Solution :
Given :
X = the number of boys in a family of four children
Families having four children are chosen randomly.
The gender distribution in the four child family are equally probable.
Thus,
X P(X) CDF
0 
= 1/16 
1 
= 1/4 
2 
= 3/8 
3 
= 1/4 
4 
= 1/16 1
Change 30 hours into minutes, then divide by 20 and 25
QUESTION A
The given points are
and 
The slope can be found using the formula;
We substitute the point to obtain;
This simplifies to
Therefore the slope is 5.
QUESTION 2
A positive slope indicates a rising line
A negative slope indicates a rising line
A zero slope means the line is horizontal.
An undefined slope means the line is vertical.
The correct answer is
A. The line rises from left to right.
Answer:
To solve the first inequality, you need to subtract 6 from both sides of the inequality, to obtain 4n≤12. This can then be cancelled down to n≤3 by dividing both sides by 4. To solve the second inequality, we first need to eliminate the fraction by multiplying both sides of the inequality by the denominator, obtaining 5n>n^2+4. Since this inequality involves a quadratic expression, we need to convert it into the form of an^2+bn+c<0 before attempting to solve it. In this case, we subtract 5n from both sides of the inequality to obtain n^2-5n+4<0. The next step is to factorise this inequality. To factorise we must find two numbers that can be added to obtain -5 and that can be multiplied to obtain 4. Quick mental mathematics will tell you that these two numbers are -4 and -1 (for inequalities that are more difficult to factorise mentally, you can just use the quadratic equation that can be found in your data booklet) so we can write the inequality as (n-4)(n-1)<0. For inequalities where the co-efficient of n^2 is positive and the the inequality is <0, the range of n must be between the two values of n whereby the factorised expresion equals zero, which are n=1 and n=4. Therefore, the solution is 1<n<4 and we can check this by substituting in n=3, which satisfies the inequality since (3-4)(3-1)=-2<0. Since n is an integer, the expressions n≤3 and n<4 are the same. Therefore, we can write the final answer as either 1<n<4, or n>1 and n≤3.
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