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2 years ago

1. Find the mean, median, mode, and range of the following set of data: 1,2,4,6,4,4

Mathematics

1 answer:

mezya [45]2 years ago

6 0

Step-by-step explanation:

the median is 4

the mean is 1+2+4+6+4+4/6

21/6=7\2

6.5 the mode is 4

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Find the distance between a point (– 2, 3 – 4) and its image on the plane x+y+z=3 measured across a line (x + 2)/3 = (2y + 3)/4

dimaraw [331]

Answer:

Distance of the point from its image = 8.56 units

Step-by-step explanation:

Given,

Co-ordinates of point is (-2, 3,-4)

Let's say

$x_1\ =\ -2$

$y_1\ =\ 3$

$z_1\ =\ -4$

Distance is measure across the line

$\dfrac{x+2}{3}\ =\ \dfrac{2y+3}{4}\ =\ \dfrac{3z+4}{5}$

So, we can write

$\dfrac{x-x_1+2}{3}\ =\ \dfrac{2(y-y_1)+3}{4}\ =\ \dfrac{3(z-z_1)+4}{5}\ =\ k$

$=>\ \dfrac{x-(-2)+2}{3}\ =\ \dfrac{2(y-3)+3}{4}\ =\ \dfrac{3(z-(-4))+4}{5}\ =\ k$

$=>\ \dfrac{x+4}{3}\ =\ \dfrac{2y-3}{4}\ =\ \dfrac{3z+16}{5}\ =\ k$

$=>\ x\ =\ 3k-4,\ y\ =\ \dfrac{4k+3}{2},\ z\ =\ \dfrac{5k-16}{3}$

Since, the equation of plane is given by

x+y+z=3

The point which intersect the point will satisfy the equation of plane.

So, we can write

$3k-4+\dfrac{4k+3}{2}+\dfrac{5k-16}{3}\ =\ 3$

$=>6(3k-4)+3(4k+3)+2(5k-16)\ =\ 18$

$=>18k-24+12k+9+10k-32\ =\ 18$

$=>\ k\ =\dfrac{13}{8}$

So,

$x\ =\ 3k-4$

$=\ 3\times \dfrac{13}{8}-4$

$=\ \dfrac{7}{4}$

$y\ =\ \dfrac{4k+3}{2}$

$=\ \dfrac{4\times \dfrac{13}{8}+3}{2}$

$=\ \dfrac{19}{4}$

$z\ =\ \dfrac{5k-16}{3}$

$=\ \dfrac{5\times \dfrac{13}{8}-16}{3}$

$=\ \dfrac{-21}{8}$

Now, the distance of point from the plane is given by,

$d\ =\ \sqrt{(x-x_1)^2+(y-y_1)^2+(z-z_1)^2}$

$=\ \sqrt{(-2-\dfrac{7}{4})^2+(3-\dfrac{19}{4})^2+(-4+\dfrac{21}{8})^2}$

$=\ \sqrt{(\dfrac{-15}{4})^2+(\dfrac{-7}{4})^2+(\dfrac{9}{8})^2}$

$=\ \sqrt{\dfrac{225}{16}+\dfrac{49}{16}+\dfrac{81}{64}}$

$=\ \sqrt{\dfrac{1177}{64}}$

$=\ 4.28$

So, the distance of the point from its image can be given by,

D = 2d = 2 x 4.28

= 8.56 unit

So, the distance of a point from it's image is 8.56 units.

4 0

3 years ago

100 POINTS!!!

PSYCHO15rus [73]

Answer:

Step-by-step explanation:

The first one is -2x + 3

The seconf one is -2x +7

Look, same slope.

7 0

1 year ago

What's the area?<br><br> C= pi/2 <br><br> A=____

kompoz [17]

The answer is actually 1.571

6 0

3 years ago

Which value can be added to the set below without changing its mean?

Grace [21]

Answer:

0 because it has no value.

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

The total interest paid on a 3-year loan at 9% interest compounded monthly is $1505.82 determine the monthly payment for the

Kruka [31]

Number of compounding periods is
n=12months×3years=36
I assume that

The total interest=
monthly payment×number of compounding periods - the amount of the present value of an annuity ordinary
I=x×n-pv

Let monthly payment be X

I =Total interest is 1505.82

The present value of an annuity ordinary is
Pv=X [(1-(1+0.09/12)^(-36))÷(0.09/12)]

now plug those in the formula of the total interest above
I=x×n-pv
1505.72=36X-X [(1-(1+0.09/12)^(-36))÷(0.09/12)]
Solve for X using Google calculator to get the monthly payment which is
X=330.72

Check your answer using the interest formula
36×330.72−330.72×((1−(1+0.09
÷12)^(−12×3))÷(0.09÷12))
=1,505.83

3 0

3 years ago