A lab is trying to determine if a new medication is effective at reducing acne breakouts. The results are displayed in the Venn Diagram below: A Venn Diagram titled Acne medicine probabilities is shown with two circles labeled used the medicine and skin cleared. Inside the used the medicine area is 20. Inside the skin cleared area is 10. In the intersection of the two circles is 30. The area outside the two circles is labeled 40. What is the probability that the person's skin cleared up given that they used the medication?
Answers
Answer: 3/5 is the probability that person's skin cleared up given that they used the medication.
Step-by-step explanation:
let S represents skin cleared and M represents medicine used.
According to the given Venn diagram,
P(S) = 40
P(M)= 50
[tex]P(M\cap S) = 30[/tex]
Thus by the definition of conditional probability,
If it is given that the skin is cleared then the probability that persons used the medicine,
P(M/S)=[tex]\frac{P(M\cap S)}{P(S)}[/tex]=30/50= 3/5.
P(M/S)=3/5.
The probability that the person's skin will clear up given that they used the medication is:
3/5What is Probability?This refers to the likelihood of an event to occur based on certain conditions.
If we want to find the probability about whether the skin will clear up is:
We would assign S to represent the skin
M to represent medicine
Hence,
P(S) = 40P(M)= 50P(MnS) = 30
Using the conditional probability rule,
P9M/S)= P(MnS)/P(S) = 30/50
=3/5
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Related Questions
An interior angle of a regular polygon has a measure of 108°. What type of polygon is it? The polygon is .
Answers
The polygon is a penthagon.
In a regular polygon with n sides, the sum of the interior angles is
[tex] 180(n-2) [/tex]
But we also know that each interior angle has a measure of 108, and of course there is a total of n angles. So, we also know that the sum of the interior angles is
[tex] 108n [/tex]
Since we have two expressions for the same quantity, these expressions must equal each other:
[tex] 180(n-2) = 108n [/tex]
To solve for n, let's start by expanding the left hand side:
[tex] 180n-360 = 108n [/tex]
Now move all terms involving n to the left hand side, and all constants to the right hand side:
[tex] 180n-108n = 360 [/tex]
Simplify the right hand side:
[tex] 72n = 360 [/tex]
And finally, divide both sides by 72:
[tex] n = \frac{360}{72} = 5 [/tex]
The correct polygon is, Pentagon
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
We have to given that;
An interior angle of a regular polygon has a measure of 108°.
Since, We know that;
In a regular polygon with n sides, the sum of the interior angles is
⇒ 180 (n - 2)
Here, The sum of the interior angles is,
⇒ 108n
Hence, We can formulate;
⇒ 108n = 180 (n - 2)
⇒ 108n = 180n - 360
⇒ 360 = 180n - 108n
⇒ 72n = 360
⇒ n = 5
Thus, It shows the Pentagon.
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Saving account has a principal of 1,800.00 it earns 6 percent interest compounded semiannually. How much is the compound interest after 1 year
Answers
A=p (1+r/k)^kt
A future value?
P principle 1800
R interest rate 0.06
K compounded semiannual 2
T time 1 year
A=1,800×(1+0.06÷2)^(2×1)
A=1,909.62
Now find the compound interest
I=A-p
I=1,909.62−1,800
I=109.62
Three painters can paint three walls in three minutes. how many painters are needed to paint 27 walls in nine minutes?
Answers
To paint 27 walls in 9 minutes, you would need 9 painters working at the same speed. This is based on the proportional relationship that each painter can paint 1 wall in 3 minutes.
Explanation:This problem can be solved with a clear understanding of proportions. Given that 3 painters can paint 3 walls in 3 minutes, it implies that each painter can paint 1 wall in 3 minutes.
Thus, in 9 minutes, a single painter can paint 3 walls.
Therefore, to paint 27 walls in 9 minutes, we would need 27/3 equals 9 painters.
It is important to note that this implies all painters are working at the same speed. This is a simple and practical example of proportions in mathematics
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Which of the sums below can be expressed as 8(2 + 7) 2+56......10+15.....16+7......16+56
Answers
8(2 + 7) = 8*2 + 8*7 = 16 + 56
Answer:
The correct answer is D) 16+56
Step-by-step explanation:
Which one of the following tin-lead soldiers has the lowest melting point? A. 60/40 B. 70/30 C. 40/60 D. 50/50
Answers
Based on this, the soldier with the lowest melting point is the one with the highest tin ratio.
Answer : (B) 70/30
You have three $1 bills, four $5 bills, and two $10 bills in your wallet. You select a bill at random. Without replacing the bill, you choose a second bill at random. Find P($5 then $10).
Answers
P(5,10)=8/72
P(5,10)=1/9
Find the terminal point p(x y) on the unit circle determined by the given value of t. t = -3 pi / 2
Answers
the terminal point on the unit circle for pi/2 is (0,1)
so that means the terminal point for -3pi/2 is also (0,1).
Answer:
It is B, just got it on a p e x
Step-by-step explanation:
A (-1,0)
B (0,-1)
C (1,0)
D (0,1)
Please Help ASAP!
Will award brainliest!
Answers
ratio of AB to DE = 30/6 = 5
do 24/6 = 4
x = 4
The points in a coordinate plane are reflected in the y-axis. In general, every point (x, y) is mapped onto what point? (___,___)
Answers
In a Cartesian coordinate system, a point (x, y) reflected over the y-axis is mapped to the point (-x, y), as the x-component changes direction in the reflection while the y-component remains the same.
Explanation:When a point is reflected across the y-axis in a Cartesian xy-coordinate system, which has orthogonal directions defined by the unit vectors i and j for the x and y axis respectively, the coordinates of the point change in a specific way. For every point whose coordinates are initially (x, y), after being reflected over the y-axis, the resultant point will have coordinates (-x, y).
This happens because the reflection over the y-axis effectively reverses the direction of the x-component of the point's position vector, changing its sign from positive to negative or vice-versa, while leaving the y-component unaffected. Therefore, after reflection, a point (x, y) is mapped onto the point (-x, y).
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Solve for x.
3:12 = x:16
2 1/4
4
64
Answers
We can set up a proportion to solve this
[tex] \frac{3}{12} \frac{x}{16} [/tex]
Cross multiply
3 x 16 = 48
48/12 = 4
The answer is 4
Hope this helps! :)
Answer:
[tex]x=4[/tex]
Step-by-step explanation:
we have
[tex]\frac{3}{12}=\frac{x}{16}[/tex]
solve for x
Cross multiply
[tex]12*x=3*16\\x=3*16/12\\x=48/12\\x=4[/tex]
Show all work to write the equations of the lines, representing the following conditions, in the form y = mx + b, where m is the slope and b is the y-intercept:
Part A: Passes through (−2, 1) and parallel to 4x − 3y − 7 = 0
Part B: Passes through (−2, 1) and perpendicular to 4x − 3y – 7 = 0
Answers
-3y = -4x + 7
y = 4/3x - 7/3....slope here is 4/3
A. a parallel line will have the same slope
y = mx + b
slope(m) = 4/3
(-2,1)...x = -2 and y = 1
sub and find b, the y int
1 = 4/3(-2) + b
1 = -8/3 + b
1 + 8/3 = b
3/3 + 8/3 = b
11/3 = b
so ur parallel line is : y = 4/3x + 11/3
B. A perpendicular line will have a negative reciprocal slope. To get the negative reciprocal of a number, u flip the number and change the sign. So our perpendicular line will need a slope of -3/4
y = mx + b
slope(m) = -3/4
(-2,1)...x = -2 and y = 1
sub and find b, the y int
1 = -3/4(-2) + b
1 = 3/2 + b
1 - 3/2 = b
2/2 - 3/2 = b
-1/2 = b
so ur perpendicular equation is : y = -3/4x - 1/2
Final answer:
The equation of the line for Part A is y = (4/3)x + 11/3, since it is parallel to the given line with a slope of 4/3. The equation for the line in Part B is y = (-3/4)x - 1/2, as it is perpendicular to the given line and the slope is the negative reciprocal of 4/3.
Explanation:
Writing Equations of Lines
To find the equation of a line in the form y = mx + b, we first need to determine the slope (m) and the y-intercept (b). For Part A, since the line needs to be parallel to 4x - 3y - 7 = 0, the slope of our line must be the same as the slope of this given line. To find the slope of the given line, we can rewrite it in slope-intercept form:
4x - 3y = 7
-3y = -4x + 7
y = (4/3)x - 7/3
The slope is 4/3. Since parallel lines have the same slope, our line's slope is also 4/3. Using the point (-2, 1) it passes through, we can substitute into the equation y = mx + b to find b:
1 = (4/3)(-2) + b
1 = -8/3 + b
b = 1 + 8/3
b = 11/3
Thus, the equation of the line for Part A is y = (4/3)x + 11/3.
For Part B, to find a line perpendicular to the given line, we need the negative reciprocal of its slope. The negative reciprocal of 4/3 is -3/4. We then use the given point (-2, 1) to find the y-intercept:
1 = (-3/4)(-2) + b
1 = 3/2 + b
b = 1 - 3/2
b = -1/2
So, the equation for the line in Part B is y = (-3/4)x - 1/2.
Orlando bought a new couch for $2,904, using the furniture store's finance plan. He will pay $121 a month for 24 months. Which equation can Orlando use to find out how much money he still owes after each month of the plan?
Select one:
a. y=2,904+121x
b. y=2904−121x
c. y=121x−2,904
d. y=121x
Answers
Which of the following is quantitative data?
eye colors of a group of people
hair colors of a group of people
heights of a group of people
genders of a group of people
Answers
Eliza Savage received a statement from her bank showing a checking account balance of $324.18 as of January 18. Her own checkbook shows a balance of $487.38 as of January 29. The bank returned all of the cancelled checks but three. The amounts of these three checks are $15.00, $77.49, and $124.28. How much did Eliza deposit in her account between January 18 and January 29?
Answers
3 checks total : 15.00 + 77.49 + 124.28 = 216.77
that amount will still need to be deducted from the bank
so 324.18- 216.77=107.41
her checkbook has a total of 487.38
487.38-107.41 = 379.97 is the amount she deposited into her account
Answer:
The amount she deposited in her account between January 18 and January 29 is $379.97
Step-by-step explanation:
Given :
Eliza showing a checking account balance of $324.18 as of January 18.
Her own checkbook shows a balance of $487.38 as of January 29.
The bank returned all of the cancelled checks but three. The amounts of these three checks are $15.00, $77.49, and $124.28.
To Find : Eliza deposit in her account between January 18 and January 29.
Solution :
Eliza showing a checking account balance of $324.18 as of January 18.
Total amount of three checks = $15.00 + $77.49+ $124.28 =$216.77
The account balance after the deduction of three checks amount
= $324.18 -$216.77 = $107.41
So, the new balance is $107.41.
Her own checkbook shows a balance of $487.38 as of January 29.
So, the amount she deposited between January 18 and January 29
= $487.38-$107.41 = $379.97
Hence , The amount she deposited in her account between January 18 and January 29 is $379.97
A wooden plank of length x is cut into 8 sections such that each section is at most 2 1/2 meters long. What is the length of the entire plank in meters?
a x ≤ 3.2 meters
b x ≤ 20 meters
c x ≥ 10.5 meters
d x ≥ 20 meters
Answers
Answer:
b
Step-by-step explanation:
Hiram raises earthworms. In a square of compost 4 ft by 4 ft, he can have 1000 earthworms. How many earthworms can he have if his square of compost has a side length that is 8 times longer?
A. 8000
B. 64,000
C. 256,000
D. 32,000
Answers
area=length times widtha
rea=4 times 4=16 square feet
so every 16 square feet is 1000 earthworms
so ratio of worms to area is 1000:16
if each side length is 8 then
8 times 8=64 area
but how many worms?
1000:16=?:64
1000/16=?/64
times both sides by 64
64000/16=?
4000=?
wat, not listed? why
if we assume it's a cube then
voluem is 4^3 or 64
1000:64 is the ratio
if 8ft then 8^3=512
so
1000:64=?:512
1000/64=?/512
512000/64=?
8000=?
I guess it was a cube then
A would be the answer
Jillian’s begins to solve a linear equation that results in a variable expression set equal to the same variable as expression. Which is the best interpretation of this solution
Answers
the equation has infinite solutions
Answer:
infinity solutions
Step-by-step explanation:
Store employees are handing out coupons. Every 10th customer gets a $1 coupon. Every 12th customer gets a $2 coupon.
Which customer is the first to receive both coupons?
Answers
correct answer 60th costumer
PLEASE HURRY!!! 30 POINTS
DIMENSIONAL ANALYSIS
A water cooler can hold 50 pt of water.
About how many liters of water can it hold?
1 L≈1.06 qt
23.6 L
26.5 L
94.3 L
106.0 L
Answers
The answer is 23.6 if I pretty sure
PLEASE HELP!!! For the given quadratic equation convert into vertex form, find the vertex, and find the value for x = 6. Show your work.
y = -2x2 + 2x +2
Answers
y = -2x^2+2x+2
y-2 = -2x^2+2x
y-2 = -2(x^2-x) ... notice the x coefficient here -1
y-2 = -2(x^2-x+1/4 - 1/4) ... take half of -1 to get -1/2, then square it to get 1/4
y-2 = -2(x^2-x+1/4)-2(-1/4)
y-2 = -2(x^2-x+1/4)+1/2
y-2-1/2 = -2(x^2-x+1/4)
y-5/2 = -2(x-1/2)^2
y = -2(x-1/2)^2+5/2
y = -2(x-0.5)^2+2.5
Answer in fraction form: y = -2(x-1/2)^2+5/2
Answer in decimal form: y = -2(x-0.5)^2+2.5
-------------------------------------------------------------------------------
Part 2) Find the vertex
The answer from part 1) leads to the answer to part 2). The nice thing about vertex form that it's easy to read off the vertex without having to do any extra work.
Vertex form is y = a(x-h)^2 + k
Match that to y = -2(x-1/2)^2+5/2 and we see that a = -2, h = 1/2, k = 5/2
The vertex is (h,k) = (1/2, 5/2) in fraction form. That's equivalent to (h,k) = (0.5, 2.5) in decimal form
Answer in fraction form: (1/2, 5/2)
Answer in decimal form: (0.5, 2.5)
-------------------------------------------------------------------------------
Part 3) Find the y value when x = 6
Plug in x = 6, to get...
y = -2x^2+2x+2
y = -2(6)^2+2(6)+2
y = -2(36)+2(6)+2
y = -72+12+2
y = -60+2
y = -58
Answer: y = -58
You thought the balance in ur cheking account was $68. When your bank statement arrives, you realize that you forgot to record a chem. The bank statement lists your balance as $26. Write and solve an equation to find out the amount of the chem that you forgot to record.
Answers
Answer is $42
Final Answer:
The amount of the check that you forgot to record is $42.
Step-by-step explanation:
Let x represents the amount which is forgotten in recording.
Bank balance + Amount of money forgotten in recording = Balance while checking account
26 + x = 68
x = 68 - 26
x = 42
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Name an angle adjacent to ∠DGE.
A. ∠FGI
B. ∠EGH
C. ∠HGJ
D. ∠JGI
Answers
------------------------------------------------
The given angle is DGE. Exactly two of the letters (D, G, and E) will be found in any adjacent angle to this given one. For example, angle FGD is adjacent to DGE because of the shared letters D and G. The two angles share the segment DG.
Similarly, angle DGE is adjacent to EGH for the same reason. Now segment EG is the overlapping shared segment. Note how "E" and "G" can be found in the given angle and the answer.
Edit: see the attached image for visual proof. The given angle is in red. The angle for the answer is in blue.
Find the circumference of a circle that has an area of 452.16 square meters. (Use 3.1416 as the value of π.)
Answers
Final answer:
The circumference of a circle with a given area is 75.40 meters
Explanation:
To find the circumference of a circle, we can use the formula C = 2πr, where C is the circumference and r is the radius. First, we need to find the radius from the given area.
The formula for the area of a circle is [tex]A = \pi r^2[/tex]
Rearranging the formula, we get [tex]r = \sqrt{(A/\pi \p).[/tex]
Now, substitute the given area (452.16 square meters) into the formula and solve for r:
[tex]r = \sqrt{(452.16/3.1416)[/tex]
= 12.00 meters
Finally, plug the value of r into the circumference formula:
[tex]C = 2\pi (12.00)[/tex]
= 75.40 meters
What reduced fraction corresponds to 92%?
Answers
The product of twenty one negative integers is negative? True of false
Answers
A mathematics journal has accepted 14 articles for publication. However, due to budgetary restraints only 9 articles can be published this month. How many ways can the journal editor assemble 9 of the 14 articles for publication? A. 726,485,760 B. 14 C. 2,002 D. 126
Answers
Answer:
A. 726,485,760
Step-by-step explanation:
A mathematics journal has accepted 14 articles for publication.
However, due to budgetary restraints only 9 articles can be published this month.
As the journals are published one by one (arranged combination), so the order matters in this case.
So permutation should be used in this case, rather than combination.
Hence, the number of ways the journal editor can assemble 9 of the 14 articles for publication is,
[tex]=\ ^{14}\text{P}_9=\dfrac{14!}{(14-9)!}=\dfrac{14!}{6!}=726,485,760[/tex]
Use the graph below to answer the question that follows:
graph of curve that passes through the following points, 0, 5; pi over 2, 2; pi, negative 1; 3 pi over 2, 2; 2 pi, 5.
What is the rate of change between the interval x = π and x = three pi over two?
Answers
The rate of change between x = π and x = three pi over two is 6/π.
Explanation:The rate of change between the interval x = π and x = three pi over two can be found by calculating the slope of the line connecting these two points on the graph. In this case, we can calculate the slope by finding the difference in y-values and dividing it by the difference in x-values:
Slope = (y₂ - y₁) / (x₂ - x₁) = (2 - (-1)) / (π - 3π/2) = (2 + 1) / (3π/2 - π) = 3 / (π/2) = 6 / π
Therefore, the rate of change between the interval x = π and x = three pi over two is 6/π.
The rate of change between x = π and x = three pi over two is 6/pi.
Explanation:The rate of change between the interval x = π and x = three pi over two can be found by determining the slope of the line connecting the two points on the graph corresponding to these x-values.
Using the coordinates (pi, -1) and (3 pi over 2, 2), we can calculate the slope as follows:
Slope = (change in y)/(change in x) = (2 - (-1))/(3 pi over 2 - pi) = 3/(pi/2) = 6/pi
So, the rate of change between x = π and x = three pi over two is 6/pi.
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Help^^^^^^^^^^^^^^^^^
Answers
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Work Shown:
I'm assuming the problem is -4*(1-x) <= -12+2x where the first term is -4 and not 4
-4*(1-x) <= -12+2x
-4*(1-x) <= -12+2x
-4+4x <= -12+2x
-4+4x-2x <= -12+2x-2x
-4+2x <= -12
-4+2x+4 <= -12+4
2x <= -8
2x/2 <= -8/2
x <= -4
To graph x <= -4, you plot a closed circle at -4. Then you shade to the left of the closed circle. This matches with choice D
Maximal use of bezels, gradients, and drop shadows make an interface highly user friendly True False
Answers
FALSE
Using too much image effects can make an interface not user-friendly.
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