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The probability of coin landing with heads is an independent event.

The probability of winning 1st and 2nd prize is a dependent event.

Independents events are events whose occurrence do not depend on each other. They are random events. The probability of a coin landing on heads is a random event.

Dependent events are events that are not random. The outcome of one event depends on the outcome of another event.

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Answer:

Step-by-step explanation:

The matrix of coefficients has one row corresponding to each equation. The constants in that row are the coefficients of the variables in the equation. Coefficients are listed in the same order on each row. A missing term is represented by a coefficient of 0.

The first attachment shows the coefficient matrix and its determinant.

__

The solution to the system of equations can be found by left-multiplying the constant vector by the inverse of the coefficient matrix.

  [tex]\textbf{A$\cdot$X}=\textbf{B}\\\\\textbf{X}=\textbf{A}^{-1}\cdot\textbf{B}[/tex]

This multiplication is shown in the second attachment. It tells us ...

  [tex]\textbf{X}=\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}3\\4\\1\end{array}\right][/tex]

The material wasted is 7915.375 sq cm.

The product of its length and breadth.

Area = length* breadth

Given:

length= 150 ac, breadth = 100 cm

d= 0.9m 5cm

r= 47.5 cm

Area of rectangle,

= l * b

= 150*100

= 15000 sq. cm

Area of Circular cloth,

= πr²

=3.14*47.5*47.5

=7084.625 sq cm.

Hence, the wasted material is = 15000-7084.625

                                                  = 7915.375 sq cm

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The weekday hours you purchased is 5 hours.

The number of weekend hours I can purchase if the weekday hours tripled is 11 hours.

2a + 10b = 220 equation 1

a + b = 26 equation 2

Where:

Multiply equation 2 by 10

10a + 10b = 260 equation 3

Subtract equation 3 from equation 2

8a = 40

a = 5 hours

(5 x 3) + b = 26

15 + b = 26

b = 26 - 15

b = 11 hours

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Answer:

y

[tex]y = - 2 x + 5[/tex]

Step-by-step explanation:

Hope this will help :)

Answer: your gonna add 3,000+ 5,000 then you will add test answer to 157.50 then you’ll put the answer for 3,000+5,000 then you’ll put that in the first box then you’ll add that number two 157.50

Step-by-step explanation:

Hope this helps

:3 have an amazing day or a beautiful day:)

After 8 years the value of the computer to be $0 if the Aaron’s mother purchases a new computer for $1750.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have:

Aaron’s mother purchases a new computer for $1750. If she claims a linear depreciation (loss of value) on the computer at a rate of $250 per year.

The above problem can be solved using concept of arithmetic sequence

The starting value = $1750

After one year = 1750 - 250 = $1500

After second year = 1500 - 250 = $1250

Common difference = 1500 - 1750 = -250

a(n) = 1750 + (n - 1)(-250)

a(n) = 0  (final value is zero given)

0 = 1750 + (n - 1)(-250)

n - 1 = 7

n = 8 years

Thus, after 8 years the value of the computer to be $0 if the Aaron’s mother purchases a new computer for $1750.

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Answer:

  x²

Step-by-step explanation:

The area of rectangle ABJH is the product of its dimensions.

__

The dimensions are given as ...

  AB = x

  AH = x

The area of ABJH is ...

  area = length × width = (x) × (x) = x²

The area of ABJH is x².

The answer of the following questions is discussed below

Area of a circle is the region covered or enclosed within its boundary. It is measured in square units.

The radius of each circle

r1= 2.5 inches.

r2= 1 inches

Area of circle large circle,

= πr1²

=3.14*2.5*2.5

=19.625 inch²

Area of small circle,

= πr2²

= 3.14*1*1

=3.14 inch²

Area of large circle minus area of small circle,

= 16.485  inch²

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In a data set, the proportion of items that are in a particular category is called the Relative Frequency

Frequency mean how often an event can occur , an relative frequency means how many times that event will occur with respect to the total number of events.

For determining Relative frequency , we need to know the frequency for a particular event and the total number of event.

The proportion of items that are in a particular category is called the Relative Frequency.

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Answer:

8 hrs.

Step-by-step explanation:

He has to spend $9, so 57+9=66. The closest multiple of 9 over 66 is 9x8=72. So, Reuben has to spend 8 hrs.

Answer:

angles in a triangle add up to 180°

5:12:13 = 30

180 ÷ 30 = 6

6 × 5 = 30°

6 × 12 = 72°

6 × 13 = 78°

angles = 30°, 72°, 78°

The experimental probability of spinning a 7 is 0%

From the complete question, we  have:

n(7) = 0

The above means that the number 7 is not on the spinner.

So, it is impossible to spin a 7

Hence, the experimental probability of spinning a 7 is 0%

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The number of ways there are to get to the point (7,4) if you have to pass through the point (2,2) is; 1266 ways

The formula to get the number of ways to get to the lattice point (x, y) (supposing x, y ≥ 0) by taking steps of one unit each either in the eastward or northward direction is exactly;

(x + y)

          = (x + y)!/(x!y!)

(   x   )

Thus, number of ways from (0, 0) to (2, 2) = (2 + 2)!/(2!2!) = 6 ways

Number of ways to get to point (7,4) from (2, 2) is;

((7 - 2) + (4 - 2))!/(2!2!) = 7!/(2!2!) = 1260

Thus, total number of ways = 1266 ways

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The angular measure L is : 47°

Angles are formed when two lines meet.

Analysis:

Firstly, we calculate for m using cosine rule.

[tex]m^{2}[/tex] = [tex]510^{2}[/tex] + [tex]820^{2}[/tex] -2(510)(820) cos 20

[tex]m^{2}[/tex] = 260100 + 672400 -83600(0.9396)

[tex]m^{2}[/tex] = 146618.56

m = [tex]\sqrt{146618.56}[/tex] = 382.9cm

using sine rule to find ∠L

382.9/sin20 = 820/sinL

sinL = 820sin20/382.9

sinL = 820(0.342)/382.9

sinL = 0.732

L = sin inverse of 0.732 = 47°

In conclusion, ∠L is 47°

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Answer:

Step-by-step explanation:

Answer:

1.5 or 3/2

Step-by-step explanation:

[tex]\frac{2x+1}{2x-1} =2\\(\frac{2x+1}{2x-1} )(2x-1)=2(2x-1)\\2x+1 = 4x-2\\2x+1-4x=4x-2-4x\\-2x+1=-2\\-2x+1-1=-2-1\\-2x=-3\\x=\frac{-3}{-2} \\=1.5 or \frac{3}{2}[/tex]

Answer:

  58.1 cm

Step-by-step explanation:

The length of each support rod can be found using the Pythagorean theorem. The geometry can be modeled by a right triangle, such that the distance from centre is one leg and half the length of the rod is the other leg of a triangle with hypotenuse equal to the radius of the grill.

__

The theorem tells us that the sum of the squares of the legs of a right triangle is the square of the hypotenuse. For legs a, b and hypotenuse c, this is ...

  c² = a² +b²

For the geometry of the grill, we can define a=7.5 and c=30. Then b will be half the length of the support rod.

  30² = 7.5 +b²

  b² = 900 -56.25 = 843.75

  b = √843.75 ≈ 29.0473

The length of each support rod is twice this value, so ...

  rod length = 2b = 2(29.0473) = 58.0947

Each support rod is about 58.1 cm long.

Answer:

-9,40

Step-by-step explanation:

Midpoint Formula:

[tex](\frac{x^{1} +x^{2} }{2},\frac{y^{1} +y^{2} }{{2} } } )[/tex]

Answer:

Midpoint = (−9,40)

Step-by-step explanation:

Answer:

There can be alot of equations for this since you didn't say anything specific. But since u didnt say anything specific, this can be one of the equations: 20 + 8, 30 - 2, 4 x 7

Answer:

*r = R/100 = 8%/100 = 0.08 per year, A = P(1 + rt)

a) A = 6000[1 + (0.08 × 5)] = 8400

b) A = $8,400.00

Answer:

  a) $2400

  b) $8400

Step-by-step explanation:

The simple interest formula can be used to find the amount of interest. The amount collected at the end of the period is the total of principal and interest.

__

The simple interest is given by the formula ...

  I = Prt . . . . . . P is the principal amount, r is the annual rate, and t is the number of years

For this investment, the interest is ...

  I = $6000·0.08·5 = $2400

The simple interest amounts to $2400.

__

The amount collected at the end of 5 years is the principal plus interest:

  P +I = $6000 +2400 = $8400

The total collected is $8400.

Answer:

-6x²+xy-6y²

Step-by-step explanation:

3y² - 4x² + xy - 2x² - 9y²

-4x²+ xy - 2x² - 6y²

-6y² + xy - 6y²

Answer:

−6x² + xy − 6y²

Step-by-step explanation:

Simplify 3y²-4x² + xy - 2x² - 9y²​

Step 1

Subtract 9y² from 3y²

−4x² +xy −2x² −6y²

Step 2

Subtract 2x²  from −4x²

−6x²  + xy  − 6y²

Answer:

58°

Step-by-step explanation:

Apply trig inverse properties

W = arccos(0.53)

W = 2[tex]\pi[/tex] - arccos(0.53)

Answer:

(f+g)(x) = 3x^2+x+1

Step-by-step explanation:
It may look hard at first, but all the question is asking you to do is add both of the equations together.

(f+g)(x) = (3x^2-1) + (x+2)
(f+g)(x) = 3x^2+x+1

Answer:

0.81

Step-by-step explanation:

how this helps!

btw: you spelled truly wrong

Using it's concept, it is found that the range of the set of numbers 10, 30, 15, 17, and 18 is of 20.

The range of a data-set is given by the difference of the greatest value by the smallest.

In the data-set 10, 30, 15, 17, and 18, we have that:

Hence the range is given by:
R = 30 - 10 = 20.

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