The Saxena family plans to install a light to illuminate part of their rectangular yard. Nikki and Dylan each proposed a differe
nt spot to place the light. The proposed placements and the lit area that each produces are shown below. Nikki's proposed placemat has a triangular light area with a base of 60 feet and height of 38 feet. Dylan's proposed placemat has a base of 60 feet and a height of 38 feet. How do Nikki's and Dylan's proposals compare? Check all that apply.
1 answer:
Options:
a. Nikki's proposed placement will light a greater area than Dylan's placement.
b. Dylan's proposed placement will light a greater area than Nikki's placement.
c. Both proposed placements will light the same sized area.
d. Nikki's proposed placement will light more than half the yard.
e. Dylan's proposed placement will light more than half the yard.
f. Dylan's proposed placement will light exactly half of the yard.
g. Nikki's proposed placement will light less than half of the yard.
Answer:
C) Both proposed placements will light the same sized area.
F) Dylan's proposed placement will light exactly half of the yard.
Step-by-step explanation:
The area of a triangle is (base x height) / 2, and both lights illuminate the same base and height = (60 x 38) / 2 = 1,140 sq ft
Both Dylan's and Nikki's proposed placement will lit exactly half of the yard. The yard's total area = 60 x 38 = 2,280 sq ft, which is twice the area lit by the lights.
You might be interested in
Answer:
a) 0.5 = 50% probability that an NPN transistor will be selected.
b) 0.3333 = 33.33% probability that it came from the cabinet that contains both types
c) 66.67% probability that it comes from the cabinet that contains only NPN transistors
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
a) What is the probability that an NPN transistor will be selected?
1/3 probability that the first cabinet is chosen. This cabinet has two transistors, both of which are NPN, so 100% probability of selecting a NPN transistor.
1/3 probability that the second cabinet is chosen. This cabinet has two transistors, both of which are PNP, so 0% probability of selecting a NPN transistor.
1/3 probability that the second cabinet is chosen. This cabinet has two transistors, one of which is NPN, so 50% probability of selecting a NPN transistor.
So
0.5 = 50% probability that an NPN transistor will be selected.
b) Given that the hobbyist selects an NPN transistor, what is the probability that it came from the cabinet that contains both types?
Here we use the conditional probability formula.
Event A: NPN transistor
Event B: From the third cabinet.
50% probability that an NPN transistor will be selected, so .
1/6 probability that it is from the third cabinet and NPN, so
The desired probability is:
0.3333 = 33.33% probability that it came from the cabinet that contains both types.
c) Given that an NPN transistor is selected what is the probability that it comes from the cabinet that contains only NPN transistors?
Either it comes from the cabinet with only NPN transistors, or it comes from the cabinet with both types of transistors. The sum of the probabilities of these outcomes is 100%. So
x + 33.33 = 100
x = 66.67
66.67% probability that it comes from the cabinet that contains only NPN transistors
The answer to the question
