Time has a total of $28 after spending half of his weekly earnings on a video game and earning $10 additional dollars for mowing
1 answer:
Given:
Time has a total of $28 after spending half of his weekly earnings on a video game and earning $10 additional dollars for mowing the lawn.
To find:
Weekly earnings at his part time job.
Solution:
Let x be the weekly earning.
He spend half of his weekly earning, i.e.,
He earns $10 additional dollars for mowing the lawn.
According to the question,
Multiply both sides by 2.
Therefore, his weekly earnings is $36.
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Answer:
Domain: set of all real numbers
Range:
Step-by-step explanation:
We have to find the domain and range of the function:
This is a quadratic function, shape of a "U", that's called a parabola.
The domain is the set of x values for which the function is defined.
The range is the set of y values for which the function is defined.
Normally, any parabola in the form has domain as "all real numbers". This is the case for this problem as well, thus,
Domain = set of all real numbers
Now, for the range, we have to look at the minimum value of the function. So, the range would be y values greater than or equal to the minimum number. Lets find the minimum value of this function.
We have to find the value of x for which the minimum occurs by using the formula:
<em><u>Note: value of a is "5" and b is "10"</u></em>
Now, we plug this into the function to find the minimum value:
So, the range is set of all real numbers greater than or equal to -5.
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