Anna is an avid reader. Her generous grandparents gave her money for her birthday, and she decided to spend at most $150.00 on b
ooks. Reading Spot is running a special: all paperback books are $8.00 and hardback books are $12.00. Anna wants to purchase at least 12 books.
1.) Write a system of inequalities to reach po represent the situation.
2.) Graph the region of the solutions to the inequality.
3.) Name two different solutions for Anna's situation.
1.) Write a system of inequalities to reach po represent the situation.
2.) Graph the region of the solutions to the inequality.
3.) Name two different solutions for Anna's situation.
2 answers:
Answer:
1) equations 1, 2, 3 and 4
2) see picture attached (the region of the solutions is in yellow)
3) x = 18.75 and y =0
y = 12.5 and x =0
Step-by-step explanation:
Let's call x the number of paperback books bought and y the number of hardback books bought.
She decided to spend at most $150.00. All paperback books are $8.00 and all hardback books are $12.00. Combining this information we get:
x*8 + y*12 ≤ 150 (eq. 1)
Anna wants to purchase at least 12 books. Mathematically:
x + y ≥ 12 (eq. 2)
On the other hand, both the number of paperback books bought and the number of hardback books bought must be positive, that is:
x ≥ 0 (eq. 3)
y ≥ 0 (eq. 4)
3) One possible solution is got if we make y = 0 and to take eq. 1 as an equality, then:
From eq. 1: x*8 = 150
x = 150/8 = 18.75
equations 2 and 3 are also satisfied
Another option is to make x = 0 and to take eq. 1 as an equality, then:
From eq. 1: y*12 = 150
y = 150/12 = 12.5
equations 2 and 4 are also satisfied
Answer:
The solutions for 3 questions are explained one after the other below.
Step-by-step explanation:
1).Let x be the number of paperback books that she buys, y be the number of hardback books that she buys.
for the first condition, i.e, she has decided to spend at most $150.00 on books,the required inequality will be :
for the second condition , i.e, she wants to purchase at least 12 books,
the required inequality will be:
2). the graph is in the attachment..
3). x,y are the two required solutions. where,
x =number of paperback books she buys.
y=number of hardback books she buys.
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Answer:
Step-by-step explanation:
Data given and notation
The info given by the problem is:
the random sample taken
represent the population mean
represent the population standard deviation
The critical region on this case is so then if the value of
we fail to reject the null hypothesis. In other case we reject the null hypothesis
Null and alternative hypotheses to be tested
We need to conduct a hypothesis in order to determine if the true mean is 5000, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Let's define the random variable X ="The compressive strength".
We know from the Central Limit Theorem that the distribution for the sample mean is given by:
Find the probability of committing a type I error when H0 is true.
The definition for type of error I is reject the null hypothesis when actually is true, and is defined as the significance level.
So we can define like this:
And in order to find this probability we can use the Z score given by this formula:
And the value for the probability of error I is givn by: