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3 years ago

Is the system of equations consistent and independent, consistent and dependent, or inconsistent?

Mathematics

1 answer:

Bess [88]3 years ago

4 0

Answer: It is consistent as the lines are intersecting lines and it has a unique solution

Step-by-step explanation:

Since we have given two systems of equation :

We need to check whether the system of equations is consistent or inconsistent.

As we know the formula for checking the consistency :

In the first equation, we have

similarly,

In the second equation, we have

So, According to the question, we have

Therfore , it is consistent as the lines are intersecting lines and it has a unique solution.

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A candidate for a US Representative seat from Indiana hires a polling firm to gauge her percentage of support among voters in he

UkoKoshka [18]

Answer:

a) The minimum sample size is 601.

b) The minimum sample size is 2401.

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 $1 - \frac{\alpha}{2}$ .

The margin of error is:

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

For this problem, we have that:

We dont know the true proportion, so we use $\pi = 0.5$ , which is when we are are going to need the largest sample size.

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

a. If a 95% confidence interval with a margin of error of no more than 0.04 is desired, give a close estimate of the minimum sample size that will guarantee that the desired margin of error is achieved. (Remember to round up any result, if necessary.)

This is n for which M = 0.04. So

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

$0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.04\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.04}$

$(\sqrt{n})^2 = (\frac{1.96*0.5}{0.04})^2$

$n = 600.25$

Rounding up

The minimum sample size is 601.

b. If a 95% confidence interval with a margin of error of no more than 0.02 is desired, give a close estimate of the minimum sample size necessary to achieve the desired margin of error.

Now we want n for which M = 0.02. So

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

$0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.02\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.02}$

$(\sqrt{n})^2 = (\frac{1.96*0.5}{0.02})^2$

$n = 2401$

The minimum sample size is 2401.

4 0

3 years ago

parker correctly answered 70% of the questions on his math test. If he answered 35 questions correctly, how many questions were

Alexandra [31]

Let the total number of questions in the math test be defined by the variable x.

Now, we know that Parker correctly answered 35 questions. These 35 questions make 70% of the total number of questions on his math test.

The information we have above can be expressed as an equation given below:

70% of x=35

This can be rewritten as:

$\frac{70}{100}x=35$

Thus, to find the total number of questions we will have to isolate x.

$\therefore x=\frac{35\times 100}{70}=50$

Therefore, there were a total of 50 questions in the math test.

4 0

3 years ago

Read 2 more answers

Write the equation of the line that

zlopas [31]

Answer:

y=-1/2x+2

Step-by-step explanation:

First, the slope of perpendicular line have negative reciprocal coefficients. In this case the coefficient is 2, The reciprocal of 2 is 1/2 and the negative of 1/2 is -1/2. So x will have a coefficient of -1/2.

Second, find the equation with a slope of -1/2 that passes through (-2,3). There are a few ways to do this. I like to plug the given x value into the expression -1/2x, so -1/2(-2) which equals positive 1 and for the line to pass through the point (-2,3) you need to add 2. So: y=-1/2x+2

8 0

2 years ago

Someone please help me

Mars2501 [29]

Answer:

x=-1,-2

Step-by-step explanation:

Multiply the given equation with (x+1) on both sides. We'll get,

x+2/x=-3

or,x^2+2=-3x

or,x^2+3x+2=0

or,x^2+2x+x+2=0

or,x(x+2)+1(x+2)=0

or,(x+2)(x+1)=0

or,x=-2,-1

4 0

3 years ago

Cody and Brad bought pizza for the class party. Cody bought 12 pizzas for $15 each.

tankabanditka [31]

Answer:

brad paid more

Step-by-step explanation:

15/12=1.25

and 12/8=1.50

so brad paid more on pizza

3 0

2 years ago

Read 2 more answers