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Ne4ueva [31]
3 years ago
11

3(x - 1) – 2(2x + 1) = 8(x - 1) What is the solution in a fraction

Mathematics
1 answer:
defon3 years ago
3 0

Answer:

1/3

Step-by-step explanation:

3(x-1)-2(2x+1)=8(x-1)

3x-3-4x-2=8x-8

3x-4x-3-2=8x-8

-x-5=8x-8

-x-8x-5=-8

-9x-5=-8

-9x=-8+5

-9x=-3

9x=3

x=3/9

simplify

x=1/3

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A coin is to be tossed as many times as necessary to turn up one head. Thus the elements c of the sample space C are H, TH, TTH,
slavikrds [6]

Answer:

Step-by-step explanation:

As stated in the question, the probability to toss a coin and turn up heads in the first try is \frac{1}{2}, in the second is \frac{1}{4}, in the third is \frac{1}{8} and so on. Then, P(C) is given by the next sum:

P(C)=\sum^{\infty}_{n=1}(\frac{1}{2} )^{n}=1

This is a geometric series with factor \frac{1}{2}. Then is convergent to \frac{1}{1-\frac{1}{2}}-1=1.. With this we have proved that P(C)=1.

Now, observe that

P(H)=\frac{1}{2}, P(TH)=\frac{1}{4},P(TTH)=\frac{1}{8},P(TTTH)=\frac{1}{16},P(TTTTH)=\frac{1}{32},P(TTTTTH)=\frac{1}{64}.

Then

P(C1)=P(H)+P(TH)+P(TTH)+P(TTTH)+P(TTTTH)=\frac{1}{2} +\frac{1}{4} +\frac{1}{8} +\frac{1}{16} +\frac{1}{32} =\frac{31}{32}

P(C2)=P(TTTTH)+P(TTTTTH)=\frac{1}{32}+\frac{1}{64} =\frac{3}{64}

P(C1\cap C2)=P(TTTTH)=\frac{1}{32}

and

P(C1\cup C2)=P(H)+P(TH)+P(TTH)+P(TTTH)+P(TTTTH)+P(TTTTTH)=\frac{1}{2} +\frac{1}{4} +\frac{1}{8} +\frac{1}{16} +\frac{1}{32} +\frac{1}{64}=\frac{63}{64}

5 0
3 years ago
Find the x-intercept of the function: f(x) = 6x - 2. Round answer to the nearest hundredth, if necessary. A) (0.39, 0) B) (1.00,
lions [1.4K]
The function f(x) = 6^(x)-2 has an x-intercept at approximately <span>(0.39, 0)
              f(x) =  0 = 6^(x) - 2
                        2  = 6^(x)
       log(2)/log(6)= x
                          x = 0.3868 = 0.39</span>
The answer to this question is A) (0.39, 0).
6 0
2 years ago
A marching band is performing in a rectangular arrangement, with a width of $w$ people. The length consists of seven less people
Norma-Jean [14]

Answer:

There are 120 people in the marching band.

Step-by-step explanation:

Let no. of people in the band be x.

In the first rectangular arrangement,

Width of rectangle (w_{1}) = w people.

Length of rectangle (l_{1}) = (w-7) people

Therefore,

no. of people in the band(x) = Area of the rectangle = Product of width and Length

x = width \times length

x = w\times (w-7)  (equation 1);

In the second rectangular arrangement,

Width of rectangle (w_{2}) = (w-3) people.

Length of rectangle (l_{2}) = (w-5) people

Therefore,

no. of people in the band(x) = Area of the rectangle = Product of width and Length

x = width \times length

x = (w-3)\times(w-5)  (equation 2);

Therefore, from equation 1 and equation 2 , we get,

w\times(w-7)=(w-3)\times(w-5)

w^{2}-7w=w^{2} - 8w + 15

Therefore,

w = 15  (equation 3)

From equation 1 and equation 3, we get

x = 15\times(15-7)

x = 120.

Therefore,

no. of people in the marching band = 120 people

8 0
3 years ago
An ellipse has a center at the origin, a vertex along the major axis at (10, 0), and a focus at (8, 0).
nekit [7.7K]

Answer:

In standard form x^2/64 + y^2/100 = 1

Step-by-step explanation:

The major axis is the y axis because 10 has a larger value than 8.  

8x8 = 64

10 x10 = 100

7 0
1 year ago
What is the product?
Setler79 [48]

Answer:

[7 38 9] is the answer

Step-by-step explanation:

Hope this helps I did my calculations and this is the answer

7 0
3 years ago
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