The likelihood that someone with symptoms and a positive test has hepatitis is therefore 0.994, or almost 99.4%.
What is the probability that an individual who has the symptoms and who reacts positively to the test actually has hepatitis?We need to apply Bayes' theorem to determine the likelihood that a person with symptoms and a positive test actually has hepatitis. Let H stand for the occurrence that the person has hepatitis and T stand for the occurrence that the test is positive. Next, we have:
P(T | H) * P(H) / P(T | H) = P(H | T) (T)
where P(H) is the prior probability of the individual having hepatitis (which is 0.8), P(H) is the likelihood of the individual testing positive, and P(T) is the probability of testing positive given that the individual has hepatitis.
We must apply the law of total probability to determine P(T):
P(T) is equal to P(T | H)* P(H) plus P(T | not H)* P. (not H)
P(T | not H) is the complement of P(H), and P(not H) is the probability of testing positive if the person does not have hepatitis (0.05). (i.e., the probability of not having hepatitis, which is 0.2).
Now that the values have been inputted, we can calculate:
P(T) = (0.94 * 0.8) + (0.05 * 0.2) = 0.752 P(H | T) = (0.94 * 0.8) / 0.752 = 0.994
Although there is a strong likelihood that this is the case, it's crucial to remember that no medical test is error-free, and false positives and false negatives can still happen.
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Notes Solve for Y, the solution cannot be negative. Please answer!
The solution to equation 1, 2, 3, 4, 5 and 6 are y = (-3/2) + 6, y = (-5/3) + 3, y = (-1/5)x + 9/5, y = (1/4)x + 3/2, y = (-7/3)x + 3 and y = 6x + 3 respectively.
How to solve for y in a linear equation?Given the linear equations in the question;
3x + 2y = 125x + 3y = 9x + 5y = 9-2x + 8y = 12-7x - 3y = -96x - y = -3To make y the subject of the formula, we need to isolate y on one side of the equation by moving all other terms to the other side.
1) 3x + 2y = 12
Subtract 3x from both sides:
3x - 3x + 2y = -3x + 12
2y = -3x + 12
Divide each term by 2
2y/2 = -3x/2 + 12/2
y = (-3/2) + 6
2) 5x + 3y = 9
Subtract 5x from both sides:
5x - 5x + 3y = -5x + 9
3y = -5x + 9
Divide each term by 3
3y/3 = -5x/3 + 9/3
y = (-5/3) + 3
3) x + 5y = 9
Subtract x from both sides:
x - x + 5y = -x + 9
5y = -x + 9
y = (-1/5)x + 9/5
4) -2x + 8y = 12
8y = 2x + 12
y = (2/8)x + 12/8
y = (1/4)x + 3/2
5) -7x - 3y = -9
-3y = 7x - 9
y = (-7/3)x + 3
6) 6x - y = -3
-y = -6x - 3
y = 6x + 3
Therefore, the formula in terms of x is: y = 6x + 3.
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Olivia had a high yield savings account, to which she makes deposits of $650 monthly. if she already has a balance of $400 in the account and she wants to save at least $7,500. How many months will it take for a Olivia to reach her goal
Olivia will need at least 11 months to reach her savings goal.
What is algebra ?
Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It involves the use of letters and symbols to represent values and quantities in mathematical equations and formulas. Algebra is used to solve problems that involve unknown quantities by using rules and operations to manipulate the symbols representing those quantities.
Let's use algebra to solve this problem. Let "m" be the number of months it will take for Olivia to reach her goal of saving at least $7,500.
In one month, Olivia will deposit $650, so after "m" months, she will have deposited:
650m
In addition to this, Olivia already has a balance of $400, so her total savings after "m" months will be:
650m + 400
We want to find how many months "m" it will take for Olivia to save at least $7,500. So we can set up the following inequality:
650m + 400 >= 7,500
Subtracting 400 from both sides:
650m >= 7,100
Dividing both sides by 650:
m >= 10.92
Since we can't have a fraction of a month, we'll round up to the next whole number. Therefore, Olivia will need at least 11 months to save at least $7,500.
Therefore, Olivia will need at least 11 months to reach her savings goal.
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Tom had 2304 picture cards. He had 3 times as many picture cards as
Cevin. Ron had 190 fewer picture cards than Kevin. How many picture cards
Did Ron have?
Let's start by using "x" to represent the number of picture cards that Cevin has. We know that Tom has 3 times as many picture cards as Cevin, so:
Tom = 3x
We also know that Tom has 2304 picture cards, so:
3x = 2304
Solving for x, we get:
x = 768
So, Cevin has 768 picture cards.
We also know that Ron has 190 fewer picture cards than Kevin, so:
Ron = x - 190
Substituting x with 768, we get:
Ron = 768 - 190
Therefore, Ron has:
Ron = 578 picture cards.
eight more than the sum of a number and 7 is 90. write the equation and define a variable.
The expression "eight more than the sum of a number and 7 is 90" can be written as: 8 + (x + 7) = 90
How to determine the algebraic expressionFrom the question, we have the following parameters that can be used in our computation:
eight more than the sum of a number and 7 is 90
Express the numbers properly
So, we have
8 more than the sum of a number and 7 is 90
Express the operators properly
8 + (x + 7) = 90
hence, the expression is 8 + (x + 7) = 90
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Simplify (4with an expponent of 4)−1 exponent too
Answer:
[tex]\frac{1}{256}[/tex]
Step-by-step explanation:
Given
[tex]\left(4^4\right)^{-1}[/tex]
We can use the power rule to multiply the exponents.
The power rule for exponents states
[tex]\left(a^b\right)^{c}=a^{bc}[/tex]
[tex]4^{4*-1}[/tex]
Multiply 4 by −1.
[tex]4^{-4}[/tex]
Rewrite the expression using the negative exponent rule.
The negative exponent rule states
[tex]a^{-b}=\frac{1}{a^b}[/tex]
[tex]\frac{1}{4^4}[/tex]
Raise 4 to the power of 4.
[tex]\frac{1}{256}[/tex]
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Ariana and Leon hung out at the mall on Saturday. They spent 1 hour shopping for clothes and 55 minutes at the food court. Then they spent 2 hours and 10 minutes at the video arcade before heading home. It was 1:40 P.M. when Ariana and Leon left the mall. What time did they start shopping for clothes?
By answering the above question, we may state that As a result, around expressions 10:35 AM, Ariana and Leon began their clothing shopping.
what is expression ?In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.
We must take the time they spent at the mall overall from the moment they departed in order to determine when Ariana and Leon began looking for clothing.
To make adding up the times easier, let's first convert all the times to minutes:
Clothing shopping takes an hour, or 60 minutes.
Restaurant: 55 minutes
In a video arcade, two hours are equal to 120 minutes plus 10 minutes.
Total time spent at the mall is 245 minutes (60 + 55 + 130).
If they left the mall at 1:40, then we need to take 245 minutes away from that time.
1:00 PM minus 245 minutes equals 10:35 AM.
As a result, around 10:35 AM, Ariana and Leon began their clothing shopping.
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There are 9 game pieces on each tic-tac-toe board. The third grade class has 4 tic-tac-toe boards. How many game pieces does the class have for all of their tic-tac-toe boards?
A) 13
B) 27
C) 36
D) 45
Answer:
C) 36.
Step-by-step explanation:
Since there are 9 game pieces in each tic-tac-toe board and the class has 4 tic-tac-toe boards, the total number of game pieces the class has is:
9 pieces/board x 4 boards = 36 pieces
Therefore, the answer is C) 36.
number that adds up to 27 and 6
Answer: 9 and 3
Step-by-step explanation: Depends the signs +/- and the problem.
Critically discuss strategies that the matric learners could implement if they did not obtain the marks they needed to enter their chosen study programmes
If matric learners do not obtain the marks they need to enter their chosen study programmes, there are several strategies they can implement to still achieve their academic and career goals:
1. Consider alternative study programmes: Matric learners who did not obtain the marks they need for their first choice of study programme should consider other programmes that may be similar or related to their original choice. They can also look at bridging courses, diploma programmes or short courses that will enable them to develop the skills and knowledge they need for their chosen career.
2. Upgrade matric results: Some learners may choose to re-write some of their matric subjects to improve their results. This can be done through night school, part-time courses or through online platforms. This will require dedication, hard work and perseverance, but it can be an effective way to meet the entry requirements for their desired study programmes.
3. Attend a tertiary institution with lower entry requirements: Matric learners who do not meet the requirements for their desired study programme at their first choice institution can consider attending another institution with lower entry requirements. This will enable them to obtain a qualification in their chosen field, which they can use to pursue further studies or career advancement.
4. Take a gap year: Taking a gap year to gain work experience or travel can provide learners with valuable skills and experiences that can enhance their application for their chosen study programme in the future. This time can also be used to upgrade their matric results or to explore other interests and career options.
In conclusion, while not obtaining the marks required to enter a chosen study programme can be disappointing, it is important for matric learners to remain positive and proactive. By considering alternative study programmes, upgrading matric results, attending institutions with lower entry requirements, or taking a gap year, learners can still achieve their academic and career goals.
When the age of Rita was equal to the present age of Shova, she was thrice as old as Shova was. If the sum of their present ages is 40 years, fing their ages.
As the total of Rita and Shova's current ages is 20, they are both 20 years old.
what is unitary method ?A mathematical strategy for resolving proportional and ratio issues is called the unitary method. Finding the value of one unit of an amount and using that value to calculate the value of additional units is what this process entails. The foundation of the unitary approach is the idea that if two quantities are equal, then their ratios must also be equal. For instance, if five apples cost $10, then the expense-to-apple ratio is 10/5 = 2. This ratio can be used to calculate the price of a varied quantity of apples.
given
According to the issue statement, Rita was three times as old as Shova when her age and Shova's current age were equal.
R - (S - R) Equals 3(S - R) (S - R)
When we simplify this solution, we obtain:
2R = 4S - 2S
2R = 2S
R = S
As a result, we are aware that Rita and Shova are both currently the same age.
Additionally, we are aware that their combined current ages are 40 years.
R + S = 40
R = S, so we can change S in the second equation to R:
R + R = 40
2R = 40
R = 20
Rita is currently twenty years old. Since R = S, Shova is 20 years old at the moment.
As the total of Rita and Shova's current ages is 20, they are both 20 years old.
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Write an equation for the relation.
X
У
Find f(50).
1
7.6
The equation is
2
4.6
3
1.6
; f(50) is
4
|-1.4
5
-4.4
3 pts
An equation for the relation is y = -3x + 10.6.
f(50) is -139.4.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At point (1, 7.6), an equation of this line can be calculated by using the point-slope form:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 7.6 = (4.6 - 7.6)/(2 - 1)(x - 1)
y - 7.6 = -3(x - 1)
y = -3x + 3 + 7.6
y = -3x + 10.6
For f(50), we have:
y = -3x + 10.6
y = -3(50) + 10.6
y = -150 + 10.6
y = -139.4
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Help me I dont know the answer
Answer: the length is 6
Step-by-step explanation:
3+3+6+6=18
3x6=18
What the Answer for this Problem
Harry has 90 mosquitoes on his uniform after the loop de loop.
What is Integration?An integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations
To find the number of mosquitoes that splat on Harry's uniform during the loop de loop, we need to integrate the mosquito density function M(x,y,z) over the curve given by the parametrization r(t):
[tex]\int _C\:M\left(x,y,z\right)\:ds\:=\:\int _{t_1}^{t_2}\:M\left(r\left(t\right)\right)\:||r'\left(t\right)||\:dt\:[/tex]
where C is the curve defined by r(t), ||r'(t)|| is the magnitude of the tangent vector to the curve, and ds is the arc length element.
We can compute the tangent vector to the curve as:
[tex]r'\left(t\right)\:=\: < 7,\:3cos\left(t\right),\:-3sin\left(t\right) >[/tex]
The magnitude of the tangent vector is:
[tex]||r'\left(t\right)||\:=\:\sqrt{7^2\:+\:3^2cos^2\left(t\right)\:+\:3^2sin^2\left(t\right)}\:=\:\sqrt{67}[/tex]
Substituting these expressions into the integral, we get:
[tex]\int _C\:M\left(x,y,z\right)\:ds\:=\:\int _0^{5\pi }\:\frac{12+3cos\left(t\right)}{\pi \sqrt{58}}\sqrt{67}\:dt\:[/tex]
[tex]\int _C\:M\left(x,y,z\right)\:ds\:\approx \:89.62[/tex]
Hence, Harry has 90 mosquitoes on his uniform after the loop de loop.
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2(d-3)+5(d+2) = 4(d+6)-11
Given:-
[tex] \sf{2(d-3)+5(d+2) = 4(d+6)-11 }[/tex][tex] \: [/tex]
Solution:-
[tex] \sf{2(d-3)+5(d+2) = 4(d+6)-11 }[/tex][tex] \: [/tex]
[tex] \sf{2d - 6 + 5d + 10 = 4d + 24 - 11}[/tex][tex] \: [/tex]
[tex] \sf{2d + 5d - 4d = 24 - 11 + 6 - 10}[/tex][tex] \: [/tex]
[tex] \sf{7d - 4d = 13+6-10}[/tex][tex] \: [/tex]
[tex] \sf \: 3d = 19-10 [/tex][tex] \: [/tex]
[tex] \sf \: 3d = 9[/tex][tex] \: [/tex]
[tex] \sf \: d = \cancel \frac{9}{3} [/tex][tex] \: [/tex]
[tex] \underline{ \boxed{ \sf{ \color{pink}d = 3}}}[/tex][tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━━
Hope it helps! :)
PLS HELP MEEEEEEEEEEEEEEEEEEEEE YOU WILL GET BRAILESS PLSSSSSSSSSSSSSSSSSSSSSSSS
Answer:whoops it’s b
Answer:
Its A I think
Step-by-step explanation:
Sarai has 39 children. She goes to the hospital and has 39 more. If she keeps having children,how many will she have in 90 days? *Hint:39 x 90*
Answer:
it 39 ×90 for sure it 3510
Look at this series: 12, 11, 13, 12, 14, 13, … What number should come next?
series: 12, 11, 13, 12, 14, 13, … What number should come next? i believe its 12
12-11=1
13-11=2
So to get 11 you subtract 1 from 12 and to get 13 you add 2 to it
If you follow that procedure the next number should be 15 if you add 2 to 13
Quadratic work problems Task 1
Answer:
Step-by-step explanation:
A. h = -2(1)² + 7(1) + 4 = 9 ft
B. use the quadratic formula to find the 2 solutions to t when
y = f(t) = -2t² + 7t + 4 = 0 a=-2, b=7, c=4
the 2 solutions for t are: -1/2, 4
halfway between t=-1/2 and t=4 is: (-1/2 + 4) /2 = 1.75 (vertex of the parabola)
so, at t = 1.75 s, the toy is at its max. height:
h = -2(1.75)² + 7(1.75) + 4 = 10.125 ft
C. Toy is in the air for 4 sec
The answer is 4 s because f(4) = 0, meaning the toy hits the ground after 4 sec
25% of 84 is what value
Answer:
21
Step-by-step explanation:
Answer:
25% of 84 is 21
Step-by-step explanation:
25% can be written as 0.25
0.25 times 84 = 21
Can someone help me please?!
Answer:
Step-by-step explanation:
a. 4x + 8
b. 14x
c. 8x + 12
d. 6x + 6y + 6z
Answer:
Step-by-step explanation:
1]4(x+2)
using distributive property ,
Multiply 4 to x and 2
4x + 8
2]4(2x+3)
using distributive property ,
Multiply 4 to 2x and 3
= 4 x 2x + 4 x 3
= 8x +12
3](6 + 8).x
= (14).x
14x
4] 6(x + y + z)
using distributive property ,
multiply 6 to x and y and z
6.x + 6.y + 6.z
6x + 6y +6z
Simplify the following expression. 8.767 - 0.36
Answer:
8.407
Step-by-step explanation:
8.767−0.36
= 8.767−0.36
=8.767+(−0.36)
= 8.407
A philanthropist pledges to donate 16% of a fund each year. If the fund initially has $708,000.00, how much will the fund have after 10 years?
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &708000\\ r=rate\to 16\%\to \frac{16}{100}\dotfill &0.16\\ t=years\dotfill &10\\ \end{cases} \\\\\\ A = 708000(1 - 0.16)^{10} \implies A=708000(0.84)^{10}\implies A \approx 123830.07[/tex]
Find the value of the variable.
Answer:
Step-by-step explanation:
Help Please help me points and brainliest!!!!
In the U.S, individuals who earn an income in the top 1 percent can be referred to as good earners The percent of top earners who are men, , is more than four and a half times the percent of top earners who are women, . Also the percent of top earners who are men, , is less than five times the percent of top earners who are women, . Write and solve a compound inequality for the top percent of earners who are women:W.
Answer:1.111
Step-by-step explanation:
Let's use the variable W to represent the percent of top earners who are women.
According to the problem statement, the percent of top earners who are men is more than four and a half times the percent of top earners who are women. Mathematically, we can write this as:
M > 4.5W
Additionally, the percent of top earners who are men is less than five times the percent of top earners who are women. This can be written as:
M < 5W
We can combine these two inequalities into a compound inequality:
4.5W < M < 5W
This means that the percent of top earners who are men is between 4.5 times and 5 times the percent of top earners who are women.
To solve for W, we can divide all three parts of the compound inequality by 4.5:
W < M/4.5 < W/0.9
Simplifying, we get:
W < 0.222M < 1.111W
Therefore, the percent of top earners who are women, W, must be less than 0.222 times the percent of top earners who are men, and also less than 1.111 times the percent of top earners who are women.
HELPPP!!!!
Who ever answers right will be marked as brainliest!
Answer:
B I did the math in my head mb if I get wrong
What is a good book?
A good book is one that makes the reader feel. It takes the reader on a compelling journey. .
What is book?A book is a medium for recording information in the form of writing or images, typically composed of many pages bound together and protected by a cover
Given is to understand what are the characteristics of good book.
A good book is one that makes the reader feel. It takes the reader on a compelling journey.
Calling a book “good” is an opinion that can be applied to any book.
Therefore, a good book is one that makes the reader feel. It takes the reader on a compelling journey.
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Eduardo has a recipe that uses 2/3 cup of flour for each bath. if he makes 4 batches, how many cups of flour will he need? How many cups of will he need in total if he makes 3 more batches
Answer: 7 batches
Step-by-step explanation:
If Eduardo makes 4 batches, he will need 2/3 x 4 = 8/3 cups of flour.
To add 3 more batches, he will need 3 x 8/3 = 8 cups of flour.
In total, Eduardo will need 8/3 + 8 = 32/3 + 8 = 32/3 + 24/3 = 56/3 cups of flour for 7 batches. Therefore, Eduardo will need 8 cups of flour if he makes 3 more batches, and he will need 56/3 cups of flour in total if he makes 7 batches.
PLSS ANSWER THIS CORRECTLY
As the x-value increases, the function decreases towards y = 0. Then the correct option is C.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as,
y = a(b)ˣ
The exponential function is given below.
f(x) = (0.4)ˣ
As x tends to positive infinity, then the value of the function is calculated as,
[tex]\rm f(x) = (0.4)^{\infty}\\\\f(x) = 0[/tex]
As the x-value increases, the function decreases towards y = 0. Then the correct option is C.
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Khloe has 53 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 306 square meters. List each set of possible dimensions (length and width) of the field.
Therefore , the solution of the given problem of area comes out to be potential dimensions are thus (19 m, 15 m) and (15 m, 19 m), or (8 m, 37 m), and (37 m, 8 m).
Explain area.Its total size can be determined by how much space is required to completely cover the outside. The nearby surroundings are taken into consideration when calculating the surface of a trapezoidal shape. The total measurements of something are determined by its surface area. The sum of the boundaries for each of a cuboid's six rectangular edges represents its internal water capacity. To calculate the size of the box, use the following method:
Here,
Let's write L for the rectangular plot's length and W for its breadth. Consequently, the rectangle plot's perimeter can be written as:
=> 2L + W = 53
Additionally, since we are aware that the rectangle plot's area is 306, we can write:
=> LW = 306
By resolving the initial solution for W, we can obtain:
=> W = 53 - 2L
When we use this formula as W's substitute in the second equation, we obtain:
=> L(53 - 2L) = 306
Increasing the left edge gives us:
=> 53L - 2L² = 306
Rearranging and condensing results in:
=> 2L² - 53L + 306 = 0
To find L, we can use the cubic formula:
=> L = [53 + √53² - 4(2)(306))] / (2(2))
=> L = [53 ± 25] / 4
=> L = 19 or L = 8
The rectangular plot's two groups of potential dimensions are thus (19 m, 15 m) and (15 m, 19 m), or (8 m, 37 m), and (37 m, 8 m).
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Which one of these pls help
The side AC is 10 units long.
How does one determine length?Measurement of length can be done in a variety of methods, including using handspan, foot span, metres, or other units including millimetres, inches, and metres. There are two types of length measurement units: There are both conventional and nonstandard length measurement units.
The Pythagorean theorem can be used to determine the length of side AC in the triangle ABC given:
AC² = AB² + BC²
AC² = 6² + 8²
AC² = 36 + 64
AC² = 100
AC = 10
As a result, the side AC is 10 units long.
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