Tell whether the triangle with the given sides lengths is a right triangle
1 answer:
If this is a right triangle, then 
where c is the hypotenuse which is ALWAYS THE LONGEST SIDE. Our longest side is 5, so we will set up Pythagorean's Theorem to see if the addition of the squares of a and b = the square of c: 
. Squaring all of that and adding on the left gives us 25=25. Because this is true, we have proven the converse of the Pythagorean Theorem here and this is a right triangle.
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Answer:
Step-by-step explanation:
A scientist was interested in studying if students beliefs about illegal drug use change as they go through college. The scientist randomly selected 104 students and asked them before they entered college if they thought that illegal drug use was wrong or o.k. Four years later, the same 104 students were asked if thought that illegal drug use was wrong or o.k. The scientist decided to perform McNemar's test. The data is below. What is the proportion of students that thought that is was wrong after college? After College ( four years later) Before College O.K. Wrong O.K. 4 17 Wrong 18 65
The number of students that thought that is was wrong before college is 18+65=83
The total number of students is 104
The proportion of students that thought that is was wrong before college is
Answer:
b) 0.2464
c) 0.0580
d) 0.2952
Step-by-step explanation:
Probability of those that purchased regular gas = 88% = 0.88
2% purchased mid grade gas
10% purchased premium gad
Given that a driver bought regular gas, 28% paid with credit card
Given that a driver bought mid grade gas, 34% paid with credit card
Given that a driver bought premium gas, 42% paid with credit card
Let R represent drivers that bought regular gas
Let M represent drivers that bought mid grade gas
Let P represent drivers that bought premium gas
Let C represent credit card payment
Let NC represent non-credit card payment
Pr(R) = 88% = 0.88
Pr(M) = 2% = 0.02
Pr(P) = 10% = 0.10
Pr(C|R) = 28%= 0.28
Pr(C|M) = 34%= 0.34
Pr(C|P) = 42%= 0.42
Pr(NC|R) = 1 - 0.28= 0.72
Pr(NC|M) = 1 - 0.34 = 0.66
Pr(NC|P) = 1 - 0.42 = 0.58
Using multiplication rule
Pr(AnB) = Pr(A) * Pr(B|A) = Pr(B) * Pr(A|B)
Using conditional probability,
P(B|A) = Pr(AnB) / Pr(A)
Pr(CnR) = Pr(R) * Pr(C|R)
= 0.88*0.28
= 0.2464
Pr(CnM) = Pr(M) * Pr(C|M)
= 0.02*0.34
= 0.0068
Pr(CnP) = Pr(P) * Pr(C|P)
= 0.10*0.42
= 0.0420
b) the probability that an automobile driver filled with regular gasoline AND paid with a credit card =
Pr(CnR)
= 0.2464
c) the probability that an automobile driver filled with premium gasoline AND did NOT pay with a credit card = Pr(P n NC) = Pr(NC|P) * Pr(P)
= 0.58 * 0.10
= 0.0580
d) The probability of those that paid with credit card is given as
Pr(CnR) + Pr(CnM) + Pr(CnP)
= 0.2464 + 0.0068 + 0.042
= 0.2952
Answer:
Step-by-step explanation:
<u>The Inverse of a Function</u>
Given a function f(x), the inverse of f, called is a function that satisfies:
The domain of f becomes the range of its inverse and vice-versa.
The procedure to find the inverse of the function is:
* Write the function as a two-variable equation:
* Solve the equation for x.
* Swap the variables
We are given the function:
Defined in the interval x ≥ -3
Note f is always negative, thus its range is f(x) ≤ 0
Now we find the inverse. Call y=f(x):
Multiplying by 2:
Squaring both sides:
Subtracting 3:
Swapping variables:
Thus:
The domain of the inverse is the range of f, thus x is restricted to
x ≤ 0