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NeX [460]
2 years ago
13

Find inverse of f(x)=(x+4)^2

Mathematics
2 answers:
Dmitry_Shevchenko [17]2 years ago
7 0

Answer:

f⁻¹(x) = -4 + √x

emmasim [6.3K]2 years ago
4 0

Answer:

f⁻¹(x) = -4 + √x

Step-by-step explanation:

Switch the positions of x and y then solve for x.

f(x)=(x+4)^2\\x=(y+4)^2\\\sqrt{x} =y+4\\\sqrt{x} -4=y

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Ostrovityanka [42]

Answer:

4

Step-by-step explanation:

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8 0
2 years ago
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The Municipal Transit Authority wants to know if, on weekdays, more passengers ride the northbound blue line train towards the c
Kitty [74]

Answer:

The 90% confidence interval  -49.8

The null hypothesis is  H_o : \mu_1 = \mu_2

The alternative hypothesis H_a  :  \mu_1 <  \mu_2

The distribution test statistics is t = -3.222

The rejection region is  p-value < \alpha

The decision rule is reject the null hypothesis

The conclusion is

      There is sufficient evidence to conclude that there are more passengers riding the 8:30  train

The p-value  is  p-value  =0.000951

Step-by-step explanation:

From the question we are told that

    The first sample size n_1 = 30

    The first sample mean is  \= x _1 = 323

    The first standard deviation is s_1 = 41

    The second sample size is n_2 = 45

    The second sample mean is  \=x_2 = 356

    The second standard deviation is s_2 = 45

given that the confidence level is 90% then the level of significance is mathematically represented as

          \alpha  = (100 -90)\%

         \alpha  = 0.10

Generally the critical value of \frac{\alpha }{2} obtained from the normal distribution table is  

   Z_{\frac{\alpha }{2} } = 1.645

Generally the pooled variance is mathematically represented as

        s^2 = \frac{(n_1 - 1)s_1^2  + (n_2 -1)s_2^2 }{n_1 + n_2 -2}

      s^2 = \frac{(30 -1)(41^2) + (45-1)45^2}{30+45 -2}

     s^2 = 1888.34

Generally the standard error is mathematically represented as

     SE =  \sqrt{\frac{s^2}{n_1} + \frac{s^2}{n_2}  }

=>  SE =  \sqrt{\frac{1888.34}{30} + \frac{1888.34}{45}  }

=>   SE =  10.24

Generally the margin of error is mathematically evaluated as  

      E =  Z_{\frac{\alpha }{2} } * SE

       E =  1.645* 10.24

       E = 16.85

Generally the 90% confidence interval is mathematically represented as

     \=x_1 -\=x_2 -E < \mu_1 -\mu_2 < \=x_1 -\=x_2 +E

     323 -356 -16.84

     -49.8

The null hypothesis is  H_o : \mu_1 = \mu_2

The alternative hypothesis H_a  :  \mu_1 <  \mu_2

Generally the test statistics is mathematically represented as

     t =  \frac{\= x_1 - \=x_2 }{SE}

=>   t = \frac{323-356}{10.24}

=>   t = -3.222

Generally the degree of freedom is mathematically represented as

     df =  n_1+n_2 -2

      df = 30 + 45 -2

     df = 73

The p-value is obtained from the student t distribution table at degree of freedom of 73 at 0.05 level of significance

    The value is  p-value  =0.000951

Here the level of significance is  \alpha =  5\%  =  0.05

Given that the p-value < \alpha then we  reject the null hypothesis

Then the conclusion is  

  There is sufficient evidence to conclude that there are more passengers riding the 8:30  train

               

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3 years ago
Which of the following inequalities is equivalent to 3-(w+2)&gt;4+2w
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3 - w - 2 > 4 + 2w  \\  - w - 2w > 4 + 2 - 3 \\  - 3w > 6 - 3 \\   \frac{ - 3w}{ - 3}  >  \frac{3}{ - 3} \\ w <  - 1
The sign at the end changes because both sides of the equation are being divided by a negative number.
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2 years ago
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Step-by-step explanation:

4-1-2-3-4-6-910191944

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What is the value of the discriminant for the quadratic equation -3=-x 2+2x
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X=3,-1 your answer is right here
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