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Mamont248 [21]
3 years ago
5

3. Jennifer writes the letters M­O­N­T­A­N­A on cards and then places the cards in a hat. What is the probability of picking a v

owel?
a.2/7
b.37
c.1/3
d.2/3
Mathematics
1 answer:
11111nata11111 [884]3 years ago
8 0
The word Montana has a total of 7 letters this number becomes our denominator because this is the total amount of letters.  Three of the letters contain vowels, this number will go on top. These letters include o, and two a (s).


This will give us the answer of 3/7. This fraction cannot be reduced any further.

The answer should result in b.

It appears the slash was forgotten to be written in the answer, try not to make this mistake on any tests!

Hope this helped! :)
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2x^3-x^2-3x=210<br> the answer is 5 but I want to know why.
mel-nik [20]

Answer:

x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}

Step-by-step explanation:

1) Move all terms to one side.

2x^{3} -x^{2} -3x-210=0

2) Factor 2{x}^{3}-{x}^{2}-3x-210 using Polynomial Division.

1 -  Factor the following.

2x^{3} -x^{2} -3x-210

2 -  First, find all factors of the constant term 210.

1,2,3,4,5,6,7,10,14,15,21,30,35,42,70,105,210

3) Try each factor above using the Remainder Theorem.

Substitute 1 into x. Since the result is not 0, x-1 is not a factor..

2*1^{3} -1^{2} -3*1-210=-212

Substitute -1 into x. Since the result is not 0, x+1 is not a factor..

2(-1)^{3} -(-1)^{2} -3*-1-210=-210

Substitute 2 into x. Since the result is not 0, x-2 is not a factor..

2*2^{3} -2^{2} -3*2-210=-204

Substitute -2 into x. Since the result is not 0, x+2 is not a factor..

2{(-2)}^{3}-{(-2)}^{2}-3\times -2-210 = -224

Substitute 3 into x. Since the result is not 0, x-3 is not a factor..

2\times {3}^{3}-{3}^{2}-3\times 3-210 = -174

Substitute -3 into x. Since the result is not 0, x+3 is not a factor..

2{(-3)}^{3}-{(-3)}^{2}-3\times -3-210 = -264

Substitute 5 into x. Since the result is 0, x-5 is a factor..

2\times {5}^{3}-{5}^{2}-3\times 5-210 =0

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

⇒ x-5

4)  Polynomial Division: Divide 2{x}^{3}-{x}^{2}-3x-210  by x-5.

                                               2x^{2}                       9x                      42

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

x-5                               |    2x^{3}                          -x^{2}                     -3x     -210

                                           2x^{3}                             -10x^{2}

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

                                                                             9x^{2}                -3x       -210

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

                                                                          42x                              -210

                                                                         42x                               -210

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

5)  Rewrite the expression using the above.

2x^2+9x+42

(2x^2+9x+42)(x-5)=0

3) Solve for x.

x=5

4)  Use the Quadratic Formula.

1 - In general, given a{x}^{2}+bx+c=0 , there exists two solutions where:

x=\frac{-b+\sqrt{b^{2} -4ac} }{2a} ,\frac{-b-\sqrt{b^2-4ac} }{2a}

2 -  In this case, a=2,b=9 and c = 42.

x=\frac{-9+\sqrt{9^2*-4*2*42} }{2*2} ,\frac{-9-\sqrt{9^2-4*2*42} }{2*2}

3 - Simplify.

x=\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}

5) Collect all solutions from the previous steps.

x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}

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The number of homeruns hit by each player on the Bobcats baseball team is listed below.
sveta [45]
Range

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What is the equation of a circle with center -4, 7 and radius 6
Kitty [74]

Answer:

( x + 4 )^2 + ( y - 7 )^2 = 36

Step-by-step explanation:

Use the circle equation, ( x - h )^2 + ( y - k )^2 = r^2

Plug in the center and radius:

( x + 4 )^2 + ( y - 7 )^2 = 6^2

Simplify:

( x + 4 )^2 + ( y - 7 )^2 = 36

So, the equation is ( x + 4 )^2 + ( y - 7 )^2 = 36

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2 years ago
What type of number is Square root of two
DochEvi [55]

Answer:

irrational

The square root of 2 is irrational.

Step-by-step explanation:

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3 years ago
In a reflection, pairs of corresponding points lie on parallel lines.<br> True or False?
Lerok [7]

The statement that: pairs of corresponding points lie on parallel lines in a reflection, is false.

<h3>What are reflections?</h3>

When a point is reflected, then the point is flipped across a point or line of reflection

When a point is reflected, the following highlights are possible

  • The corresponding points can line on the same line
  • The corresponding points can line on parallel lines

Using the above highlights, we can conclude that the statement is false.

This is so because, corresponding points are not always on parallel lines

Read more about reflection at:

brainly.com/question/23970016

6 0
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