Which step in the proof has a flow?

Three vertices of parallelogram WXYZ are X(–2,–3), Y(0, 5), and Z(7, 7). Find the coordinates of vertex W

Serhud [2]

The coordinates of the vertex W are (5 , -1)

Step-by-step explanation:

In the parallelogram, the diagonal bisect each other

To find a missing vertex in a parallelogram do that:

Find the mid-point of a diagonal whose endpoints are given
Use this mid-point to find the missing vertex
The mid point rule is $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

∵ WXYZ is a parallelogram

∴ Its diagonals are WY and XZ

∵ The diagonal bisect each other

- That mean they have the same mid-point

∴ They intersect each other at their mid-point

∵ x = (-2 , -3) and z = (7 , 7)

∴ $x_{1}$ = -2 and $x_{2}$ = 7

∴ $y_{1}$ = -3 and $y_{2}$ = 7

- Substitute them in the rule of the mid point to find the

mid-point of XZ

∴ $M_{XZ}=(\frac{-2+7}{2},\frac{-3+7}{2})=(2.5 , 2)$

∴ The mid-point of diagonals WY and XZ is (2.5 , 2)

Let us use it to find the coordinates of vertex W

∵ W = (x , y) and Y = (0 , 5)

∴ $x_{1}$ = x and $x_{2}$ = 0

∴ $y_{1}$ = y and $y_{2}$ = 5

- Equate 2.5 by the rule of the x-coordinate of the mid-point

∵ $2.5=\frac{x+0}{2}$

- Multiply both sides by 2

∴ 5 = x + 0

∴ 5 = x

∴ The x-coordinate of point W is 5

- Equate 2 by the rule of the y-coordinate of the mid-point

∵ $2=\frac{y+5}{2}$

- Multiply both sides by 2

∴ 4 = y + 5

- Subtract 5 from both sides

∴ -1 = y

∴ The y-coordinate of point W is -1

The coordinates of the vertex W are (5 , -1)

Learn more:

You can learn more about the mid-point in brainly.com/question/10480770

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3 years ago

We have n = 100 many random variables Xi ’s, where the Xi ’s are independent and identically distributed Bernoulli random variab

777dan777 [17]

Answer:

(a) The distribution of $X=\sum\limits^{n}_{i=1}{X_{i}}$ is a Binomial distribution.

(b) The sampling distribution of the sample mean will be approximately normal.

(c) The value of $P(\bar X>0.50)$ is 0.50.

Step-by-step explanation:

It is provided that random variables $X_{i}$ are independent and identically distributed Bernoulli random variables with p = 0.50.

The random sample selected is of size, n = 100.

(a)

Theorem:

Let $X_{1},\ X_{2},\ X_{3},...\ X_{n}$ be independent Bernoulli random variables, each with parameter p, then the sum of of thee random variables, $X=X_{1}+X_{2}+X_{3}...+X_{n}$ is a Binomial random variable with parameter n and p.

Thus, the distribution of $X=\sum\limits^{n}_{i=1}{X_{i}}$ is a Binomial distribution.

(b)

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

The sample size is large, i.e. n = 100 > 30.

So, the sampling distribution of the sample mean will be approximately normal.

The mean of the distribution of sample mean is given by,

$\mu_{\bar x}=\mu=p=0.50$