Which events are mutually exclusive?

Answer:

Step-by-step explanation:

Since our interval is given as it is, we are in QIII. That interval is equivalent to 270 degrees to 360 degrees, which is QIII. If we draw this right triangle in QIII and label it accordingly, the side adjacent to the reference angle is sqrt2 and the hypotenuse is 2. We know this because the cosine ratio is defined as the side adjacent to the reference angle over the hypotenuse of the right triangle. That means that we have to find the missing side in order to determine the other 2 main trig ratios. Using Pythagorean's Theorem, we have

[tex]2^2=\sqrt{2}^2+b^2[/tex] and

[tex]4=2+b^2[/tex] so

[tex]b=\sqrt{2}[/tex]. But since it is for a value that, in QIII is negative, it is [tex]-\sqrt{2}[/tex]

Now we can find the sin and tan of that reference angle. Sin is defined as the side opposite the reference angle over the hypotenuse, so

[tex]sin\theta=\frac{-\sqrt{2} }{2}[/tex] and tan, which is defined as side opposite the reference angle over the side adjacent to the reference angle, then

[tex]tan\theta=\frac{-\sqrt{2} }{\sqrt{2} }=-1[/tex]

Answer:

a) 0.3140

b) 0.3098

c) 0.3447

Step-by-step explanation:

Given data :

p = 4% = 0.04

Assuming selections are independent for next 150 pieces

n = 150

a) Probability that 7,8,9 will be selected

P( 7,8,9 ) = 0.3140

b) probability that 7,8,9 will be selected using Poison approximation

P( 7,8,9 ) = 0.3098

c) using normal approximation to determine the probability from ( a )

P ( 7,8,9 ) = 0.3447

Attached below is the detailed solution

Answer:

30 cm ^3

Step-by-step explanation:

Volume = Length x Width x Height

L and W =6cm^2

H=5cm

Hope this helps!

Answer: if you roll a fair 6 sided for a large number of times the average would be 3.5

Step-by-step explanation:

Khan

Answer:

too difficult 99%(95%) fraction and decimal of 26.5 and (-36)

The answer would be A

Answer:

It would be A

Step-by-step explanation:

Once again the shape does not rotate or flip it stays the same but moves on the coordinate plane.

it would be 100.889, darling. hope this helps. <3

f(x) times g(x) = 8x^2+8x-6

(2x-1) times (4x+6) = 8x^2+8x-6

====================================================

Explanation:

The functions f(x) and g(x) are linear functions. The result of f(x) ___ g(x) is some quadratic function.

It's very likely that the answer is a multiplication sign because of the general template of

(linear)*(linear) = (quadratic)

For example, x*3x = 3x^2.

Let's see if the two functions multiply out to 8x^2+8x-6 or not.

-----------------------

f(x) * g(x) = ( f(x) ) * ( g(x) )

f(x) * g(x) = ( 2x-1 ) * ( 4x+6 )

f(x) * g(x) = y * ( 4x+6 ) ......... let y = 2x-1

f(x) * g(x) = 4xy + 6y   ......... distribute

f(x) * g(x) = 4x( y ) + 6( y )

f(x) * g(x) = 4x( 2x-1 ) + 6( 2x-1 ) .... replace y with 2x-1

f(x) * g(x) = 8x^2-4x  + 12x-6  .... distribute twice more

f(x) * g(x) = 8x^2+8x-6

We end up getting the correct result. So this confirms that a multiplication sign is needed to fill in the blank.

Answer:

(a) No solution

(b) Infinitely many solution

(c) No solution

(d) Infinitely many solution

Step-by-step explanation:

Solving (a):

[tex]2x + 10y = 9[/tex] --- (1)

[tex]3x + 15y = 13[/tex] --- (2)

Multiply (1) by 1.5

1.5 * [[tex]2x + 10y = 9[/tex]]

[tex]3x + 15y = 13.5[/tex] --- (3)

Subtract 2 and 3

[tex]3x - 3x + 15y - 15y = 13.5 - 13[/tex]

[tex]0 = 0.5[/tex]

The above is false; Hence, the system has no solution

Solving (b):

[tex]2x + 8y = 5[/tex] --- (1)

[tex]3x + 12y = 7.5[/tex] -- (2)

Multiply 1 by 1.5

1.5 * [[tex]2x + 8y = 5[/tex]]

[tex]3x + 12y = 7.5[/tex]

Subtract 2 and 3

[tex]3x - 3x + 12y - 12y = 7.5 - 7.5[/tex]

[tex]0 = 0[/tex]

The above implies that the system has infinitely many solutions

Solving (c):

[tex]y = 3 - x[/tex]

A second equation is required to solve for (c)

Solving (d):

[tex]5x - 8y = -1[/tex] --- (1)

[tex]-\frac{5}{2}x+ 4y = \frac{1}{2}[/tex] --- (2)

Multiply (2) by 2

[tex]-5x + 8y = 1[/tex] --- (3)

Add 1 and 3

[tex]5x - 5x -8y + 8y = -1 + 1[/tex]

[tex]0 = 0[/tex]

The above implies that the system has infinitely many solutions

Step-by-step explanation:

[tex] \: \:\huge\mathfrak\purple{Answer...} \\ \\ here \: is \: your \: solution \\ \\ area \: of \: parallelogram = base \times height \: \\ \\ base = 10cm \: \\ \\ height = 6cm \: \\ \\ aera \: of \: pralelogram = 10 \times 6 \: \\ \\ area \: = 60 \: cm.sq \\ \\ \huge\mathfrak\red{hope \: it \: helps...}[/tex]

9514 1404 393

Answer:

  x = -29/6 = -4 5/6

Step-by-step explanation:

The equation simplifies to ...

  ln(-3x·4) = ln(58)

Taking antilogs, the equation becomes ...

  (-3x)(4) = 58

Dividing by -12 shows us the value of x.

  x = -58/12

  x = -29/6 = -4 5/6

__

The applicable rule of logarithms is ...

  ln(ab) = ln(a) +ln(b)

Answer:

7x - 4x = 21

3x = 21

x = 21÷3

x = 7

Answer:

c

Step-by-step explanation:

Answer:

A is the answer

Step-by-step explanation:

Answer:

152

Step-by-step explanation:

Answer:

664 miles by only going to work not coming back.

Step-by-step explanation:

Answer:

Q1

[tex]by \ pythagoras \ theorem : \\(3x +1 )^2 = (3x - 1)^2 +x^2\\\\9x^2 + 6x +1 = 9x^2 + 1 -6x +x^2\\\\9x^2 + 6x +1 = 10x^2 + 1 -6x \\\\ 10x^2 + 1 -6x - 9x^2 -6x -1 = 0 \\\\x^2 -12x = 0\\x(x - 12) = 0\\x = 0, 12\\since \ length \ cannot \be \ 0, x = 12\\OJ = 3x + 1 = 3(12) +1 = 37[/tex]

Q2

[tex]by \ pythagoras \ thm, \\(7x -12) ^2 = (5x +10)^2 +(2x)^2\\\\49x^ 2 +144 - 168x = 25x^2 +100+ 100x +2x^2\\\\49x^ 2 +144 - 168x - 25x^2 -100- 100x -2x^2 = 0\\\\22x^2 -268x -44 = 0\\11x^2 - 134x - 22 = 0\\x=12.0154[/tex]

Answer:

Lets choose y

Plug in

Answer:

I'll choose 'x' variable first to eliminate because -

Step-by-step explanation:

Eqn.1 → -3x - 8y = -24

Eqn.2 → 3x - 5y = 45

If we'll add both the equations , then '3x' would be getting cancelled first.

⇒ [tex](-3x - 8y) + (3x - 5y) = (-24) + (45)[/tex]

⇒ [tex]3x - 3x - 8y - 5y = 45 - 24[/tex]

⇒ [tex]-13y = 21[/tex]

⇒ [tex]y = \frac{-21}{13}[/tex]

Putting the value of y in eqn.2 ,

⇒ [tex]3x - 5(\frac{-21}{13}) = 45[/tex]

⇒ [tex]3x + \frac{105}{13} = 45[/tex]

⇒ [tex]3x = 45 - \frac{105}{13}[/tex]

⇒ [tex]3x = \frac{585 - 105}{13} = \frac{480}{13}[/tex]

⇒ [tex]x = \frac{480}{13 \times 3} = \frac{480}{39}[/tex]

Reducing the fraction gives ,

⇒ [tex]x = \frac{160}{13}[/tex]

Answer:

13 miles

Step-by-step explanation:

                                                 12 miles

                Home --------------------------------------------------------Library

                     |

5 miles          |

                     |

                     |

                     |

                School

We can draw an imaginary line betwen school and library. by using the pythagoras theorem, because it is a right triangle. the distance between school and library is 13.

Answer:

X=41

Step-by-step explanation:

40x40 =1600

9x9=81

1600+81=1681

[tex] \sqrt{1681} [/tex]

=41

Answer:

15.38%

Step-by-step explanation:

There are 4 7's in a deck of 52 cards.

There are 4 Aces in a deck of 52 cards.

4+4 = 8

8/52, or 15.38%

=================================================

Explanation:

There are four cards labeled "7", and four cards that are aces. We have 4+4 = 8 cards that we want to find. This is out of 52 total.

The probability we're after is 8/52 = (4*2)/(4*13) = 2/13

2/13 = 0.1538 = 15.38% approximately

Answer:

x = 2, y = -1.

Step-by-step explanation:

2x + y = 3

x  -   y  = 3

Adding the 2 equations eliminates y:

3x = 6

x = 2.

Substitute for x in the first equation:

2(2) + y = 3

y = 3 - 4

y = -1.

Check the results by substitution in equation 2:

2 - (-1)

= 2 + 1 = 3 .

Checks OK.

9514 1404 393

Answer:

  28

Step-by-step explanation:

Corresponding sides are proportional.

  x/42 = 22/(22+11)

  x = 42(2/3)

  x = 28

Answer:

their graphed

Step-by-step explanation:

Answer:

  x = 2.5 or 7.5

Step-by-step explanation:

Subtract 3/4.

  |5 -x| = 10/4 = 2.5

This resolves to two equations:

The solutions are x = 2.5 or 7.5.

Answer:

[tex]x^2 -6x +c \ is \ the \ perfect \ square\\=> x^2 -6x + c = (x -k)^2\\=>x^2 -6x+c = x^2 -2kx + k^2\\Equating \ the \ like \ terms,\\-6x = -2kx\\k = 3\\substituting \ k \ in \ (x-k) = (x-3)\\x^2 -6x +c = (x-3)^2\\\\X^2 - 6x + c = x^2 -6x +9 \\\\=> c = 9[/tex]

opion. b

Answer:

b

Step-by-step explanation:

Answer:

[tex]cos x =\frac{adjacent}{hypotenuse} = \frac{11}{20}\\\\x = cos^{-1} (\frac{11}{20} ) = 56.63[/tex]

x= 57°