Therefore in this question the probability that he is innocent is 0.1743
What is probability?The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Here,
In this case, let G represent the state of guilt and H represent the state of innocence.
and Let K stand for the situation where the truth serum shows that someone is guilty.
We are aware that 90% of the guilty suspects receive just verdicts, i.e. P(K|G)=0.9.
Additionally, we know that innocent suspects are mistakenly identified 1% of the time, or P(K|H)=0.01.
When a suspect is chosen from a group of suspects, of whom 5% committed a crime, and the serum suggests that the suspect is guilty, we must determine the likelihood that the suspect is innocent.
We must therefore determine the probability P(H|K).
A group of people was chosen for the suspect, of which 5% were criminals.
so the probability that selected person is guilty is
P(G) = 0.05
Therefore, the probability that selected person is not guilty is
P(H) = 1 – P(G) = 1 – 0.05 = 0.95
Then,
Using Bayes' Theorem, we get
P(H|K) =[tex]\frac{P(H)P(K|H)}{P(H)P(K|H) + P(G)P(K|G)}[/tex]
= [tex]\frac{0.95*0.01}{0.95*0.01 + 0.05*0.9}[/tex] =0.1743
Therefore in this question the probability that he is innocent is 0.1743
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Is the system of equations consistent and independent, consistent and dependent, or inconsistent?
y=−x+1
2y=−2x+2
Select the correct answer from the drop-down menu.
After solving the equations it will the infinite solutions, then it is a consistent system.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations.
A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
As per the given information in the question,
The equations are,
y = -x + 1 (i) and,
2y = -2x + 2 (ii)
Divide equation (ii) by 2
y = -x + 1 (iii)
Solve equation (i) and (iii)
The value of x and y will be 0 which means that it has infinite solution, then it is a consistent system.
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The width of a claroom i 4meter le than the length. It area i 45cm*45cm. Find the dimenion of the claroom
The dimensions of the classroom are a width is 5 m and a length is 9 m.
We have been given that the width of a classroom is 4m less than the length its area is 45m², then.
L= 4 + W
Area = 45, so
L x W = 45
Now substituting the value of L, we get.
(4+W) W=45,
Now simplifying this we get.
4W + W² =45
W² + 4W - 45 = 0, this is a quadratic equation
Now solving this we get the factors 9 and -5,
(W+9) and (W-5) = 0
Thus, W= -9 or W= 5, since the width cannot be negative,
So, it is width = 5
So, length = 9 m
In physics and arithmetic, the dimension of a mathematical space (or item) is informally defined as the minimal range of coordinates to specify any factor within it. therefore, a line has a dimension of one (1D) due to the fact handiest one coordinate is wanted to specify a factor on it – for instance, the point at 5 on more than a few lines. A floor, together with the boundary of a cylinder or sphere, has a size of two (2d) because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the floor of a sphere. A two-dimensional Euclidean area is a -dimensional area on the aircraft. The internal of a dice, a cylinder, or a sphere is 3-dimensional (3-d) due to the fact 3 coordinates are had to find a factor inside these spaces.
In classical mechanics, area and time are distinct classes and seek advice from absolute space and time. That theory of the sector is a four-dimensional space however not the only one that was discovered as essential to explain electromagnetism. The four dimensions (4D) of spacetime encompass activities that are not really described spatially and temporally, however as a substitute are acknowledged relative to the movement of an observer. Minkowski's area first approximates the universe without gravity; the pseudo-Riemannian manifolds of fashionable relativity describe spacetime with depend and gravity. 10 dimensions are used to describe the superstring principle (6D hyperspace + 4D), eleven dimensions can describe supergravity and M-principle (7D hyperspace + 4D), and the kingdom-space of quantum mechanics is an infinite-dimensional feature area.
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function rule to find f(10).
Answer:
[tex]f(10) = 103[/tex]
Step-by-step explanation:
f(x) = 3+10x
when x is 10, we have
3+10*10
= 103
:]
Find MK
Problem # 37
Please help!
Answer:
17.5
Step-by-step explanation:
Since the triangles are similar, the side lengths are proportional. One way we can solve this is by finding the scale factor for the triangle on the left to the triangle on the right. We can use the two corresponding sides that we know.
Let x = the scale factor
385x = 175 Divide both sides by 385
x = [tex]\frac{175}{385}[/tex] Simplify by dividing the numerator and the denominator by 35
x = [tex]\frac{5}{11}[/tex]
Take the corresponding side of MK and multiply it by [tex]\frac{5}{11}[/tex] to find MK
38.5 x [tex]\frac{5}{11}[/tex] = 17.5
One thousand tickets are sold at $5 each. One ticket will be randomly selected and the winner will receive a color television valued at $375. What is the expected value for a person that buys one ticket?
Multiple choice:
-$4.62
-$1.00
$1.00
$4.62
Answer:
Hope this helps, Good Luck! :)
Step-by-step explanation:
EV = - + prob(win)*win
= -5 + 1/1000 * 375
= -4.62
The requried, the expected value for a person that buys one ticket is approximately -$4.62. The correct answer is option A. -$4.62.
To calculate the expected value, we need to consider the probability of winning the color television and the corresponding value of the prize. We can then subtract the cost of buying the ticket to find the expected value.
Given:
Cost of one ticket = $5
Value of the color television (prize) = $375
Number of tickets sold = 1000
The probability of winning the color television is 1 out of 1000, as only one ticket will be selected out of the total 1000 tickets sold.
Expected Value (EV) = (Probability of winning * Value of prize) - Cost of the ticket
EV = (1/1000 * $375) - $5
EV = $0.375 - $5
EV = -$4.625
Rounded to two decimal places, the expected value for a person that buys one ticket is approximately -$4.62. The correct answer is option A. -$4.62.
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Two friends, Montraie and Serenity, took summer jobs. The equation y=19.2x represents Montraie's earnings in dollars and cents, y, for working x hours. Serenity earned $748.60 in 38 hours.
Use the dropdown menu and answer-blank below to form a true statement.
Montraie earns $___ per hour ___ (more or less) than Serenity.
Comparing the two friends earning Montraie earns $ 0.5 per hour less than Serenity
How to compare the earnings of the two friendsThe word problem that has to do with earnings of two friends Montraie and Serenity is solved by putting the problem in equation form
The equations are generated as follows
The equation for the earning for Montraie is y = 19.2x
Using the equation in 38 hours Montraie will earn
y = 19.2 * 38
y = 729.6
This means that Montraie earns 19.2 per hour
For Serenity the earning per hour is solved
= 748.60 / 38
= 19.7
comparing both earnings
Serenity earning - Montaie earning
= 19.7 - 19.2
= 0.5
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4/6 x 3/5 in the simplest form.
Answer:
Step-by-step explanation:
2/5
(10x12) + (5x11) + (12x12) = Y
Answer:
Y= 319 hope you have the best rest of the day of your life ever. can i have brainliest
Step-by-step explanation:
Steps for Solving Linear Equation
(10×12)+(5×11)+(12×12)=Y
Multiply 10 and 12 to get 120. Multiply 5 and 11 to get 55. Multiply 12 and 12 to get 144.
120+55+144=Y
Add 120 and 55 to get 175.
175+144=Y
Add 175 and 144 to get 319.
319=Y
Swap sides so that all variable terms are on the left hand side.
Y=319
PART A: Given the rate at which the zookeeper is giving the animals hay and grain, on which day will she have the same amount of grain and hay remaining? Explain how you determined your answer
Given the rate at which the zookeeper is giving the animals hay and grain, on which day will she have the same amount of grain and hay remaining is 6 days.
Every three days, one pound of hay and one pound of feed are used.
10 pounds of grain and 8 pounds of hay are present.
There are 6 pounds of hay and 6 pounds of grain left on the sixth day.
A rate in mathematics is the comparison of two related values expressed in different units.
The numerator of the ratio indicates the rate of change in the other (dependent) variable if the denominator of the ratio is written as a single unit of one of these quantities, and if it is assumed that this quantity may be modified systematically (i.e., is an independent variable).
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7.Show that quadrilateral FGHJ is a trapezoid, but is not a parallelogram.
Answer:
FJ is -3/1
Step-by-step explanation:
And in order to be a trapezoid, just one pair of sides needs to be parallel.
What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest form in the box.
Answer:
-1
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]
Define two points on the line:
Let (x₁, y₁) = (-2, 0)Let (x₂, y₂) = (0, -2)Substitute the defined points into the slope formula:
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-0}{0-(-2)}=\dfrac{-2}{2}=-1[/tex]
Therefore, the slope of the line is -1.
If 16* = find the value of x. 1 64 7
Answer:it's 16 or 4 I can't confirm
Step-by-step explanation:
What is the standard form of the equation of the circle with the given center (-6,8) and radius r=10
Answer:
(x+6)^2 + (y-8)^2 = 10^2
or
(x+6)^2 + (y-8)^2 = 100
Step-by-step explanation:
Equation of a circle in standard form: (x-h)^2 + (y-k)^2 = r^2
(h,k) represent the center of the circle
h = -6
k = 8
r = the length of the radius
10^2 = 100
I need help please!! Is 16% the correct answer?
Answer:
No, 16% is not the right answer.
It's:
Cars under 25 mph / Total Number of Cars
Cars under 25 mph:
I count 42 I think.
Total Number:
42 + 7 + 1 = 50
42 / 50 = .84
.84 * 100 = 84%
So, 84% of cars are moving below the speed limit.
Ue the ditributive property to rewrite the expreion a a multiple of a um of two number with no common factor. 24 18
36 is a multiple of two numbers added together without a common factor.
What is a common factor?When a number is exactly divided by a divisor, that divisor is known as a factor of that number.
Alternatively, a factor of a number is an exact divisor of the provided number.
A number's factors are either less than or equal to the supplied number; they cannot be bigger. Every number is a factor of itself, and the common factor of all numbers is 1.
A number can be divided exactly by numerous divisors if it is a multiple of the divisor, therefore when we determine the factors of two or more numbers, we discover that some factors are common. As an illustration, the factors of 35 are 1, 5, 7, 35 while those of 45 are 1, 3, 5, 9, 15, 45. 1 and.
Hence, 36 is a multiple of two numbers added together without a common factor.
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solve for x -12x-14=24
PLEASE HELP NOW ILL DO ANYTHING
Answer: x= 38/11
Step-by-step explanation: x-12x-14=24
-11x-14=24
Add 14 to both sides
simplfy
-11x=38
Divide both sides by the same factor
x=11-38/11
Answer:
3
Step-by-step explanation:
Translate and solve the following: three more than the difference of 6s and 5s is equal to the sum of 12 and 6.
Therefore, the value of "s" that satisfies the given equation three more than the difference of 6s and 5s is equal to the sum of 12 and 6. is 15/4.
What are linear equations?A linear equation is one where the variable's maximum power is 1. To put it another way, a linear equation is one that has the form axe + b = 0, where a and b are constants and x is the variable.
The speed of an item travelling straight forward or the pace at which a population is increasing are two examples of real-world scenarios that are equal to the frequently modelled using linear equations. They are rather easy to resolve, and the answers may be obtained by applying fundamental algebraic strategies such isolating the variable and running calculations on both sides of the problem.
In several disciplines, including physics, engineering, and economics, linear equations are used extensively.
How to solve?
Let "s" be the unknown value that we are trying to find.
3 + (6s - 5s) = 12 + 6
3 + (6s - 5s) = 12 + 6
3 + 1s = 18
4s = 15
s = 15/4
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The lengths of two sides of a triangle are 8 cm and 10 cm. Identify the range of possible lengths for the third side.
Given that the first two sides of a triangle are 8 cm and 10 cm in length, the third side's range of potential lengths will be [2,18].
What is range?When the sample maximum and minimum are subtracted, the range of a collection of data is the difference between the greatest and lowest values. It uses the same units as the data to express itself. The difference between the highest and lowest values for a given data collection is the range in statistics. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3. As a result, the range can also be thought of as the distance between the highest and lowest observation.
Here,
The minimum length can be,
=10-8
=2 cm
The maximum length can be,
=10+8
=18 cm
(10-8)<x<(10+8)
2<x<18
The range of possible lengths for the third side will be [2,18] as The lengths of two sides of a triangle are 8 cm and 10 cm.
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According to last year's 7th grade standards test results 73% of the students and John's graduating class passed the math section. If 400 students took the test how many students did not pass the math section.
Answer:175
Step-by-step explanation:
parallelogram fghj was dilated and translated to form similar parallelogram f'g'h'j'. what is the scale factor of the dilation? 4 8
The scale factor of the dilation is s = 4 units .
Given :
parallelogram fghj was dilated and translated to form similar parallelogram f'g'h'j'.
To find scale factor between figures, find two corresponding sides and write the ratio of the two sides.
The value of y is same through the distance of F to G.
So, FG = change in x coordinates
FG = -2 - ( -4 )
= -2 + 4
= 2
F'G' = 3 - ( - 5 )
= 3 + 5
= 8
Let s be the scale factor
s = F'G' / FG
= 8 / 2
= 4
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what are three powers that have values greater than 120 and less than 130. ?
Answer: 11^2, 5^3, 2^7
Step-by-step explanation:
11^2= 121
5^3= 125
2^7= 128
in the simplex method, the pivot column is the column with the most negative number (to the left of the vertical bar) in the bottom row. why?
The most negative number corresponds to the variable that has the largest impact on the Value of the objective function. So, maximizing it first is most efficient.
What is pivot column in simplex method?
The Simplex method's pivot column is selected by the fundamental variable's biggest reduced cost coefficient. 4. The highest ratio of right side parameters to positive coefficients in the pivot column determines the pivot row in the Simplex approach.
A location of a leading entry in the matrix's echelon structure. A pivot is a non-zero number that is either transformed into a leading 1 and then used to make 0s, or it is utilized in a pivot position to create 0s.
The element of a matrix or array chosen first by an algorithm (such as Gaussian elimination, simplex algorithm, etc.) to do particular computations is known as the pivot or pivot element.
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in order to conduct an experiment, four subjects are randomly chosen from a group of 20 people . how many differenty groups of four subjects are pssoibke
The total number different groups of four subjects are possible are 4845 ways.
Define the term combination?A combination is indeed a selection of all or a portion of a group of items, regardless of the sequence in which the items are chosen.The formula for the combination is-
ⁿCr = n!/r!(n - r)!
We are wondering in how many distinct options there are to choose 4 subjects out of 20;
n = 20
r = 4.
Sequence is not important because the topics can be arranged in any order and still form the same group, hence we must use a combination:
Review the combination's definition:
²⁰C₄ = 20!/4!(20 - 4)!
²⁰C₄ = 20!/4!16!
²⁰C₄ = 4845
Thus, the total number of different groups four subject groupings is 4845.
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loverdale Middle School is buying new helmets for the football team. Each helmet costs $89.95. How much money does the school spend if they buy 45 of these football helmets?
Answer:
$4047.75
Step-by-step explanation:
If each helmet costs $89.95 and there are 45 of these helmets, you would multiply $89.95 x 45. Plug this into a calculator and you get $4047.75.
what is the slope of the line tangent to f(x)= x-sin(x) at x= pi
The slope of the line tangent to the given function would be m= 2.
What is the slope of the function?
If the function f(x) is given then differentiation will give you the gradient or slope for the tangent at any point.
The given function is f(x) = x - sinx
Now differentiating the above function with respect to x.
f'(x) = 1 - cosx
Now put x = π, we get
Slope = 1 - cos(π)
= 1 - (-1)
= 1 + 1
Slope (m) = 2.
Hence, the slope of the line tangent to the given function would be m= 2.
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Solve x for this diagram
Answer:
x = 20
Step-by-step explanation:
the 3 unknown angles form a right angle and sum to 90° , that is
x + 2x + x + 10 = 90
4x + 10 = 90 ( subtract 10 from both sides )
4x = 80 ( divide both sides by 4 )
x = 20
Answer:
x = 20°
Step-by-step explanation:
From the picture we know that x + 2x + x + 10 = 90°
x + 2x + x + 10 = 90
4x = 80
x = 80 : 4
x = 20°
--------------------
check
20 + 2 x 20 + 20 + 10 = 90
90 = 90
the answer is good
Kayden's math teacher said that each
question answered correctly on a test would
be worth 7 points. Answer the questions
below regarding the relationship between
the number of questions correct and the
score on the test.
Step-by-step explanation:
Kayden's math teacher said that each question answered correctly on a test would be worth 7 points. Answer the questions below regarding the relationship between the number of questions correct and the score on the test.
Since 00 questions correct gets you 00 points on the test, the function will have a yy-intercept of 0.0.
The rate at which points are earned is 7 points per question, so the slope of the function should be 7.7.
\text{Function Rule:}
Function Rule:
V(x)=7x
V(x)=7x
Plug x=11 Into Rule:
V(11)=7(11)=77
Correct Answer:
The independent variable, x, represents the number of questions correct, and the dependent variable is the score on the test, because the score on the test depends on the number of questions correct.
A function relating these variables is V(x) =V(x)= 7x7x.
So V(11) =V(11)= 7777, meaning 1111 questions correct will earn 7777 points on the test
Step 1: we know that angle a b c is-congruent-to angle f g h because all right angles are congruent. step 2: we know that angle b a c is-congruent-to angle g f h because corresponding angles of parallel lines are congruent. step 3: we know that line segment b c is-congruent-to line segment g h because it is given. step 4: triangle a b c is-congruent-to triangle f g h because of the asa congruence theorem. aas congruence theorem. third angle theorem. reflexive property.
Based on the given steps the triangle ABC will be Congruent to triangle FGH because of the AAS Congruence .
What is AAS Congruence ?
the two triangle are said to be congruent based on the AAS Congruence when 2 angles and 1 non included side in one triangle are congruent to corresponding 2 angles and 1 non included side in another triangle.
So , in the question , based on the given steps we can say that ,
the two angles that are congruent is angle G and B , and angle A and angle F .
and the side that is congruent is BC = GH .
So the triangle ABC and triangle FGH are congruent by AAS congruence .
Therefore , the correct option is (b) AAS Congruence Theorem .
The given question is incomplete , the complete question is
Step 1: we know that angle a b c is-congruent-to angle f g h because all right angles are congruent.
Step 2: we know that angle b a c is-congruent-to angle g f h because corresponding angles of parallel lines are congruent.
Step 3: we know that line segment b c is-congruent-to line segment g h because it is given.
Step 4: triangle a b c is-congruent-to triangle f g h because of the
(a) ASA congruence theorem.
(b) AAS congruence theorem.
(c) Third angle theorem.
(d) Reflexive property.
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18 2/6 Use the number line to round the mixed number to the nearest whole number.
Answer: The nearest whole number is 18
Step-by-step explanation: because 18 2/6 is closer to 18 than 19.
2x - 7 + 3x + 10 > x - 6 + 8x - 11 PLEASE SOLVE "STEP BY STEP" AND SHOW ME THE WORK!
thank you!
Answer:
x<5
Step-by-step explanation:
2x-7+3x+10>x-6+8x-11
5x+3>9x-17
5x-9x>-17-3
-4x>-20
x<5
Answer:
x < 5
Step-by-step explanation:
step 1: simplify both sides of the inequality.
5x + 3 > 9x − 17
step 2: subtract 9x from both sides.
5x + 3 − 9x > 9x − 17 − 9x − 4x + 3 > − 17
step 3: subtract 3 from both sides.
−4x + 3 − 3 > − 17 −3 − 4x > − 20
step 4: divide both sides by -4.
-4x/-4 > -20/-4
x < 5