Answer:
A. principal interviewed the 25 students who scored highest on a reading test.
D. For a report on the exercise habits of adults, Sergio talked to 30 adults at a local fitness center.
E. Josh asked the first 25 people he met at the dog park if they preferred dogs or cats.
Step-by-step explanation:
Biased means if the selection of every unit does not have an equal chance of being selected in a sample.
The sample is said to be good if choosing the unit is unbiased. The sample is said to be unbiased if the selection of each unit is independent.
Option A is an example of data selected in a biased way because principal chose only those student who scored the highest marks on reading test.
Options B and C are unbiased as here a selection of each number and name of the student has an equal chance of being selected.
Option D is biased because Sergio talked adults at a local fitness center where people go for maintaining their health. So, there is a chance of the selection of fitted adults more than unfitted adults.
Option E is biased because Josh met people at the dog park where dog lovers are more than a cat lover.
Answers:
(a) p + m = 5
0.8m = 2
(b) 2.5 lb peanuts and 2.5 lb mixture
Explanations:
(a) Note that we just need to mix the following to get the desired mixture:
- peanut (p) - peanuts whose amount is p
- mixture (m) - mixture (80% almonds and 20% peanuts) that has an amount of m; we denote this as
By mixing the peanuts (p) and the mixture (m), we combine their weights and equate it 5 since the mixture has a total of 5 lb.
Hence,
p + m = 5
Note that the desired 5-lb mixture has 40% almonds. Thus, the amount of almonds in the desired mixture is 2 lb (40% of 5 lb, which is 0.4 multiplied by 5).
Moreover, since the mixture (m) has 80% almonds, the weight of almonds that mixture is 0.8m.
Since we mix mixture (m) with the pure peanut to get the desired mixture, the almonds in the desired mixture are also the almonds in the mixture (m).
So, we can equate the amount of almonds in mixture (m) to the amount of almonds in the desired measure.
In terms mathematical equation,
0.8m = 2
Hence, the system of equations that models the situation is
p + m = 5
0.8m = 2
(b) To solve the system obtained in (a), we first label the equations for easy reference,
(1) p + m = 5
(2) 0.8m = 2
Note that using equation (2), we can solve the value of m by dividing both sides of (2) by 0.8. By doing this, we have
m = 2.5
Then, we substitute the value of m to equation (1) to solve for p:
p + m = 5
p + 2.5 = 5 (3)
To solve for p, we subtract both sides of equation (3) by 2.5. Thus,
p = 2.5
Hence,
m = 2.5, p = 2.5
Therefore, the solution to the system is 2.5 lb peanuts and 2.5 lb mixture.
Answer:
20
Step-by-step explanation:
Divisors of 100
1, 2, 4, 5, 10, 20, 25, 50, 100
2 x 5 x r will give you this as well as 10r
