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Arturiano [62]
3 years ago
13

Find the experimental probability of getting the letter e when a letter is drawn at random from this text:

Mathematics
1 answer:
MrMuchimi3 years ago
5 0

Answer:

0.17647 or 17.647%

Step-by-step explanation:

You have to count the total number of letters in the text:

The text has 102 letters. Do not count punctuation signs and spaces.

Now count the total number the letter “e” appears.

The letter “e” appears 18 times.

So the experimental probability of getting the letter e when a letter is drawn at random from the text:

<em>"In English l, the letter e appears most frequently among alphabetical characters, in these lines, it appears eighteen times."</em>

is

18/102 = 0.17647 or 17.647%

'

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Solve the system by graphing.<br><br> 3x+8y=16<br><br> 3x+8y=-64
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<em>4x-4y=8</em>

<em>or</em>

<em>y = -3x - 10 </em>

<em>P(0,-10) and P(-2, -4) on this line: Plot and connect with the Line.</em>

<em></em>

<em> </em>

<em>y = x - 2</em>

<em>P(0, -2) and (2,0) on this line: Plot and connect with the Line.</em>

<em>P(-2,-4) is the ordered pair that is the solution for this system of EQs</em>

<em>On may CHECK by substituting x= -2 and y = -4 into the EQs of these Lines</em>

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<em>Hope this helps!!!</em>

7 0
3 years ago
Find the roots of:
Elena-2011 [213]

\large\displaystyle\text{$\begin{gathered}\sf \pmb{1) \  2x^3-7x^2+8x-3=0 } \end{gathered}$}

Synthetic division is used since the equation is of the third degree. The divisors of -3 are 1, -1, 3, +3. So:

  | 2  -7    8  -3

<u>1 |      2   -5   3</u>

  | 2   -5    3  0

<u> 1 |      2     -3   </u>

    2   -3     0

So the factorization is (x-1)² (2x-3)=0. So:

                     \bf{ x_1=x_2=1 \qquad x_2=\dfrac{3}{2}  }

\large\displaystyle\text{$\begin{gathered}\sf \pmb{2) \  x^3-x^2-4=0 } \end{gathered}$}

Synthetic division is used since the equation is of the third degree. The divisors of -4 are 1, -1, 2, -2, 4, -4. So:

      |  1  -1  0  -4

  <u>2  |     2  2     </u>

         1  2  2  0

So the factorization is (x-2)(x²+x+2)=0 . When calculating the discriminant of the trinomial, it is concluded that it has no roots since the result is negative. So you only have one solution.

                   \bf{ 1^2-4(2)(2)=1-16=-15 < 0 \quad \Longrightarrow \quad x=2 }

\large\displaystyle\text{$\begin{gathered}\sf \pmb{3) \  6x^3+7x^2-9x+2=0 } \end{gathered}$}

Synthetic division is used since the equation is of the third degree. The divisors of 2 are 1, -1, 2, -2. So:

   | 6    7       9      2

<u>-2 |      -12    10     -2</u>

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So the factorization is (x+2)(6x²-5x+1)=0 . The quadratic equation is solved by the general formula:

         \bf{ x_{2, 3}&=\dfrac{5\pm \sqrt{(5)^2-4(6)(1)}}{2(6)}=\dfrac{5\pm \sqrt{25-24}}{12}=\dfrac{5\pm 1}{12} }}

                     \large\displaystyle\text{$\begin{gathered}\sf  \begin{matrix} x_1=-2&\ \ \ \ \ \ x_{2}=\dfrac{6}{12} \qquad &\ \ \ x_3=\dfrac{4}{12}\\ &\ \ \ x_2=\dfrac{1}{2} \qquad &x_3=\dfrac{1}{3} \end{matrix} \end{gathered}$}

6 0
2 years ago
Your 6 1/4 year investment of $40,000 at 14% compounded quarterly is worth how much now?
KengaRu [80]
The formula to be used here is:

F = P(1+i)ⁿ
where 
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Let's find i first which has to be converted to compounded annually.

i = (1 + r/m)^m - 1
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i = (1 + 0.14/4)⁴ - 1 = 0.1475

Thus,
F = (40000)(1+0.1475)^(6 1/4)
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4 0
3 years ago
Question 1 (1 point)<br> Divide using any method.<br> -3x3 + 4.x2 + 2x – 5)<br> (x - 2)
valkas [14]

Answer:Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of

0

.

x

+

1

4

x

2

-

2

x

-

5

Divide the highest order term in the dividend

4

x

2

by the highest order term in divisor

x

.

4

x

x

+

1

4

x

2

-

2

x

-

5

Multiply the new quotient term by the divisor.

4

x

x

+

1

4

x

2

-

2

x

-

5

+

4

x

2

+

4

x

The expression needs to be subtracted from the dividend, so change all the signs in

4

x

2

+

4

x

4

x

x

+

1

4

x

2

-

2

x

-

5

-

4

x

2

-

4

x

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

4

x

x

+

1

4

x

2

-

2

x

-

5

-

4

x

2

-

4

x

-

6

x

Pull the next terms from the original dividend down into the current dividend.

4

x

x

+

1

4

x

2

-

2

x

-

5

-

4

x

2

-

4

x

-

6

x

-

5

Divide the highest order term in the dividend

−

6

x

by the highest order term in divisor

x

.

4

x

-

6

x

+

1

4

x

2

-

2

x

-

5

-

4

x

2

-

4

x

-

6

x

-

5

Multiply the new quotient term by the divisor.

4

x

-

6

x

+

1

4

x

2

-

2

x

-

5

-

4

x

2

-

4

x

-

6

x

-

5

-

6

x

-

6

The expression needs to be subtracted from the dividend, so change all the signs in

−

6

x

−

6

4

x

-

6

x

+

1

4

x

2

-

2

x

-

5

-

4

x

2

-

4

x

-

6

x

-

5

+

6

x

+

6

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

4

x

-

6

x

+

1

4

x

2

-

2

x

-

5

-

4

x

2

-

4

x

-

6

x

-

5

+

6

x

+

6

+

1

The final answer is the quotient plus the remainder over the divisor.

4

x

−

6

+

1

x

+

1

Step-by-step explanation:

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Step-by-step explanation:

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