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QveST [7]
1 year ago
5

Geometry please help!

Mathematics
1 answer:
o-na [289]1 year ago
6 0

Answer:

x = 3

Step-by-step explanation:

Angle S and Angle T are consecutive interior angles. Therefore, we know that T + S = 180°.

First, we need to solve for T, and since angles S and T are consecutive interior angles, we know that T + S = 180°. If we reorganize the equation to include the things we know (S = 105°), then we get 180° - 105° = 75°. So T is 75°.

Now, we use T = 75° and the information given to us in the picture to set up an equation. 75 = 24x + 3. Now, we can find x by isolating it. Do this by:

1) Subtracting 3 from both sides to give you 72 = 24x. We do this to get rid of the 3 from the "x side", but we must also do it to the other to keep the equation true. This moves the 3 from the "x side" to the other since we're trying to isolate x.

2) Divide 24 by both sides to get 3 = x. We use the same logic as we did for 3, except this time we divide since that's the opposite of multiplying.

In conclusion, x = 3.

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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
Please help! I will mark you as brainliest!
lisov135 [29]

Answer:

7/9

Step-by-step explanation:

Think of 1 as being 9/9. The difference between 9/9 and 2/9 is 7/9, which is the answer

8 0
3 years ago
Read 2 more answers
Which one of these diagrams shows its reference angle in standard position?
Svetach [21]

Answer:

A

Step-by-step explanation:

MARK AS BRAINLIEST!!

3 0
3 years ago
Write an explicit function for f(x) <br> Can anyone help me with this please I’ll mark as brainliest
stiv31 [10]

Answer:

Explicit Function:

Any function which when expressed in terms of the independent variable is called an explicit function. For example, if we write y=f(x)

, then the dependent variable y is given in terms of the independent variable x by the function f(x). Thus y=f(x) is an explicit function. But, g(x,y)=c

is not explicit as it is a combination of both x and y. Such a function is called implicit.

Step-by-step explanation:

What is meant by implicit function?

An implicit function is a function that is defined by an implicit equation. That means the equation contains several variables, including dependent and independent. In other words, it is an equation that relates one of the variables, recognized as the value of the function, with the others regarded as the arguments.

What is an explicit function?

An explicit function is a function that is represented in terms of an independent variable. For example, y = 4x – 7 is explicit where y is a dependent variable and is dependent on the independent variable x.

How do you know if a function is implicit?

If a function is written in the form f(x, y) = 0, we can say that the given function is implicit.

What is implicit function differentiation?

We differentiate or find the derivative for both sides of the equation in implicit function differentiation.

What is explicit and implicit?

In general, “explicit” means clearly stated, whereas “implicit” refers to proposed and not stated directly.

5 0
3 years ago
Which expression can be used to find the surface area of the following rectangular prism?
PolarNik [594]

Answer:

C.

Step-by-step explanation:

3 times 2 is 6, 2 times 5 is 10, 5 times 3 is 15. However you need 2 for each since there are 3 sets of two equal faces. So it will be 6+6+10+10+15+15

4 0
3 years ago
Read 2 more answers
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