Using probability concepts, it is found that:
a) 0.43 = 43% probability that the patient experiences neither depression nor weight gain.
b) 0.3929 = 39.29% probability that the patient experiences depression given that the patient experiences weight gain.
c) 0.275 = 27.5% probability that the patient experiences weight gain given that the patient experiences depression.
d) No.
e) No.
---------------------
Conditional probability is an important part of the exercise.The formula is:[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
P(B|A) is the probability of event B happening, given that A happened. [tex]\mathbf{P(A \cap B)}[/tex] is the probability of both A and B happening. P(A) is the probability of A happening.----------------------
40% experience depression, thus [tex]P(A) = 0.4[/tex]28% experience weight gain, thus [tex]P(B) = 0.28[/tex]11% experience both, thus: [tex]P(A \cap B) = 0.11[/tex]Item a:
The probability of experiencing at least one of them is:[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.4 + 0.28 - 0.11 = 0.57[/tex]
The probability of none is:[tex]p = 1 - P(A \cup B) = 1 - 0.57 = 0.43[/tex]
0.43 = 43% probability that the patient experiences neither depression nor weight gain.
Item b:
This probability is: [tex]P(A|B)[/tex].Using conditional probability:[tex]P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.11}{0.28} = 0.3929[/tex]
0.3929 = 39.29% probability that the patient experiences depression given that the patient experiences weight gain.
Item c:
Similar to b, thus:[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.11}{0.4} = 0.275[/tex]
0.275 = 27.5% probability that the patient experiences weight gain given that the patient experiences depression.
Item d:
[tex]P(A \cap B) \neq 0[/tex], thus, the events are not mutually exclusive.
Item e:
We have that: [tex]P(A \cap B) = 0.11[/tex]Also: [tex]P(A)P(B) = 0.4(0.28) = 0.112[/tex][tex]P(A \cap B) = P(A)P(B)[/tex], thus, the are not independent.A similar problem is given at https://brainly.com/question/21421475
It takes Sara 5 1/2hours to drive to her aunt's
house. She has already driven 3 1/2 hours.
How much longer does Sara have left to
drive?
Answer:
2 hours
Step-by-step explanation:
To solve this question, we can convert the fraction into decimal form momentarily, so that 5 1/2 is now 5.5, and 3 1/2 is now 3.5. We know that Sara has already driven 3.5 hours, and it takes 5.5 to get to her aunts house. To dins how much longer Sara has left to drive, simply subtract the total amount of hours by the hours already completed:
5.5 - 3.5 = 2.0
Meaning, Sara has 2 hours left to drive
Hope this helps :)
What is the area of the rectangle?
Answer:
Area = 396 units²
Step-by-step explanation:
Let's assume:
Length = 2c - 5
Width = 5c + 9
Perimeter = 2(L + W) = 106 units
Thus:
2[(2c - 5) + (5c + 9)] = 106
Find the value of c
2[2c - 5 + 5c + 9] = 106
2[7c + 4] = 106
14c + 8 = 106
14c = 106 - 8
14c = 98
Divide both sides by 14
c = 98/14
c = 7
✔️Area of the rectangle = Length × Width
Area = (2c - 5)(5c + 9)
Plug in the value of c
Area = (2×7 - 5)(5×7 + 9)
Area = (14 - 5)(35 + 9)
Area = (9)(44)
Area = 396 units²
the difference of twelve and three times a number and negative 4
Answer:The answer is going to be 3 and this is how we came to that determination:
We are to subtract 3 times the number from 7 times the number and have it equal 12. So here is the the mathematical sentence to help us get the answer:
7X-3X=12 ; now we are going to subtract the 3 from the 7 on the left hand side of the equal sign:
4X=12 ; now we will divide each side of the equal sign by 4:
4X/4=12/4 and get X =3 ; to prove 3 is the number we are looking for, we will substitute it for X in our original sentence:
7(3)-3(3)=12
21–9=12
12=12
3 is our answer.
Step-by-step explanation:
Please anyone help me on this
Answer:
a.) x²+h²+2xh-8x-8h
b.) h+2x-8
Step-by-step explanation:
A.) you just plug in x+h wherever there's an x
which means you have
(x+h)²-8(x+h)
simplify and get
x²+h²+2xh-8x-8h
we already know what f(x+h) is so we just need to subtract f(x) we have
x²+h²+2xh-8x-8h-x²+8x
simplify and get
h²+2xh-8h
Divide this by h and get
h+2x-8
Answer:
h+2x-8
Step-by-step explanation:
iiiiiiii aaaaaaammmmm ssssuuuurrree
Carson draws a scale drawing of a city park and a parking lot. The city park is in the shape of a right triangle with logs that are 3 inches and 4 inches. The parking lot is in a shape of a rectangle with
dimensions of 15 inches and 25 inches. The scale for the drawing is 1 inch 40 feet.
Answer:
6,000 & 19,200
(14, 5) , (21, 3) , (26, 8) , (33, 6) , (38, 11) , ( _____ , _____ ) , ( _____ , _____ ) , (57, 12) , (62, 8) , (69, 15) , (74, 11)
fill in the sequence
Answer:
(45,9), (50, 14)
Step-by-step explanation:
the y-axis' pattern is subtract 2 and add 5.
the x-axis' pattern is add 7 then add 5.
So we get (45, 9) and (50, 14)
a) 25 + 97 - 72
46 -19 + 55
185 - 82 + 39
Answer:
254
Step-by-step explanation:
Add everytin step by step.
solve 4(x+7)-5x+2=10
Answer:
x = 20
Step-by-step explanation:
4(x + 7) - 5x + 2 = 10
open the parenthesis
4 * x + 4 * 7 - 5x + 2 = 10
4x + 28 - 5x + 2 = 10
combine like terms
-x + 30 = 10
subtract 30 from both sides of the equation
-x + 30 - 30 = 10 - 30
-x = 10 - 30
-x = -20
mutiply the equation by -1
-1 * -x = -20 * -1
x = 20
This graph represents Andre's distance from his bicycle
as he walks in a park.
Decide whether the following statements are true or
false.
The graph has multiple horizontal intercepts: T or F
A horizontal intercept of the graph represents the time when Andre was with his bike: T or F
A minimum of the graph is (17, 1): T or F
The graph has two maximums: T or F
About 21 seconds after he left his bike, he was the farthest away from it, at about 8.3 feet: T or F
Answer:
True
True
False
False
True
The graph describes Andres movement in the park relative to the position
of his bike with time.
The correct responses are;
The graph has multiple horizontal intercept: FA horizontal intercept of the graph represent the time when Andre was with his bike: T A minimum of the graph is (17, 1): TThe graph has two maximums: TAbout 21 seconds after he left his bike, he was the farthest away from it, at about 8.3 feet: TReasons:
1. The graph has only one horizontal x and y-intercept at the origin of the graph, the correct option is false, FAn horizontal line of the graph represents a stationary point on the graph, the x-intercept represent the points when Andre is next to his bike, therefore;
2. At the horizontal intercept of the graph, Andre was with his bike, the correct option is true, TThe point with coordinates (17, 1) represent a local minimum of the graph, therefore;
3. Point (17, 1) is a minimum of the graph, the correct option is true, TThe maximum points are points having higher vertical coordinate values compared to the surrounding points.
4. Therefore, the points (9, 8), and (21, 8.3) represent two maximum points on the graph, the correct option is true, TThe point that gives the highest value of the maximum points, which is at (21, 8.3) is the point at which he was farthest away from the bike.
5. Therefore, he was farthest away from his bike at 8.3 feet, 21 seconds after he left his bike. The correct option is true, TLearn more here
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Given that 9x – 8y = 16
Find x when y = -8
Give your answer as an improper fraction in its simplest form.
Answer:
x=-16/3
Step-by-step explanation:
9x-8(-8)=16
9x+64=16
9x=-48
x=-48/9
x=-16/3
A line passes through the point (2, 1) and has a slope of -5/2
Write an equation in slope-intercept form for this line.
Answer:
[tex]y = -\frac{5}{2}x +6[/tex]
Step-by-step explanation:
Given
[tex]m = -\frac{5}{2}[/tex] -- slope
[tex](x_1,y_1) = (2,1)[/tex] --- point
Required
Determine the line equation
In slope intercept form, a line equation is:
[tex]y - y_1 = m(x - x_1)[/tex]
This gives:
[tex]y - 1 = -\frac{5}{2}(x - 2)[/tex]
Open bracket
[tex]y - 1 = -\frac{5}{2}x +5[/tex]
Add 1 to both sides
[tex]y - 1+1 = -\frac{5}{2}x +5+1[/tex]
[tex]y = -\frac{5}{2}x +6[/tex]
Deshawn bought 2 packs of markers each pack has 8 markers he gave 3 markers to ami how many markers does deshawn have left?
Answer:
13
Step-by-step explanation:
2(8)-3= 13
if my answer helped please mark as brainliest.
One month Lucy rented 2 movies and video games for a total of $40. The next month she rented 5 movies and 3 video games for a total of $25. Find the
rental cost for each movie and each video game.
Answer:
the first month it was 10 each for a video game and the 2nd month it was
How many yards are in 1 mile 300 feet
Answer:
1860?
Step-by-step explanation:
one mile is 5280 feet
add 300 feet and its
5580 feet but then divide by 3 to get in yards
1860 yards is the answer
A rectangular prism has a length of 6 cm, a width of 5 cm, and a depth of 4 cm. What is its volume? PL HURRY IT IS TIMED
Answer:
The answer should be 120
Step-by-step explanation: hope this helps
please be quick i need this done
Answer:
8.8
Step-by-step explanation:
kids cheating in tests.....
8.7749643787
8.8(1dp)
As an investment, a couple bought a house for 2.7 million. Two years later sold it for $5 million what was their profit
please help answer gets brainliest
Answer:
you got to go back to the question before that and then you will know.
Step-by-step explanation:
Loyalty requires you to dismiss all of your personal goals permanently.
Answer:
Step-by-step explanation:
show the rest
Answer:
False
Step-by-step explanation:just took the test
what is the slope of the line that passes through these points shown in the table
x= -1, 0, 1, 2
y= -5, -3, -1, 1
Answer:
m=2
Step-by-step explanation:
(0,-3) (2,1)
y2-y1 1+3. 4
x2-x1 2-0. 2
4/2= 2
Help
How many 1/8 cup servings are there in 3/4 cup salad dressing
Answer:
6
Step-by-step explanation:
divide 3/4 by 1/8 (same as multiplying by 8)
this gives you 6
I need help with this one
Answer:
(2/3)^3
8/27 in^3
Step-by-step explanation:
Answer:
3
0.29629629629in³
Step-by-step explanation:
To find the volume of a cube you multiply the length by the width by the height. Since all the sides of the cube are the same, its the same measure multiplied three times, ie. to the power of three.
(2/3)³=0.29629629629in³
five hundred and fifty four thousandths in number form
i need for homework
Answer:
54.0054
Step-by-step explanation:
hope it helps you
please mark me as brainlist
HELP FAST PLEASE!!!!
Deshawn surveyed two boys from each kickball team in his coed (boys and girls) kickball league to find out how many games the attended during the 10-game season. Which of the following generalizations could be valid based on the sample?
Answer:
75% of the guys is valid and half the boys in the league attended all the games is also valid. 80% of the games is not valid and so is 70% of the games.
Step-by-step explanation:
I took the test :)
Answer:
The Screenshot has the answer to the problem.
Step-by-step explanation:
Solve for the coefficient a in vertex form for the parabola in Daredevil Danny’s practice jump
Answer:
-8/25 or -0.32Step-by-step explanation:
Vertex is (25, 32)The function in vertex form:
y = a(x - 25)² + 32x- intercepts are 15 and 35:
0 = a(15 - 25)² + 32 or 0 = a(35 - 25)² + 320 = a*100 + 32100a = - 32a = -32/100a = -8/25 or -0.32Under her cell phone plan, Autumn pays a flat cost of $48 per month and $5 per gigabyte. She wants to keep her bill at $68.50 per month. Write and solve an equation which can be used to determine gg, the number of gigabytes of data Autumn can use while staying within her budget.
Answer:
Equation: 68.50=48+5x Answer: 4gigabytes
Step-by-step explanation:
You have to add the flat cost and the cost per gigabyte together. Then set it equal to her maximum amount and solve.
The equation to calculate the number of gigabytes will be 68.50=48+5x. The number of gigabytes will be 4.1 GB
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that under her cell phone plan, Autumn pays a flat cost of $48 per month and $5 per gigabyte. She wants to keep her bill at $68.50 per month.
The expression can be written as below:
68.50=48+5x
5x = 68.5 - 48
5x = 20.5
x = ( 20.5 / 5 ) = 4.1 Gb
Therefore, the equation to calculate the number of gigabytes will be 68.50=48+5x. The number of gigabytes will be 4.1 GB
To know more about an expression follow
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Brandon rode in a taxi that charges a flat fee of $2.25 and an additional $0.40 per mile of his trip. If he paid $6.80 for the cab ride, how many miles did he travel? (HOW DID YOU GET YOUR ANSWER SHOW YOUR WORK!!)
A. 11 3/8
B. False
C. 1/5
D. 61.5
E. True
F. 3/25
G. 62.4
Answer:
11 [tex]\frac{3}{8}[/tex] miles.
Step-by-step explanation:
To find how many miles Brandon rode, we can create an equation in slope-intercept form: y = mx + b
$2.25 is the flat fee, or the unchanging variable. This is our y-intercept, or b.
$0.40 is the changing variable, as it changes value depending on the amount of miles ridden. This is our slope, or m.
We know Brandon spent $6.80 on the cab ride. So, this is our y.
We get the equation: 6.80 = 0.40x + 2.25.
To solve, first subtract 2.25 from both sides of the equation:
6.80 - 2.25 = 0.40x + 2.25 - 2.25
We get: 4.55 = 0.40x
Now, just divide by 0.40 on both sides:
4.55 ÷ 0.40 = 0.40x ÷ 0.40
We get: 11.375 = x
So, Brandon rode for 11.375 miles. When converted to a mixed number, we get 11 [tex]\frac{3}{8}[/tex] .
I would appreciate brainliest, if not that's ok!
Learn with an example
Write an equation to describe the sequence below. Use n to represent the position of a term
in the sequence, where n = 1 for the first term.
1, 4, 16, ...
Write your answer using decimals and integers.
an =
yn-1
Submit
Work it out
Not feeling ready yet? These can help:
Answer:
Step-by-step explanation:
Because dividing any term by the previous term gives a constant this is a geometric sequence of the form an=y^(n-1). Since each term is four times the previous term y=4 so
an=4^(n-1)
If m <CGB = 79°, then what is m <DGB?
Answer:
∠DGB = 101°
Step-by-step explanation:
Given:
∠CGB = 79°
Find:
∠DGB
Computation:
We know that CD is a straight line
So,
∠CGB + ∠DGB = 180
79 + ∠DGB = 180
∠DGB = 101°
factorise fully 18e^2f^3-12e^2f
Answer:
[tex]18e^2f^3-12e^2f = 6e^2f(3f^2-2)[/tex]
Step-by-step explanation:
Given
[tex]18e^2f^3-12e^2f[/tex]
Required
Factorize:
[tex]18e^2f^3-12e^2f[/tex]
Express 18 as 6 * 3 and 12 as 6 * 2
[tex]18e^2f^3-12e^2f = 6*3e^2f^3-6*2e^2f[/tex]
Factor out 6
[tex]18e^2f^3-12e^2f = 6(3e^2f^3-2e^2f)[/tex]
Factor out [tex]e^2[/tex]
[tex]18e^2f^3-12e^2f = 6e^2(3f^3-2f)[/tex]
Factor out f
[tex]18e^2f^3-12e^2f = 6e^2f(3f^2-2)[/tex]