davidson family wants to expand its rectangular patio, which currently measures 15 ft by 12 ft. they want to extend the length a
2 answers:
<h2>Answer</h2>
Which simplifies to:
Let the number of feet they are going to expand the width and length of the patio. So the new width of the patio will be
and the new length
.
Remember that the area of a rectangle is <u>width times length</u>, so the length of our expanded patio will be . But, we also know form our problem that they want to increase the total area of the patio by 160 ft2. The actual area of the patio is
, so the expanded area of the patio will be
.
Now we can equate the expanded area of the patio and simplify:
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(Points plotted and connected in picture below)
Slope: 9
The slope represents the total cost depending on the number of DVDs ordered.
Y-intercept: 6
Slope: 9
The slope represents the total cost depending on the number of DVDs ordered.
Y-intercept: 6
Answer:
(a) The probability that exactly 5 of the 6 consumers recognize the brand name is 0.0369.
(b) The probability that all of the selected consumers recognize the brand name is 0.0041.
(c) The probability that at least 5 of the selected consumers recognize the brand name is 0.041.
(d) The events of 5 customers recognizing the brand name is unusual.
Step-by-step explanation:
Let <em>X</em> = number of consumer's who recognize the brand.
The probability of the random variable <em>X</em> is, P (X) = <em>p</em> = 0.40.
A random sample of size, <em>n</em> = 6 consumers are selected.
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> and <em>p</em>.
The probability mass function of <em>X</em> is:
(a)
Compute the value of P (X = 5) as follows:
Thus, the probability that exactly 5 of the 6 consumers recognize the brand name is 0.0369.
(b)
Compute the value of P (X = 6) as follows:
Thus, the probability that all of the selected consumers recognize the brand name is 0.0041.
(c)
Compute the value of P (X ≥ 5) as follows:
P (X ≥ 5) = P (X = 5) + P (X = 6)
= 0.0369 + 0.0041
= 0.041
Thus, the probability that at least 5 of the selected consumers recognize the brand name is 0.041.
(d)
An event is considered unusual if the probability of its occurrence is less than 0.05.
The probability of 5 customers recognizing the brand name is 0.0369.
This probability value is less than 0.05.
Thus, the events of 5 customers recognizing the brand name is unusual.