Shown is a circle with centre O. ABC is a straight line. Angle CBD is 146 degrees
Find the size of angle AOD.
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Related Questions
Disk drives have been getting larger. Their capacity is now often given in terabytes (TB) where 1 TB = 1000 gigabytes, or about a trillion bytes. A survey of prices for external disk drives found the data shown in chart. For this data, we want to predict Price from Capacity. A). Find the slope estimate b1. _________B). Find the intercept b0. ___________C). Write equation that predicts Price from Capacity - price= ______ + (_____) capacityD). What would you predict price of a 20.0 TB disk? _______
Answers
To compute the slope, intercept, and equation to predict the Price, we will use the formulae below:
For the equation
\(\bar{y}=b(\bar{x})+a\)For the slope
\(b=r(\frac{S_y}{S_x})\)For the intercept
\(a=\bar{y}-b\bar{x}\)In this case, we have the following data given:
\(\begin{gathered} \bar{x}=7.611,S_x=9.85,r=0.987 \\ \bar{y}=784.173,S_y=1419.89 \end{gathered}\)Part A
Upon substituting the above into the formula, we will have
\(b=0.987(\frac{1419.89}{9.85})=141.41\)Hence slope = 141.41
Part B
\(\begin{gathered} a=\bar{y}-\bar{bx} \\ a=784.173-141.41(7.611) \\ a=-292.099 \end{gathered}\)Hence, Intercept =-292.099
PART C
The equation that can be used to predict Price from Capacity
\(\begin{gathered} \text{Price}=\text{intercept}+(\text{slope)capacity} \\ \text{Price}=-292.099+(141.41)\text{capacity} \end{gathered}\)Therefore, the equation is
Price=-292.099+(141.41)capacity
Part D
To predict the price of a 20.0TB disk, we will simply set the capacity= to 20 and then simplify
\(\begin{gathered} P_{20TB}=-292.099+141.41(20) \\ P_{20TB}=2536.10 \end{gathered}\)Hence, the predicted price is=2536.10
true/false. A large container is full of ball bearings with mean diameter 2.5003 centimeters (cm). This is within the specifications for acceptance of the container by the purchaser. By chance, an inspector chooses 100 bearings from the container that have mean diameter 2.5009 cm. Because this is outside the specified limits, the container is mistakenly rejected.
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The answer is False because It is possible that the true mean diameter of all the bearings in the container is still within the specified limits, even though the sample mean of 100 bearings is outside the specified limits
The statement that "an inspector chooses 100 bearings from the container that have mean diameter 2.5009 cm. Because this is outside the specified limits, the container is mistakenly rejected" is not accurate. The mean diameter of 2.5009 cm is calculated from a sample of 100 bearings, and it is only an estimate of the true mean diameter of all the bearings in the container. It is possible that the true mean diameter of all the bearings in the container is still within the specified limits, even though the sample mean of 100 bearings is outside the specified limits.
In order to make a decision about whether to reject or accept the container, the inspector should use statistical techniques that take into account the sample size and the level of precision required.
It's also important to note that the tolerance of 0.0006 cm is a very small margin, and it's likely that the manufacturing process can't achieve such a precision. The inspector should consider if the sample size and the precision required are aligned with the manufacturing process.
Therefore, The answer is False because It is possible that the true mean diameter of all the bearings in the container is still within the specified limits, even though the sample mean of 100 bearings is outside the specified limits.
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Impliment the function Indy4Vec that takes in four 3 dimentional vectors each represented as an array and tells whether they are linearly independent. Hint: This is a bit of a trick question.
v1=np.array([-1,3,4])
v2=np.array([6,-2,9])
v3=np.array([3,8,5])
v4=np.array([5,6,7])
assert Indy4Vec(v1, v2, v3, v4) == False, "Problem 1.3, Your code said that four linearly dependent vectors were independent"
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The output will be False as expected since the function always returns False for any input vectors.
To implement the function Indy4Vec that checks whether four 3-dimensional vectors are linearly independent, you can use the concept that four vectors in a three-dimensional space are always linearly dependent. Therefore, the function should always return False. Here's the implementation in Python:
def Indy4Vec(v1, v2, v3, v4):
return False
This implementation simply returns False regardless of the input vectors, as it is guaranteed that four vectors in a three-dimensional space are linearly dependent. The assertion provided in the question confirms that the function should return False when tested with the given vectors.
You can use the function as follows:
v1 = np.array([-1, 3, 4])
v2 = np.array([6, -2, 9])
v3 = np.array([3, 8, 5])
v4 = np.array([5, 6, 7])
result = Indy4Vec(v1, v2, v3, v4)
print(result) # Output: False
The output will be False as expected since the function always returns False for any input vectors.
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- 2 (k+ 3) > - 2k - 7
Answers
Answer:
-2 (k+3) > -2k -7 --> -2k-6 > -2k-7
+2k +2k
-6 > -7 = No Solution
Step-by-step explanation:
A triangle has side lengths of (7.4b + 6.3c) centimeters, (1.1b + 8.7d) centimeters, and (3.5d + 2.1c) centimeters. Which expression represents the perimeter, in centimeters, of the triangle? 17.1cd + 12bd 5.6d + 150 + 8.5b Submit Answer 9.8bd + 13.7bc + 5.6cd 12.2d + 8.5b + 8.40
Answers
Answer:
This might help you.....
Graph DEF and its image when you translate DEF using vector
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Answer:
The image coordinates are D'(8, 5), E'(12, 3) and F'(10,0)
Step-by-step explanation:
Given the vertices of △ DEF are D (2, 5), E (6, 3), and F (4, 0). We have to translate the triangle using the vector (6, 0)
Now, translation by vector (6, 0)
D (2, 5)=D'(2+6, 5+0)=D'(8, 5)
E (6, 3)=E'(6+6, 3+0)=E'(12, 3)
F (4, 0)=F'(4+6, 0+0)=F'(10,0)
Now, we have to label the coordinate of the triangle or to get image of triangle after translation.
Hence, The image coordinates are D'(8, 5), E'(12, 3) and F'(10,0)
Step-by-step explanation:
Solve there Systems of equations. Step - by - Step 2x + y = 15
3x - y = 5
Answers
Answer:
2x+y=15, 6x+3y=45
3x-y=5, 6x-2y=10
Y=35, plug it in, x=-10
Step-by-step explanation:
Get some pointsss :)
Answers
\(2 + \frac{19}{30} = \frac{60 + 19}{30} = \frac{79}{30} \)
Answer:\( \frac{79}{30} = 2 \frac{19}{30} \)
Answer:
79/30
Step-by-step explanation:
the whole number is 60/30. If we add that to the already existing 19/30 we get 79/30.
please help me lol.
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which of the following is equivalent to this expression? 6*6^2*6^2
a) 6^6
b) 6^3
c) 6^4
d) 6^5
Answers
Choice D ) 6^5
Explanation :
They both equal to 7776
find the derivative of the function. _2. f(x)=x’arctan 5x _3. y = arctan x + 1+ sin x 4. Find the indefinite integral: S dx 2x-5 Find the indefinite integral by completing the square: 2x dx
Answers
1. To find the derivative of the given function, f(x) = x’ arc tan 5x, we use the product rule of differentiation given as:(f(x)g(x))' = f(x)g'(x) + f'(x)g(x)Here, f(x) = x', and g(x) = arctan 5x.
We can find the derivative of the given function using the above formula. Thus, f(x)g(x) = x' arc tan 5x, and f'(x) = 1.
Also, g'(x) = 5/(1 + 25x²). Hence, the derivative of the given function is given as: (x' arc tan 5x)'
= f(x)g'(x) + f'(x)g(x)
= arctan 5x + 5x'/(1 + 25x²).
2. To find the derivative of the given function,
y = arctan x + 1+ sin x,
we use the sum and product rule of differentiation. Thus, the derivative of the given function is given as:
dy/dx = d/dx(arctan x) + d/dx(1) + d/dx(sin x)
Here, d/dx(arctan x)
= 1/(1 + x²), d/dx(1)
= 0, and d/dx(sin x)
= cos x. Thus, we get,dy/dx = 1/(1 + x²) + 0 + cos x = cos x/(1 + x²) + 1/(1 + x²).
3. To find the indefinite integral of the given function, S dx/(2x-5), we can use the method of partial fractions.
First, we factorize the denominator of the given function as (2x - 5)
= 2(x - 5/2).
Thus, the given function can be written as:
S dx/(2x-5)
= A/(x - 5/2), where A is a constant to be determined. Multiplying both sides by (x - 5/2), we get:
S = A(x - 5/2) dx/(x - 5/2)
= A dx. Integrating both sides, we get:
S = A ln|x - 5/2| + C,
where C is the constant of integration. Hence, the indefinite integral of the given function is given as:
S dx/(2x-5)
= ln |x - 5/2|/2 + C.
4. To find the indefinite integral of the given function, S 2x dx/(2x² - 8x + 8),
we can use the method of completing the square.
First, we complete the square of the denominator as:
2x² - 8x + 8
= 2(x² - 4x + 4 - 4 + 8)
= 2(x - 2)² + 4.
Thus, the given function can be written as:
S 2x dx/(2x² - 8x + 8)
= S 2x dx/[2(x - 2)² + 4].
Now, we substitute x - 2
= 2tan(t) to get:
S 2x dx/[2(x - 2)² + 4]
= S 2(2tan(t) + 2) sec²(t) dt/[(2tan(t) + 2)² + 4]
= S [2(1 + tan²(t))] dt/[2(tan(t) + 1)²]
= S dt/tan²(t)
= - cot(t) + C.
Hence, the indefinite integral of the given function is given as:
S 2x dx/(2x² - 8x + 8)
= -cot(t) + C
= -cot(arctan(x - 2)) + C
= -x/(x - 2) + C.
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In ΔNOP, the measure of ∠P=90°, NP = 35, ON = 37, and PO = 12. What ratio represents the sine of ∠N?
Answers
Answer:
12/37
Step-by-step explanation:
SOH - CAH - TOA
O = opposite
A = adjacent
H = hypotenuse
Sin = O/H
Sin N = 12/37
Answer:Find sin N
sinN=
hypotenuse/opposite
12/37
Step-by-step explanation:
The mean distance of the earth from the sun (let's call it d) is 93 million miles. The distance varies as much as 1.6 million miles. Write the equation that describes the possible distances of the earth from the sun, using as distance unit millions of miles.
Use d as the variable
(this is copy-pasted from the textbook)
Answers
Answer:
The equation that can be used to describe the possible distances of the Earth from the Sun, with the distances given in million of miles is;
d = 93 ± 1.6
Step-by-step explanation:
The parameters given are;
The mean distance of the Earth from the Sun, d = 93 million
The amount by which the distance varies = 1.6 million
Therefore, the equation that can be used to describe the possible distances of the Earth from the Sun, with the distances given in million of miles is given as follows;
d = 93 ± 1.6
Therefore, the range of values for the distance of the Earth from the Sun can be presented as follows;
93 - 1.6 ≤ d ≤ 93 + 106
Which gives
91.4 ≤ d ≤ 94.6
Please someone tell me the answer of these questions
Answers
Answer:
VERTICALLY OPP ANGLES
Step-by-step explanation:
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why would your weight be less on the moon than on earth even though your mass would not change.
Answers
The weight is less on the moon than on the Earth due to the force of gravity being less on the moon.
What is weight and what factors affect it?Weight can be defined as the force with which the center of the Earth, or even the center of a satellite planet such as Earth attracts a body towards its center. This is determined by:
The mass, which is constantThe force of gravity, which changes according to the planet.This makes your weight to be less in the moon as the force of gravity there is also less.
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The probability that a health nurse will find a client at home on a particular day is 0.7. what is the probability that on two home visits made by the nurse in a day, she will find each client at home?
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The probability that the nurse will find the two patients is P = 0.49.
How to find the probability?
We know that the probability that the nurse finds the client on a particular day is 0.7
So, each time that the nurse goes that a home, that probability is the same and is independent of what happened before.
So if the nurse goes to two houses, the probability that she will find the client on the first home is 0.7
And the probability that she will find the client on the second home is 0.7
Then the joint probability (the product of the two individual ones) is:
P = 0.7*0.7 = 0.49
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The function can be used to determine one leg length, b, of a right triangle given the other leg length, a. The function can be used to find the area of a right triangle. Which statements are true? Check all that apply. The function is one way to compose the functions. The function is one way to compose the functions. g(b(a)) can be used to find the area of the triangle based on side length a. b(g(a)) can be used to find the area of the triangle based on side length a. g(b(a)) can be used to find side length a given the area of the triangle. b(g(a)) can be used to find side length a given the area of the triangle.
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Both g(b(a)) and b(g(a)) can be utilized to find the area of the triangle when one side length is known. However, neither g(b(a)) nor b(g(a)) can be used to find the side length a given the area of the triangle.
We are given a function that can be used to determine one leg length, b, of a right triangle given the other leg length, a, as well as find the area of a right triangle. We are asked to determine which statements are true. Firstly, it is important to note that we are only dealing with one function, not multiple functions. Therefore, the statement "The function is one way to compose the functions" is not applicable and is not true. Moving on to the other statements, we see that g(b(a)) can be used to find the area of the triangle based on side length a. This is true because the function can find the length of one leg (b) and then use that length along with the given length of the other leg (a) to calculate the area of the triangle.
We have b(g(a)) can be used to find the area of the triangle based on side length a. This statement is not true because the function g(a) does not give us the length of the other leg of the triangle, which is needed to calculate the area. Lastly, g(b(a)) can be used to find side length a given the area of the triangle and b(g(a)) can be used to find side length a given the area of the triangle. These statements are not true because the function only allows us to find the length of one leg, not the length of both legs simultaneously.
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Answer:
a and c
Step-by-step explanation:
Formula One race cars can reach speeds of approximately 100 meters per second. What is this speed in meters per minute? 0. 6 meters per minute 1. ModifyingAbove 6 with Bar meters per minute 600 meters per minute 6,000 meters per minute.
Answers
Answer:
1.6667 meters per minute
Step-by-step explanation:
To convert meters per second into meters per minute, let's first think about the difference between seconds and minutes.
There are 60 seconds in one minute, so to find our meters per minute speed, we will divide the distance by 60.
100 / 60 = 1.6667 meters per minute
Hope this helped!
Answer:
it is d my guy :)
Step-by-step explanation:
What value of x does not satisfy the equation sin 2x + sinx = 0? (a) 7/2 (b) 3/2 (c) 271 (d) 3 (e) All Satisfy What value of x does not satisfy the equation sin x + sin x = 0 ? (a) 7/2 (b) 31/2 (c) (d) 2 (e) All Satisfy
Answers
For the first equation, the value of x that does not satisfy the equation sin 2x + sin x = 0 is (c) 271.
For the second equation, all values of x satisfy the equation sin x + sin x = 0, and the answer is (e) All Satisfy.
How to find the value of x?For the first equation of Trigonometry, sin 2x + sin x = 0, we can use the identity sin 2x = 2 sin x cos x to rewrite it as:
2 sin x cos x + sin x = 0
Factoring out sin x, we get:
sin x (2 cos x + 1) = 0
So the equation is satisfied when sin x = 0 or 2 cos x + 1 = 0. Solving the second equation for cos x, we get:
2 cos x = -1
cos x = -1/2
So the equation is satisfied when sin x = 0 or cos x = -1/2.
The values of x that satisfy these conditions are x = nπ (where n is an integer) and x = (2n+1)π/3 (where n is an integer).
Therefore, the value of x that does not satisfy the equation sin 2x + sin x = 0 is (c) 271.
For the second equation, sin x + sin x = 0, we can simplify it to:
2 sin x = 0
This equation is satisfied when sin x = 0, which occurs at x = nπ (where n is an integer).
Therefore, all values of x satisfy the equation sin x + sin x = 0, and the answer is (e) All Satisfy.
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MATH PROBLEM!! PLEASE HELP!!
Explain your answer please
Answers
========================================
Work Shown:
Use law of cosines to find angle B
b^2 = a^2 + c^2 - 2*a*c*cos(B)
9^2 = 6^2 + 12^2 - 2*6*12*cos(B)
81 = 36 + 144 - 144*cos(B)
81 = 180 - 144*cos(B)
81 - 180 = -144*cos(B)
-99 = -144*cos(B)
-144*cos(B) = -99
cos(B) = (-99)/(-144)
cos(B) = 0.6875
B = arccos(0.6875)
B = 46.5674634422102
B = 47 when rounding to the nearest whole number
Make sure your calculator is in degree mode.
arccos is the same as inverse cosine often labeled \(\cos^{-1}\) on calculators.
I need help with my homework please it’s 3 parts to this question I will post the rest into the answer tab
Answers
Since there are a adults and c children
Since there are 187 tickets sold
Then the number of adults and children is 187
Add a and c, then equate the sum by 187
\(a+c=187\rightarrow(1)\)Since the price of each adult's ticket is $25
Since the price of each child ticket is $13
Since the total revenue is $3223
Then multiply a by 25, c by 13, then add the products and equate the sum by $3223
\(25a+13c=3223\rightarrow(2)\)Now, we have a system of equations to solve it
Multiply equation (1) by -13 to make c equal in values and opposite in signs to eliminate it
\(\begin{gathered} -13(a)+-13(c)=-13(187) \\ -13a-13c=-2431\rightarrow(3) \end{gathered}\)Add equations (2) and (3)
\(\begin{gathered} (25a-13a)+(13c-13c)=(3223-2431) \\ 12a=792 \end{gathered}\)Divide both sides by 12
\(\begin{gathered} \frac{12a}{12}=\frac{792}{12} \\ a=66 \end{gathered}\)Substitute a by 66 in equation (1) to find c
\(66+c=187\)Subtract 66 from both sides
\(\begin{gathered} 66-66+c=187-66 \\ c=121 \end{gathered}\)The answers are:
a) The system of equations is
\(\begin{gathered} a+c=187 \\ 25a+13c=3223 \end{gathered}\)b) There were 66 adult tickets sold
c) There were 121 children's tickets sold
Can anyone help? Last day of school today and I'm getting all my assignments done.
Answers
Help me with this!!!
Answers
300. Because the distance is still 100 in between.
i need help on figuring this out and the answer plz!!
Answers
Answer:
$76
Step-by-step explanation:
The amount changed is the total amount of the whole entire thing.
Therefore, we use absolute value or simply find the difference.
21 - (-55) = 76
So the bank account changed $76 over the 2 days.
Given f(x)=2x^2-3x+1, determine the value of 3f(-2x)
Answers
Answer:
Step-by-step explanation:
3f(-2x)= 3[2(-2x)^2-3(-2x)+1]
=3[2(4x^2)+6x+1]
=3[8x^2+6x+1]
=24x^2+18x+3
For the following, Let Ln denote the left-endpoint sum using n subintervals. Compute the indicated left sum for the given function on the indicated interval. (Round your answer to four decimal places.): L4 for f(x)=1/x−1 on [3,4] L4= L6 for f(x)=1/x(x−1) on [2,5].
Answers
We need to calculate the indicated left sum for the given function on the indicated interval for the given value of L4 and L6.1. For \(f(x) = \frac{1}{x} - 1\) on [3,4] L4 We need to calculate L4, where Ln denotes the left-end point add using n sub intervals.
\(L_4 = \sum_{i=1}^3 \left( \frac{1}{x_1 - i \Delta x} - 1 \right) \Delta x\)
where \(\Delta x = \frac{b - a}{n} = \frac{4 - 3}{4} = \frac{1}{4}\)
Then we have f(x) evaluated at x = 3, 3+Δx, 3+2Δx and 3+3Δx, so we get:
\(\xi^3 + \Delta x^3 + 2 \Delta x^3 + 3 \Delta x f(\xi) \left( \frac{1}{\xi} - 1 \right) \\\\= \frac{1}{3} f(\xi) \left( \frac{1}{\xi} - 1 \right) - \frac{11}{4} = -0.3875\)
Therefore, the value of L4 for f(x)=1/x-1 on [3,4] is -0.3875 (rounded to 4 decimal places).
2. L6 for f(x)=1/x(x−1) on [2,5] Now, we need to find L6 for \(f(x) = \frac{1}{x} - 1\) on [2,5]. Ln denotes the left-end point sum using n sub intervals.
\(L_6 = \sum_{i=1}^6 \left( \frac{1}{x_i - i \Delta x} - 1 \right) \Delta x\)
where Δx=b−a/n=5−2/6=1/2
Then we have f(x) evaluated at x = 2, 2+Δx, 2+2Δx, 2+3Δx, 2+4Δx, and 2+5Δx,
so we get :
\(\xi^2 + \Delta x^2 + 2 \Delta x^2 + 3 \Delta x^2 + 4 \Delta x^2 + 5 \Delta x^2 f(\xi) \left( \frac{1}{\xi} (1 - \xi) \right) \\\\= \frac{1}{6} f(\xi) \left( \frac{1}{\xi} (1 - \xi) \right) = 0.625\)
Therefore, the value of L6 for \(f(x) = \frac{1}{x} - 1\) on [2,5] is 0.625 (rounded to 4 decimal places).
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the r command for calculating the critical value of the distribution with 7 degrees of freedom is "qt(0.95, 7).". True/False
Answers
True. The r command "qt(0.95, 7)" calculates the critical value of the distribution with 7 degrees of freedom at a significance level of 0.05 and a two-tailed test. The "qt" function in R is used to find the critical value of a t-distribution for a given probability and degrees of freedom.
In this case, the command returns the critical value of the t-distribution with 7 degrees of freedom at a significance level of 0.05, which can be used to perform hypothesis testing or confidence interval calculations. It is important to note that the critical values of the t-distribution change as the degrees of freedom change, and different significance levels require different critical values. Answering in more than 100 words, it is necessary to understand the concept of degrees of freedom in statistics. Degrees of freedom represent the number of independent observations that are available for estimation in a statistical model. The number of degrees of freedom depends on the sample size, the number of parameters being estimated, and any constraints on the model. In general, more degrees of freedom lead to greater precision in estimates and narrower confidence intervals.
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A sequence can be generated by using fn = 2f(n-1)+1, where f1 = 4 and n is a whole number greater than 1. What are the first four terms in the sequence?
Answers
Answer:
{9,19,39,79}
Step-by-step explanation:
Recursive Sequences
The recursive sequence can be identified because each term is given as a function of one or more of the previous terms. Being n an integer greater than 1, then:
f(n) = 2f(n-1)+1
f(1) = 4
To find the first four terms of the sequence, we set n to the values {2,3,4,5}
For n=2f(2) = 2f(1)+1
Since f(1)=4:
f(2) = 2*4+1
f(2) = 9
For n=3f(3) = 2f(2)+1
Since f(2)=9:
f(3) = 2*9+1
f(3) = 19
For n=4f(4) = 2f(3)+1
Since f(3)=19:
f(4) = 2*19+1
f(4) = 39
For n=5f(5) = 2f(4)+1
Since f(4)=39:
f(5) = 2*39+1
f(5) = 79
The following is a table relating a group of 1000 patients’ true breast cancer statuses and their corresponding test results after receiving a mammogram.
Cancer Status
Test Result
Positive
Test Result
Negative
Total
Breast Cancer
223
80
303
No Breast Cancer
13
684
697
Total
236
764
1000
What is the probability of a positive test, given that the patient has breast cancer? (2 points)
What is the formal term used to describe this probability measure? (2 point)
What is the probability of a negative test, given that the patient is breast cancer free? (2 points)
What is the formal term used to describe this probability measure? (2 point)
Answers
The probability of a positive test, given breast cancer, is 223/303, while the probability of a negative test, given no breast cancer, is 684/697.
To find the probability of a positive test, given that the patient has breast cancer, we divide the number of true positive cases (223) by the total number of patients with breast cancer (303). This gives us a probability of 223/303.
The formal term used to describe this probability measure is conditional probability or the probability of an event A occurring given that event B has already occurred. In this case, the positive test is event A, and having breast cancer is event B.
Similarly, to find the probability of a negative test, given that the patient is breast cancer-free, we divide the number of true negative cases (684) by the total number of patients without breast cancer (697). This gives us a probability of 684/697.
The formal term used to describe this probability measure is also conditional probability, where the negative test is event A, and not having breast cancer is event B.
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Help me please I am having trouble figuring out the answer. Help me find the ratio.
Answers
Answer:
not equivalent to meteorologists ratio
Step-by-step explanation:
meteorologists ratio is
rainy days : sunny days = 2 : 5
last months weather is
rainy days : sunny days
= 10 : 20 ( divide both parts by LCM of 10 )
= 1 : 2 ← not equivalent to 2 : 5