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3 years ago

8-2b=-2/3(12b+6) solve

2 answers:

7 0

We have to mutiply factor -2/3 times every agument from the parenthesis.
$8-2b=- \frac{2*12b}{3}- \frac{2*6}{3} \\ 8-2b= -8b-4 \\$ /+8b
8+6b=-4 /-8
6b=-12 /:6
b=-2 - its the answer

pishuonlain [190]3 years ago

6 0

$8-2b=-\frac { 2 }{ 3 } \left( 12b+6 \right) \\ \\ 8-2b=-\frac { 2 }{ 3 } \cdot 12b-\frac { 2 }{ 3 } \cdot 6\\ \\ 8-2b=-\frac { 24 }{ 3 } b-\frac { 12 }{ 3 } \\ \\ 8-2b=-8b-4\\ \\ -2b+8b=-4-8\\ \\ 6b=-12\\ \\ b=\frac { \left( -12 \right) }{ 6 } \\ \\ \therefore \quad b=-2$

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There are 9,481 eligible voters in a precinct. 500 were selected at random and asked to indicate whether they planned to vote fo

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Answer:

The confidence limits for the proportion that plan to vote for the Democratic incumbent are 0.725 and 0.775.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

Of the 500 surveyed, 350 said they were going to vote for the Democratic incumbent.

This means that $n = 500, \pi = \frac{350}{500} = 0.75$

80% confidence level

So $\alpha = 0.2$ , z is the value of Z that has a pvalue of $1 - \frac{0.2}{2} = 0.9$ , so $Z = 1.28$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.75 - 1.28\sqrt{\frac{0.75*0.25}{500}} = 0.725$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.75 + 1.28\sqrt{\frac{0.75*0.25}{500}} = 0.775$

The confidence limits for the proportion that plan to vote for the Democratic incumbent are 0.725 and 0.775.

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3 years ago

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Step-by-step explanation:

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A padlock has the digits 0 through 9 arranged in a circle on its face. A combination for 0 1 2 3 4 6 5 7 8 9 this padlock is fou

stepan [7]

Answer:

The total numbers of possible combinations are 3430.

Step-by-step explanation:

Consider the provided information.

A combination for 0 1 2 3 4 6 5 7 8 9 this padlock is four digits long. Because of the internal mechanics of the lock, no pair of consecutive numbers in the combination can be the same or one place apart on the face.

Here, for the first digit we have 10 choices.

For the second digit we have 7 choices, as the digit can't be the same nor adjacent to the first digit.

For the third digit we have 7 choices, as the digit can't be the same nor adjacent to the second digit.

For the fourth digit we have 7 choices, as the digit can't be the same nor adjacent to the third digit.

So the number of choices are:

$10\times 7\times 7\times 7=10\times 7^3\\10\times 343=3430$