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2 years ago

The variance Var(x) for the binomial distribution is given by equation :

Mathematics

1 answer:

aliina [53]2 years ago

6 0

Answer: d. np(1 - p).

Step-by-step explanation:

Let x be any binomial variable which represents the number of success such that $X\sim B(n, p)$ , where n is the sample size or the total number of trials and p is the probability of getting success in each trial .

Then, the mean E(x) and the variance Var(x) for the binomial distribution is given by equation :

$E(x)=\mu=np$

$Var (x)=\sigma^2=np(1-p)$

where n is the sample size or the total number of trials and p is the probability of getting success in each trial .

Therefore , the correct option is option d. np(1 - p) .

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Which is the graph of the linear inequality y < 3x + 1? On a coordinate plane, a solid straight line has a positive slope and

stepan [7]

For this case we have the following inequality: y < 3x + 1

What we must do is to evaluate a point of the Cartesian plane and verify if it is in the shaded region.

The shaded region represents the solution of the system of equations.

For the point (0, 0) we have:

0 < 3(0) + 1

0 < 0 + 1

0 < 1

Therefore, the point (0, 0) is in the shaded region because it satisfies the inequality.

Then, the points that are on the line, are not part of the solution because the sign is of less strict.

Hope I helped ~~Laurel

6 0

2 years ago

Read 2 more answers

Circle the common factors of 18W and 30WZ

Alex

Answer:

6, 6w, 3w, z and w.

Step-by-step explanation:

The common factors are those values that can divide 18w and 30wz perfectly.

Take a look at 6, 6 can divide both perfectly to give 3w and 5wz respectively.

We move on to 6w, this can also work perfectly to yield 3 and 5z.

6xz is not a factor as both values do not contain any x term.

3z is not a factor. Although 30wz has a z term, 18w does not.

3w is a factor as it can give 10z and 6 when used to divide the terms.

Z is not a factor as the 18w term does not contain a z term.

10w is not a term as it can not divide 18w perfectly

w is a term as it can divide both 18w and 30wz perfectly to yield 18 and 30z respectively.

6 0

2 years ago

What is the simplest form of RootIndex 3 StartRoot 27 a cubed b Superscript 7 Baseline EndRoot?

Vinvika [58]

Answer: $3ab\sqrt[3]{b^4}$

Step-by-step explanation:

Given the following expression:

$\sqrt[3]{27a^3b^7}$

You need to apply the Product of powers property, which states that:

$(a^m)(a^n)=a^{(m+n)$

Then, you can rewrite the expression as following:

$=\sqrt[3]{27a^3b^4b^3}$

The next step is to descompose 27 into its prime factors:

$27=3*3*3=3^3$

Now you must substitute $3^3$ inside the given root. Then:

$=\sqrt[3]{3^3a^3b^4b^3}$

You need to remember that, according to Radicals properties:

$\sqrt[n]{a^n}=a^{\frac{n}{n}}=a^1=a$

Therefore, the final step is to apply this property in order to finally get the expression is its simplest form. This is:

$=3^{\frac{3}{3}}a^{\frac{3}{3}}b^{\frac{4}{3}}b^{\frac{3}{3}}=3ab^{\frac{4}{3}}b=3ab\sqrt[3]{b^4}$

3 0

2 years ago

Read 2 more answers

Which of the following is the graph of y = negative StartRoot x EndRoot + 1? On a coordinate plane, an absolute value curve curv

mestny [16]

Answer:

B. On a coordinate plane, an absolute value curve curves up and to the right in quadrant 4 and starts at y = 1.

Step-by-step explanation:

Graph of the function:

y = -√x + 1

The domain is x ≥ 0, the range y ≤ 1

Correct answer choice is B

On a coordinate plane, an absolute value curve curves up and to the right in quadrant 4 and starts at y = 1.

The graph is attached

7 0

2 years ago

Read 2 more answers

A region R in the xy-plane is given. Find equations for a transformation T that maps a rectangular region S in the uv-plane onto

Gre4nikov [31]

$\begin{cases}y=2x-2\\y=2x+2\end{cases}\implies\begin{cases}-2x+y=-2\\-2x+y=2\end{cases}$

For these lines, let $u=-2x+y$ .

$\begin{cases}y=2-x\\y=4-x\end{cases}\implies\begin{cases}x+y=2\\x+y=4\end{cases}$

And for these, let $v=x+y$ .

Now,

$\begin{cases}u=-2x+y\\v=x+y\end{cases}\implies \begin{bmatrix}u\\v\end{bmatrix}=\underbrace{\begin{bmatrix}-2&1\\1&1\end{bmatrix}}_{\mathbf T}\begin{bmatrix}x\\y\end{bmatrix}$

The vertices of $S$ in the x-y plane are (0, 2), (2/3, 10/3), (2, 2), and (4/3, 2/3). Applying $\mathbf T$ to each of these yields, respectively, (2, 2), (2, 4), (-2, 4), and (-2, 2), which are the vertices of a rectangle whose sides are parallel to the u-v plane.

6 0

2 years ago