Line segment QR is dilated to create line segment Q'R' using the dilation rule DT,1.5. Point T is the center of dilation. Line segment Q R is dilated to create line segment Q prime R prime. The length of R T is 6 and the length of R prime R is y. What is y, the distance between points R and R'?

The question is incomplete. The complete question is :

In a survey of women in a certain country ( ages 20-29), the mean height was 62.9 inches with a standard deviation of 2.81 inches.  Answer the following questions about the specified normal distribution.  (a) What height represents the 99th percentile?  (b) What height represents the first quartile?  (Round to two decimal places as needed)

Solution :

Let the random variable X represents the height of women in a country.

Given :

X is normal with mean, μ = [tex]62.9[/tex] inches and the standard deviation, σ = [tex]2.81[/tex] inches

Let,

[tex]$Z=\frac{X - 62.9}{2.81}$[/tex] , then Z is a standard normal

a). Let the [tex]99th[/tex] percentile is = a

The point a is such that,

[tex]$P(X<a)=0.99$[/tex]

[tex]$P \left( Z < \frac{a-62.9}{2.81} \right) = 0.99$[/tex]

From standard table, we get : [tex]P( Z < 2.3263) =0.99[/tex]

∴ [tex]$\frac{(a-62.9)}{281} = 2.3263$[/tex]

  [tex]$a= (2.3263 \times 2.81 ) +62.9$[/tex]

     = 6.536903 + 62.9

     = 69.436903

     = 69.5 (rounding off)

Therefore, the height represents the [tex]99th[/tex] percentile = 69.5 inches.

b). Let b = height represents the first quartile.

It is given by :

[tex]P( X < b) =0.25[/tex]

[tex]$P \left( Z < \frac{(b-62.9)}{2.81} \right) = 0.25$[/tex]

From the standard normal table,

[tex]P( Z < -0.6745) =0.99[/tex]

∴ [tex]$\frac{(b-62.9)}{2.81}= 0.6745$[/tex]

[tex]$b=(0.6745 \times 2.81) +62.9$[/tex]

  = 1.895345 + 62.9

   = 64.795345

   = 64.8 (rounding off)

Therefore, the height represents the 1st quartile is 64.8 inches.

Answer:

Học sinh nam là 21 học sinh, số học sinh nữ là 15 học sinhH

Step-by-step explanation:

Tỉ số giữa nam và nữ là x/y = 7/5 => x/7 = y/5

áp dụng tính chất của dãy tỉ số bằng nhau, ta được:  

x/7 = y/5 => x-y =/7-5 = 6/2 = 3

Vì x/7 = 3 => x = 21

y/5 = 3 => y= 15

Vậy số học sinh nam là 21 học sinh, số học sinh nữ là 15 học sinh

Answer:

12 minutes

Step-by-step explanation:

Given

[tex]s_1 = 10mi/h[/tex] --- walk speed

[tex]s_2 = 20mi/h[/tex] --- jog speed

[tex]d = 2\ miles[/tex] --- distance

Required

The time to walk the given distance

Time is calculated as:

[tex]Time = \frac{distance}{speed}[/tex]

In this case, the speed is the speed at which she walks.

So, we have:

[tex]Time = \frac{d}{s_1}[/tex]

Substitute known values

[tex]Time = \frac{2mi}{10mi/h}[/tex]

[tex]Time = 0.2hr[/tex]

Convert to minutes

[tex]Time = 0.2 * 60mins[/tex]

[tex]Time =12mins[/tex]

Step-by-step explanation:

In this problem, all we have to do is replace x and y with the values we've been given.

It can be helpful to think of 3x as 3 * x (which is the same exact thing), so I'll write it out that way.

3*x - 4*y

(replace)

3*4 - 4*3

(multiply (doing this step first because of PEMDAS))

12 - 12

(subtract)

0

Answer:

0

Answer: 0

Step-by-step explanation:

Concept:

Here, we need to understand the idea of evaluation.  

When encountering questions that gave you an expression with variables, then stated: "If x = a, y = b, z = c" (a, b, c are all constants), this means you should substitute the value given for each variable back to the expression.

Solve:

Given

3x - 4y

x = 4, y = 3

Substitute value of x and y

3(4) - 4(3)

Simplify multiplication

12 - 12

Final subtraction

0

Hope this helps!! :)

Please let me know if you have any questions

Answer:

17) The answer is option B. 273.8 m^2

16) The answer is option A. 2.9887

Step-by-step explanation:

Answer: C=25.12

Step-by-step explanation:

[tex]\displaystyle\ \Large \boldsymbol{} if \ \ equal \ \pi =3,14 \ \ then \\\\\pi r^2=3,14r^2\\\\3,14r^2=50,24 \\\\ r^2=16 \\\\ r=4 \Longrightarrow C= 2\pi r=2\cdot 3,14\cdot 4=25.12 \\\\\\ Answer : C=25.12[/tex]

Answer:

Pentagon = 72°

Octagon = 45°

Step-by-step explanation:

To solve for the measure of one exterior angle in a regular pentagon;

n = number of sides

180 - (180 x n-2/n)

180 - (180 x 5-2/5)

180 - (180 x 3/5)

180 - (540/5)

180 - 108

Exterior angle = 72°

To solve for the measure of one exterior angle in a regular octagon;

n = number of sides

180 - (180 x n-2/n)

180 - (180 x 8-2/8)

180 - (180 x 6/8)

180 - (1080/8)

180 - 135

Exterior angle = 45°

Answer:

135

Step-by-step explanation:

Multiply 2 1/4 by 3/4 by 1 1/4 to get 2 7/64.

Then, multiply 1/4 by 1/4 by 1/4 to get 1/64.

Then divide 2 7/64 by 1/64 to get 135.

Hope this helps!

If there is something wrong, just let me know.

Answer:

Step-by-step explanation:

Adjacent to the undetermined angle is 6, and the hypotenuse has been given. We can conclude, after looking at our SOHCAHTOA, that we will be using cosine(CAH) to solve this problem.

Let the unspecified angle be [tex]\theta\\[/tex] (This sign is called theta, which is just a sign for angle)

Lets start!

cos[tex]\theta\\[/tex] = adj/hyp

cos[tex]\theta\\[/tex] = 6/13

[tex]\theta\\[/tex] = [tex]cos^{-1}[/tex](6/13)

[tex]\theta\\[/tex] = 62.5

[tex]\theta\\[/tex] = 63

Hope that helped!

We have to find the circumference

[tex]\\ \rm\longmapsto C=2\pi r[/tex]

[tex]\\ \rm\longmapsto C=2\dfrac{22}{7}(14)[/tex]

[tex]\\ \rm\longmapsto C=44(2)[/tex]

[tex]\\ \rm\longmapsto C=88cm[/tex]

Answer:

The domain is the whole R-{0} and the range is R

Answer:

Step-by-step explanation:

Function 2 has a slope of 1.1 while function 1 has a slope of just 1.

Answer:

Y = 2x - 4

(2,-4)

gradient= 2

y-intersept = -4

Answer:

Top right option

Step-by-step explanation:

multiplying the digits, you get the volume, which is 3/4

Answered by GAUTHMATH

Answer:

a+b+c +90+90 = 540

Step-by-step explanation:

A five sided figure has interior angles that add to 540

a+b+c +90+90 = 540

Answer:

[tex]Slope = \frac{31}{29}[/tex]

Step-by-step explanation:

Step 1:  Define the slope formula

[tex]Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Step 2:  Find the slope

[tex]Slope = \frac{71-9}{32-(-26)}[/tex]

[tex]Slope = \frac{62}{58}[/tex]

[tex]Slope = \frac{31}{29}[/tex]

Answer:  [tex]Slope = \frac{31}{29}[/tex]

Answer:

x=-2

Step-by-step explanation:

g(x) = x-2

Let g(x) = -4

-4 =x-2

Add 2 to each side

-4+2 = x-2+2

-2 = x

Answer:

x = -2

Step-by-step explanation:

g(x) = -4

g(x) = x - 2

-4 = x - 2

+2      +2

-2 = -x

Answer:

x = 45

Step-by-step explanation:

The angles labeled with the pink x are the same.  Line V and Line X are parallel and alternate interior angles are equal when the lines are parallel.

We know the 3 angles inside the triangle and the sum of the angles of a triangle are 180

x+x+ 2x = 180

4x= 180

4x/4 = 180/4

x = 45

Answer:

Step-by-step explanation:

44.4--0.4=-44

Answer: [tex]9\times 11\ ft^2[/tex]

Step-by-step explanation:

Given

Height is [tex]2\ ft[/tex] more than its width

Suppose the width is [tex]x[/tex]. So, height becomes [tex]x+2[/tex]

Area of the painting is [tex]99\ ft^2[/tex]

Area is the product of width and height

[tex]\therefore 99=x(x+2)\\\Rightarrow 99=x^2+2x\\\Rightarrow x^2+2x-99=0\\\Rightarrow x^2+11x-9x-99=0\\\Rightarrow (x+11)(x-9)=0\\\Rightarrow x=-11,9[/tex]

Neglect the negative values

[tex]\text{Width =}9\ ft\\\text{height =}9+2=11\ ft[/tex]

Answer:

Which angle are you talking about please?

Answer:

X ≥ 3

Step-by-step explanation:

Let the number of grapes you'll buy be X, you need to buy at leaF 3 pounds so:

X ≥ 3

Answered by Gauthmath

Answer:

75 degrees

Step-by-step explanation:

Use trigonometry

we are given opposite(27) and hypotenuse(28), so use sin

sin=opp/hyp

sin(x)=27/28

x=arcsin(27/28)

x=74.64111442

Answer:

1) 6а-9b=3(2a-3b)

2)8a-12b=4(2a-3b)

3) 5ab-5ac=5a(b-c)

4) 6ax+6ay=6a(x+y)

Answer:

D

Step-by-step explanation:

graph it

Answer:

x=9

Step-by-step explanation:

4(x-2)=2x+10

<=> 4x-8=2x+10

<=> 2x=18

<=>x=9

Answer:

x=3 the explanation is above

Answer:

It's A

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd\displaystyle\ \Large \boxed{ \boxed{\boldsymbol{Rule : a^{-1}=\frac{1}{a} }}} \\\\\\\\ (2+3)^{-1} \times (2^{-1}+2^{-1}) = \\\\1)\ (2+3)^{-1}=5^{-1}=\frac{1}{5} \\\\2)\ 2^{-1}+2^{-1}=\frac{1}{2} +\frac{1}{2} } =1 \\\\3)\ \frac{1}{5} \cdot 1=\boxed{\frac{1}{5} }[/tex]