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2 years ago

Solve x -2/3(3x - 4) + 3x = 5/6 is x -19/6, 11/6, 21/6, 29/6

Mathematics

1 answer:

Tanzania [10]2 years ago

3 0

Answer:

x=-11/12

Step-by-step explanation:

Given an equation for x

x -2/3(3x - 4) + 3x = 5/6

We are asked to find the value of x.

We use equation rules to solve

To get rid of denominator in fraction, let us multiply the whole equation by 6.

6x-4(3x-4) +18x = 5

Simplify:

-6x+18x+16 =5

12x = 5-16 = -11

x = -11/12

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2 years ago

Fast Food and Gas Stations Forty percent of all Americans who travel by car look for gas stations and food outlets that are clos

Andrei [34K]

Answer:

mean $\mu = 10$ variance $\sigma^2 = 6$

The binomial random variable x fall into this interval ranges from

- 5 to 5

$P(6 \le x \le 14) = 0.8969$

Step-by-step explanation:

From the question we are told that

The sample size is $n = 25$

The percentage that look for gas stations and food outlets that are close to or visible from the highway is $p = 0.40$

Generally the mean is mathematically represented as

$\mu = n * p$

=> $\mu = 0.40 * 25$

=> $\mu = 10$

The variance is mathematically represented as

$\sigma^2 = np(1- p )$

=> $\sigma^2 = 25 * 0.40(1- 0.40 )$

=> $\sigma^2 = 6$

The standard deviation is mathematically evaluated as

$\sigma = \sqrt{\sigma^2}$

$\sigma = \sqrt{6}$

$\sigma = 2.45$

The interval is evaluated as

$p\pm 2 \sigma$

=> $p - 2 \sigma\ \ \ , \ \ \ p + 2\sigma$

=> $0.40 - 2 *2.45\ \ \ , \ \ \ 0.40 + 2* 2.45$

=> $-4.5\ \ \ , \ \ \ 5.3$

The binomial random variable x fall into this interval ranges from

- 5 to 5

Generally

$P(6 \le x \le 14) = P(\frac{ x - \mu }{\sigma } \le \frac{14 - 10}{{2.45}} ]-P[ \frac{ x - \mu }{\sigma } \le \frac{6 - 10}{2.45 } ]$

$P(6 \le x \le 14) = P(Z \le 1.63 ]-P[ Z \le -1.63 ]$

$P(6 \le x \le 14) = [1- P(Z > 1.63 ]] -[1- P[ Z > -1.63 ]]$

From the z-table

$P(Z > 1.63 ) = 0.051551$

And

$P(Z >- 1.63 ) =0.94845$

=> $P(6 \le x \le 14) = [1-0.051551] -[1-0.94845]$

=> $P(6 \le x \le 14) = 0.8969$

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