Does the following scenario describe a dependent or independent sequence of events: Flipping a coin and getting a "heads" and then flipping a second coin and getting a "heads".

The correct transformation that describes why rectangles ABCD and A′B′C′D′ are similar is Rectangle ABCD was dilated by a scale factor of 5 to form rectangle A′B′C′D′.

Dilation is a transformation that changes the size of an object while maintaining its shape. In this case, the coordinates of rectangle ABCD were multiplied by a scale factor of 5 to obtain the coordinates of rectangle A′B′C′D′.

This means that each side length of rectangle ABCD was multiplied by 5 to get the corresponding side length of rectangle A′B′C′D′.

The reflection across the y-axis and the rotation of 90° counterclockwise would result in different shapes and orientations, not maintaining the similarity between the two rectangles.

The dilation by a scale factor of 15 or 1/5 would also change the proportions and not result in a similar rectangle.

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Answer:

In Geometry, the cross-section is defined as the shape obtained by the intersection of solid by a plane. The cross-section of three-dimensional shape is a two-dimensional geometric shape. In other words, the shape obtained by cutting a solid parallel to the base is known as a cross-section.

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

no

Answer:

decimal   fraction    percent

0.0855 171/2000  8.55%

Step-by-step explanation:

Answer:

f(x)=x(x-6)(x+3)

Step-by-step explanation:

Answer: (a)- \(0.99\ \text{units}\)

Step-by-step explanation:

Given

Central angle is \(57^{\circ}\)

The radius of the unit circle is \(1\ \text{unit}\)

Arc length is given by

\(\Rightarrow l=\dfrac{\theta}{360^{\circ}}\times 2\pi r\)

Put the values

\(\Rightarrow l=\dfrac{57}{360}\times 2\pi \cdot1\\\\\Rightarrow l=0.99\ \text{units}\)

Answer:

-12 -4x^2

Step-by-step explanation:

f(x) = -6 -2x^2

We want to find 2f(x) so multiply each term by 2

2f(x) = 2 (  -6 -2x^2)

      Distribute

       = -12 -4x^2

Answer:

10.7

Step-by-step explanation:

Since this is a right triangle, we can use trig functions to calculate the hypotenuse.

We know the opposite side from the angle labeled 59 degrees.

sin 59 = opp side / hypotenuse

sin 59 = 9.2/x

x = 9.2/ sin 59

x = 10.733

Answer:

B

Step-by-step explanation:

let's list everything out.

$35 for school supplies

$17.5 has already been used

$17.5 is left

pens only come in packs of 12

one pack of pens is $5

ok, so we know its definitely not C or D because they are less than 12

42 is not divisible by 12

since packs only come in 12's then it must be B.

good luck my friend!

Answer:

A) \(x=-1\pm\sqrt{\frac{13}{6}}\)

Step-by-step explanation:

\(\displaystyle x=\frac{-12\pm\sqrt{12^2-4(6)(-7)}}{2(6)}\\\\x=\frac{-12\pm\sqrt{144+168}}{12}\\\\x=\frac{-12\pm\sqrt{312}}{12}\\\\x=\frac{-12\pm2\sqrt{78}}{12}\\\\x=-1\pm\frac{\sqrt{78}}{6}\\\\x=-1\pm\sqrt{\frac{78}{36}}\\\\x=-1\pm\sqrt{\frac{13}{6}}\)

Answer:

To find the length of AB, we can use the property that two tangents to a circle from the same external point are equal. This means that AB = AD. Substituting the given values, we get:

8x = x + 9

Solving for x, we get:

x = 1.5

Therefore, AB = 8x = 8(1.5) = 12.

To check our answer, we can use the Pythagorean theorem on triangle ABD, since AB is perpendicular to BD at the point of tangency. We have:

AB^2 + BD^2 = AD^2

Substituting the values, we get:

12^2 + BD^2 = (1.5 + 9)^2

Simplifying, we get:

BD^2 = 56.25

Taking the square root of both sides, we get:

BD = 7.5

Hence, the length of AB is 12 and the length of BD is 7.5.

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The equation is solved and the distribution property is given by

a) A = 5x + 15

b) B = x² - 3x

c) C = x² + 6x + 8

d) D = x² - 10x + 25

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

A = 5 ( x + 3 )

On simplifying the equation , we get

A = 5 ( x ) + 5 ( 3 )

A = 5x + 15

b)

B = x ( x - 3 )

On simplifying the equation , we get

B = x ( x ) - x ( 3 )

B = x² - 3x

c)

C = ( x + 4 ) ( x + 2 )

On simplifying the equation , we get

C = ( x + 4 ) ( x ) + ( x + 4 ) ( 2 )

C = x² + 4x + 2x + 8

C = x² + 6x + 8

d)

D = ( x - 5 ) ( x - 5 )

On simplifying the equation , we get

D = ( x - 5 ) ( x ) + ( x - 5 ) ( -5 )

D = x² - 5x - 5x + 25

D = x² - 10x + 25

Hence , the equations are solved

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The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

72 = 2³ × 3²

48 = 2⁴ × 3

48 = 2⁴ × 3

48 = 2⁴ × 3

The GCD of the crayons is 2³ × 3 , which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = 2³ × 3 × 5

The GCD of the drawing paper is also 2³ × 3 , which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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Answer:

12

Step-by-step explanation:

The figure is a right triangle with hypotenuse = QS

The  base from the graph = 4 units
(or you can just subtract the x-coordinates 2 - (-2) = 4)

The height from the graph is 3 units
(Or you can subtract the y-coordinates: 1 - (-2) = 3)

Since this is a right triangle the square of the hypotenuse = sum of squares of the other two sides

QS² = 3² + 4² = 9 + 16 = 25

QS, the hypotenuse = √25 = 5

The perimeter = sum of the sides = 3 + 4 + 5 = 12 units

To find the number of terms in a geometric progression, we can use the formula:

n = log[size of last term / size of first term] / log[common ratio]

In this case, the first term is 2, the last term is 256, and the common ratio is 4/2 = 2. Plugging these values into the formula, we get:

n = log[256/2] / log[2] = log[128] / log[2] = 7

Therefore, there are 7 terms in the geometric progression 2, 4, 8, ..., 256.

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Answer:

I think it is d but you didn't gimme a picture

a) Using the given recurrence,

\(x_2 = \dfrac{{x_1}^3-1}4 = \dfrac{(-1)^3-1}4 = -\dfrac12 = -0.5\)

\(x_3 = \dfrac{{x_2}^3-1}4 = \dfrac{\left(-\frac12\right)^3-1}4 = -\dfrac9{32} = -0.28125\)

b) Proceeding as above, you'll find that successive values of \(x_n\), starting at n = 7, gravitate towards a solution of about -0.254102.

Future value of annuity due is calculated using

From the question, we are given

Hence,

Future Vlaue of annuity due will be

Answers.

Answer:

\( \sqrt{55}\)

Step-by-step explanation:

Given is a right angled triangle.

Therefore, by Pythagoras theorem:

\( {x}^{2} = {8}^{2} - {3}^{2} \\ = 64 - 9 \\ = 55 \\ x = \sqrt{55} \)

\(\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\[-0.35em] ~\dotfill\\\\ \underline{\ln(2)+\ln(8)}-\ln(4)\implies \underline{\ln(2\cdot 8)}-\ln(4)\implies \ln(16)-\ln(4) \\\\\\ \ln\left(\cfrac{16}{4} \right)\implies \ln(4)\)

The overtime rate of pay is K10.25.

The overtime rate of pay can be calculated by multiplying the basic rate pay by the time-and-a-quarter factor. In this case, the basic rate pay is K8.20.

To determine the overtime rate of pay, we need to calculate one-quarter (1/4) of the basic rate pay, and then add that amount to the basic rate pay. One-quarter of K8.20 is calculated as (1/4) * K8.20 = K2.05.

By adding the calculated overtime amount to the basic rate pay, we get the overtime rate of pay: K8.20 + K2.05 = K10.25.

Therefore, the overtime rate of pay is K10.25.

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Answer:

x=1

Step-by-step explanation:

y=3x so just add 1+3=4 then add veriable y=4x

Each number should be dragged to a box to complete the table as follows;

Kilometers     Meters

1                        1,000

2                       2,000

3                       3,000

5                       5,000

8                       8,000

In Science and Mathematics, a conversion factor can be defined as a number that is used to convert a number in one set of units to another, either by dividing or multiplying.

Generally speaking, there are one (1) kilometer in one thousand (1,000) meters. This ultimately implies that, a proportion or ratio for the conversion of kilometer to meters would be written as follows;

Conversion:

1 kilometer = 1,000 meters

2 kilometer = 2,000 meters

3 kilometer = 3,000 meters

4 kilometer = 4,000 meters

5 kilometer = 5,000 meters

6 kilometer = 6,000 meters

7 kilometer = 7,000 meters

8 kilometer = 8,000 meters

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Let,

X1 = Patient that is Critical

X2 = Patient that is Serious

X3 = Patient that is Stable

D = Dead Patient

V = Survived Patient

Using Baye's Formula:

Let,

P(X2, V) = the probability that the patient who survived was categorized as serious upon arrival.​

We are given,

P(X1) = 0.12

P(X2) = 0.27

P(X3) = 1 - (0.12 + 0.27) = 0.61

P(X1,V) = 1 - P(X1,D) = 1 - 0.43 = 0.57

P(X2,V) = 1 - P(X2,D) = 1 - 0.26 = 0.74

P(X3,V) = 1 - P(X3,D) = 1 - .05 = 0.95

We now solve for the probability that the patient who survived was categorized as serious upon arrival,

The probability that the patient who survived was categorized as serious upon arrival is 0.2357.

Answer: 71.57

Step-by-step explanation:

You are going to use SOH CAH TOA to find the angle

because the opposite and adjacent are the sides from the reference angle use TOA (tanΘ=opp/adj)

TanΘ=\(\frac{9}{3}\)

now use that tan^-1 (9/3) on your calculator (make sure your calc is in degree mode)

71.57

Answer:

Noah would need to work 30 hours to equal Mason's earning for 40 hours

Step-by-step explanation:

Mason;

8.10 x 40 = 324

324 ÷ 10.80 = 30 hours.

Helping in the name of Jesus.

Answer:

30 hours

Step-by-step explanation:

40 times 8.10 is 324 and 324 divided by 10.8 is 30 hours

Answer:

20° and 70°

Step-by-step explanation:

complimentary angle sum to 90°

let x be the compliment then the angle is 3x + 10 , so

x + 3x + 10 = 90 , that is

4x + 10 = 90 ( subtract 10 from both sides )

4x = 80 ( divide both sides by 4 )

x = 20

3x + 10 = 3(20) + 10 = 60 + 10 = 70

the 2 angle measures are 20° and 70°

Answer:

4x² + 22x - 12

Step-by-step explanation:

A = bh/2

A = (4x - 2)(2x + 12)/2

A = (8x² + 48x - 4x - 24)/2

A = (8x² + 44x - 24)/2

A = 4x² + 22x - 12