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Inessa [10]
3 years ago
12

Solve each of the following equations for x. 2^x − 1 = 0

Mathematics
1 answer:
AlekseyPX3 years ago
3 0

Answer:

The solution to the equation is x = 0

Step-by-step explanation:

Hi there!

First, let´s write the equation:

2ˣ - 1 = 0

To solve it for x, let´s add 1 to both sides of the equation:

2ˣ = 1

Apply log to both sides of the equation

log(2ˣ) = log(1)

Apply logrithm property: log(2ˣ) = x log(2)

x log(2) = log(1)

x log(2) = 0

x = 0

The solution is x = 0

Let´s check the solution:

2ˣ - 1 = 0

x = 0

2⁰ - 1 = 0

1 - 1  = 0

0 = 0

The solution is correct!

Have a nice day!

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Is this multiple choice? I know that a is correct.

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if the product of 4 and a number is decreased by 12, the result is twice the opposite of the number. Find the number. EXPLAIN PL
ELEN [110]
Answer:  The number is:  "2 " .
__________________________________________
Explanation:
__________________________________________
Write the expression; which is an equation, as follows:
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     " 4x <span>− 12 = 2(-x) " ;  in which "x" represents "the number for which we shall                                       solve" .
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Note:  

If the "number" = "x" ;  the "opposite of the number"  =  " -x " ;
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Rewrite as:  " 4x <span>− 12 = -2x " ;
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     →  Add "12" ; & add "2x" ; to EACH SIDE of the equation:

                      4x − 12 + 12 + 2x = -2x + 12 + 2x ;

           to get:    6x  = 12  ;
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 Now, divide each side of the equation by "6" ; 
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Let us check our answer, by plugging in "2" for "x" in our original equation:
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Hannah claims that people who live in southern states spend 9 hours more per week outside than do people in northern states. She
vova2212 [387]

Answer:

b. Hannah is likely to be incorrect because 9 is not contained in the interval.

Step-by-step explanation:

Hello!

Hannah estimated per CI the difference between the average time that people spend outside in southern states and the average time people spend outside in northern states.

The CI is a method of estimation of population parameters that propose a range of possible values for them. The confidence level you use to construct the interval can be interpreted as, if you were to calculate 100 confidence interval, you'd expect that 99 of them will contain the true value of the parameter of interest.

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Meaning that with a 99% confidence level you'd expect the value of the difference between the average time people from southern states spend outside than the average time people from northern states spend outside is included in the interval [0.4;8.0]hs.

Now, she claims that people living in southern states spend 9 more hours outside than people living in northern states, symbolized μ₁ - μ₂ > 9

Keep in mind that if you were to test her claim, the resulting hypothesis test would be one-tailed

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I hope this helps!

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