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evablogger [386]
3 years ago
13

Angle x is such that sin x = a + b and cos x = a − b, where a and b are constants.

Mathematics
2 answers:
Mazyrski [523]3 years ago
3 0

Answer:

Step-by-step explanation:

sin x=a+b

cos x=a-b

sin²x+cos²x=(a+b)²+(a-b)²=2a²+2b²

or 2a²+2b²=1

a²+b²=1/2 which is constant for all values of x

(ii)

\frac{\sin x}{\cos x}=\frac{a+b}{a-b}\\\tan x=\frac{a+b}{a-b}=2\\a+b=2a-2b\\b+2b=2a-a\\or a=3b

trasher [3.6K]3 years ago
3 0

Answer:25

Step-by-step explanation:

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What is the chance of rolling a 4 with a single die four times in a row?
BlackZzzverrR [31]

Answer:

16.66

Step-by-step explanation:

5 0
3 years ago
According to the US Bureau of labor statistics, 7% of US female workers between 16 and 24 years old are paid at the minimum wage
vladimir1956 [14]

Answer:

The Null Hypothesis is  H_o:k_o = 0.07

The alternative hypothesis is  H_a :k_o \ne 0.07

Decision rule

    If the test staistics is  greater than the critical value of significance level then H_o is accepted else H_o  is rejected

With the above in mind

       The critical value of the significance level which is obtained from the table is

     t_{0.05} = 1.645

Now since the critical value of significance level is greater than the test  staistics then the null hypothesis will be rejected

Conclusion

The information is not enough to back the claim that state differs from the nation

Step-by-step explanation:

From the question we are told that

The percentage of US female workers paid at the minimum wage or less is  k_o = 7% = 0.07

  The sample size is  n =  500

    The number paid minimum wage or less is  x = 42

    The significance level is \alpha  =5%  = 0.05

Now the probability of getting a US female workers paid at the minimum wage or less is mathematically represented as

         \= k = \frac{x}{n}

substituting value

        \= k = \frac{42}{500}

        \= k = 0.084

The Null Hypothesis is  H_o:k_o = 0.07

The alternative hypothesis is  H_a :k_o \ne 0.07

Generally the test statistics is mathematically evaluated as

        z =  \frac{\=  k  - k_o}{\sqrt{\frac{k_o(1-k_o)}{n} } }

substituting value

      z =  \frac{0.084  - 0.07}{\sqrt{\frac{0.07 (1-0.07)}{500} } }

     z =  1.23

Now the Decision rule is stated as  

        If the test staistics is  greater than the critical value of significance level then H_o is accepted else H_o  is rejected

With the above in mind

       The critical value of the significance level which is obtained from the table is

     t_{0.05} = 1.645

Now since the critical value of significance level is greater than the test  staistics then the null hypothesis will be rejected

   So the conclusion will be

   The information is not enough to back the claim that state differs from the nation

 

4 0
3 years ago
What is the mean absolute deviation of the data set?<br> {12, 17, 12, 8,6)
ser-zykov [4K]

Answer:The mean absolute deviation of the set of data is

2.24

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Step-by-step explanation:

8 0
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Help please i only got 4 minutes​
Zinaida [17]

Answer:

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Step-by-step explanation:

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2 years ago
A regular room has an area of 313 1/2 feet the length is 12 1/2 feet what is the width of the room
swat32
You need to divide 313.5/12.5=25.08 so the width is 25.08 feet
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