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Kruka [31]
3 years ago
12

An angle theta is in​ ________ _______ if its vertex is at the origin of a rectangular coordinate system and its initial side co

incides with the positive​ x-axis
Mathematics
1 answer:
romanna [79]3 years ago
6 0

We know that in standard position, the vertex of the angle should lie at the origin and its initial side is always fix along the positive x- axis. Please see the attached image.

We can see that the vertex of the angle is at the origin O and the initial side OB is along the positive x axis. This is the standard position of an angle.

Therefore, we have

An angle theta is in​ standard position if its vertex is at the origin of a rectangular coordinate system and its initial side coincides with the positive​ x-axis.

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WILL MARK BRAINLIST FOR ANSWER!!!!!!!!!!<br> |2 1/3 x+0.3|=3.5
Natalija [7]
THE ANSWER ISSSS


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6 0
3 years ago
The amount of money spent on textbooks per year for students is approximately normal.
Ostrovityanka [42]

Answer:a

a

   336.04    <  \mu < 443.96

b

  The  margin of error will increase

c

The  margin of error will decreases

d

The 99% confidence interval is  0.4107 <  p  < 0.4293

Step-by-step explanation:

From the question we are  told that

   The sample size  n =  19

    The sample mean is  \= x  = \$\  390

    The  standard deviation is  \sigma =  \$ \  120

 

Given that the confidence level is  95% then the level of significance is mathematically represented as

           \alpha = 100 -  95

          \alpha  =  5 \%

          \alpha  =  0.05

Next we obtain the critical value of \frac{\alpha }{2} from the normal distribution table

    So  

         Z_{\frac{\alpha }{2} } =  1.96

The  margin of error is mathematically represented as

      E =  Z_{\frac{\alpha }{2} } *  \frac{\sigma}{\sqrt{n} }

=>    E = 1.96 *  \frac{120}{\sqrt{19} }

=>   E = 53.96

The 95% confidence interval is  

     \= x  -  E  <  \mu < \= x  +  E

=>   390  -   53.96   <  \mu < 390  -   53.96

=>  336.04    <  \mu < 443.96

When the confidence level increases the Z_{\frac{\alpha }{2} } also increases which increases the margin of error hence the confidence level becomes wider

Generally the sample size mathematically varies with margin of error as follows

         n  \  \ \alpha  \ \  \frac{1}{E^2 }

So if the sample size increases the margin of error decrease

The  sample proportion is mathematically represented as

       \r p  =  \frac{210}{500}

       \r p  = 0.42

Given that the confidence level is 0.99 the level of significance is  \alpha =  0.01

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

      Z_{\frac{\alpha }{2} }  =  2.58

  Generally the margin of error is mathematically represented as

       E =  Z_{\frac{\alpha }{2} }*  \sqrt{ \frac{\r p (1- \r p )}{n} }

=>   E =  0.42 *  \sqrt{ \frac{0.42 (1- 0.42 )}{ 500} }

=>     E =  0.0093

The 99% confidence interval  is

     \r p  -  E <  p  < \r p  +  E

     0.42  -  0.0093 <  p  < 0.42  +  0.0093

     0.4107 <  p  < 0.4293

 

4 0
3 years ago
How many solutions does the following equation have?<br> -5(2+1) = –22 + 10
Igoryamba

Answer:

0 real # solution

Step-by-step explanation:

b^2-4ac<1 is equal to 0 real number solution and

-5(2+1)=-22+10

-5(2+1)=-12

which is less than 1

7 0
3 years ago
Divide 25.84 divide by 4
Nadusha1986 [10]
I believe it is 6.46
6 0
3 years ago
Read 2 more answers
In Bobby’s school, math grades for the year are calculated from assignments, tests and a final exam. Assignments count 30%, test
jarptica [38.1K]

Answer:

A) Bobby's overall grade is 70.4%

Step-by-step explanation:

To solve this problem we must calculate the percentages each grade represents from the overall grade. Therefore:

assignment = 85*30% = 85*30/100 = 25.5%

tests = 72*20% = 72*20/100 = 14.4%

exam = 61*50% = 61*50/100 = 30.5%

total = assignment + tests  + exam

total = 25.5 + 14.4 + 30.5 = 70.4

Bobby's overall grade is 70.4%. Therefore the correct answer is A).

7 0
3 years ago
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