7. Two similar containers are such that the capacity of the larger container is 5 litres...
(a) Figure 2 shows a cuboid and a cone (not drawn to scale). Edge AB has length 26 cm, and the diagonal AC has length 42 cm. The radius r of the cone is 12 cm, the height h is 16 cm and the slant height l is 20 cm. D 26 cm B 1= 20 cm h=16 cm 42 cm r= 12 cm Figure 2 Give your answers to each of the following to two significant figures. (1) Find...
Figure 2 shows a cuboid and a prism (not drawn to scale). Edges CD and BF have length 12 cm, and the diagonal BD has length 32 cm. The area A of the top of the prism is 96 cm2 and the perimeter p is 48 cm. area A is 96 cm2 perimeter p is 48 cm 12 cm 32 cm 12 cm Figure 2 Give your answers to each of the following to two significant figures. (i) Use Pythagoras'...
2, Sarah uses 5ķups of flour for every 2 loaves of bread she bakes. What is the unit rate of cups of flour per loaf of bread? Using this unit rate, how many cups of flour will Sarah need to make 5 loaves of 3. Rosie bought some tickets to a concert and found out that she could not go. She decided to sell them on line. Rosie wanted to markup the price 7% to make some money. If she...
Show work please Optimization problems 1. (5 points) Find two nonnegative numbers whose sum is 25 and so that the product of one number and the square of the other number is a maximum. 2. (5 points) Build a rectangular pen with two parallel partitions using 300 feet of fencing. What dimensions will maximize the total area of the pen? (5 points) An open rectangular box with square base is to be made from 48 ft.2 of material. What dimensions...
Consider water being drained from a cylindrical container of diameter D through a hole in the cap, of diameter d, as shown below. Let A be a point on the surface of the water and let B be a point right at the hole. The level of water is h above the hole. If the height of the water level is h = 24 cm, what is the value of vB2−vA2, in SI units? If the diameters are d =...
Let X be normally distributed with mean 100 cm and standard deviation 5 cm. (a) On the diagram below, shade the region representing P(X > 105). (2) (b) Given that P(X < d) = P(X > 105), find the value of d. (2) (c) Given that P(X > 105) = 0.16 (correct to two significant figures), find P(d < X < 105). (2) (Total 6 marks) 2. A test has five questions. To pass the test, at least three of...
please help with all questions not partly Question 10 Which of the folowing statements is/are true A. A sphere bas radius 3s units. A right circular cylinder has height 4 times its radius, which is a units Te tio of the volue of the eylinder to the splere is 1:9 B. Consider a circle with dismeter dunits and a sare with diagonal d units. Ifa y crauls romd the circle ance and an ant crawls romd the square once, the...
3. [25 marks] Some female psychology students were investigating whether intelligence depends on brain size. They each took a standard test that measured verbal IQ and also underwent an MRI scan to measure their brain size. The resulting data is below, file named IQBrain.csv. IQ BrainV 132 816.932 132 951.545 90 928.799 136 991.305 90 854.258 129 833.868 120 856.472 100 878.897 71 865.363 132 852.244 112 808.02 129 790.619 86 831.772 90 798.612 83 793.549 126 866.662 126 857.782...
2. A 4-lane expressway (onee direction) is carrying a total volume of 4500 veh/h when an incident occurs resulting in the closure of two lanes. If it takes 1.5 h to clear the obstruction, determine the following: Assuming that the capacity of the highway is 2200 veh/h/In i. The maximum queue length that will be formed ii. The total delay ii. The number of vehicles that will be affected by the incident iv. The average individual delay. 7:38 PM Task-1...
4. Suppose that a student performed the experiment and calculations perfectly as directed except that, unknown to the student, the balance was not zeroed but weighed 0.100 g too high throughout the experiment. Would the calculated val- ue for the density of the unknown liquid be correct? That is, would it be equal to, higher than, or lower than the true value. Explain your answer in clear and correct English. 16 LABORATORY EXPERIMENTS IN GENERAL CHEMISTRY ed in question 4...