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Determine whether the lines L1 and L2 are parallel, skew, or intersecting. L1:x=9+6t,y=12-3t,z=3+9t L2:x=4+16s, y=12-8s, z=16+20s parallel skew intersecting If they intersect, find the point of intersection. (If an answer does not exist, enter DNE.)

Answers

Answer 1

Answer:

Answer:

L1 and L2 are skew

Step-by-step explanation:

Since the equation of the line is

L1:x=9+6t,y=12-3t,z=3+9t

L2:x=4+16s, y=12-8s, z=16+20s

then if they intersect each other , they will have both in that point P=(xp , yp ,zp) then

1)9+6t = 4+16s

2) 12-3t =2-8s

3) 3+9t = 16+20s

adding 2*2) to 1)

9+6*t + 24-6t = 4+16*s + 4-16*s

33 = 8

since this is not possible , the error comes from our assumption that the lines intersect each other

then they are skew or parallel. They are parallel if their corresponding vectors are parallel , that is

L1 (x,y,z) = (9,12,3) + (6,-3,9)*t

L1 (x,y,z) = (4,2,16) + (16,-8,20)*t

then if they are parallel

(16,-8,20)= k*(6,-3,9)

16=6*k

-8 = -3*k

20= 9*k

since there is no k that satisfy for x , y and z simultaneously then L1 and L2 are not parallel

therefore L1 and L2 are skew

Answer 2

Answer:

Final answer:

The lines L1 and L2 are neither parallel nor intersecting. Upon comparing their direction vectors and attempting to find a common solution, it is determined that they are skew.

Explanation:

In order to determine whether two lines in three dimensions are parallel, skew, or intersecting, we compare their direction vectors. The given lines L1 and L2 are in the form of parametric equations. The direction vectors for the lines are d1 = <6, -3, 9> for L1 and d2 = <16, -8, 20> for L2. To determine if they are parallel, we check if there is a constant ratio between the corresponding terms. This isn't the case here, so the lines are not parallel.

For skew lines, they neither intersect or are parallel. Since we have already confirmed the lines are not parallel, to confirm if they are skew we must try to find a common solution (point of intersection). If we cannot, then they are skew. However, solving the equations does not give a common solution, so they do not intersect either. Hence, the lines are skew.

Learn more about Analysis of Lines in 3D here:

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A large tank is filled to capacity with 600 gallons of pure water. Brine containing 5 pounds of salt per gallon is pumped into the tank at a rate of 6 gal/min. The well-mixed solution is pumped out at a rate of 12 gallons/min. Find the number A(t) of pounds of salt in the tank at time t. A(t)

Answers

Salt flows into the tank at a rate of

(5 lb/gal) * (6 gal/min) = 30 lb/min

The volume of solution in the tank after t min is

600 gal + (6 gal/min - 12 gal/min)*(t min) = 600 - 6t gal

which means salt flows out at a rate of

(A(t)/(600 - 6t) lb/gal) * (12 gal/min) = 2 A(t)/(100 - t) lb/min

Then the net rate of change of the salt content is modeled by the linear differential equation,

$A'(t)=30-(2A(t))/(100-t)$

Solve for A:

$A'+(2A)/(100-t)=30$

Multiply both sides by the integrating factor, $\frac1{(100-t)^2}$ :

$(A')/((100-t)^2)+(2A)/((100-t)^3)=(30)/((100-t)^2)$

$\left(\frac A{(100-t)^2}\right)'=(30)/((100-t)^2)$

Integrate both sides:

$\frac A{(100-t)^2}=(30)/(100-t)+C$

$\implies A(t)=30(100-t)+C(100-t)^2$

The tank starts with no salt, so A(0) = 0 lb. This means

$0=30(100)+C(100)^2\implies C=-\frac3{10}$

and the particular solution to the ODE is

$A(t)=30(100-t)-\frac3{10}(100-t)^2=\frac3{10}t(100-t)$

In a study of 788 randomly selected medical malpractice lawsuits, it was found that 494 of them were dropped or dismissed. Use a 0.05 significance level to test the claim that most medical malpractice lawsuits are dropped or dismissed.Which of the following is the hypothesis test to be conducted?
A.
Upper H 0 : p less than 0.5
Upper H 1 : p equals 0.5
B.
Upper H 0 : p greater than 0.5
Upper H 1 : p equals 0.5
C.
Upper H 0 : p equals 0.5
Upper H 1 : p not equals 0.5
D.
Upper H 0 : p equals 0.5
Upper H 1 : p less than 0.5
E.
Upper H 0 : p not equals 0.5
Upper H 1 : p equals 0.5
F.
Upper H 0 : p equals 0.5
Upper H 1 : p greater than 0.5
What is the test statistic?
Z =
(Round to two decimal places as needed.)
What is the conclusion about the null hypothesis?
A. Reject the null hypothesis because the P-value is greater than the significance level, alpha.
B. Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, alpha.
C. Fail to reject the null hypothesis because the P-value is greater than the significance level, alpha.
D. Reject the null hypothesis because the P-value is less than or equal to the significance level, alpha.
What is the final conclusion?
A.There is sufficient evidence to support the claim that most medical malpractice lawsuits are dropped or dismissed.
B.There is not sufficient evidence to support the claim that most medical malpractice lawsuits are dropped or dismissed.
C.There is sufficient evidence to warrant rejection of the claim that most medical malpractice lawsuits are dropped or dismissed.
D.There is not sufficient evidence to warrant rejection of the claim that most medical malpractice lawsuits are dropped or dismissed.

Answers

Answer:

Step-by-step explanation:

A. Upper H 0 : p equals 0.5

Upper H 1 : p not equals 0.5

B. Using the tests promotion formula, we have (p - P) / √P(1-P)

Where p (sample promotion) = 494/788 = 0.6269, P (population proportion) = 0.5,

(0.6269 - 0.5) / (√0.5(1-0.5))

0.1269/ √(0.5 (0.5))

0.1269/ √0.25

0.1269/0.5

Test statistics is equal to 0.2538

C. We will use the p value to determine our result, thus the p value at 0.05 level of significance is 0.79965, thus we fail to reject the null hypothesis because the P-value is greater than the significance level, alpha.

Then we conclude that There is not sufficient evidence to support the claim that most medical malpractice lawsuits are dropped or dismissed.

In a systematic review with a meta-analysis, researchers combine the results of each of the individual studies to create a larger sample size (and therefore greater power), then re-run the statistics to capture the true magnitude of the effect. The single-effect measure calculated and reported when the results from all the studies are combined is called what?

Answers

Answer:

Power analysis

Step-by-step explanation:

Power analysis is a significant part of test structure. It permits us to decide the example size required to recognize an impact of a given size with a given level of certainty. On the other hand, it permits us to decide the likelihood of recognizing an impact of a given size with a given degree of certainty, under example size requirements. On the off chance that the likelihood is unsuitably low, we would be shrewd to adjust or forsake the analysis.

The principle reason underlying power analysis is to assist the analyst with determining the littlest example size that is appropriate to recognize the impact of a given test at the ideal degree of hugeness.

If I buy cart 1 containing 350 pairs of shoes, I buy cart 2 containing 1000 pairs of shoes, what is the ratio of cart 1 to 2.

Answers

Answer:

7:20

Step-by-step explanation:

350:1000

35:100

5:20

Ans 5:20

Answer:

7:20

Step-By-Step Explanation:

Cart 1

350

Cart 2

1000

Ratio

350:1000

and divide both by 5

70:200

and divide both by 10

7:20

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Answers

Answer:

-3.9

Step-by-step explanation:

Mrs Perry shares out 21 biscuits betweenGemma and Zak in the ratio 1 : 6
How many biscuits does each child get?
biscuits.
Gemma gets
biscuits and Zak gets