Answer:
... I
... II
Step-by-step explanation:
Given that John is packing books into boxes to send to his cousins in case they are snowed in and want to do some light reading.
Let x represent the number of small books and y the number of large books.
The box capacity is either 15 small books or 8 large books
i.e. we have 
No of books is atleast 350 and no of boxes he needs is atleast 35
Total no of books = ... I
is the first inequality
Next is he wants 35 boxes.
One box can hold either 15 small books or 8 large books.
For x books no of boxes required = x/15 and for y book no of boxes is y/8
Total no of boxes is atleast 35
... II
Answer:
16 years
Step-by-step explanation:
If the salary at the first job is modeled by ...
y1 = 25000 +800x . . . . . salary after x years
and that of the second job is modeled by ...
y2 = 23000(1.032^x)
The salaries will be equal when ...
y2 = y1
23000(1.032^x) = 25000 +800x
There are no algebraic methods for solving an equation like this. However, a graphing calculator can give a pretty good estimate of the solution. It shows us that the equations give the same salary after about 15.3 years. If raises are given once per year, then ...
the salary of the second job will surpass the salary of the first job after 16 years.
_____
<em>Additional comments</em>
It isn't until after more than 25 years that total earnings at the second job exceed those at the first job. That time period is even longer if the effect of inflation is taken into account.
A spreadsheet can also provide a good answer to this question, either by listing the yearly salaries in a table, or by searching for a value of x that will make the salaries the same.
3 + 0.3 + 0.03 + 0.09 should be your answer
Consistent means 1 solution
inconsistent means no solutions....because they are parallel lines
equivalent means infinite solutions...because they are the same line
y = 3x - 2 3x - y = 4
-y = -3x + 4
y = 3x - 4
both equations have the same slope but different y intercepts....this means they are parallel lines and have no solutions ....INCONSISTENT
=======================
1/2y = -x + 5 2y = -4x + 20
y = -2x + 10 y = -2x + 10
same equation.....same line...infinite solutions...EQUIVALENT
===================
y = -x + 4 x = -y - 6
y = -x - 6
same slope, different y intercepts....parallel lines......no solutions...this means INCONSISTENT
==================
y = 4x + 2 y = 6x - 10
different slopes, different y intercepts...one solution...CONSISTENT
==================
y = 2x + 1 y = -2x + 3
different slopes, different y intercepts...one solution...CONSISTENT
=================
-2x + 5y = 0 y = 2/5x
5y = 2x
y = 2/5x
same line....infinite solutions....EQUIVALENT
Answer:
The probability that at least one of the children get the disease from their mother is 0.7125.
Step-by-step explanation:
We are given that a human gene carries a certain disease from the mother to the child with a probability rate of 34%.
Suppose a female carrier of the gene has three children. Assume that the infections of the three children are independent of one another.
Let Probability that children get the disease from their mother = P(A) = 0.34
SO, Complement of the event "At least one of the children get the disease from their mother"= P(A') = 1 - P(A)
where A' = event that children do not get the disease from mother.
So, P(A') = 1 - P(A) = 1 - 0.34 = 0.66
Now, probability that at least one of the children get the disease from their mother = 1 - Probability that none of the three children get disease from their mother
= 1 - P(X = 0)
= 1 - (0.66 
0.66 0.66)
= 1 - 0.2875 = <u>0.7125</u>
