step explanation:

From the question we are told that

   The  proportion that live with their parents is  \r p  =  0.142

   The  sample  size is n =  125

   

Given that there are two possible outcomes and that this outcomes are independent of each other then we can say the Recent census data follows a Binomial distribution

  i.e  

       X   \  \~ \ B( \mu ,  \sigma )

Now the mean is evaluated as

      \mu  =  n *  \r p

      \mu  =  125 *  0.142

      \mu  =  17.75

Generally the proportion that are not staying with parents is  

      \r  q  =  1 -  \r  p

= >    \r  q  =  0.858

The standard deviation is mathematically evaluated as

     \sigma  =  \sqrt{n * \r p  *  \r q }

     \sigma  =  \sqrt{ 125 *  0.142 * 0.858  }

    \sigma  = 3.90

Given the n is large  then we can use normal approximation to evaluate the probability as follows  

     P(14 <  X  <  20 ) =  P( \frac{ 14 -  17.75}{3.90}

Now applying continuity correction

      P(14 <  X  <  20 ) =  P( \frac{ 13.5 -  17.75}{3.90}  < \frac{  X  - \mu }{\sigma } < \frac{ 19.5 -  17.75}{3.90}   )

Generally  

    \frac{  X  - \mu }{\sigma }  =  Z  ( The  \ standardized \ value  \  of  X )

    P(14 <  X  <  20 ) =  P( \frac{ 13.5 -  17.75}{3.90}  < Z< \frac{ 19.5 -  17.75}{3.90}   )

     P(14 <  X  <  20 ) =  P( -1.0897   < Z<  0.449 }   )

    P(14 <  X  <  20 ) =   P( Z<  0.449   ) - P(Z  <   -1.0897)

So  for the z -  table  

         P( Z<  0.449   ) =  0.67328

         P(Z  <   -1.0897)  = 0.13792

 P(14 <  X  <  20 ) =   0.67328 -  0.13792    

  P(14 <  X  <  20 ) =  0.5354  

     

6 0
3 years ago
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sleet_krkn [62]

Answer:

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Step-by-step explanation:

This is a common, GCF question and the question becomes, what number is the GCF of 40 and 24.

40= 2x2x2x5

24=2x2x2x3

Both share 2x2x2, which is 8 so the largest number of pencils in each pack is 8.

5 0
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Answer $2.84

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