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Marizza181 [45]

3 years ago

14

Calculate the mean and variance of the sample data set provided below. show and explain your steps. round to the nearest tenth.

14, 16, 7, 9, 11, 13, 8, 10

1 answer:

eimsori [14]3 years ago

6 0

Mean = (14 + 16 + 7 + 9 + 11 + 13 + 8 + 10) ÷ 8 = 11

Variance =
[ (14-11)²+(16-11)²+(7-11)²+(9-11)²+(11-11)²+(13-11)²+(8-11)²+(10-11)² ]/7 = 9.71

Answer: 9.71

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Identify any solutions to the system given below.

alekssr [168]

Answer: The system of equations have many solutions and the correct options are A,B and D.

Explanation:

The given equations are,

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

$3y=15-6x$ .... (2)

Simplify the second equation.

$3y+6x=15$

$3(y+2x)=15$

Divide both sides by 3.

$2x+y=5$

It is same as equation (1). Since equation (1) and (2) are same, therefore all the points lies on the line or which satisfies the equation are the solution of the given system of equations.

Test the points whether the point lies on the line or not.

Check for point A(6,-7).

$2(6)+(-7)=5$

$5=5$

LHS and RHS are equal, therefore the point A is the solution of the system of equations.

Check for point B(2,1).

$2(2)+(1)=5$

$5=5$

LHS and RHS are equal, therefore the point B is the solution of the system of equations.

Check for point C(-2,-9).

$2(-2)+(-9)=5$

$-13=5$

LHS and RHS are not equal, therefore the point C is not the solution of the system of equations.

Check for point D(-4,13).

$2(-4)+(13)=5$

$5=5$

LHS and RHS are equal, therefore the point D is the solution of the system of equations.

Therefore the options A,B and D are correct.

3 0

4 years ago

Read 2 more answers

There are 8 cakes and we are dividing them into pieces. Each piece will be ⅕ of a cake. How many pieces will there be in all? Wr

natta225 [31]

Answer:

40

Step-by-step explanation:

8 piece of cakes times 5 pieces per cake = 40 pieces for the total cakes

7 0

2 years ago

Identify a function rule for the following ordered pairs:

Andreas93 [3]

2x-4 D it can be your answer if you multiply correctly and you do it

5 0

3 years ago

The green triangle is a dilation of the red triangle with a scale factor of s=13 and the center of dilation is at the point (4,2

Arada [10]

Given:

Scale factor $s=\dfrac{1}{3}$

Center of dilation = (4,2)

To find:

The coordinates of the points C' and A.

Solution:

We know that, if a figure is dilated with a scale factor k and the center of dilation is at the point (a,b), then

$(x,y)\to (k(x-a)+a,k(y-b)+b)$

The scale factor is $\dfrac{1}{3}$ and the center of dilation is at (4,2).

$(x,y)\to (\dfrac{1}{3}(x-4)+4,\dfrac{1}{3}(y-2)+2)$ ...(i)

Suppose the vertices of red triangle are A(m,n), B(10,14) and C(-2,11).

Using rule (i), we get

$C(-2,11)\to C'(\dfrac{1}{3}(-2-4)+4,\dfrac{1}{3}(11-2)+2)$

$C(-2,11)\to C'(\dfrac{1}{3}(-6)+4,\dfrac{1}{3}(9)+2)$

$C(-2,11)\to C'(-2+4,3+2)$

$C(-2,11)\to C'(2,5)$

Hence, the coordinates of Point C' are C'(2,5).

Let us assume that point A is A(m,n).

Using rule (i), we get

$A(m,n)\to A'(\dfrac{1}{3}(m-4)+4,\dfrac{1}{3}(n-2)+2)$

From the given figure it is clear that the image of point A is (8,4).

$A'(\dfrac{1}{3}(m-4)+4,\dfrac{1}{3}(n-2)+2)=A'(8,4)$

On comparing both sides, we get

$\dfrac{1}{3}(m-4)+4=8$

$\dfrac{1}{3}(m-4)=8-4$

$(m-4)=3(4)$

$m=12+4$

$m=16$

And,

$\dfrac{1}{3}(n-2)+2=4$

$\dfrac{1}{3}(n-2)=4-2$

$(n-2)=3(2)$

$n=6+2$

$n=8$

Therefore, the coordinates of point A are (16,8).

4 0

3 years ago

Find 16% of 370. Round to the nearest 10th if necessary.

svetoff [14.1K]

Multiply 370 by 0.16 get get 16%

370 x 0.16 = 59.2%

8 0

3 years ago