A school fair ticket costs $8 per adult and $1 per child. On a certain day, the total number of adults (a) and children (c) who went to the fair was 30, and the total money collected was $100. Which of the following options represents the number of children and the number of adults who attended the fair that day, and the pair of equations that can be solved to find the numbers? (4 points) 20 children and 10 adults Equation 1: a + c = 30 Equation 2: 8a + c = 100 10 children and 20 adults Equation 1: a + c = 30 Equation 2: 8a − c = 100 10 children and 20 adults Equation 1: a + c = 30 Equation 2: 8a + c = 100 20 children and 10 adults Equation 1: a + c = 30 Equation 2: 8a − c = 100

which of the following sets of data would produce the largest value for an independent-measures t statistic? the two sample means are 10 and 20 with variances of 20 and 25 the two sample means are 10 and 20 with variances of 120 and 125 the two sample means are 10 and 12 with sample variances of 20 and 25 the two sample means are 10 and 12 with variances of 120 and 125

Whit h equation best represents this situation the number 98 increased by an unknown number equal to 120

For every corresponding pair of cross sections, the area of the cross section of a sphere with radius r is equal to the area of the cross section of a cylinder with radius and height 2r minus the volume of two cones, each with a radius and height of r. a cross section of the sphere is and a cross section of the cylinder minus the cones, taken parallel to the base of cylinder, is the volume of the cylinder with radius r and height 2r is and the volume of each cone with radius r and height r is 1/3 pie r^3. so the volume of the cylinder minus the two cones is therefore, the volume of the cylinder is 4/3pie r^3 by cavalieri's principle. (fill in options are: r/2- r- 2r- an annulus- a circle -1/3pier^3- 2/3pier^3- 4/3pier^3- 5/3pier^3- 2pier^3- 4pier^3)