All categories

4 years ago

A randomly selected sample of 100 students had an average grade point average (GPA) of 3.2 with a standard deviation of 0.2.

Mathematics

1 answer:

alexdok [17]4 years ago

5 0

Answer:

A. 0.020

Step-by-step explanation:

we calculate the standard error of the sample mean with the formula,

$E=\frac{s}{\sqrt{n} }$ ,

with E= standard error of the sample mean

s= standard deviation

n= sample

So,

s= 0.2

n= 100

$E=\frac{0.2}{\sqrt{100} } =\frac{0.2}{10}=0.02$

You might be interested in

Solve using algebreic methods y=x^2+5x, y=7-x

adelina 88 [10]

Answer:

x = 1 and x = -7

Step-by-step explanation:

Given that,

$y=x^2+5x$ ...(1)

and

y = 7 -x ....(2)

Put the value of y from equation (2) in (1)

$7-x=x^2+5x\\\\x^2+5x-7+x=0\\\\x^2+6x-7=0\\\\x^2+7x-x-7=0\\\\x(x+7)-1(x+7)=0\\\\(x-1)(x+7)=0$

So,

x = 1 and x = -7

Hence, the solution of the given equations is x = 1 and x = -7

6 0

3 years ago

Consider the matrix A. A = 1 0 1 1 0 0 0 0 0 Find the characteristic polynomial for the matrix A. (Write your answer in terms of

dusya [7]

Answer with Step-by-step explanation:

We are given that a matrix

$A=\left[\begin{array}{ccc}1&0&1\\1&0&0\\0&0&0\end{array}\right]$

a.We have to find characteristic polynomial in terms of A

We know that characteristic equation of given matrix $\mid{A-\lambda I}\mid=0$

Where I is identity matrix of the order of given matrix

I= $\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$

Substitute the values then, we get

$\begin{vmatrix}1-\lambda&0&1\\1&-\lambda&0\\0&0&-\lambda\end{vmatrix}=0$

$(1-\lambda)(\lamda^2)-0+0=0$

$\lambda^2-\lambda^3=0$

$\lambda^3-\lambda^2=0$

Hence, characteristic polynomial = $\lambda^3-\lambda^2=0$

b.We have to find the eigen value for given matrix

$\lambda^2(1-\lambda)=0$

Then , we get $\lambda=0,0,1-\lambda=0$

$\lambda=1$

Hence, real eigen values of for the matrix are 0,0 and 1.

c.Eigen space corresponding to eigen value 1 is the null space of matrix $A-I$

$E_1=N(A-I)$

$A-I=\left[\begin{array}{ccc}0&0&1\\1&-1&0\\0&0&-1\end{array}\right]$

Apply $R_1\rightarrow R_1+R_3$

$A-I=\left[\begin{array}{ccc}0&0&1\\1&-1&0\\0&0&0\end{array}\right]$

Now,(A-I)x=0[/tex]

Substitute the values then we get

$\left[\begin{array}{ccc}0&0&1\\1&-1&0\\0&0&0\end{array}\right]\left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right]=0$

Then , we get $x_3=0$

And $x_1-x_2=0$

$x_1=x_2$

Null space N(A-I) consist of vectors

x= $\left[\begin{array}{ccc}x_1\\x_1\\0\end{array}\right]$

For any scalar $x_1$

$x=x_1\left[\begin{array}{ccc}1\\1\\0\end{array}\right]$

$E_1=N(A-I)=Span(\left[\begin{array}{ccc}1\\1\\0\end{array}\right]$

Hence, the basis of eigen vector corresponding to eigen value 1 is given by

$\left[\begin{array}{ccc}1\\1\\0\end{array}\right]$

Eigen space corresponding to 0 eigen value

$N(A-0I)=\left[\begin{array}{ccc}1&0&1\\1&0&0\\0&0&0\end{array}\right]$

$(A-0I)x=0$

$\left[\begin{array}{ccc}1&0&1\\1&0&0\\0&0&0\end{array}\right]\left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right]=0$

$\left[\begin{array}{ccc}x_1+x_3\\x_1\\0\end{array}\right]=0$

Then, $x_1+x_3=0$

$x_1=0$

Substitute $x_1=0$

Then, we get $x_3=0$

Therefore, the null space consist of vectors

$x=x_2=x_2\left[\begin{array}{ccc}0\\1\\0\end{array}\right]$

Therefore, the basis of eigen space corresponding to eigen value 0 is given by

$\left[\begin{array}{ccc}0\\1\\0\end{array}\right]$

5 0

3 years ago

Write slope intercept equation passing through (-5,0) and (0,4/5)

pav-90 [236]

First find the slope by calculating rise (change in x) over run (change in y).

(4/5)-0/0-(-5)

(4/5)/5=0.16

The y intercept is 4/5. We know this because y interceot is the value of y when x is 0.

Then plug this into y=mx+b where m is slope andb is y intercept.

Final answer: y=0.16x+0.8 or y= 4/25x+ 4/5

3 0

3 years ago

Find the value of x:

slega [8]

Answer:

x = 20

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Using ΔAHC , then

∠ACH = 180 - (2x + 100) = 180 - 2x - 100 = 80 - 2x

∠ECD = ∠ACB ( vertical angles are congruent ), thus

∠ECD = ∠ACH + ∠HCB, that is

3x = 80 - 2x + x

3x = 80 - x ( add x to both sides )

4x = 80 ( divide both sides by 4 )

x = 20

7 0

4 years ago

David make 17 dollars in an hour and works 25 hours each week Linda makes 25 dollars in and hour and works 17 hours how much do

MA_775_DIABLO [31]

Answer:

Total earned= $850

Step-by-step explanation:

Giving the following information:

David makes 17 dollars in an hour and works 25 hours each week Linda makes 25 dollars in an hour and works 17 hours.

<u>To calculate the total earned, we need to use the following formula:</u>

Total earned= 17*25 + 25*17

Total earned= $850

8 0

3 years ago