answer:To solve this problem, we will calculate the points scored by each player step by step and then sum them up to find the total points scored by Jon, Jack, and Tom together. 1. **Calculating Jack's Points:** - Jon scored 3 points. - Jack scored 5 points more than Jon. - Therefore, Jack's points can be calculated as: [ text{Jack's Points} = text{Jon's Points} + 5 = 3 + 5 = 8 ] 2. **Calculating the Points of Jon and Jack Together:** - We already know Jon scored 3 points and Jack scored 8 points. - The total points scored by Jon and Jack together is: [ text{Jon and Jack Together} = text{Jon's Points} + text{Jack's Points} = 3 + 8 = 11 ] 3. **Calculating Tom's Points:** - Tom scored 4 points less than the total points of Jon and Jack together. - Therefore, Tom's points can be calculated as: [ text{Tom's Points} = text{Jon and Jack Together} - 4 = 11 - 4 = 7 ] 4. **Calculating the Total Points Scored by Jon, Jack, and Tom:** - To find the total points, we add up the points scored by each of them: [ text{Total Points} = text{Jon's Points} + text{Jack's Points} + text{Tom's Points} = 3 + 8 + 7 ] - Simplifying the above, we get: [ text{Total Points} = 3 + 8 + 7 = 18 ] Therefore, the total points scored by Jon, Jack, and Tom together is boxed{18}.

answer:1. **Identify Information:** - Kolya lives on the 5th floor in apartment number 83. - Vasya lives on the 3rd floor in apartment number 169. - Each floor has 4 apartments. 2. **Determine the Number of Apartments Below Kolya's Floor:** - Since Kolya lives on the 5th floor, the floors below him are: the 1st, 2nd, 3rd, and 4th floors. - Each of these floors has 4 apartments. So, the number of apartments on the floors below the 5th: [ text{Total apartments} = 4 (text{floors}) times 4 (text{apartments per floor}) = 16 text{ apartments} ] 3. **Locate the Apartment Number of Kolya on His Floor:** - Kolya is in apartment number 83. - Apartments are presumably numbered sequentially starting from 1. - The first 16 apartments are on the floors below the 5th floor, so the numbering on the 5th floor starts from 17: [ text{First apartment on 5th floor} = 16 + 1 = 17 ] Therefore, number of apartments on 5th floor till 83 is [ n_a = 83 - 16 = 67 ] Number of apartments on 4 floors [ 4*4 = 16 ] 4. **Define the Floor of Vasya:** - Vasya lives on the 3rd floor in apartment number 169. - We already know each floor has 4 apartments: So we calculate, Number of apartments on 5th floor [ 5 x 4 = 20 ] ] Number of apartment of Vasya ] n_b = 169 - 37 = 135 ] So, solution calculate the apartment on particular ` To sum up, the number is the operation in between (boxed{4})

answer:Given the point's rectangular coordinates ((3, -4, 2)), we have: [ 3 = rho sin phi cos theta, -4 = rho sin phi sin theta, 2 = rho cos phi. ] For the new spherical coordinates ((rho, theta + pi, phi)): [ x = rho sin phi cos(theta + pi) = -rho sin phi cos theta = -3, y = rho sin phi sin(theta + pi) = -rho sin phi sin theta = 4, z = rho cos phi = 2. ] Thus, the rectangular coordinates of the point with spherical coordinates ((rho, theta + pi, phi)) are (boxed{(-3, 4, 2)}).

answer:Step 1: The nine points divide the circumference of the circle into nine equal small arcs, each with measure frac{360^circ}{9} = 40^circ. Step 2: Each tip of the star cuts off a minor arc which consists of four small arcs (as adjusted in the draft). Thus, [ widehat{Arc} = 4 times 40^circ = 160^circ. ] Step 3: The angle at each tip of the star is half of the arc it intercepts (because it is an inscribed angle), which gives [ text{Angle at tip} = frac{1}{2} times 160^circ = 80^circ. ] Step 4: Sum up the angles at all nine tips: [ text{Total sum} = 9 times 80^circ = 720^circ. ] Conclusion: The sum of the angle measurements at the nine tips of the star is boxed{720^circ}.