If Alice tests positive and the experts are right on the population prevalence, the probability that Alice has the disease is 0.489.
In the given question, a new disease has been observed, and experts believe that 1% of the population have it.
A test is developed that has 95% true positive rate and 1% false positive rate.
From the given data,
Let E be the event that a patient has a disease and F be the event that a patient has tested positive.
Then according to Bayes' theorem we have,
P(E/F) = P(E)P(E/F)}/(P(E)P(E/F)+P(E')P(F/E')
P(E/F) = (1*95)/(1*95)*(99*1)
P(E/F) = 95/194
P(E/F) = 0.489 (approx.)
Hence, the probability that Alice has the disease 0.489.
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Match the following factored-form quadratics with their equivalent standard form
The factored quadratic functions with their equivalent standard form are given as follows:
1. e -> x² - 3x - 10 = (x - 5)(x + 2)
2. a -> x² + 7x - 10 = (x + 5)(x + 2).
3. c -> x² - 7x + 10 = (x - 5)(x - 2).
4. d -> x² - 2x - 63 = (x - 9)(x + 7)
5. f -> x² + 2x - 63 = (x + 9)(x - 7).
6. b -> x² + 16x + 63 = (x + 7)(x + 9).
How to factor a quadratic function?A quadratic function is defined as follows:
y = ax² + bx + c.
A quadratic function can be factored as a function of it's roots x* and x**, as follows:
y = a(x - x*)(x - x**).
For item a, the function is given as follows:
y = x² + 7x + 10.
The coefficients are given as follows:
a = 1, b = 7, c = +10.
The discriminant is of:
D = 7² - 4(1)(10)
D = 49 - 40
D = 9.
Hence the first root is of:
x = (-7 - square root of 9)/2
x = -5.
The second root is of:
x = (-7 + square root of 9)/2
x = -2.
Meaning that the factored expression is given as follows:
y = (x + 5)(x - 2).
Matched with the second expression of column A.
The same procedure is followed for the remaining quadratic functions.
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Find the equation of the line that passes through (1,3) and is perpendicular to y=1−2x. Leave your answer in the form y=mx+c
Answer:
The equation of the line that passes through (1,3) and is perpendicular to y=1−2x is y=1/2x+5/2
Step-by-step explanation:
We can rewrite the original equation as y=-2x+1
To find an equation's perpendicular slope, you take the reciprocal of it and negate it, therefore the perpendicular slope is -2 -> 1/-2 -> 1/2
So far, we have y=1/2x+b, but to find the y-intercept, b, we would need to plug in (1,3) and solve for b:
y=1/2x+b
3=1/2(1)+b
3=1/2+b
5/2=b
Therefore, your final equation is y=1/2x+5/2
y^2=1/5(x-4), (24,2)
⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ a(1)=20 a(n)=a(n−1)−17 third term
The third term of the arithmetic sequence will be negative 14.
What is an arithmetic sequence?A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.
Let a₁ be the first term and d be a common difference.
Then the nth term of the arithmetic sequence is given as,
aₙ = a₁ + (n - 1)d
The first term is 20 and the common difference is calculated as,
aₙ = aₙ₋₁ - 17
aₙ - aₙ₋₁ = - 17
d = - 17
Then the third term is calculated as,
a₃ = 20 + (3 - 1) (-17)
a₃ = 20 + 2 (-17)
a₃ = 20 - 34
a₃ = - 14
The third term of the arithmetic sequence will be negative 14.
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Dominic invested $93,000 in an account paying an interest rate of 6. 8% compounded monthly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $202,800?
The standard deviation equation ( 1 + 6.8)% × 93000 > 202800
What is standard deviation?
Your dataset's standard deviation serves as a gauge of its degree of variability. It displays the typical difference between each outcome and the mean.
While a high standard deviation indicates that values are frequently distant from the mean, a low standard deviation indicates that values are typically grouped close to the mean.
( 1 + 6.8)% × 93000
= 202800
Then we get n ≈ 12,
the equation ( 1 + 6.8)% × 93000 > 202800
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Solve for x: 0.4x - 3 = 1.4
Answer: x = 11
Step-by-step explanation:
First, add 3 to both sides
0.4x - 3 = 1.4
+3 +3
0.4x = 4.4
Then, divide each side by 0.4 to isolate x
x = 11
Please help- thank you!!
Answer: u = -3
Step-by-step explanation:
To solve the equation, we will isolate the u variable by simplifying and using inverse operations.
Given:
4(3u + 5) = 2(2u - 2)
Distribute the 4 and the 2:
12y + 20 = 4u - 4
Subtract 20 from both sides of the equation:
12y = 4u - 24
Subtract 4u from both sides of the equation:
8u = -24
Divide both sides of the equation by 8:
u = -3
WAT IS GOOGOLPLEX PLZ HLP
Answer:
number
equivalent to ten raised to the power of a googol.
Step-by-step explanation:
A googolplex is the number 10, or equivalently, 10. Written out in ordinary decimal notation, it is 1 followed by 10¹⁰⁰ zeroes; that is, a 1 followed by a googol zeroes
please no links or anything but the correct answer!
Answer:
sinD ≈ 0.44
Step-by-step explanation:
sinD = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{CE}{CD}[/tex] = [tex]\frac{39}{89}[/tex] ≈ 0.44 ( to the nearest hundredth )
"Jose wants to put wall-to-wall carpeting in a rectangular room that measures 11 feet by 12 feet. The carpet costs $4.12 per square foot. How much will it cost for Jose to buy the carpet for the room? Write your answer in the box. you may use the sketch area to draw a diagram or show where, if you would like!"
links will be reported
Answer:
$543.84
Step-by-step explanation:
Find the area of the room:
11*12 = 132ft^2
Multiply the area by the cost per square foot:
132*4.12 = 543.84 dollars
99 Divided by 2=48 r1 is that true or faulse
Answer:
Yes, the answer is 'True'
Write 1 and 6/7 as an improper fraction.
Answer:
13/7
Step-by-step explanation: YW :)
Answer:
[tex] \frac{13}{7} [/tex]
Step-by-step explanation:
7×1+6/7
13/7
plz mark as brainliest
Estimate how many times larger 1.9 • 10^-8 is than 4.2 • 10^-13
Answer:
Step-by-step explanation:
a.[tex]1.9[/tex]·[tex]10^{-8}[/tex]=190000·[tex]10^{-13}[/tex]
b.so 190000÷4.2=4523
c.finally, about 4523 times
hola me pueden ayudar es para hoy pliss doy coronita ✨
Answer:
Step-by-step explanation:
A. 62
B. 58
C. -19
13yd 2ft 6in x 15 =
i need to know the answer to this problem
Using the unit conversion and converting all the distance units to inches, The final answer is 7575 inches.
What do you mean by unit conversion?Divide the smaller unit's value by the quantity of smaller units required to create the larger unit. Multiply to change from a larger to a smaller unit. Divide to change from a smaller unit to a larger one. We need to convert between units in order to ensure accuracy and prevent measurement misinterpretation. For example, we do not measure a pencil's length in kilometers. In this situation, one must convert from kilometers (km) to centimeters (cm).
What do you mean by equations?An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A collection of one or more linear equations containing the same variables is known as a system of linear equations in mathematics.
13 yard = 468inches
2ft = 24 inches
total 268+24+13 = 505inches
505*15 = 7575 inches
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Please help me literally need this to be answered in 2 hours P-L-E-A-S-E !!
Answer:
Yeah with that type of problem
Step-by-step explanation:
You aint getting answered for the next 4 hours <3
#11 Please answer the question
Answer:
Step-by-step explanation:
The two given angles are called remote interior angles. They share 1 line with each other and each of them shares the other line making them up with the remote exterior angle (x)
x is the sum of the two interior angles
x = 88 + 46
x = 134
Solve for c.
c2−9 = b2
what is the area of 3 2/3 X 2
Answer:
7.33333333333
Step-by-step explanation:
this was easy i did it in my head
Someone please help with this! I’ll give brainliest.
With full working
Answer:
k = -2
Step-by-step explanation:
The value of k is -2
cuz the point D is marked at (1,-2)
Question 9(Multiple Choice Worth 1 points)
(05.06 LC)
The net of a solid figure is shown below:
Four squares are shown side by side in a row. The second square has a square above it and a square below it. All the squares have side length equal to 4 inches
Which calculation will give the total surface area of the solid figure?
6 ⋅ 4 ⋅ 4 square inches
4 ⋅ 6 ⋅ 6 square inches
6 ⋅ 4 ⋅ 4 ⋅ 4 square inches
4 ⋅ 6 ⋅ 6 ⋅ 6 square inches
PLEASE HELP
you can use a calculator to try and multiply all of them so multiply 6x4 and then it will give you the answer then once you have that answer multiply it with the 4 im pretty sure but if not then sorry
You spin the spinner once what is p (even)
Answer:
???
Step-by-step explanation:
inadequate info a pic is needed :)
Answer:
50%
Step-by-step explanation:
real answer
Solve for x. Assume that lines which appear tangent
Answer:
Step-by-step explanation:
Join line EG with a straight edge.
Put a point in the middle of the circle.
Call it O.
GO and EO form a central angle.
GOE = 120 degrees
Any point on the circumference of a circle that is on the same side of EG as the peak of the central angle = 1/2 the central angle. It's much easier to do this with an example
Arc EOG = 120 degrees. The Central angle = the arc.
EFG = 1/2 EOG
EFG = 1/2 120
EFG = 60
11x + 5 = 60 Given
-5 -5 Subtract 5 from both sides.
11x = 55 Divide by 11
x = 55/11
x = 5
Which of the following best describes the figure with vertices (1, -4), (-2, 1), (3, 4) and (5, 2)?
Answer fast pls
Square
Parallelogram
Quadrilateral
Rectangle
Answer choices
The best description of the figure with the vertices given is, C. Quadrilateral
How to find the figure ?The figure given is a Quadrilateral firstly because it has 4 vertices and therefore 4 points. A Quadrilateral has four points as well which means this figure is a Quadrilateral.
The figure is not a Parallelogram because no two values of y are the same. A Parallelogram would have two points that have the same y value as there would be parallel lines involved.
To find out if the shape is a rectangle or square, find the lengths of the vertices using a distance calculator.
The length of (1, -4), and (-2, 1) is:
= 5.83 units
The length of (-2, 1), and (3, 4) is:
= 5.83 units
The length of (5, 2) and (3, 4) is:
= 2.82 units
The length of (5, 2) and (1, -4 ) is:
= 7.21 units
The shape is neither a square nor a rectangle so it is a quadrilateral.
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The point N(-2,-3) is rotated 270° clockwise about the origin. What are the coordinates of N'?
A. (-3,-2)
B. (-3,2)
C. (3,-2)
The coordinate of N' is (2, -3)
Now, According to the question:
We have the point n (-2, -3) and we need to rotate it 270 degrees clockwise about the origin.
When rotating 270 clockwise about the origin you switch the x and y coordinate and use the opposite sign of the original y coordinate.
A(x, y) becomes A' (-y, x)
This means that point N becomes:
N (-2, -3) => N'(-(-2), (-3))
=> N'(2,- 3)
Hence, The coordinate of N' is (2, -3)
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Professor Curie is using the radioactive isotope Francium-223 in her research. This
isotope has a half-life of 22 minutes, which means that every 22 minutes the sample has
half the radioactivity it did in the previous interval. If Professor Curie has 15 grams of
Francium-223, which explicit formula describes how the isotope decays?
This formula describes how the amount of Francium-223 (N(t)) decays over time (t). The initial amount of Francium-223 is 15 grams, and each 22 minutes the amount is halved.
Step 1: Start with the formula
N(t) = 15 * (1/2)^(t/22).
Step 2: Substitute the value for N(t). For example, if you want to find the amount of Francium-223 after 44 minutes,
N(44) = 15 * (1/2)^(44/22).
Step 3: Calculate the fraction (1/2)^(44/22). This is equal to (1/2)^2, or 1/4.
Step 4: Multiply the initial amount of Francium-223 (15) by the fraction (1/4). The result is
15 * (1/4) = 3.75 grams.
The formula N(t) = 15 * (1/2)^(t/22) describes how the amount of Francium-223 (N(t)) decays over time (t). The initial amount of Francium-223 is 15 grams, and each 22 minutes the amount is halved. To calculate the amount of Francium-223 after a certain time, substitute the value for N(t). Then calculate the fraction (1/2)^(t/22) and multiply it by the initial amount of Francium-223 (15). The result is the amount of Francium-223 after the specified time. For example, after 44 minutes, the amount of Francium-223 is 15 * (1/4) = 3.75 grams.
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What is the nth term rule of the linear sequence below?
6, 13, 20, 27, 34, . . .
Answer:
7n - 1
Step-by-step explanation:
notice that the difference between adjacent terms is 7.
so nth term is given by:
nth term = first term + (n-1)×difference (n is any number)
= 6 + (n-1)7
= 6+ 7n -7
= 7n - 1
hope this helps :-))
the cost per box!! please help (will mark first answer as brainliest!)
Answer:
$1.20
Step-by-step explanation:
Just divide $3.60 by 3. If that's the price of 3 boxes, dividing it by 3 will estimate it to how much 1 box will cost.
Answer:
$1.20 per box
Step-by-step explanation:
Hope this helps :)
How doe etimation help you place the decimal point in a product correctly?Explain
By counting the numbers of figures after the decimal points before you locate the product and shifting the decimal point from the rear to the front in the order you previously counted it after you find the product, an estimation can help you place the decimal point in a product correctly.
What is Estimation?A high number of a certain number is estimated to be the closest whole number or significant number.
When estimating, the use of decimal points aids in separating the fractional portion from the entire figure.
For instance, we have a total of three integers after the decimal point if we want to calculate the product of 4.23 and 2.1.
4.23
× 2.1
4 2 3
________
8 4 6
8 8 8 3
Therefore, we shall move the decimal point three places, working our way from the back to the front.
The result of 4.23 and 2.1 is 8.883 then.
We can therefore say that we completely understand how estimating helps you accurately set the decimal point in a product.
Therefore, by counting the numbers of figures after the decimal points before you locate the product and shifting the decimal point from the rear to the front in the order you previously counted it after you find the product, an estimation can help you place the decimal point in a product correctly.
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Correct question:
How does estimation help you place the decimal Point in a product correctly?
In the 2-man bobsled competiton in the olympics, the gold medalists were about 0.2 seconds faster than the silver medalists, and the silver medalists were about 0.14 seconds faster than the bronze medalists. Which gap in time was larger? By how much?
The difference in timing was greater since the silver medalists finished around 0.14 seconds ahead of the bronze medalists.
what is unitary method ?The unit technique is a strategy for addressing issues that entails first figuring out the value of a specific unit, then dividing that value to figure out the needed value. Simply put, the unit method is employed to derive a single system value from a multiple that is supplied. For example, 40 pens might cost 400 rupees, which is equal to the cost of one pen. This procedure could follow a regular procedure. a single nation. anything has a distinct identity. Its adjoint and reciprocal are equal in terms of mathematics, algebra, linear algebra, computational equations, or algebra of matrices or operators.
given
time separation of gold medalists by silver medalists is equal to 0.14 minus 0.2, or 0.11.
The difference in timing was greater since the silver medalists finished around 0.14 seconds ahead of the bronze medalists.
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