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2 years ago

Solve x2 = 12x – 15 by completing the square. Which is the solution set of the equation?

2 answers:

4 0

The answer is x = 6 + √21. The general form of quadratic function is ax2 + bx + c = 0. So, the equation x2 = 12x – 15 in the general form will be look like: x2 - 12x + 15 = 0. Now, move the number term on the right side of the equation: x2 - 12x = -15. Since b = 12, (b/2)2 = (12/2)2 = (6)2 = 36. Add this number on the both side of equation: x2 - 12x + 36 = -15 + 36. From here: (x-6)2 = 21. Take square root on both sides: x - 6 = √21. Solve for x: x = 6 + √21

Nady [450]2 years ago

3 0

For this case we have the following polynomial:
$x ^ 2 = 12x - 15
$
The first thing to do is to place the variables on the same side of the equation.
We have then:
$x ^ 2 - 12x = -15
$
We complete the square by adding the term (b / 2) ^ 2 on both sides of the equation.
We have then:
$x ^ 2 - 12x + (-12/2) ^ 2 = -15 + (-12/2) ^ 2
$
Rewriting we have:
$x ^ 2 - 12x + (-6) ^ 2 = -15 + (-6) ^ 2

x ^ 2 - 12x + 36 = -15 + 36
 
(x-6) ^ 2 = 21$
$x-6 =+/- \sqrt{21}$
Therefore, the solutions are:
$x = 6 - \sqrt{21}$
$x = 6 + \sqrt{21}$
Answer:
the solution set of the equation is:
$x = 6 - \sqrt{21}$
$x = 6 + \sqrt{21}$

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In the 2000 presidential election, three candidates split the vote as follows:

Lera25 [3.4K]

Answer:

c 23 and 0.46 are statistics and 0.484 is a parameter

True. For this case the value 0.46 represent t statistic since from the sample obtained we can calculate the sample proportion of people who voted for Gore like this:

$\hat p_{Gore]=\frac{X}{n}=\frac{23}{50}=0.46$

Where X represent the people with the characteristic desired in the random sample selected.

So then we can say that 23 and 0.46 represent statistics since comes from the sample. And the value 0.484 is obtained from the population so then represent a parameter.

Step-by-step explanation:

Previous concepts

A parameter is any "numerical quantity that characterizes a given population or some aspect of it". For this case we are interested on proportions and we denote the population proportion by $p$

A statistic is "used to estimate the value of a population parameter". In other words is just an estimation of the population parameter of interest. Four our case the sample proportion denoted by $\hat p$ represent the statistic for this case.

Solution for the problem

a 0.46 and 0.484 are statistics

False. 0.484 is not an statistic since it's the outcome from the original population and would represent the parameter "proportion of people who vote for Gore"

b 50 and 23 are statistics and 0.484 is a parameter

False. The sample size is not an statistic is just a value selected in order to calculate the statistic.

c 23 and 0.46 are statistics and 0.484 is a parameter

True. For this case the value 0.46 represent t statistic since from the sample obtained we can calculate the sample proportion of people who voted for Gore like this:

$\hat p_{Gore]=\frac{X}{n}=\frac{23}{50}=0.46$

Where X represent the people with the characteristic desired in the random sample selected.

So then we can say that 23 and 0.46 represent statistics since comes from the sample. And the value 0.484 is obtained from the population so then represent a parameter.

6 0

2 years ago

Сумму чисел 165 и 633 уменьшили в несколько раз получили 266. Чему равно неизвестное число?

Whitepunk [10]

Answer:

Step-by-step explanation:

The sum of 165 and 633 will be

165+633=798

When the sum is reduced to 266, it means the sum is reduced by 798/266=3

The sum is reduced three times.

Therefore, as per the question, this sum was reduced three different times

4 0

2 years ago

A machine produces parts that are either defect free (90%), slightly defective (3%), or obviously defective (7%). Prior to shipm

AURORKA [14]

Answer:

(a) 0.0686

(b) 0.9984

Step-by-step explanation:

Given that a machine produces parts that are either defect free (90%), slightly defective (3%), or obviously defective (7%).

Let A, B, and C be the events of defect-free, slightly defective, and the defective parts produced by the machine.

So, from the given data:

P(A)=0.90, P(B)=0.03, and P(C)=0.07.

Let E be the event that the part is disregarded by the inspection machine.

As a part is incorrectly identified as defective and discarded 2% of the time that a defect free part is input.

So, $P\left(\frac{E}{A}\right)=0.02$

Now, from the conditional probability,

$P\left(\frac{E}{A}\right)=\frac{P(E\cap A)}{P(A)}$

$\Rightarrow P(E\cap A)=P\left(\frac{E}{A}\right)\times P(A)$

$\Rightarrow P(E\cap A)=0.02\times 0.90=0.018\cdots(i)$

This is the probability of disregarding the defect-free parts by inspection machine.

Similarly,

$P\left(\frac{E}{A}\right)=0.40$

and $\Rightarrow P(E\cap B)=0.40\times 0.03=0.012\cdots(ii)$

This is the probability of disregarding the partially defective parts by inspection machine.

$P\left(\frac{E}{A}\right)=0.98$

and $\Rightarrow P(E\cap C)=0.98\times 0.07=0.0686\cdots(iii)$

This is the probability of disregarding the defective parts by inspection machine.

(a) The total probability that a part is marked as defective and discarded by the automatic inspection machine

$=P(E\cap C)$

$= 0.0686$ [from equation (iii)]

(b) The total probability that the parts produced get disregarded by the inspection machine,

$P(E)=P(E\cap A)+P(E\cap B)+P(E\cap C)$

$\Rightarrow P(E)=0.018+0.012+0.0686$

$\Rightarrow P(E)=0.0986$

So, the total probability that the part produced get shipped

$=1-P(E)=1-0.0986=0.9014$

The probability that the part is good (either defect free or slightly defective)

$=\left(P(A)-P(E\cap A)\right)+\left(P(B)-P(E\cap B)\right)$

$=(0.9-0.018)+(0.03-0.012)$

$=0.9$

So, the probability that a part is 'good' (either defect free or slightly defective) given that it makes it through the inspection machine and gets shipped

$=\frac{\text{Probabilily that shipped part is 'good'}}{\text{Probability of total shipped parts}}$

$=\frac{0.9}{0.9014}$

$=0.9984$

(c) The probability that the 'bad' (defective} parts get shipped

=1- the probability that the 'good' parts get shipped

=1-0.9984

=0.0016

5 0

2 years ago

shanti wrote the predicted values for a data set using the line of best fit y = 2.55x – 3.15. she computed two of the residual v

Delvig [45]

The question asks us to determine the values for a and b in the linear equation. Linear equation in the slope-intercept form is : y = a x + b. This equation is: y = 2.25 x - 3.15. The slope: a = 2.25 and the y-intercept is: b = -3.15. Answer: a = 2.25 and b = - 3.15.

8 0

2 years ago

Read 2 more answers

What are the differences among an experiment, a study, and a survey? Complete the explanation of the differences by selecting th

artcher [175]

Answer:

The full question is

What are the differences among an experiment, a study, and a survey?

1. In an observational study, randomization of subjects ______

A. occurs

B. does not occur

We understand randomization as a random process of assigning experimental subjects to treatment groups. Through this process, we have more control about variables which are not related to the experiment.

In an observational study, the researcher doesn't change anything, he or she studies the events as they are, without using any randomization process.

Therefore, the right answer here is B. 

2. A survey _______

A. poses no interference on subjects

B. makes inferences about a population

A survey poses no interference on subjects, actually if it does, then that survey is not reliable. An important charactersitic of a survey is that it must be objective, that way it will be reliable enough to use it in the research.

Therefore, the right answer is A.

3. In an experiment, ___________ to discern differences in a response variable.

A. treatment is imposed

B. inferences are made

C. randomization does not occur

Experiments are characterized by having certain "stimulus" at least in one group of subjects, that way researches compare data sets to prove their hypothesis.

Therefore, the right answer here is A.

8 0

2 years ago