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
The equation of the function is f(x) = -5x + 10
<h3>How to determine the function equation?</h3>
The points are given as:
x-intercept at (2,0) and a y-intercept at (0,10)
A linear function is represented as:
y = mx + b
Where b is the y-intercept.
The y-intercept at (0,10) means that:
b = 10
So, we have:
y = mx + 10
The x-intercept at (2,0) means that:
x = 2, when y = 0
Substitute these values in y = mx + 10
0 = 2m + 10
Subtract 10 from both sides
2m = -10
Divide both sides by 2
m = -5
Substitute m = -5 in y = mx + 10
y = -5x + 10
Hence, the equation of the function is y = -5x + 10
Read more about linear functions at:
brainly.com/question/4025726
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Answer:
a ^ (1/12)
Step-by-step explanation:
a ^ (1/3)
---------------
a ^ (1/4)
We know that b^ c / b^ d = b ^ (c-d)
a^ (1/3 - 1/4)
getting a common denominator
1/3 *4/4 - 1/4*3/3 = 4/12 - 3/12
a^ (4/12 - 3/12)
a ^ (1/12)
85 is the answer. 2+ 78 = 80 + 5 += 85.