Last year there were 221 students and 13 teachers at Hillard School. This year there are 272 students. The principal wants to ke
2 answers:
Answer:
Step-by-step explanation:
Let x be the number of required teachers this year.
We have been given that last year there were 221 students and 13 teachers at Hillard School. This year there are 272 students.
Since the principal wants to keep the same student-to-teacher ratio as last year, so we will use proportions to solve for x as proportions states that two fractions are equal.
Upon substituting number of students and teachers this year in our proportion we will get,
Therefore, the principal can use the proportion to find the number of teachers needed this year.
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Answer:
0.0008
Step-by-step explanation:
The formula for a hypergeometric probability is
where N is the population, A is the number of objects of type A, B is the number of objects of type B, n is the sample size and x is the number of successes.
In this problem, N is 13. A is 5, since there are 5 objects drawn, and B is 8, since there are 8 remaining objects.
The sample size, n, is 5, and x is 5:
To solve inequalities algebraically, first, you have to graph the lines disregarding the inequalities for a while.
For line 3x-y-7 <0, let's disregard < first and change it to =, such that 3x-y-7=0. Rearranging, y=3x-7. If you plot this equation, that would be the blue line in the equation. To know which of side of the line is the solution, you substitute a random point into the equality. For example, let's use point (5,20).
3x-y-7<0
3(5)-20-7<0
-12<0, this is true. Therefore, all the space to the left of the blue line is a solution (blue region).
We do the same for the other equation (orange line). Let's use the same point (5,20) to test.
x+5y+3≥0
5+5(20)+3≥0
108≥0, this is true, Therefore, everything above the orange line is a solution (orange region).
The overlapped area of the two shaded regions is presented as green in the picture. This is the exact solution of this system of linear equations.
For line 3x-y-7 <0, let's disregard < first and change it to =, such that 3x-y-7=0. Rearranging, y=3x-7. If you plot this equation, that would be the blue line in the equation. To know which of side of the line is the solution, you substitute a random point into the equality. For example, let's use point (5,20).
3x-y-7<0
3(5)-20-7<0
-12<0, this is true. Therefore, all the space to the left of the blue line is a solution (blue region).
We do the same for the other equation (orange line). Let's use the same point (5,20) to test.
x+5y+3≥0
5+5(20)+3≥0
108≥0, this is true, Therefore, everything above the orange line is a solution (orange region).
The overlapped area of the two shaded regions is presented as green in the picture. This is the exact solution of this system of linear equations.