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goldenfox [79]
3 years ago
7

What is the solution 8x-3(2x-4)=3(x-6)

Mathematics
2 answers:
SVETLANKA909090 [29]3 years ago
7 0
16x^2 - 32x -3x +12 = 3x-18
X= 30
yanalaym [24]3 years ago
5 0

Answer:

x = 30

General Formulas and Concepts:

<u>Pre-Alg</u>

  • Order of Operations: BPEMDAS
  • Equality Properties

Step-by-step explanation:

<u>Step 1: Define equation</u>

8x - 3(2x - 4) = 3(x - 6)

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Distribute:                                   8x - 6x + 12 = 3x - 18
  2. Combine like terms:                   2x + 12 = 3x - 18
  3. Subtract 2x on both sides:        12 = x - 18
  4. Add 18 to both sides:                 30 = x
  5. Rewrite:                                       x = 30

<u>Step 3: Check</u>

<em>Plug in x to verify it's a solution.</em>

  1. Substitute:                    8(30) - 3(2(30) - 4) = 3(30 - 6)
  2. Multiply:                        240 - 3(60 - 4) = 3(30 - 6)
  3. Subtract:                       240 - 3(56) = 3(24)
  4. Multiply:                        240 - 168 = 72
  5. Subtract:                       72 = 72
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Jack is at the zoo looking up at a monkey
sasho [114]

The height of the pole at which the monkey is at the top is 10.2 feet.

<h3>Trigonometric ratio</h3>

Trigonometric ratio is used to show the relationship between the angles and sides of a right angled triangle.

Let h represent the height of the pole, hence using trigonometric ratio:

tan(23) = h/24

h = 10.2 feet

The height of the pole at which the monkey is at the top is 10.2 feet.

Find out more on Trigonometric ratio at: brainly.com/question/4326804

4 0
2 years ago
The number of events is 29​, the number of trials is 298​, the claimed population proportion is​ 0.10, and the significance leve
Nina [5.8K]

Answer:

z=\frac{0.0973 -0.1}{\sqrt{\frac{0.1(1-0.1)}{298}}}=-0.155  

p_v =2*P(Z  

And we can use excel to find the p value like this: "=2*NORM.DIST(-0.155;0;1;TRUE)"

So the p value obtained was a very high value and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is not significantly different from 0.1 .  

Step-by-step explanation:

1) Data given and notation

n=298 represent the random sample taken

X=29 represent the events claimed

\hat p=\frac{29}{298}=0.0973 estimated proportion

p_o=0.1 is the value that we want to test

\alpha=0.05 represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the proportion is 0.1 or no.:  

Null hypothesis:p=0.1  

Alternative hypothesis:p \neq 0.1  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.0973 -0.1}{\sqrt{\frac{0.1(1-0.1)}{298}}}=-0.155  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

p_v =2*P(Z  

And we can use excel to find the p value like this: "=2*NORM.DIST(-0.155;0;1;TRUE)"

So the p value obtained was a very high value and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is not significantly different from 0.1 .  

We can do the test also in R with the following code:

> prop.test(29,298,p=0.1,alternative = c("two.sided"),conf.level = 1-0.05,correct = FALSE)

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