Answer:
-11/12
Step-by-step explanation:
slope for points (x1,y1) and (x2,y2)
slope=(y2-y1)/(x2-x1)
(x,y)
(-12,15)
(0,4)
x1=-12
y1=15
x2=0
y2=4
slope=(4-15)/(0-(-12))=-11/(0+12)=-11/12
Answer:
The probability that they have the disease given that the test came back positive is 0.6899.
Step-by-step explanation:
Let A represent the event that the prevalence of a certain disease is 0.09
Let D be the event in which those patients are tested who already have the disease then the probability of B
P (D) = 0.9
Let F be the event in which those patients are tested who do not have the disease then the probability of F
P (F) = 0.96
The tree diagram helps explain the events and their probabilities.
A 0.09 -----------0.9 (D)= P(D/A) (positive test)
⇅------------0.1 ( negative test)
⇅
1----- ⇅
⇅
⇅
B 0.91 ------------0.96 (F)= P(F/ B) (negative test)
----------------0.04 P (G/B) (positive test)
By Bayes Theorem
P (A/ D)= P (A). P(D/A)/ P (A). P(D/A)+P (B) P(G/ B)
P (A/ D)= 0.09 (0.9)/ 0.09 (0.9)+ (0.91)(0.04)
P (A/ D)= 0.081/ 0.081+0.0364
P (A/ D)= 0.081/ 0.1174
P (A/ D)= 0.6899
The probability that they have the disease given that the test came back positive is 0.6899.
Answer:
The door has a width of 6.26 feet, with a height of 12.52 feet.
Step-by-step explanation:
You can solve this by taking two pieces of information we're given:
1) the diagonal size of the doorway is 14 feet
2) the height of the doorway twice its width
First lets describe the width and height using the diagonal length. We can do that with the Pythagorean theorem:
w² + h² = 14²
Now we can use the relationship between the width and height to eliminate one variable:
w² + (2w)² = 14²
w² + 4w² = 14²
5w² = 196
w² = 39.2
w ≈ 6.26
So the door has a width of 6.26 feet, with a height of double that, 12.52 feet.
That is all correct, good job!
Let area to be painted = X m²
Rate for Allen = X / 16 m² / h
Rate for Brianne = X / 18 m² / h
Combined rate
X/16 + X/18 m² / h
[ 18X + 16X ] / 144 m² / h
34 X / 144 m² / h
time = X / [ 34 X / 144 ] h
time = 144 / 34 h
time = 4 h 14 min
