Bob wants to plant a 7 foot by 10 foot garden with a uniform border of petunias around the outside and still have 28 square feet
2 answers:
Answer:
The petunia border width is 1.5 feet.
Step-by-step explanation:
Let’s define x as the border width in feet,
Given,
The garden measurements are 7 feet by 10 feet,
Thus, the dimensions of the central area without the border are (7 - 2x) feet by (10 - 2x) feet.
Therefore, the central area = (7 - 2x)(10 - 2x)
According to the problem,
( Combine like terms )
( Middle term splitting )
By applying the zero product principle,
4x - 6 or x - 7 = 0
⇒ x = 1.5 or x = 7
Since the width cannot equal the garden dimensions,
It follows that the border width would be 1.5 feet.
Answer:
1.5 feet
Step-by-step explanation:
Bob is planning to create a garden that measures 7 feet by 10 feet.
Area = square feet
He intends to plant petunias in a uniform border around the garden while ensuring there is a leftover area of 28 square feet for tomatoes and roses in the center.
This requires factoring 28 so that both the length and width remain under 10 and 7 feet.
28 = 2 x 2 x 7
This indicates that the width can be 4 feet and 7 feet the length for the area meant for tomatoes.
Thus, we find that the garden reduces feet on every side, meaning the deduction on each side is
feet.
Similarly, the width is also reduced by feet, resulting in a width reduction of 1.5 feet on each side.
Consequently, the petunia border should be 1.5 feet wide throughout.
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Complete Question
The complete question appears in the first uploaded image
Answer:
a) Yes, selecting 15 corresponds to a binomial experiment
b)
c)
d)
Regarding question a:
For an experiment to qualify as binomial
the trials have to be independent
each trial must yield one of two possible outcomes
Given that the selection of 15 individuals is random, we ascertain that the trials are independent and the outcomes are “either the individual saves for retirement or does not save for retirement.”
Therefore, we conclude that the selection of 15 people at random is indeed a binomial experiment.
In question b:
The probability that all selected adults do not save for retirement is mathematically modeled as
r = 15 implies all selected adults
n refers to the population size equating to 15
From the problem, p = 0.20
and q can be calculated as
=>
=>
Thus
Regarding question c:
The probability that exactly five of the selected adults do not save for retirement is mathematically modeled as
In relation to question d:
The probability that at least one of the selected adults opts not to save for retirement can be mathematically expressed as