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3 years ago

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.