The population of a town increased from 3600 in 2006 to 4500 in 2011. Find the absolute and relative (precent) increase.

Answer:

up is equal to 5/ 6

left side is equal to 3/4

Step-by-step explanation:

1/6 + 1/6+ 1/6+ 1/6+ 1/6= 5/6

1/4 + 1/4 + 1/4= 3/4

Given :

Two points [tex]P_1(-2,3,2)\ and\ P_2(1,2,0)[/tex] .

To Find :

The direction of [tex]P_1P_2[/tex] and midpoint of line segment [tex]P_1P_2[/tex] .  

Solution :

Direction of [tex]P_1[/tex] and [tex]P_2[/tex] is given by :

[tex]\vec{D}=\dfrac{P_2-P_1}{|P_2-P_1|}\\\\\vec{D}=\dfrac{(-2i+3j+2k)-(i+2j+0)}{P_2-P_1}\\\\\vec{D}=\dfrac{-3i+j+2k}{\sqrt{3^2+1^2+2^2}}\\\\\vec{D}=\dfrac{-3i+j+2k}{\sqrt{14}}[/tex]

Now , mid point is given by :

[tex]M(\dfrac{-2+1}{2},\dfrac{3+2}{2},\dfrac{2+0}{2})\\\\M(\dfrac{-1}{2},\dfrac{5}{2},1)[/tex]

Hence , this is the required solution .

Answer:

28 (0,2,4,14,28)

34 (0,2,17,34)

42 (0,2,6,7,21,42)

the greatest common factor is 2 because it's the greatest number that can be divided by 28, 34 and 42

Answer:

-15

Step-by-step explanation:

-10+-9=-19+4=-15

Here are the expressions on the left matched with the simplifed form on the right:

Here are some mathematical rules:

Also, this sign | | indicates that the number is postive.

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Question:

Express each vector as a product of its length and direction.

[tex]\frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k[/tex]

Answer:

[tex]\frac{1}{\sqrt{2}}[/tex] [tex](\frac{1}{\sqrt{3}}i - \frac{1}{\sqrt{3}}j - \frac{1}{\sqrt{3}}k)[/tex]

Step-by-step explanation:

A vector v can be expressed as a product of its length and direction as follows;

v = |v| u

Where;

|v| = length/magnitude of v

u = unit vector in the direction of v

---------------------------------------------------------------------------------------

Let the given vector be v, i.e

[tex]v = \frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k[/tex]

(i) The length/magnitude |v| of vector v is therefore,

|v| = [tex]\sqrt{(\frac{1}{\sqrt{6}})^2 + (-\frac{1}{\sqrt{6}})^2 + (-\frac{1}{\sqrt{6}})^2[/tex]

|v| = [tex]\sqrt{(\frac{1}{6}) + (\frac{1}{6}) + (\frac{1}{6})[/tex]

|v| = [tex]\sqrt{(\frac{3}{6})[/tex]

|v| = [tex]\sqrt{(\frac{1}{2})[/tex]

|v| = [tex]\frac{1}{\sqrt{2}}[/tex]

(ii) The unit vector u in the direction of vector v, is therefore,

u = [tex]\frac{v}{|v|}[/tex]

[tex]u = \frac{\frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k}{\frac{1}{\sqrt{2}}}[/tex]

[tex]u = \sqrt{2}(\frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k)[/tex]

[tex]u = (\frac{\sqrt{2}}{\sqrt{6}}i - \frac{\sqrt{2}}{\sqrt{6}}j - \frac{\sqrt{2}}{\sqrt{6}}k)[/tex]

[tex]u = (\frac{1}{\sqrt{3}}i - \frac{1}{\sqrt{3}}j - \frac{1}{\sqrt{3}}k)[/tex]

Therefore, the vector can be expressed as a product of its length and direction as:

|v| u = [tex]\frac{1}{\sqrt{2}}[/tex] [tex](\frac{1}{\sqrt{3}}i - \frac{1}{\sqrt{3}}j - \frac{1}{\sqrt{3}}k)[/tex]

Answer:

-17 × 0 = 0

every number multiplied by 0 is equal to 0

the first two professors did not know if everyone wanted coffee because the third professor had to choose yes or no if he wanted coffee. the first two professors were waiting for the third to say something, and when he said no, they knew he did not want coffee. if one of the first two professors said no, the answer would be no.

Answer:

modulus of  |9+40i|  is 41

Step-by-step explanation:

Let z = 9+40i

then

|z| = [tex]\sqrt{9^{2}+40^{2} }[/tex]

   = [tex]\sqrt{81+1600}[/tex]

   = [tex]\sqrt{1681}[/tex]

   = 41

|z| = 41

Answer:

Step-by-step explanation:

1. |9+40i| = 41

2. |-10+24i| = 26

Step-by-step explanation:

r+4r=24+1

5r=25

r=25/5

r=5

Answer:

r = 5

Step-by-step explanation:

r + 4r - 1 = 24

r + 4r = 25

5r = 25

r = 5

Answer:

The equation of the sphere with center (-3, 2 , 5) and radius 4 is [tex](x+3)^{2} +(y-2)^{2} + (z-5)^{2} = 16[/tex]

The intersection of the sphere with the yz- plane gave the equation [tex](y-2)^{2} + (z-5)^{2} = 7[/tex] which is a 2D- circle with center (0,2,5) and radius [tex]\sqrt{7}[/tex].

Step-by-step explanation:

The equation of a sphere of radius r, with center (a,b,c) is given by

[tex](x-a)^{2} +(y-b)^{2} + (z-c)^{2} = r^{2}[/tex]

where, [tex]x,[/tex] [tex]y,[/tex] and [tex]z[/tex] are the coordinates of the points on the surface of the sphere.

Hence, the equation of the sphere with center,  (-3, 2 , 5) and radius 4 becomes

[tex](x-a)^{2} +(y-b)^{2} + (z-c)^{2} = r^{2}[/tex]

[tex](x-(-3))^{2} +(y-(2))^{2} + (z-(5))^{2} = 4^{2}[/tex]

Then,

[tex](x+3)^{2} +(y-2)^{2} + (z-5)^{2} = 16[/tex]

This is the equation of the sphere with center (-3, 2 , 5) and radius 4,

Now, for the intersection of this sphere with the yz- plane,

The [tex]yz -[/tex]plane is where [tex]x = 0[/tex], then we set [tex]x = 0[/tex]

Them the equation [tex](x+3)^{2} +(y-2)^{2} + (z-5)^{2} = 16[/tex] becomes

[tex](0+3)^{2} +(y-2)^{2} + (z-5)^{2} = 16[/tex]

[tex](3)^{2} +(y-2)^{2} + (z-5)^{2} = 16\\9 +(y-2)^{2} + (z-5)^{2} = 16\\(y-2)^{2} + (z-5)^{2} = 16 - 9\\(y-2)^{2} + (z-5)^{2} = 7[/tex]

This equation is the equation of a 2D- circle with center (0,2,5) and radius [tex]\sqrt{7}[/tex]

This is the part of the sphere that intersects with the yz-plane.

Answer:

He did not check for extraneous solutions.

Step-by-step explanation:

He solved the equation correctly and obtained solutions -2 and -5, but there is one final step he did not do.

Every time you square both sides of an equation to solve it, you must check for extraneous solutions. If he did, he would have eliminated x = -5.

Answer: He did not check for extraneous solutions.

Answer:

6Y

Step-by-step explanation:

We need to solve the statement ' Thrice the product of two and "Y" '.

Thrice means 3 times and product means multiply. It means we have to multiply 3,2 and Y.

Let the result is R. It can be calculated as follows :

[tex]R=3\times 2\times Y[/tex]

We know that, 3×2 = 6

So,

[tex]R=6Y[/tex]

Hence, Thrice the product of two and "Y" is 6Y.

Answer:

(2)

Step-by-step explanation:

We can use the points (-4, 0) and (0, 2) to solve.

Slope formula: y2-y1/x2-x1

2-0/0-(-4)

2/4

1/2

Best of Luck!

Answer:

b = 12

Step-by-step explanation:

15 - 2b = -9

Minus 15 to both sides

-2b = -24

Divide both sides by -2

b = 12

Answer:

i think is the second one

Step-by-step explanation:

Answer:

$818,3

Step-by-step explanation:

16.7% in decimal is 0.167

= 0.167 x $4900

= $818,3

Answer:

y = 2/7x + 7

Step-by-step explanation:

We start off by putting the original equation into slope-intercept form. Subtract 7x from both sides, then divide both sides by -2. Your new equation should be y = -7/2x - 8. It's important to know that when two lines are perpendicular, their slopes (m) are opposite reciprocals of each other.  So -7/2 becomes 2/7. The first part of your final equation is y = 2/7x + b.

Next, we need to find the y intercept (b). You need to plug the x and y values from the given coordinate point (-7,5) into your final equation. You should end up with: 5 = 2/7(-7) + b. Then, solve for b.

5 = -14/7 + b

5 = -2 + b

7 = b

Finally, plug the b value into your final equation and you will have your answer.

Answer:

C

Step-by-step explanation:

2/3=66 therefore it also equals 2/3%

Answer: C

Step-by-step explanation:

First find the decimal of 2/3  

Divide it  2/3 = 0.6666666

Now multiply it by 100 to convert it to a percent  

You get 66.66..%  which is the same as 66 2/3%

Answer:

rational numbers and irrational numbers

Step-by-step explanation:

Answer:

x = -8

Step-by-step explanation:

[tex]6(x - 1) = 9(x + 2)[/tex]

Expand :

[tex]6(x - 1) = 6x - 6 \\ 9(x + 2) = 9x + 18[/tex]

[tex]6x - 6 = 9x + 18[/tex]

Collect like terms and simplify

[tex]6x - 9x = 18 + 6 \\ - 3x = 24[/tex]

Divide both sides of the equation by -3

[tex] \frac{ - 3x}{ - 3} = \frac{24}{ - 3} \\ x = - 8[/tex]

Answer:

Step-by-step explanation:

6x - 6 = 9x + 18

-3x - 6 = 18

-3x = 24

x = -8 is the solution

Answer:

1. RATIO SCALE

2. INTERVAL SCALE

3. NOMINAL SCALE

4. ORDINAL SCALE

Step-by-step explanation:

The scales are:

- Nominal Scale

- Ordinal Scale

- Interval Scale

- Ratio Scale

Rule: Each scale will be used exactly once.

For number 1, the description is that of a Ratio Scale because size comparisons can be made between values on the scale, such as the example given - that one value is twice as big as another value.

For number 2, the description is that of an Interval Scale because the values of data measured on the scale can be ranked e.g. Yes ranks as 1, No ranks as 2, Indifferent ranks as 3 and there is meaningful difference (not numerical difference) between scale points.

For number 3, the description is that of a Nominal Scale, because it says obviously that the values of data measured on this scale can be in form of names (watch out for keywords like this when reading through) and cannot be rank ordered! A good example is the following data set:

- Yellow, Brown, Purple, Cream, Fustian Pink

For number 4, the description is that of an Ordinal Scale. A keyword "rank" is to be given attention here, even as the statement is straightforward and gives just a simple information.

Answer:

10 x 10 x 10 x 10.

Step-by-step explanation:

2(5)^4

10^4

Expanded form; 10*10*10*10.

Answer:

10 x 10 x 10 x 10

Step-by-step explanation:

Answer:

Step-by-step explanation:

Product—Multiplication

Sum— Addition

Difference—Subtraction

Quotient—Division

Quantity— Parenthesis

Answer:

The value of m + k = [tex]5+\frac{1}{2}[/tex] = [tex]\frac{11}{2}[/tex].

Step-by-step explanation:

We are given that C is the midpoint of segment AB where A(-3,m) , B (4, -1) , and C (k, 2).

As we know that the mid-point formula states that;

Mid-point = [tex]\frac{a+b}{2}[/tex]

This means that;

Mid-point of AB = [tex]\frac{A+B}{2}[/tex]

C(k, 2) = [tex](\frac{-3+4}{2}, \frac{m+(-1)}{2} )[/tex]

C(k, 2) = [tex](\frac{1}{2}, \frac{m-1}{2} )[/tex]

This means that;

[tex]k = \frac{1}{2}[/tex]  and  [tex]2=\frac{m-1}{2}[/tex]

[tex]k = \frac{1}{2}[/tex]  and  [tex]m-1=4[/tex]

[tex]k = \frac{1}{2}[/tex]  and  [tex]m = 4+1 = 5[/tex]

So, the value of m + k = [tex]5+\frac{1}{2}[/tex] = [tex]\frac{11}{2}[/tex].

Answer:

for the first question at the top, x=10

Step-by-step explanation:

x+3+9x=8x+23

(subtract 8x from both sides)

x+3+x=23

(combine the x terms)

2x+3=23

(subtract 3 from both sides)

2x=20

(divide by 2 from each side)

x=10

Answer:

Coordinate A ins not intercepting any axis.

Step-by-step explanation:

For a coordinate to intercept an axis, it will be in the form [tex](a, b)\ such\ that:\ a=0, b \in \mathbb{R},\ or:a\in \mathbb{R}, b=0.[/tex]

Since in (3, 6), none of the components are 0, it is not intercepting any axes.

Answer:

7

Step-by-step explanation: