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2 years ago

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Determine which of (a)-(d) form a solution to the given system for any choice of the free parameter. (HINT: All parameters of a

solution must cancel completely when substituted into each equation.) 3x1 + 8x2 − 14x3 = 9 x1 + 3x2 − 4x3 = 1

2 answers:

Alecsey [184]2 years ago

8 0

Answer:

Please see attachment

Ksju [112]2 years ago

8 0

Question:

The options are;

(a) (9 - 2s1, 3 + 3s1, s1)

solution

not a solution

(b) (-4 - 5s1, s1, -(3 + s1)/2)

solution

not a solution

(c) (11 + 10s1, -3 - 2s1, s1)

solution

not a solution

(d) ((6 - 4s1)/3, s1, -(7 - s1)/4)

solution

not a solution

Answer:

The options that form a solution of the given system are;

(b) and (c)

Step-by-step explanation:

Here we have

3·x₁ + 8·x₂ − 14·x₃ = 9

x₁ + 3·x₂ − 4·x₃ = 1

(a) (9 - 2·s₁, 3 + 3·s₁,s₁)

3·(9 - 2·s₁) + 8·(3 + 3·s₁) − 14·s₁ = 4s₁+51

Not a solution

(b) (-4 - 5s₁, s₁, -(3 + s1)/2)

3·(-4 - 5s₁) + 8·(s₁) − 14·-(3 + s1)/2 = 9

(-4 - 5s₁) + 3·(s₁) − 4·-(3 + s1)/2 = 2

Solution

(c) (11 + 10s₁, -3 - 2s₁, s₁ )

3·(11 + 10s₁) + 8·(-3 - 2s₁) − 14·s₁ = 9

(11 + 10s₁) + 3·(-3 - 2s₁) − 4·s₁ = 2

Solution

(d) ((6 - 4s1)/3, s1, -(7 - s1)/4)

3·(6 - 4s1)/3+ 8·s1− 14·-(7 - s1)/4 = 0.5s₁ +30.5

Not a solution

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According to a "how to stop bullying" Web site, 15% of students report experiencing bullying one to three times within the most

AlekseyPX

Answer:

His 95% confidence interval is (0.065, 0.155).

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

For this problem, we have that:

$n = 186, \pi = 0.11$

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 $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.11 - 1.96\sqrt{\frac{0.11*0.89}{186}} = 0.065$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.11 + 1.96\sqrt{\frac{0.11*0.89}{186}} = 0.155$

His 95% confidence interval is (0.065, 0.155).

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1 year ago

The finances of a group of pet owners were analyzed to determine how much they were spending on their pet(s) each year. A graph

kvv77 [185]

Answer:

Option D.

Step-by-step explanation:

In the given graph x-axis represents the number of owners and y-axis represents yearly cost of pets, in hundreds.

It is given that the graph passes through the points (1,15), (3,7) and (10,0).

We need to check whether (4.5, 6) is a realistic solution for the function or not. (4.5,6) point represents

Number of owners = 4.5

yearly cost of pets = 6

It is realistic that owners spend $600 a year on their pet(s).

Number of owners can not be a fraction value. So, it is not realistic to have 4.5 owners.

Therefore, the correct option is D.

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2 years ago

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Researchers from Dartmouth Medical School conducted a study in 2003 to look at the connection between watching actors smoking in

docker41 [41]

Answer:

The 95% confidence interval for the proportion of adolescents who tried smoking for the first time because of exposure to smoking in the movies is (0.37, 0.40).

Step-by-step explanation:

A confidence interval is an interval estimate of the population parameter. The confidence interval has a certain probability of consisting the true value of the parameter.

The (1 - <em>α</em>) % confidence interval for the population proportion (<em>p</em>) is given by:

$CI=\hat p\pm z_{\alpha/2}\times \sqrt{\frac{\hat p(1-\hat p)}{n}}$

The information provided is:

$n = 6522\\\hat p=0.38\\z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use a <em>z</em>-table for the critical value.

Construct the 95% confidence interval for the proportion of adolescents who tried smoking for the first time because of exposure to smoking in the movies as follows:

$CI=\hat p\pm z_{\alpha/2}\times \sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.38\pm 1.96\times \sqrt{\frac{0.38(1-0.38)}{6522}}\\=0.38\pm 0.0118\\=(0.3682, 0.3918)\\\approx (0.37, 0.40)$

Thus, the 95% confidence interval for the proportion of adolescents who tried smoking for the first time because of exposure to smoking in the movies is (0.37, 0.40).

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2 years ago

Explain how you can find 3x584 using expanded form

nasty-shy [4]

<em>I believe what you need to do is multiply 3 by each number.
To start, 3*584 is 1752. Expanded form written out would be (3*500)+(3*80)+(3*4). Simply multiply all the numbers and then add them together. 3*500=1,500; 3*80=240; 3*4=12. 1,500+240=1740+12=1752. Hope this helps! :)</em>

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2 years ago

Which statements are true regarding triangle LMN? Check all that apply.

dimaraw [331]

Answer:

$NM = x$

$LM = x\sqrt{2}$

$tan (45) = 1$

Step-by-step explanation:

Step 1: Pythagoras Theorem

Pythagoras theorem relates the three sides of the triangle in such a way that the sum of the square of base and perpendicular is equal to hypotenuse, such as:

$LM^{2} =LN^{2} +NM^{2}$

Step 2: Trigonometric Functions

Only for a right angle triangle following three trigonometric relations are valid

$sin (\theta) = \frac{opposite}{hypotenuse}$

$cos (\theta) = \frac{adjacent}{hypotenuse}$

$tan (\theta)=\frac{sin (\theta)}{cos (\theta)} = \frac{opposite}{adjacent}$

Step 3: Verifying all the possible answers

A: Since, LN = x and using $tan (45) =1$

we can calculate

$tan (\theta)= \frac{opposite}{adjacent}$

$tan (45)= \frac{NM}{x} =1$

therefore, NM = x (true)

B: As NM = x therefore it can not be equal to $x\sqrt{2\\}$ .

C: Using Pythagoras Theorem

$LM^{2} =LN^{2} +NM^{2}$

$LM^{2} =x^{2} +x^{2}$

$LM^{2} =2x^{2}$

$LM = \sqrt{2x^{2}} = x\sqrt{2}$

It can also be proved using trigonometric relation

$cos (45) = \frac{x}{LM}$

$LM = \frac{x}{cos (45)}$

As, $\frac{1}{cos (45)}= \sqrt{2}$

Therefore

$LM = x\sqrt{2}$

D and E:

Using same approach similar to part A

Since, LN = x and NM = x

we can calculate

$tan (\theta)= \frac{opposite}{adjacent}$

$tan (45)= \frac{x}{x} =1$

Therefore, $tan (45) = 1$ and not equal to $\frac{\sqrt{2} }{2}$

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2 years ago

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