Step 1) Identify the legs and the hypotenuse of the right triangle. | The legs have length '14' and 48 are the legs. The hypotenuse is X. See Picture | The hypotenuse is red in the diagram below: Steps 2 and 3 | Step 2) Substitute values into the formula (remember 'c' is the hypotenuse) | A2 + B2 = C2 142 + 482 = x2 | Step 3) Solve for the unknown | | Problem 2) Use the Pythagorean theorem to calculate the value of X. Round your answer to the nearest tenth.
When you add the values 3, 5, 8, 12, and 20 and then divide by the number of values, the result is 9.6. Which term best describes this value: average, mean, median, mode, or standard deviation? Answer: 9.6 is the average of the numbers listed and is also the mean of this data. 4. Answer the next four questions using the following set of numbers.
The random sample of 65 satisfaction rating yields a sample mean of x = 42.954. Assuming that S = 2.64, use critical values to test H0 versus Ha at each of a = 10, .05, .01 and .00l. MU = 42, N = 65, X-bar = 42.954, sigma = 2.64 Z= (x-bar – mu)/(sigma/sqrt n) Z = (42.954 – 42)/(2.64/sqrt65 = 2.9134. Wk4/Assignment 9.13 continued Critical upper tail = Z – scores for 1.2816, 1.6449, 2.3263 and 3.092 for a = 0.10, 0.05, 0.01 and 0.001. Since 2.9134>1.2816, 1.6449 and 2.3263, I rejected H0 and accepted Ha at 1 = 0.10, 0.05, and 0.01 and concluded that the mean rating exceeds 42.
Solve the triangle. Given: A = 48° C = 97° a = 12 B = 35° b = 9.2 c = 16.0 5. The given measurements produce one triangle. Given: a = 7, b = 5, A = 70° C = 67.8, B = 42.1, c = 6.8 6. x×tan62 = (x+300)×tan53 = perpendicular x = 300×tan53/(tan62-tan53) = 719.0295 yards AB = (x+300/cos53 = 1019.0295/cos53 = 1693.3 yards Distance between A and B is 1693.3 yards 7. Given: sides, 5,6,7 in miles Island A = 78.46° Island B = 135.58° Island C = 57.12° Given the information… From Island B I would travel a Northwest Bearing to Island C. 8.
Problems Answer Grade Problem-1 a x+y=56 /3 b x+y=56 x+3x=56 56/4= 14 x=14 56-14=42 y=42 check 14+42=56 or 14+(14*3)=56 /3 c before we use elimination, we simplify the second equation by dividing by 25,000: new equation for b): 7x + 8y = 288 in order to eliminate a variable, multiply the first equation by -7: new equation for a): -7x + -7y = -266 Elimination: add the two equations and the x's cancel out: y = 22 x = 38-22 = 16 /3 d For the first equation, the intercepts are (56, 0) and (0,56). The intercept for the second equation is (0, 0). The lines would intersect at (14, 42) /3 Problem-2 a x+y=38 /3 b $175,000x+$200,000y=$7,200,000 /3 c Before we use elimination, we simplify the second equation
The combination of antacid and base that is added will add up to .004 mol. 1. Since I am adding the antacid first, and then adding the same .05 M NaOH to get to equivalence, whichever antacid neutralizes the most base (ie- is the strongest) will require the least amount of extra base to reach equivalence. That would be the CVS brand, at .0199L (for simplicity, all volumes will be expressed in L, even though the chart is in mL). The weakest would require the most extra base, and that would be the Rennies, at .0244L.
Find the value of C that makes the equation true. (Sea level is 3,963 miles from the center of the Earth.) I plugged in the numbers where they go and then multiplied and the answer is C=1,570,536,900 Use the value of C you found in the previous question to determine how much the object would weigh in Death Valley (282 feet below sea level). First multiply 3963 * 5280 which equals 20,924,640. Next, w=1570536900(20924640 – 282)^-2.
The Collapse of Easter Island “Rapa Nui” Table of Contents 1. The Island; Geography, Environmental Facts, Early Settlers 2. Evolution of the Island 3. The Collapse The islands of the Pacific can be catoragized into two groups: those off Australia, Indonesia, Melanesia, and New Guinea – and those that are located within the Polynesian Triangle. This is an imaginary triangle with sides 4,000 miles long that link Hawaii, Easter Island and New Zealand.
Begin by writing the corresponding linear equations, and then use back-substitution to solve your variables. 10–1301–8001 159–1 x,y,z=( , , ) 10–1301–8001 159–1 = x-13z=15y-8z=9z=-1 = x-13(-1)=15y-8(-1)=9z=-1 = x=2y=1z=-1 x,y,z=(2 , 1 , -1) Determinants and Cramer’s Rule: 2. Find the determinant of the given matrix. 8–2–12 8–2–12 = 8*2 - (-1)(-2) = 16 - 2 = 14 3. Solve the given linear system using Cramer’s rule.
P(1+r/2)(1+r/2) Next step is to multiply the squared quantity. P(1+(r/2)+(r/2)+(r2/4)) Then carry out FOIL. P(1+(2r/2)+(r2/4)) Combine like terms. P+(2Pr/2)+(Pr2/4) Distribute P throughout the trinomial 4P+4Pr+Pr2 Simplified. 4 Now, unlike traditional polynomials, the one used above is not in descending order of the variables.