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Nitella [24]
3 years ago
11

two sides of a triangle measures 20 centimeters and 30 centimeters which of the following could be the measure of the third side

Mathematics
1 answer:
brilliants [131]3 years ago
6 0
To find the third side of a triangle (there are two answers you could get), you need to use the Pythagorean formula: a^2+b^2=c^2.  First answer, 20^2+30^2=c^2.  Solve for c.  c=36.06.  The second answer, 20^2+b^2=30^2.  Solve for b.  b=26.36.
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Step-by-step explanation:

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Find each angle measure in the figure<br><br><br><br>The angle measures are ___°, ___° And ___°.​
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Maths!
Ber [7]

Answer:

(1) Variance = 4.5 and Standard deviation = 2.121.

(2) Variance = 4.5 and Standard deviation = 2.121.

(3) The effect on the measure of dispersion if each value is changed uniformly ​is that it remains unchanged.

Step-by-step explanation:

We are given with the following set of data below;

              X                     X-\bar X                   (X-\bar X)^{2}

              5                   5 - 8 = -3                     9

              5                   5 - 8 = -3                     9

              8                   8 - 8 = 0                      0

             10                  10 - 8 = 2                     4

             10                  10 - 8 = 2                     4

             10                  10 - 8 = 2                     4

              9                   9 - 8 = 1                       1

              9                   9 - 8 = 1                       1

         <u>     6     </u>              6 - 8 = -2             <u>        4       </u>          

Total <u>    72     </u>                                         <u>       36       </u>

<u>Firstly, the mean of the above data is given by;</u>

              Mean, \bar X  =  \frac{\sum X}{n}

                              =  \frac{72}{9}  = 8

(1)Now, the variance of the given data is;

            Variance  =  \frac{\sum (X-\bar X)^{2} }{n-1}

                                  =  \frac{36}{9-1}  = 4.5

So, the standard deviation, (S.D.)  =  \sqrt{\text{Variance}}

                                                        =  \sqrt{4.5} = 2.12

(2) Now, each value is added by 2; so the new data set is given by;

              X                     X-\bar X                   (X-\bar X)^{2}

              7                   7 - 10 = -3                     9

              7                   7 - 10 = -3                     9

             10                  10 - 10 = 0                     0

             12                  12 - 10 = 2                     4

             12                  12 - 10 = 2                     4

             12                  12 - 10 = 2                     4

              11                  11 - 10 = 1                       1

              11                  11 - 10 = 1                       1

         <u>     8     </u>              8 - 10 = -2             <u>        4       </u>          

Total <u>    90     </u>                                         <u>       36       </u>

<u>Firstly, the mean of the above data is given by;</u>

              Mean, \bar X  =  \frac{\sum X}{n}

                              =  \frac{90}{9}  = 10

(1)Now, the variance of the given data is;

            Variance  =  \frac{\sum (X-\bar X)^{2} }{n-1}

                                  =  \frac{36}{9-1}  = 4.5

So, the new standard deviation, (S.D.)  =  \sqrt{\text{Variance}}

                                                                =  \sqrt{4.5} = 2.12

(3) The effect on the measure of dispersion if each value is changed uniformly ​is that it remains unchanged as we see in the case of variance or standard deviation.

4 0
3 years ago
Hayley has $155 in savings, and her brother Hank has $230. Hayley is saving $10 each week, and her brother is spending $15 each
Sindrei [870]

Answer:

After 3 weeks they both will have the same amount in their savings account.

Step-by-step explanation:

Given:

Amount saved by Haley = $155

Amount saved by Hank = $230

Amount saving each week by Haley = $10

Amount spending each week by Hank = $15

We need to find Number of weeks when both both will have same amount in savings account.

Solution:

Let Number of week be 'x'.

Total Amount of Haley can be calculated by Amount saved by Haley plus Amount saving each week by Haley multiplied by number of weeks.

framing in equation form we get;

Total Amount of Haley = 155+10x

Also;

Total Amount of Hank can be calculated by Amount saved by Hank minus Amount spending each week by Hank multiplied by number of weeks.

framing in equation form we get;

Total Amount of Hank = 230-15x

Now we need to find the number of weeks when both will have same amount.

To find the same we will have to make both the equation equal.

So we can say.

155+10x=230-15x

On Solving above equation we get;

We will combine the like terms together;

10x+15x =230-155\\\\25x = 75

Now Dividing both side by 25 using Division property of equality we get;

\frac{25x}{25} = \frac{75}{25}\\\\x=3 \ weeks

Hence, After 3 weeks they both will have the same amount in their savings account.

4 0
3 years ago
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