If x is directly proportional to y, and x = 4.5 when y = 3, find

(i) an equation connecting x and y

(ii) the value of x when y = 6,

(iii) the value of y when x = 12.

Answer:

Step-by-step explanation:

First you take your smallest number, which in this case is 4 - then you find your maximum number which is 14. Then we can list these numbers on a piece of paper and cross a number out from each side until you reach the middle number which would be 8. Then you go from the min to the middle number which would be 5. Then you repeat between the max number and the middle number which is 11. So your minumum would be 4, max would be 14, Q1 would be 5 Median would be 8 and Q3 would be 11. Let me know if I got it right! I haven't done it for a while, but I am pretty sure this is correct..

The missing values are:

Minimum value = 4 ,

Q₁ = 5 ,

Median = 6,

Q₃ = 11

Maximum value = 14.

The set of values known as quartiles divides a batch of data into four equal portions.

We have,

Minimum value = 4

Now, arrange the data in ascending order

4,4,5,5, 6, 6, 8, 10, 11, 11, 12, 14

Then, Quartiles

Q₁ = [ (n+1)/4]th term

   = (12+1) / 4

  = 3.25th term

  = 3rd term + 0.25 ( 4th term - 3th term)

  = 5 + 0.25 (5 -5)

   = 5

Now, Median = (N/2)th term

           = 12 /2

           = 6th term

          = 6

and, Q₃ = [3(n+1)/4]th term

   = 3 × 3.25

   = 9.75

   = 9th term + 0.75( 10th term - 9th term)

   = 11 + 0.75 (10 -10)

   = 11

and, Maximum value = 14

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Answer:

340°

Step-by-step explanation:

To convert radians to degrees, multiply by [tex]\frac{180}{\pi }[/tex] since a full circle is 360° or

2[tex]\pi[/tex] radians.

[tex](\frac{17}{\pi } )[/tex] x [tex]\frac{180}{\pi }[/tex]

Factor [tex]\pi[/tex] out 0f 17[tex]\pi[/tex]

[tex]\frac{\pi (17)}{9}[/tex] x [tex]\frac{180}{\pi }[/tex]

Cancel the common factor "[tex]\pi[/tex]"

Rewrite the expression as:

[tex]\frac{17}{9}[/tex] x 180

Factor 9 out of 180.

[tex]\frac{17}{9}[/tex] x(9(20))

Cancel out the common factor "9"

Rewrite the expression as:

17 x 20

=340°

Answer:

1,1. 4,4. 5,5 and. 6,6

Step-by-step explanation:

Because they are all the same numbers :)

Answer:

2

Step-by-step explanation:

Following the substitution rules:

O becomes P and

E becomes F

because they are vowels(a,e,i,o,u) change to next letter.

C becomes A

L becomes J

G becomes E

because constants change to the letter two before the given letter.

So COLLEGE becomes APJJFEF

so it now has 2 vowels.

1. Convert 8cm³ into m³

= 8.0E-6 m³

(divide the volume value by 1e+6)

2. Convert 0.7m³ into cm³

= 700000 cm³

(multiply the volume value by 1e+6)

3. Convert 4000000cm³ into m³

= 4 m³

(divide the volume value by 1e+6)

1. - 3p^3 + 7p^2 - 3

2. 5a^3 - 5a^2

3. 6 + 7n^3

4. - 6n^3

5. a^2 + 2r^4

6. 9r^3 + 2r^4

7. 1

8. 6x^4 - 6x

9. - 7k^4 - 11k^2 + 6

10. 2n^5 - 2n^4 + 3n + 3

11. 14a^5 + 14a^4 - 10a^3 - 16a

12. - 14n^4 - 7n^2 + 8n + 7

13. 18x^5 + 6x^4 + 12x^3

14. 7r^3 - 3r^2 + 20r

15. 8n - 8n^4

16. - 2x^5 + 10x^4 + 5x + 14

17. 4x^5 - 15x^3 - 11x - 1

18. 5a^5 + 23a^2 - 11a

19. 15v^5 + 4v^3 - 24v^2

20. 2b^4 + 15b^3 - 3

Answer:

On a linear graph, the rate of change is called the slope of a line

Step-by-step explanation:

Hope this helps

The complete statement is, on a linear graph, the rate of change is called the slope of a line.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

From the above concepts we now know that, on a linear graph, the rate of change is called the slope of a line.

It can also be defined as, (y₂ - y₁)/(x₂ - x₁).

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Answer:

please where's the diagram

Answer:

angle HMS = 62 degrees

x = 13 degrees

AT = 28

Step-by-step explanation:

angle SHM and angle HMS are both inside the triangle SMH.

We want to find the angle of HMS. We know that the sum of the angles in the triangle adds up to 180 degrees. There are two angles that we already know.

Angle SHM = 28 (given)

Angle HSM = 90 (because it is a right angle which is always 90 degrees, right angles are formed at two perpendicular lines)

Angle HMS = x (we let angle HMS be a variable as we don't know the value for it)

x + 90 + 28 = 180

x = 62 ddegrees

HMS is 62 degrees

TSA is a right angle in triangle AST because it is formed by two perpendicular lines. Right angles always equal 90 degrees.

10x - 40 = 90

10x = 130

x = 13 degrees

AT and HT are both congruent sides. We know this because the figure we are given is a kite. In a kite, we have two pairs of sides that are congruent to each other.  HT is congruent to AT while HM is congruent to AM.

So,

8x - 4 = 2x + 20

Subtraact 2 x from both sides

6x - 4 = 20

Add 4 to both sides

6x = 24

Divide 6 on both sides.

x = 4

Plug x back to AT.

AT = 2(4) + 20 = 28

Answer:

3+18=21

Step-by-step explanation:

first see the second number

let us assume as x & y

3+ (3×6)= 21

3+18=21Step-by-step explanation:

Answer:

3+18

Step-by-step explanation:

3x6 is 18, so 18 is 6 times the first number. If you add 3 and 18, its equal to 21.

Answer:

2 and 3

Step-by-step explanation:

So, 24=2x2x2x3

42=2x3x7

3 and 2

Answer:

2 and 3

Step-by-step explanation:

prime factors for 42: 2, 3, and 7

prime factors for 24: 2,2,2 and 3

Answer:The penguin will walk 75.15 feet in 45 seconds.

It will take the penguin 26.95 seconds to walk 45 feet.

Through cross multiplication we can determine the unknown quantity we need

Step-by-step explanation:

Answer:

See below ~

Step-by-step explanation:

The function can be written as :

Answer:

33

Step-by-step explanation:

area of large triangle = 117

117-(30)-(12*5/2)-(8*6/2)

= 33

The exact area of the shaded region is 33 units²

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure.

Given is a figure, we need to find the area of the shaded region.

For finding the same, we will first find the area of the big triangle and then find the areas of the small parts in it having shape, triangle and a rectangle,

The area of the big triangle = 1/2 x 18 x 13 = 117 units²

The area of the two small triangles =

1/2 x 6 x 8 = 24 units²

and

1/2 x 12 x 5 = 30 units²

Now, the area of the square = 5 x 6 = 30 units²

The area of the shaded region = 117-(24+30+30) = 33 units²

Hence, the exact area of the shaded region is 33 units²

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Answer:

(4,-8) is the only correct solution because it is the only one to have a Y value of -8

3x+y=5 & 5x-4y=-3

3x+5x=8x+y-4y=-3

           8x+y-4y=-3

     8x+3y=-3

         -3     -3

8x=-6

x = 1 and y = 2.

Step-by-step explanation:

to do this, i changed the form of one of the equations so it was in the y= form then plugged it into the pther equation to solve for x. once i had x i plugged it into one of the equation to get y! hope this helps

Answer:

54%

Step-by-step explanation:

Answer:

x=-2

Step-by-step explanation:

Hey there!

In order to solve this equation, you need to combine like terms

The equation after combining the x terms and the contants will look like this

10x+3=12x+7

Now you have to take 10x away from both sides

3=2x+7

Now bring all the constants to the left side

3-7=2x

Simplify

-4=2x

divide 2 on both sides to get x by itself

x=-2

So, the answer is x=-2

Answer:

5.5

Step-by-step explanation:

6 x 5.5 = 33

The solution for r is 5.5

Answer:

r = 5.5

Step-by-step explanation:

6r=33

1. divide both sides by 6

6/6=1

33/6= 5.5

2. r=5.5

The standard deviation of the dataset is the square root of the variance

The mean and the standard deviation of the dataset are 24.6 and  5.70, respectively

The dataset is given as;

25, 24, 32, 16, 22, 34. 19. 27, 18, 29

Calculate the mean using:

μ = Sum/Count

So, we have:

μ = (25+ 24+ 32+ 16+ 22+ 34+ 19+ 27+ 18+ 29)/10

Evaluate

μ = 24.6

The standard deviation is then calculated using:

[tex]\sigma =\sqrt{ \frac{\sum(x - \mu)^2}{n}[/tex]

So, we have:

[tex]\sigma = \sqrt{\frac{(25 - 24.6)^2 + .................. + (27- 24.6)^2 + (18- 24.6)^2 + (29- 24.6)^2}{10}}[/tex]

Evaluate

[tex]\sigma = \sqrt{32.44}[/tex]

Evaluate the square root

[tex]\sigma = 5.70[/tex]

Hence, the mean and the standard deviation of the dataset are 24.6 and  5.70, respectively

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Answer:

76.6%

Step-by-step explanation:

345/450 * 100%

I hope it helps and sorry if I'm wrong

Answer:

They are the same.

Step-by-step explanation:

1.1 and 1.10 are both the same, actually. There is just an extra 0 at the end. For example, 2 and 2.0 are the same, because 0 is 0, and it doesn't change your answer. The 0 could go on as in 1.100000000 but it will still equal 1.1 .

Hope this helped :)

Answer:

83.6

Step-by-step explanation:

just use your calculator

Answer:

83.6

Step-by-step explanation:

It's simple, just type it in the calculator and you'll get the answer

Answer:

yes

Step-by-step explanation:

yes

Answer:

x = 10.76 cm

Step-by-step explanation:

[tex]\frac{7}{sin(40^{o} )} =\frac{x}{sin(81^{o} )}[/tex]

[tex]x=\frac{7sin(81^{0}) }{sin(40^{o} )} =10.76cm[/tex]

Hope this helps

Answer:

After 3 years, Dakota will have $674.09 total.