A 20-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 6 feet
1 answer:
You might be interested in
Answer:
The width of the box is 6.7 cm
The maximum volume is 148.1 cm³
Step-by-step explanation:
The given parameters of the box Jorge is asked to build are;
The maximum girth of the box = 20 cm
The nature of the sides of the box = 2 square sides and 4 rectangular sides
The side length of square side of the box = w
The length of the rectangular side of the box = l
Therefore, we have;
The girth = 2·w + 2·l = 20 cm
∴ w + l = 20/2 = 10
w + l = 10
l = 10 - w
The volume of the box, V = Area of square side × Length of rectangular side
∴ V = w × w × l = w × w × (10 - w)
V = 10·w² - w³
At the maximum volume, we have;
dV/dw = d(10·w² - w³)/dw = 0
∴ d(10·w² - w³)/dw = 2×10·w - 3·w² = 0
2×10·w - 3·w² = 20·w - 3·w² = 0
20·w - 3·w² = 0 at the maximum volume
w·(20 - 3·w) = 0
∴ w = 0 or w = 20/3 = 6.
Given that 6. > 0, we have;
At the maximum volume, the width of the block, w = 6. cm ≈ 6.7 cm
The maximum volume, , is therefore given when w = 6.
cm = 20/3 cm as follows;
V = 10·w² - w³
= 10·(20/3)² - (20/3)³ = 4000/27 = 148.
The maximum volume, = 148.
cm³ ≈ 148.1 cm³
Using a graphing calculator, also, we have by finding the extremum of the function V = 10·w² - w³, the coordinate of the maximum point is (20/3, 4000/27)
The width of the box is;
6.7 cm
The maximum volume is;
148.1 cm³
Answer:
The expected value of this game is -$0.26.
Step-by-step explanation:
Expected value:
Each possible earning/loss multiplied by it's probability.
Probability:
Number of desired outcomes divided by the number of total outcomes.
In this question, the order in which the numbers are chosen is not important. So we use the combinations formula to solve.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
Probability of winning:
Desired outcomes:
The 6 correct numbers, so
Total outcomes:
6 numbers from a set of 21. So
Probability:
Expected value
probability of earning 40,000.
probability of losing 1. So
The expected value of this game is -$0.26.
Answer:
a) There is a 45.53% probability that a person who walks by the store will enter the store.
b) There is a 41.07% probability that a person who walks into the store will buy something.
c) There is a 18.70% probability that a person who walks by the store will come in and buy something.
d) There is a 58.93% probability that a person who comes into the store will buy nothing.
Step-by-step explanation:
This a probability problem.
The probability formula is given by:
In which P is the probability, D is the number of desired outcomes and T is the number of total outcomes.
The problem states that:
123 people walked by the store.
56 people came into the store.
23 bought something in the store.
(a) Estimate the probability that a person who walks by the store will enter the store.
123 people walked by the store and 56 entered the store, so .
So
There is a 45.53% probability that a person who walks by the store will enter the store.
(b) Estimate the probability that a person who walks into the store will buy something.
56 people came into the store and 23 bought something, so .
So
There is a 41.07% probability that a person who walks into the store will buy something.
(c) Estimate the probability that a person who walks by the store will come in and buy something.
123 people walked by the store and 23 came in and bought something, so .
So
There is a 18.70% probability that a person who walks by the store will come in and buy something.
(d) Estimate the probability that a person who comes into the store will buy nothing.
Of the 56 people whom came into the store, 23 bought something. This means that 56-23 = 33 of them did not buy anything. So:
There is a 58.93% probability that a person who comes into the store will buy nothing.