The grade appeal process at a university requires that a jury be structured by selecting eight individuals randomly from a pool of eight students and nine faculty. What is the probability a jury of all students?

Answer:

Step-by-step explanation:

F(x) = (x - 2)(x - 9)(x + 4)²(x + 5)

The term "dilation" refers to a transformation. The height of the pre-image is 24.4 mm.

The term "dilation" refers to a transformation that is used to downsize an item. Dilation is a technique for making items appear bigger or smaller. The picture produced by this transformation is identical to the original shape.

Let the dilation factor of the trapezoid be x.

Now, if we write the area of the pre-image trapezoid, it can be written as,

[tex]\text{Area of trapezoid} = \dfrac{(a+b)}{2}h = 49\rm\ mm^2[/tex]

As we know the dilation is applicable to dimensions, therefore, the area of the trapezoid which is the image can be written as,

[tex]\text{Area of Image trapezoid} = \dfrac{(ax+bx)}{2}hx[/tex]

                                      [tex]= \dfrac{x(a+b)}{2}hx\\\\=\dfrac{(a+b)}{2}h\cdot x^2\\\\=49\cdot x^2[/tex]                  

Now, if we calculate the scale factor(x) of the dilation we will get,

[tex]{\text{Area of trapezoid}}={\text{Area of Image trapezoid}}\\\\x^2 \cdot 49 = 784\\\\x = 4[/tex]

Further, the scale factor applied to the height of the image can be written as,

The height of the Image = 4 × Height of pre-image

                                          = 4 × 6.1 = 24.4 mm

Hence, the height of the pre-image is 24.4 mm.

Learn more about Dilation:

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Answer:

24.4 mn

Step-by-step explanation: I took the quiz

Answer:

-8d+13

Step-by-step explanation:

Add and Multiply all of the numbers without variables:

3x4+1

Use PEMDAS to solve (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction):

3x4=12

12+1=13

Now you have your answer:

-8d+13

Answer:

-8d+13

Step-by-step explanation:

Multiply first:

3x4=12

Add:

12+1=13

Add equations:

-8d+13

The correct answer is -8d+13

Answer:

83°

Step-by-step explanation:

? = (1/2)[m(arc)DE + m(arc)RF]

? = (1/2)[106° + 60°]

? = 83°

Answer:

He would have 48

Step-by-step explanation:

1 set: 8

2 sets: 16

3 sets: 24

4 sets: 32

5 sets: 40

5 sets: 48

OR

{4(8)} + 2(8)

32 + 2(8)

32 + 16

48

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Answers

48

Steps

4+2=6

8 times 6= 48

We are given with a complex no. and need to simplify it , so let's start !!!

Let's assume that :

[tex]{:\implies \quad z=\sf \dfrac{6+2\iota}{3-\iota}}[/tex]

Now , Rationalizing the denominator or in other words multiplying and dividing [tex]{z}[/tex] by the conjugate of the denominator

[tex]{:\implies \quad z=\sf \dfrac{6+2\iota}{3-\iota}\times \dfrac{3+\iota}{3+\iota}}[/tex]

[tex]{:\implies \quad z=\sf \dfrac{(6+2\iota)(3+\iota)}{(3-\iota)(3+\iota)}}[/tex]

[tex]{:\implies \quad z=\sf \dfrac{6(3+\iota)+2\iota (3+\iota)}{(3)^{2}-(\iota)^{2}}\quad \qquad \{\because (a-b)(a+b)=a^{2}-b^{2}\}}[/tex]

[tex]{:\implies \quad z=\sf \dfrac{18+6\iota +6\iota +2(\iota)^{2}}{9-(-1)}\quad \qquad \{\because (\iota)^{2}=-1\}}[/tex]

[tex]{:\implies \quad z=\sf \dfrac{18+12\iota -2}{10}}[/tex]

[tex]{:\implies \quad z=\sf \dfrac{16+12\iota}{10}}[/tex]

[tex]{:\implies \quad z=\sf \dfrac{16}{10}+\dfrac{12\iota}{10}}[/tex]

[tex]{:\implies \quad {\bf \therefore}\quad \underline{\underline{z=\bf \dfrac{8}{5}+\dfrac{6}{5}\iota}}}[/tex]

Hence , Option B) (8/5) + (6/5)i is correct :D

Answer: 8/5+6/4i

Proof of validity is shown below.

Answer:

25978

Step-by-step explanation:

There are 26 letters in the alphabet and 999 numbers with 3 digits so I multiplied and got the answer

Please mark Brainlest if I helped

Answer:

Yes

Step-by-step explanation:

9/21 SIMPLIFIED= 3/7

6/14 SIMPLIFIED= 3/7

Answer:

24x²

Step-by-step explanation:

6 x 4x² = 24(x)(x) = 24x²

Answer:

x = [tex]\frac{3}{2}[/tex]y + 20

[Given]

4x - 6y = 20

[Add 6y to both sides of the equation]

4x = 6y + 20

[Divide both sides of the equation by 4]

x = [tex]\frac{6}{4}[/tex]y + 20

[Simplify [tex]\frac{6}{4}[/tex], both 6 and 4 are divisible by 2]

x = [tex]\frac{3}{2}[/tex]y + 20

Answer:

We use a variety of different notations to express the derivative of a function. In (Figure) we showed that if f(x)=x^2-2x, then f^{\prime}(x)=2x-2. If we had expressed this function in the form y=x^2-2x, we could have expressed the derivative as y^{\prime}=2x-2 or \frac{dy}{dx}=2x-2. We could have conveyed the same information by writing \frac{d}{dx}(x^2-2x)=2x-2. Thus, for the function y=f(x), each of the following notations represents the derivative of f(x):

f^{\prime}(x), \, \frac{dy}{dx}, \, y^{\prime}, \, \frac{d}{dx}(f(x)).

In place of f^{\prime}(a) we may also use \frac{dy}{dx}\Big|_{x=a} Use of the \frac{dy}{dx} notation (called Leibniz notation) is quite common in engineering and physics. To understand this notation better, recall that the derivative of a function at a point is the limit of the slopes of secant lines as the secant lines approach the tangent line. The slopes of these secant lines are often expressed in the form \frac{\Delta y}{\Delta x} where \Delta y is the difference in the y values corresponding to the difference in the x values, which are expressed as \Delta x ((Figure)). Thus the derivative, which can be thought of as the instantaneous rate of change of y with respect to x, is expressed as

\frac{dy}{dx}=\underset{\Delta x\to 0}{\lim}\frac{\Delta y}{\Delta x}.

Step-by-step explanation:

Answer:

I'm pretty sure it's D) 8x = 6x + 0.50

Answer:

Graph 1 (big) shows that it has the biggest number which means that graph 1 (big) is the correct answer!

Step-by-step explanation:

Answer:

Multiply 54 by 6

Step-by-step explanation:

Remember the Order of Operations:

Parentheses

Exponents

Multiplication/Division (Whichever comes first)

Addition/Subtraction (Whichever comes first)

In this case, we can start by looking inside of the parentheses.

There are two signs; addition and multiplication.

Now we look back to the order of operations (PEMDAS), and see that multiplication comes before addition, therefore you should first multiply 54 by 6.

Answer:

98

Step-by-step explanation:

71 + 9 + 18 = ( 71 + 9 ) + 18     Group numbers that add to 10 to make it easier

                 = 80 + 18

                 = 98

If you have any questions, you can ask them in the comments section of this answer. If you could mark this answer as brainliest, I would greatly appreciate it.

Answer:

45⁰

Step-by-step explanation:

We need to find n first.

we are given that GQH is 90⁰ which means that the sum of GQL and LQK should 90⁰ because these are angles on a straight line which adds up to 180⁰.

so,

(4n-15) + 3n = 90⁰

Take the -15 to the other side after opening the brackets.

4n + 3n = 90⁰ + 15

7n = 105⁰

Divide it by 7 for both sides.

n = 15⁰

Now substitute n=15⁰ in you LQK equation.

4n -15

(4×15) -15

60⁰ - 15

45⁰

Answer:

it is letter B and then it is letter a

Answer:

yellow = 33.3 %

green = 20%

orange = 30%

red = 16.6%

Step-by-step explanation:

all in all there are 30 cards

10 ➗ 30 = 0.333 = 33.3%

6 ➗ 30 = 0.20 = 20%

9 ➗ 30 = 0.30 = 30%

5 ➗ 30 = 0.166 = 16.6%

Answer:

  a > c

Step-by-step explanation:

The Transitive Property of Inequality can be written as ...

  If a > b and b > c, then a > c.

Based on the above, we can conclude from your premises that a > c.

Answer:

45 years

Step-by-step explanation:

Let the sum be x and CI=2x

We know that

CI=P(1+100R)T

2x=x(1+100R) ^15

(1+100R)^15=2                

Let m be the number of years.

Therefore,

x(1+100R)m=8x

(1+100R)m=23

(1+100R)m=[(1+100R)^15]3          

From eqn(1)

(1+100R)m=(1+100R)45

On comparing both power, we get

m=45 years

Answer:

81.60 is your selling price

Step-by-step explanation:

60% = 0.60

0.60 x 51 = 30.60

51 + 30.60 = 81.60

Answer:

4m and 6m

Step-by-step explanation:

factors of 24: 2, 3, 4, 6, 8, 12

now just go through each and find one that fits the description

Answer: A

Step-by-step explanation:

The change in the y coordinates is 0, but the change in the x coordinates is 8.

Answer:

8*(4^n)

where n is the nth number

equation ar^n

where a is first term

r common ratio.

The length of the diagonal of the rectangular prism is 14.7 feet to the nearest tenth.

In a three-dimensional space prism is a polyhedron where two ends are similar.

Given:

The dimensions of the right rectangular prism:

Length l = 10cm

Width w = 4cm

Height h = 10cm

The length of the diagonal of the rectangular prism,

= √(l² + w² + h)

= √{(10)² + (4)² + (10)²}

= 14.69

= 14.7 feet.

Therefore, the length of the diagonal is  14.7 feet.

To learn more about the prism;

https://brainly.com/question/12649592

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Step-by-step explanation:

To find the area of a rectangle, we simply need to multiply its length by its width. The area is simply the width of a rectangle times height. Area = h × h, Area = h2. Hence for a square, the area is the square of its sides.

Answer:

5.2 hours

Step-by-step explanation:

divide the total distance by how fast

td/speed

3250/625=5.2hrs

Step-by-step explanation:

Two meals are the different

Answer:

5*3*4 = 60, so 60 different main meals could be ordered.