A point (x,y) is a distance of 6 units from the x-axis. It is a distance of 5 units from the point (8,3). It is a distance [tex]\sqrt{n}[/tex] from the origin. Given that x<8, what is n?

Answers

Answer 1

Answer: n = 52

Step-by-step explanation:

when we have two vectors (x,y) and (a,b) the distance between the vectors is:

D = √( (x - a)^2 + (y - b)^2)

now, we know that:

1) the distance between (x, y ) and the x-axis is 6 units.

The nearest point to (x, y) in the x-axis is the point (x, 0) so we have:

D = 6 = √( (x - x)^2 + (y - 0)^2) = √y^2

so y can be 6 or -6.

So we know that y = 6, and now we can write our point as (x, +-6)

2) The distance between our point and (8, 3) is 5 units:

D = √( (x - 8)^2 + (y - 3)^2) = 5.

And we know that the distance from the origin, (n, n) is:

D = √n = √(x^2 + y^2}

n = x^2 + y^2

Now, we should start with:

√( (x - 8)^2 + (y - 3)^2) = 5

first suppose that y = -6, then:

√( (x - 8)^2 + (-6 - 3)^2) = √( (x - 8)^2 + (-9)^2) = 5.

√( (x - 8)^2 + 81) = 5.

Then we must have that:

and we know that √25 = 5

so (x-8)^2 + 81 = 25

this can never happen, so we can discard y = -6

Now the second case, if y = 6,

√( (x - 8)^2 + (6 - 3)^2) = 5.

√( (x - 8)^2 + (3)^2) = 5.

√( (x - 8)^2 + 9) = 5.

here:

(x - 8)^2 + 9 = 25

(x - 8)^2 = 16

(x - 8) = √16 = +-4

So again we have two cases:

if x - 8 = 4, then:

x = 4 + 8 = 12

but we must have x < 8, so this can be discarded.

now, if x - 8 = -4 then:

x = -4 + 8 = 4, this is an acceptable answer, then our point is (4, 6)

And we have:

n = 4^2 + 6^2 = 16 + 36 = 52


Related Questions

A rectangular window is 48 in long and 36 in wide. Lisa
would like to buy a screen for the window. The cost of
the screen is based on the number of square feet the
screen is. Use the facts to find the area of the window in
square feet.
Conversion facts for length
1 foot (ft) 12 inches (in)
1 yard (yd) = 3 feet (ft)
1 yard (yd) = 36 inches (in)
2
Х
$
?

Answers

Length=48inBreadth=36in

[tex]\\ \sf\longmapsto Area=Length\times Breadth[/tex]

[tex]\\ \sf\longmapsto Area=48(36)[/tex]

[tex]\\ \sf\longmapsto Area=1728in^2[/tex]

[tex]\\ \sf\longmapsto Area=144ft^2[/tex]

[tex]\\ \sf\longmapsto Area=48yard^2[/tex]

Which statements about the sum of the interior angle measures of a triangle in Euclidean and non-Euclidean geometries are true? A. In Euclidian geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is less than 180 degrees. B. In Euclidian geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is greater than 180 degrees. C. In Euclidian geometry the sum of the interior angle measures of a triangle is less than 180 degrees, but in hyperbolic geometry the sum is equal to 180 degrees. D. In Euclidian geometry the sum of the interior angle measures of a triangle is greater than 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees. E. In Euclidian geometry the sum of the interior angle measures of a triangle is 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees.

Answers

Answer:

its b and e

Step-by-step explanation:

The statements given in options B and E are   true so options B and E are right options.  

Given some statements we have to determine that which of the following statements are true

The given statements are as follows

A. In Euclidean geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is less than 180 degrees.

B. In Euclidean geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is greater than 180 degrees.

C. In Euclidean geometry the sum of the interior angle measures of a triangle is less than 180 degrees, but in hyperbolic geometry the sum is equal to 180 degrees.

D. In Euclidean geometry the sum of the interior angle measures of a triangle is greater than 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees.

E. In Euclidean geometry the sum of the interior angle measures of a triangle is 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees.

We know some facts about each type of geometry

In Euclidean geometry  plane is used to plot the points and line.

In spherical geometry uses the sphere to plot the points and circles

Elliptical geometry is such a geometry where no parallel lines exists.

The sum of interior angles of a triangle is dependent on the type of geometry we are dealing with   and they can be written down in the following points

In Euclidean geometry the sum of interior angles of  a triangle is 180° In spherical or elliptical geometry the sum of interior angles of a triangle is more than 180°  In hyperbolic geometry  the sum of interior angles  of a triangle is less than 180°  

So from the above observations we can conclude that statements given in options B and E are   true so options B and E are right options.  

For more information please refer to the link given below

https://brainly.com/question/4637858

Consider the following information. 1 hour = 3.6 · 10^3 seconds 1 day = 24 hours 1 year = 3.65 · 10^2 days Use scientific notation to calculate the number of seconds in 3 days.

Answers

Answer:

2.592 x 10^5

Step-by-step explanation:

1st step: Calculate for 1 day.

if 1 hour = 3.6 X 10³

24 hrs = (3.6 x 10³) X (2.4 x 10¹)

= 3.6 x 2.4 X 10⁴

= 8.64 x 10⁴

2nd Step: Calculate for 3 days;

if 1 day = 8.64 x 10⁴

3 days = (8.64 x 10⁴) X (0.3 x 10¹)

= 8.64 x 0.3 x 10^5

= 2.592 x 10^5

Consider the following ordered data. 6 9 9 10 11 11 12 13 14 (a) Find the low, Q1, median, Q3, and high. low Q1 median Q3 high (b) Find the interquartile range.

Answers

Answer:

Low             Q1                Median              Q3                 High

6                  9                     11                      12.5                14

The interquartile range = 3.5

Step-by-step explanation:

Given that:

Consider the following ordered data. 6 9 9 10 11 11 12 13 14

From the above dataset, the highest value = 14  and the lowest value = 6

The median is the middle number = 11

For Q1, i.e the median  of the lower half

we have the ordered data = 6, 9, 9, 10

here , we have to values as the middle number , n order to determine the median, the mean will be the mean average of the two middle numbers.

i.e

median = [tex]\dfrac{9+9}{2}[/tex]

median = [tex]\dfrac{18}{2}[/tex]

median = 9

Q3, i.e median of the upper half

we have the ordered data = 11 12 13 14

The same use case is applicable here.

Median = [tex]\dfrac{12+13}{2}[/tex]

Median = [tex]\dfrac{25}{2}[/tex]

Median = 12.5

Low             Q1                Median              Q3                 High

6                  9                     11                      12.5                14

The interquartile range = Q3 - Q1

The interquartile range =  12.5 - 9

The interquartile range = 3.5

What is the solution (x, y) to this system of linear equations? 2x – 3y = –6 x + 2y = 11

Answers

Answer:

x = 3, y = 4

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

2x +6x = 3y + 2y = 11
8x = 5y= 11

8x= 11
X= 11/8 or 1.375

5y= 11
Y= 11/5 or 2.2


Maybe ^ haven’t done these in a while.

A Prefeitura da Cidade Feliz doou um
terreno para a Comunidade Viver Bem
discutir projetos que deveriam ser
implantados no local. Após um planejamento
participativo, ficou acertado que 45% da área
total desse terreno serão destinados a uma
creche;
3%,
para banheiros públicos e 12%
para uma academia de ginástica comunitária.
A sobra da área, que é de 960m² será
utilizada para uma pequena praça com
parque de lazer. Qual é a área total ocupada
pela creche, banheiros públicos e academia
de ginástica comunitária?

Answers

Aqui temos a seguinte divisao de terreno:

creche + banheiros + academia = 45% + 3% + 12% = 60%

O que sobra: Fazendo a conta, 100 - 60 = 40, restará 40%

No enunciado informa que sobraram 960m².

Logo concluimos que 40% = 960m²

Sendo assim, regra de 3:

   m²                %

  960   --------   40

    X     --------   60

40X = 960 . 60

X = 57600/40

X = 1440

Logo 1440m² é destinado para: creche, banheiros públicos e academia

de ginástica comunitária.

O terreno tem um total de 1440 + 960 = 2400m²

para cada espaço - novamente diversas regra de 3:

→ creche = 45%

    m²                  %

  2400   --------   100

    X        --------    45

X = 108000/100 = 1080

 

→ banheiros públicos  = 3%

    m²                  %

  2400   --------   100

    X        --------    3

X = 7200/100 = 72

→ academia de ginástica comunitária = 12%

    m²                  %

  2400   --------   100

    X        --------    12

X = 28800/100 = 288

provando:

60% = 1440m²  (visto acima)

creche - 1080

banheiros - 72

academia - 288

1080 + 72 + 288 = 1440 (60%)

WORTH 100 POINTS!
The function h(x) is quadratic and h(3) = h(-10) = 0. Which could represent h(x)?

1) h(x) = x2 - 13x - 30
2) h(x) = x2 - 7x - 30
3) h(x) = 2x2 + 26x - 60
4) h(x) = 2x2 + 14x - 60

Answers

Answer:

h(x) = 2x^2 +14x -60

Step-by-step explanation:

A quadratic is of the form

h(x) = ax^2 + bx +c

h(3) = h(-10) = 0

This tells us that the zeros are at x=3 and x = -10

We can write the equation in the form

h(x) = a( x-z1)(x-z2) where z1 and z2 are the zeros

h(x) = a(x-3) (x- -10)

h(x) = a(x-3) (x+10)

FOIL

h(x) = a( x^2 -3x+10x-30)

h(x) = a(x^2 +7x -30)

Let a = 2

h(x) = 2x^2 +14x -60

It means

zeros are 3 and -10

Form equation

y=x²-(3-10)x+(-10)(3)y=x²+7x-30

Multi ply by 2

y=2x²+14x-60

Option D

All of Ralph’s ranch land was divided equally among his six children whose daughter land portion of the ranch land was divided among her four children how much of Roslyn was in Inherited by 1 of Lynn’s children

Answers

Answer: 1/24 of Ralph's land

Step-by-step explanation:

Ralph gave each of his children a 6th of his land.

= 1/6

Lynn being his daughter got 1/6 of his land. She then shared it to her 4 children.

Children got 1/4 of Lynn's land which is 1/6 of Ralph's land.

Lynn's children therefore got;

= 1/4 * 1/6

= 1/24 of the land

What is the volume of a sphere, to the nearest cubic inch, if the radius equals 5 inches? Use π = 3.14.

Answers

Answer:

V = 523 in^3

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

V = 4/3 ( 3.14) * 5^3

V = 523.33333repeating

Rounding to the nearest inch^3

V = 523 in^3

Answer:

[tex] 523.6 {in}^{3} [/tex]

Step-by-step explanation:

[tex]v = \frac{4}{3} \pi {r}^{3} \\ = \frac{4}{3} \pi \times 5 \times 5 \times 5 \\ = 523.6 {in}^{3} [/tex]

467,768 round it to
the hundreds place

Answers

Answer:

467,800

Step-by-step explanation:

When nearing to the hundred you look at the number 6. It’s greater than 5 so the previous number 7 turns into 8 and the numbers 6 and 8 became 0.

The answer is 467,800

What is the prime factorization of 75

Answers

Step-by-step explanation:

The prime fractorization of 75 is 3×5×5 or 3×52

how many 50 cents coins are there in $10:50​

Answers

Answer:

21

Step-by-step explanation:

you divide 10.50 by 50

Nhà trường muốn đánh giá tỉ lệ chăm học của sinh viên (trong một tuần). Khảo sát 236 sinh viên thì thấy có 32 sinh viên chăm học. Hãy ước lượng khoảng đối xứng cho tỉ lệ sinh viên chăm học của trường với độ tin cậy 95%

Answers

Answer:

can't understand the language

Ashton needs to rent a car while on vacation. The rental company charges $19.95, plus 18 cents for each mile driven. If Ashton only has $50 to spend on the car rental, what is the maximum number of miles she can drive?

Answers

Answer:

166.9 miles or 166 miles

Step-by-step explanation:

We can form an equation like this:

19.95 + .18x = 50

In this equation, "x" is the number of miles.

=> 19.95 - 19.95 +.18x = 50 -19.95

=> .18x = 30.05

=> .18x/.18 = 30.05/.18

=> x = 166.9

Ashton can drive 166.9 miles.

**Note: We cannot round the answer to 167, as she would not have enough money to drive the extra 0.1 mile.

Is the number 7 included in the following interval: (2,7] *

Answers

Answer:

yes number 7 is included in this interval .

............

Question: Complete the point-slope equation of the line through (1,3)and (5,1). Use exact numbers. Equation: y-3=(Answer ?)

Answers

Answer:

y - 3 = -1/2(x - 1)

Step-by-step explanation:

Hey there!

Well point slope form is,

[tex]y - y_{1} = m(x - x_{1})[/tex]

We can use the point (1,3)

y - 3 = m(x - 1)

Now we need to find slope with the following formula,

[tex]\frac{y^2-y^1}{x^2-x^1}[/tex], we’ll use the points (1,3) and (5,1).

[tex]\frac{1-3}{5-1}[/tex]

-2/4

Slope or m = -1/2

y - 3 = -1/2(x - 1)

Hope this helps :)

Dan weighs 205 pounds but is only 5 feet 8 inches tall. Evan is 6 feet tall. How much would you expect Evan to weigh if they have the same height/weight ratio? WILL MARK BRAINLIST

Answers

Answer:

Around 217 pounds

Step-by-step explanation:

Let's convert the height into inches.

5 feet 8 = [tex]5\cdot12 + 8 = 60 + 8 = 68[/tex]

6 feet [tex]= 6\cdot12 = 72[/tex].

We can set up a proportion

[tex]\frac{205}{68} = \frac{x}{72}[/tex]

We can use the cross products property to find x.

[tex]205\cdot72=14760\\\\\\14760\div68\approx217[/tex]

Hope this helped!

Answer:

217.0588235 lbs

Step-by-step explanation:

Convert ft inches to inches

5 ft = 5*12 = 60 inches

5 ft 8 inches = 68 inches

6 ft = 6*12 = 72 inches

We can use ratios to solve

205 lbs        x lbs

------------- = ----------------

68 inches     72 inches

Using cross products

205 * 72 = 68x

Divide by 68

205 *72/68 = x

217.0588235 lbs

For this year's fundraiser, students at a certain school who sell at least 75 magazine subscriptions win a prize. If the fourth grade students at this school sell an average (arithmetic mean) of 47 subscriptions per student, the sales are normally distributed, and have a standard deviation of 14, then approximately what percent of the fourth grade students receive a prize

Answers

Answer:

The percentage is  k  =  2.3%

Step-by-step explanation:

From the question we are told that

  The  population mean is  [tex]\mu = 47[/tex]

    The  standard deviation is  [tex]\sigma = 14[/tex]

Given that the sales are normally distributed and that students at a certain school who sell at least 75 magazine subscriptions win a prize then the  percent of the fourth grade students receive a prize is mathematically represented as

     [tex]P(X > 75) = P(\frac{X - \mu }{\sigma } > \frac{75 - \mu }{\sigma })[/tex]

Generally

     [tex]\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of \ X )[/tex]

So

   [tex]P(X > 75) = P(Z > \frac{75 - 47 }{14 })[/tex]

   [tex]P(X > 75) = P(Z > 2)[/tex]

From the standardized normal distribution table  

      [tex]P(Z > 2) =0.023[/tex]

=>   [tex]P(X > 75) = 0.023[/tex]

The  percentage of the fourth grade students receive a prize is  

  k =  0.023 * 100

   k  =  2.3%

   

10 times as much as 9

Answers

Answer:

90

Step-by-step explanation:

10 x 9

=> 90

10 times 9 is 90.

plz hep me to prove the following relations:​

Answers

Step-by-step explanation:

[taking alpha = a]

L.H.S.

(1-sin⁴a)/cos⁴a

= 1/cos⁴a-sin⁴a/cos⁴a

= sec⁴a-tan⁴a

= (sec²a+tan²a)(sec²a-tan²a)

= (1+tan²a+tan²)(1) [as sec²a=1+tan²a]

= 1+2tan²a

= R.H.S. [Proved]

Write an expression to represent: Four less than the product of one and a number xxx

Answers

Answer:

xxx-4

Step-by-step explanation:

(1×xxx)-4

yietisyksykd

Answer:

(1xxx)-4

Step-by-step explanation:

Since 1 and xxx are multiplied, they produce 1xxx and eventually 4 is subtracted so 1xxx-4 and I put the brackets just to make it clear about what is going on in the expression

The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of 7 cm/s. When the length is 12 cm and the width is 5 cm, how fast is the area of the rectangle increasing?

Answers

Answer:

129 m/s^2

Step-by-step explanation:

The length of a rectangle is increasing at a rate of 9m/s

dL/dt = 9m/s

The width is increasing at a rate of 7m/s

dw/dt= 7m/s

The formular for solving the area of a rectangle is length × width

Therefore, to calculate how fast the rectangle is increasing we will apply the product rule

dA/dt= L × dw/dt + W × dl/dt

= 12×7 + 5×9

= 84+45

= 129m/s^2

Hence the area of the rectangle is increasing at 129m/s^2

HHHHHHHheeellllllppppp MEMEMEMEMMEMEMEMEMEEEEEEEE PLLLZZZZ

Answers

First plug in the numbers for x and y
-2.31-(-5.9)
When a negative is being subtracted you replace it with an addition symbol. So, now the equation is -2.31+5.9
Answer: 3.59

Calcule o valor de x nas equações literais: a) 5x – a = x+ 5a b) 4x + 3a = 3x+ 5 c) 2 ( 3x -a ) – 4 ( x- a ) = 3 ( x + a ) d) 2x/5 - (x-2a)/3 = a/2 Resolva as equações fracionárias: a) 3/x + 5/(x+2) = 0 , U = R - {0,-2} b) 7/(x-2) = 5/x , U = R - {0,2} c) 2/(x-3) - 4x/(x²-9) = 7/(x+3) , U = R - {-3,3}

Answers

Answer:

1) a) [tex]x = \frac{3}{2}\cdot a[/tex], b) [tex]x = 5-3\cdot a[/tex], c) [tex]x = -a[/tex], d) [tex]x = \frac{5}{2}\cdot a[/tex]

2) a) [tex]x = -\frac{3}{4}[/tex], b) [tex]x = -5[/tex], c) [tex]x = 3[/tex]

Step-by-step explanation:

1) a) [tex]5\cdot x - a = x + 5\cdot a[/tex]

[tex]5\cdot x - x = 5\cdot a + a[/tex]

[tex]4\cdot x = 6\cdot a[/tex]

[tex]x = \frac{3}{2}\cdot a[/tex]

b) [tex]4\cdot x + 3\cdot a = 3\cdot x + 5[/tex]

[tex]4\cdot x - 3\cdot x = 5 - 3\cdot a[/tex]

[tex]x = 5-3\cdot a[/tex]

c) [tex]2\cdot (3\cdot x - a) - 4\cdot (x-a) = 3\cdot (x+a)[/tex]

[tex]6\cdot x -2\cdot a -4\cdot x +4\cdot a = 3\cdot x +3\cdot a[/tex]

[tex]6\cdot x -4\cdot x -3\cdot x = 3\cdot a -4\cdot a +2\cdot a[/tex]

[tex]-x = a[/tex]

[tex]x = -a[/tex]

d) [tex]\frac{2\cdot x}{5} - \frac{x-2\cdot a}{3} = \frac{a}{2}[/tex]

[tex]\frac{6\cdot x-5\cdot (x-2\cdot a)}{15} = \frac{a}{2}[/tex]

[tex]\frac{6\cdot x - 5\cdot x+10\cdot a}{15} = \frac{a}{2}[/tex]

[tex]2\cdot (x+10\cdot a) = 15 \cdot a[/tex]

[tex]2\cdot x = 5\cdot a[/tex]

[tex]x = \frac{5}{2}\cdot a[/tex]

2) a) [tex]\frac{3}{x} + \frac{5}{x+2} = 0[/tex]

[tex]\frac{3\cdot (x+2)+5\cdot x}{x\cdot (x+2)} = 0[/tex]

[tex]3\cdot (x+2) + 5\cdot x = 0[/tex]

[tex]3\cdot x +6 +5\cdot x = 0[/tex]

[tex]8\cdot x = - 6[/tex]

[tex]x = -\frac{3}{4}[/tex]

b) [tex]\frac{7}{x-2} = \frac{5}{x}[/tex]

[tex]7\cdot x = 5\cdot (x-2)[/tex]

[tex]7\cdot x = 5\cdot x -10[/tex]

[tex]2\cdot x = -10[/tex]

[tex]x = -5[/tex]

c) [tex]\frac{2}{x-3}-\frac{4\cdot x}{x^{2}-9} = \frac{7}{x+3}[/tex]

[tex]\frac{2}{x-3} - \frac{4\cdot x}{(x+3)\cdot (x-3)} = \frac{7}{x+3}[/tex]

[tex]\frac{1}{x-3}\cdot \left(2-\frac{4\cdot x}{x+3} \right) = \frac{7}{x+3}[/tex]

[tex]\frac{x+3}{x-3}\cdot \left[\frac{2\cdot (x+3)-4\cdot x}{x+3} \right] = 7[/tex]

[tex]\frac{2\cdot (x+3)-4\cdot x}{x-3} = 7[/tex]

[tex]2\cdot (x+3) -4\cdot x = 7\cdot (x-3)[/tex]

[tex]2\cdot x + 6 - 4\cdot x = 7\cdot x -21[/tex]

[tex]2\cdot x - 4\cdot x -7\cdot x = -21-6[/tex]

[tex]-9\cdot x = -27[/tex]

[tex]x = 3[/tex]

Given: x - 5 > -2. Choose the solution set.

Answers

Answer: x>3

Step-by-step explanation:

x-5>2

x>+5-2

x>3

The curve y=2x^3+ax^2+bx-30 has a stationary point when x=3. The curve passes through the point (4,2).

(A) Find the value of a and the value of b.

#secondderivative #stationarypoints


Answers

A stationary point at x = 3 means the derivative dy/dx = 0 at that point. Differentiating, we have

dy/dx = 6x ² + 2ax + b

and so when x = 3,

0 = 54 + 6a + b

or

6a + b = -54 … … … [eq1]

The curve passes through the point (4, 2), which is to say y = 2 when x = 4. So we also have

2 = 128 + 16a + 4b - 30

or

16a + 4b = -96

4a + b = -24 … … … [eq2]

Eliminate b by subtracting [eq2] from [eq1] and solve for a, then for b :

(6a + b) - (4a + b) = -54 - (-24)

2a = -30

a = -15   ===>   b = 96

7(a-1)=45 what is the answer to that equation????

Answers

Answer: a = 52/7

Step-by-step explanation:

remove the parentheses, move the constant to the right, calculate, then divide both sides

Answer:

The answer is, a = 52/7, or a = 7.42 in decimal form

Follow the steps below for better explanation:

How many adults must be randomly selected to estimate the mean FICO​ (credit rating) score of working adults in a​ country? We want ​% confidence that the sample mean is within points of the population​ mean, and the population standard deviation is .

Answers

Answer: hello below is the complete question

How many adults must be randomly selected to estimate the mean FICO (credit rating) score of working adults in a country? We want 90% confidence that the sample mean is within 4 points of the population mean, and the population standard deviation is 66. Round up to the nearest whole number

answer : 737 adults

Step-by-step explanation:

confidence interval = 90% = 0.9

( E ) = 4

standard deviation = 66

first we have to calculate the value of a

a = 1 - confidence interval

  = 1 - 0.9 = 0.10      hence  a / 2 = 0.05

next find the value of Z a/2 from table

Z[tex]_{0.05}[/tex]  = 1.645

The number of Adults selected can be determined using this relation

N = [tex](Z_{a/2} * (s/E))^2[/tex]

   = [tex](Z_{0.05} * ( 66/4))^2[/tex]

   = 737

A study was conducted to determine whether magnets were effective in treating pain. The values represent measurements of pain using the visual analog scale. Assume that both samples are independent simple random samples from populations having normal distributions. Use a significance level to test the claim that those given a sham treatment have pain reductions that vary more than the pain reductions for those treated with magnets.
n xbar s
Sham 20 0.41 1.26
Magnet 20 0.46 0.93

Answers

Answer and Step-by-step explanation: The null and alternative hypothesis for this test are:

[tex]H_{0}: s_{1}^{2} = s_{2}^{2}[/tex]

[tex]H_{a}: s_{1}^{2} > s_{2}^{2}[/tex]

To test it, use F-test statistics and compare variances of each treatment.

Calculate F-value:

[tex]F=\frac{s^{2}_{1}}{s^{2}_{2}}[/tex]

[tex]F=\frac{1.26^{2}}{0.93^{2}}[/tex]

[tex]F=\frac{1.5876}{0.8649}[/tex]

F = 1.8356

The critical value of F is given by a F-distribution table with:

degree of freedom (row): 20 - 1 = 19

degree of freedom (column): 20 - 1 = 19

And a significance level: α = 0.05

[tex]F_{critical}[/tex] = 2.2341

Comparing both values of F:

1.856 < 2.2341

i.e. F-value calculated is less than F-value of the table.

Therefore, failed to reject [tex]H_{0}[/tex], meaning there is no sufficient data to support the claim that sham treatment have pain reductions which vary more than for those using magnets treatment.

please find the answer

Answers

Answer:

I hope this is correct but 8.5 or 8 1/2 Units

Answer:

i think it is 8 1/2.

Step-by-step explanation:

my reasoning is that because v=lwh. the length is 4 and hw is 2 1/8. so i multiplied those together.

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