Answer:
See explanation
Step-by-step explanation:
1. 400 students in total.
Category 1: Students which rode the bus (180)
Category 2: Students that were freshmen (115)
Let x be the number of students in both categories. Then
- 180 - x students rode the bus and were not freshmen
- 115 - x students were freshmen and didn't ride the bus
So, 115 - x = 25
x = 90
Thus,
- 90 students rode the bus and were freshmen
- 90 students rode the bus and were not freshmen
- 25 students were freshmen that did not ride the bus
- 400 - 90 - 90 - 25 = 195 students didn't rode the bus and were not freshmen
2. 350 students in total.
Category 1: Students bought pizza (168)
Category 2: Students that were sophomores (123)
Let x be the number of students in both categories. Then
- 168 - x students that bought pizza and were not sophomores
- 123 - x students were sophomores and didn't buy pizza
So, 123 - x = 32
x = 91
Thus,
- 91 students bought pizza and were sophomores
- 77 students bought pizza and were not sophomores
- 32 students were sophomores that did not buy pizza
- 350 - 91 - 77 - 32 = 150 students didn't buy pizza and were not sophomores
Given that triangle ABC has been dilated to form triangle A'B'C' and the vertices of ABC are A(5,3), B(3,7), C(1,4) and vertices of A'B'C' isA'(7.5, 4.5), B'(4.5, 10.5), C'(1.5,6)
then the scale factor for dilation will be as follows:
Taking corresponding vertices SAY A (5,3) and A'(7.5, 4.5)
the scale factor will be:
7.5/5=4.5/3=1.5
Answer: 1.5
3/6 because the smaller the denominator the bigger the fraction.
(88sin20)(t - 16t²) = 0
(8(0.3090169944)(t - 16t²) = 0
(2.472135955)(t - 16t²) = 0
2.472135955t - 39.55417528t² = 0