1. Let u= (0, -2,3), v= (1,4, 1). Evaluate a) the projection proju(v) of v over u And b) the area of the parallelogram whose sides are parallel to u and v.
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A: Given that A(1,1,1) and O(0,0,0) Find a parameterization
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A: The set of all directed line segments that are equivalent to a given directed line segment PQ \ is a…
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A: Consider the following figure.
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A: To find the area of the parallelogram formed by two vectors
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Q: If L is a line through 0 and if ŷ is the orthogonal projection of y onto L, then || ŷ|| gives the…
A: To state whether the given statement is true or false : By definition, we know that, if L is a line…
Q: 16. Let y = and u = B Compute the distance from y to the line through u and the origin.
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Q: 47. Sketch the triangle with vertices at the origin 0, P = (3,3,0), and Q = (0, 3,3), and compute…
A: The triangle OPQ formed by the three points P (3, 3, 0), Q (0, 3, 3) and origin O (0, 0, 0) is shown…
Q: find the projection of v onto u. Draw a sketch
A: We first find the dot product And the square of the magnitude of u is
Q: Let →a=⟨−2,0⟩ and →b=⟨−5,5⟩ Find the projection of →b→ onto →a ( , )???
A: Recall: Projection of b→ onto a→ , proja→b→=a→.b→a→.a→a→
Q: Let j = and i = Compute the distance from j to the line through u and the 9. origin.
A: Given that y→=-39 and u→=12. To find the distance from y→ to the line through u→ and the origin, we…
Q: Find the area of the triangle with vertices P=(1,1,0), Q=(0,2,1) and R=(2,0,0).
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Q: Sketch the triangle with vertices at the origin O, P = (3, 3, 0), and Q = (0, 3, 3), and compute its…
A: The area of the triangle using the cross products is defines as Area=12v×u Here, v is the vector…
Q: Calculate the area of the triangle defined by u = (1, 6, 2), v = (3, 0, 5). [A3]
A: Here we have to calculate the area of the triangle having vectors, u→=(1,6,2) and v→=(3,0,5)
Q: (a) Find the length of the projection of w onto v given that w = (4,7) and v = (1,1).
A: Given: w=4i+7j, v=i+j we know that projectionp→ of w onto v is given by p→=w.→v→v→2v→
Q: Let y = and u = | Compute the distance from y to the line through u and the origin.
A: Compute the distance from y = [-3,9] to the line through u = (1,2) and the origin.
Q: 6- Give ā = [A, B]and b = [F,E], find VProj(b onto d) and SProjd onto b). Resolve a into…
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Q: 1.) Use Green's Theorem to evaluate the triangle with vertices (0,0), (1,2), and (0,2). $4x² ydx +…
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Q: find the projection of u onto v and the projection of v onto u
A: Given vectoru=3,-2 , v=-2,1
Q: Derive the frenet frame, curvature and torison o the binormal indicatrix of hypocycloid?
A: We need to Derive the fernet frame, curvature and torsion o the binormal indicatrix of hypocycloid.
Q: Find the point E that partitions the directed segment CD in a ratio of 1:5, given the points C(4,-2)…
A: Given that the line segment CD is cut by a point (x, y) in the ratio 1:5given that points C(x1, y1)…
Q: 1. If C₁ is the segment from (x₁, y₁) to (x2, y2), find Ja x dy - y dx in terms of the four…
A: Using Green 's theorem line integral to double integral
Q: 2. Suppose that T, U, and V are the points where the incircle of AABC touches the sides BC, AC, and…
A: 2) Formula Used : Ceva's Theorem : For any ∆ABC AT , BU and CV intersect at a point O, if ATVB…
Q: 28. Given: WX ZY and Zs Z and Y are supplementary WXYZ is a parallelogram Prove: ZRYS RVST
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Q: Let R= (1,5). Calculate the length of OR. %3D
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Q: IfL is a line through 0 and if ŷ is the orthogonal projection of y onto L, then || ŷ||l gives the…
A: The given statement is "If L is a line through 0 and if y^ is the orthogonal projection of y onto L,…
Q: If SV = 7w - 25 and UV = 2w + 5, find SV in parallelogram RSTU. R U =AS Submit
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Q: 3) Consider the line L in R? spanned byp = (6). Let PL(u) be the orthogonal %3D projection of the u…
A: b = 4
Q: In(x + y) dA where R is the triangle with vertices (1,0), (1,1), (0, 1).
A: Let - I=∫∫Rln(x+y)dA Where R is triangle with vertices (1,0),(1,1),(0,1) Equation of line joining…
Q: If L is a line through 0 and if f is the orthogonal projection of y onto L, then || F|| gives the…
A: Option B is correct.
Q: Find the coordinates of point P along the directed line segment AB so that AP to PB is the given…
A: Given, The coordinates of point P along the directed line segment AB so that AP to PB is…
Q: Evaluate O ry*da + x°dy, where C is the rectangle with vertices (0,0), (1,0), (1,5), and (0,5)
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Q: O FIND THE -く,2,3> VOLUME oF TIAE PARALLEL EPIPED WITH VECTURS J = <4,10,87 w - <1,0,17 and AS…
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Q: Suppose that u = (0, 1,-2) and v = (1, 0, 1). Compute the projection of u onto v. Enter the…
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Q: IfL is a line through 0 and if ŷ is the orthogonal projection of y onto L, then || §|| gives the…
A: Given statement is
Q: 3. Find the surface area of the parallelepiped with adjacent edges u = (4, 7, -8), v = (-2, 5, 11),…
A: Solution :18
Q: 28. Find the volume of the parallelepiped having edges PQ, PR, and PS if the points P, Q. R, and S…
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Q: Which of the letters B, O, K, I, V, F, X, D, L, and Y are their own images under a rotation by an…
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Q: Find the angle planes 3xx + z=land radans between the Sy +z=. in
A: We use dot product between Normal vectors of given planes to find angle between these two planes
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A: It is given that the length of two sides of a triangle is a and b, respectively. It is known that…
Q: What point divides the directed line segment AB into a 2:3 4. ratio? 3- -2- 456 89 10 11 12 13 14 15…
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Q: Compute : fr (Re z – 3z) dz where r is a directed line segment from z = 0 to z = i .
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Q: show that if ||u||=||v||, and u and v are not parallel, then u+v and u-v are perpendicular.
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Q: Let ā = (4, – 1) and b = (– 2,0). Find the projection of 5 onto ā. proj, 5 %3D
A: Let a→=4,-1 and b→=-2,0 To find projection of b→ on a→
Q: Show that the points E(2, 2, 2), F(2, 0, 1), G(4, 1, -1) and H(4, 3, 0) are coplanar and that they…
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Q: find the projection of v onto u. Draw a sketch
A: Evaluate u·v,u·u and obtain the projection as shown below:…
Q: 7. What additional piece is needed to prove JMLK is a rhombus ?
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Q: Let a = (- 3, – 5) and b {1, 2). Find the projection of b onto a. proj; b = >
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Q: Show that a triangle with vertices (x,Y;), (x2,y2), and (x;,y;) has area + x,y3 + X3Y, – X,Y3 – X,Y,…
A:
Q: Find the COM of the laminas in Figure 26 obtained by removing squares of side 2 from a square of…
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- A congressional committee is composed of 10 members: 6 Republicans and 4 Democrats. On any given vote, members vote independently. Whereas Republicans always vote their party line, Democrats vote their party line with probability .8, and vote Republican with probability .2. On a rainy day only 3 committee members (selected w/o replacement) were present. Let X = number of Democrats present Y = Number who voted Democratic that day Find the marginal pdf of X, i.e., P[X=k] for k=0, 1, 2, 3. Display E[X] and VAR[X]. Determine the conditional probability that P[ Y=j | X=k] for k=3 and j=0,1,2,3 Display the table of joint probabilities fX,Y(i,j) for 0 ≤ j ≤ i, i=0,1,2,3 Display the marginal pdf of Y. Is it recognizable? Compute E[Y]and VAR[Y]. Determine the conditional expectation of Y given that X=x, for x=0,1,2,3.…A school Psychologist is interested in the effect of violent television programs on a child's agression depending on if the show is a cartoon or not. Eighty children were recruited and were divided into equal groups. Half of the children watched a violent television program while the other half watched a non- violent program. Half of the children watched a cartoon while the other half watched a show that was not a cartoon. The children were then placed in a small group and the researcher measured the level of agressiveness of each child. A) z- test B) t - test C) test independent samples D) T - TEST RELATED SAMPLES E) ANOVA F) FACTORIAL ANOVA G) repeated measures ANOVA H) pearson correlation i) chi squareThe 2019-2020 flu season was especially tough. By the end of the season, an estimated total of 49 million people in the United States had contracted the flu, of whom an estimated 79,000 died from the flu. Assume that the US population was 300,000,000 during the 2019-2020 flu season and that during the season, a total of 2.9 million Americans died from all causes (including the flu). Assume the population of the US remained the same at the midpoint of the season. Report mortality rates per 100,000. Be sure to express the measure in the correct format. a.What was the proportionate mortality rate from flu during the 2019-2020 flu season? b.What was the case fatality rate from flue during the 2019-2020 flu season?
- The 2019-2020 flu season was especially tough.By the end of the season, an estimated total of 49 million people in the United States had contracted the flu, of whom an estimated 79,000 died from the flu. Assume that the US population was 300,000,000 during the 2019-2020 flu season and that during the season, a total of 2.9 million Americans died from all causes (including the flu). Assume the population of the US remained the same at the midpoint of the season. Report mortality rates per 100,000. Be sure to express the measure in the correct format. c.What was the flu-related mortality rate during the 2019-2020 flu season? d.What is the all-cause mortality rate during the 2019-2020 flu season? e.In a country with an age distribution that is much younger than in the US, the proportionate mortality rate from flu in 2019 was 5%. Based on this information alone, can we determine that the risk of dying from flu in 2019 was higher in this country compared to the US? Why or why not?The germination rate of seeds is defined as the proportion of seeds that, when properly planted and watered, sprout and grow. A certain variety of grass seed usually has a germination rate of 0.80, and a company wants to see if spraying the seeds with a chemical that is known to change germination rates in other species will change the germination rate of this grass species. (a) Suppose the company plans to spray a random sample of 400 seeds and conduct a two-sided test of 0: 0.8Hpusing = 0.05. They determine that the power of this test against the alternative 0.75pis 0.69. Interpret the power of this test.(b) Describe two ways the company can increase the power of the test. What is a disadvantage of each of these ways? (c) The company researchers spray 400 seeds with the chemical and 307 of the seeds germinate. This produces a 95% confidence interval for the proportion of seeds that germinate of (0.726, 0.809). Use this confidence interval to determine whether the test described in…Suppose that the lifetime, X, and brightness, Y, of a light bulb are modeled as continuous random variables. Let their joint pdf be given by:f(x,y)=λ_1λ_2e^{-λ_1x-λ_2y},x,y>0 •Are lifetime and brightness independent?•Are lifetime and brightness uncorrelated?
- An ecologist is considering two different positions in which to setup his solar energy collector. He takes two identical collector places one in each of the positions and measure the energy in at collected as 10 consecutive days. Days 1 2 3 4 5 6 7 8 9 10 Position X 2.6 5.4 3.2 5.0 4.3 2.7 2.6 3.9 6.0 1.6 POSITION y 2.8 5.1 3.1 6.0 4.6 3.2 2.9 4.5 6.2 2.2 Test whether the difference of mean is significance ? what will be the answerWhen looking at the data for graduate school admissions between men and women, it is shown that about 45% of men are admitted but only 38% of women. However, when the data is broken down by school it turns out that, within each school, the women are admitted at higher rates than the men. This could happen because I. The women apply in higher numbers to schools with lower acceptance rates. II. The women apply in higher numbers to schools with higher acceptance rates III. The men apply in higher numbers to schools with lower acceptance rates IV. The men apply in higher numbers to schools with higher acceptance ratesA researcher wants to find the effect of a special diet on systolic blood pressure. A sample of 7 adults was selected to start them on this diet for 3 months. Based on this information, can it be stated that systolic blood pressure changes with the special diet? Based on the findings of the test carried out, it is possible to conclude that...... A. systolic blood pressure does not change with special diet B. systolic blood pressure changes with special diet C. systolic blood pressure is lower with the special diet D. systolic blood pressure is higher with the special diet E. It is not possible to conclude anything regarding systolic blood pressure with the special diet
- The variable with the largest positive Pj – Zj value is the a. artificial variable b. entering variable c. slack variable d leaving variableAUA wants to know whether recent alumni students from MBA class earn significantly more than recent alumni from BAB class. They take a sample of several students and ask the amount of their monthly salaries in USD (Sheet 32). What can AUA conclude at alpha=0.05? Sheet 32 MBA BAB 515 300 450 420 620 380 630 450 570 420 590 490 750 510 560 470 480 530 250 570 320 480 450 620 625 190 350 280 450 350 570 250 Select one: a. t(stat)=1.92, which is greater than t(cr)=1.7, therefore, we can conclude that MBA graduates earn more BAB graduates. b. t(stat)=1.89, which is greater than t(cr)=1.75, therefore, we can conclude that MBA graduates earn more BAB graduates. c. t(stat)=2.07, which is greater than t(cr)=1.69, therefore, we cannot conclude that MBA graduates earn more BAB graduates. d. t(stat)=2.07, which is greater than t(cr)=1.69, therefore, we can conclude that MBA graduates earn more BAB graduates.Suppose you are interested in the percentage of students who had burrito for lunch in your statistics class. There are a total of 120 students in your class. Instead of asking each student whether they had burrito for lunch, you randomly picked 36 students from the class and found that 11 students had burrito for lunch. What is the parameter of interest?