Answer:
0.0748 = 7.48% probability that he is guilty
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Tests indicates guilty
Event B: Person is guilty
Probability that the test indicates that the person is guilty:
4/5 = 0.8 of 1/100 = 0.01(person is guilty)
1 - 0.9 = 0.1 of 1 - 0.99(person is not guilty). So
[tex]P(A) = 0.8*0.01 + 0.1*0.99 = 0.107[/tex]
Test indicates guilty and the person is guilty;
0.01 of 0.8. So
[tex]P(A \cap B) = 0.01*0.8 = 0.008[/tex]
What is the probability that he is guilty?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.008}{0.107} = 0.0748[/tex]
0.0748 = 7.48% probability that he is guilty
The required value is [tex]\simeq0.925 \ or \ 92.5[/tex]%.
Probability:Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are to happen, using it.
Let [tex]T_G[/tex] and [tex]T_I[/tex] denote the test result being guilty or innocent respectively.
And, [tex]G[/tex] and [tex]I[/tex] denote that the person is guilty or innocent respectively.
Given that: [tex]P\left ( T_G\mid I \right )=\frac{4}{5}[/tex]
[tex]P\left ( T_I\mid I \right )=\frac{9}{10}\Rightarrow P\left ( T_G\mid I \right )=1-\frac{9}{10}=\frac{1}{10}[/tex]
[tex]P(G)=\frac{1}{100} \\ \therefore P(I)=1-P(G) \\ =1-\frac{1}{100} \\ =\frac{99}{100}[/tex]
Now, the required probability is,
[tex]P(I\mid T_G)=\frac{P\left ( T_G\mid I \right )\times P(I)}{P(T_G\mid I)\times P(I)+P\left ( T_G\mid G \right )\times P(G)}[/tex]
[tex]=\frac{\frac{1}{10}\times\frac{99}{100}}{\left ( \frac{1}{10}\times \frac{99}{100}\right )+\left ( \frac{4}{5}\times\frac{1}{100} \right )} \\ =\frac{0.099}{0.099+0.008} \\ =\frac{0.099}{0.107} \\ =0.92523 \\ \simeq 0.925 \\ or \ 92.5%[/tex]
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Which of the following would increase if the professional football players were removed from the data set?
Answer:
the standard deviation of the residuals
Step-by-step explanation:
The removal of the professional football players will cause the correlation, and consequently r2 to become closer to 0 due to the fact that the high school athletes tend to show no association between the number of energy drinks consumed and the number of pull ups that can be done. The slope of the regression line will also be nearly 0 without the professional football players. The standard deviation of the residuals, however, will increase without the presence of the professional football players because the remaining scatter about the new regression line will be greater due to the loss of the 4 professional football players which all had small residuals.
The option that will increase if the football players were removed from the data set is the standard deviation of the residuals
What is standard deviation?It should be noted that standard deviation simply means the difference between the observed data and the predicted values.
In this case, the standard deviation of the residual will increase if the football players were removed from the data set as the removal of the professional football players will cause the correlation.
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The area of a square mural is 144x2 - 72x + 9. What is the length of one side
of the mural?
Answer:
-0.25 units
Step-by-step explanation:
144x^2 - 72x + 9 = 0
common factor: 9
16x^2 - 8x + 1 = 0
(4x + 1)^2 = 0
4x +1 = 0
4x = -1
x = -0.25 units
Calculate the finance charge for a credit card that has an average daily balance of Php5,600 and a monthly interest rate of 1.35 %
Answer:The simplest way to calculate a finance charge is: balance X monthly rate
Step-by-step explanation:
i thinkk
500 X .015 = $7.50
The finance charge for a credit card that has an average daily balance of 5,600 and a monthly interest rate of 1.35 % is $75.6.
What is the finance charge?The finance charge is the product of an average daily balance to the monthly interest rate.
finance charge = balance x monthly rate
The simplest way to calculate a finance charge = balance x monthly rate
= 5,600 x 0.0135
= $75.6
Thus, the finance charge for a credit card that has an average daily balance of 5,600 and a monthly interest rate of 1.35 % is $75.6.
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the two rectangular plots of land have properties side lengths what is the perimeter of the smaller rectangle A. 28 B. 32 C. 36 D. 76
Answer:
I think that it would be b 32
I need the answer , help me please
Carissa folds 32 TShirts in 8 minutes. How many TShirts can she fold in 20 minutes?
Answer:
5
Step-by-step explanation:
Answer:
80 TShirts in 20 minutes
Step-by-step explanation:
32/8 = 4 Tshirts in a minute
4 x 20 = 80 TShirts in 20 minutes
Using the photo above, describe what type of symmetry it has.
a. if it has reflection symmetry, draw all lines of symmetry.
b. if it has rotational symmetry, what is all the angle of rotational symmetry (the smallest)
c. if has translational symmetry, what is shape is getting repeated
9514 1404 393
Answer:
b) rotational symmetry: multiples of 120°
Step-by-step explanation:
The figure does not have a line of symmetry, or a point of symmetry. However, rotating it 1/3 turn (120°) will make it look like itself. Hence, it has rotational symmetry of degree 3. A rotation of any multiple of 120° will map the figure to itself.
PLEASE HELP ASAP!!! URGENT
Verify the identity. Sinx/1-cosx = cscx+cotx
Please use the answers shown in the image !! Thank you !!
Answer:
1) [tex]\frac{\sin x}{1-\cos x} = \csc x + \cot x[/tex]
2) [tex]\frac{\sin x}{1-\cos x} = \frac{1}{\sin x} + \frac{\cos x}{\sin x}[/tex]
3) [tex]\frac{\sin x}{1-\cos x} = \frac{1+\cos x}{\sin x}[/tex]
4) [tex]\frac{\sin x}{1-\cos x} = \frac{\sin x \cdot (1+\cos x)}{\sin^{2}x}[/tex]
5) [tex]\frac{\sin x}{1-\cos x} = \frac{\sin x\cdot (1+\cos x)}{1-\cos^{2}x}[/tex]
6) [tex]\frac{\sin x}{1-\cos x} = \frac{\sin x\cdot (1+\cos x)}{(1+\cos x)\cdot (1-\cos x)}[/tex]
7) [tex]\frac{\sin x}{1-\cos x} = \frac{\sin x}{1-\cos x}[/tex]
Step-by-step explanation:
Now we proceed to show all steps needed to demonstrate the trigonometric identity:
1) [tex]\frac{\sin x}{1-\cos x} = \csc x + \cot x[/tex] Given.
2) [tex]\frac{\sin x}{1-\cos x} = \frac{1}{\sin x} + \frac{\cos x}{\sin x}[/tex] Identities for cosecant and cotangent functions.
3) [tex]\frac{\sin x}{1-\cos x} = \frac{1+\cos x}{\sin x}[/tex] [tex]\frac{a}{b}+\frac{c}{b} = \frac{a+c}{b}[/tex]
4) [tex]\frac{\sin x}{1-\cos x} = \frac{\sin x \cdot (1+\cos x)}{\sin^{2}x}[/tex] Existence of additive inverse/Modulative property.
5) [tex]\frac{\sin x}{1-\cos x} = \frac{\sin x\cdot (1+\cos x)}{1-\cos^{2}x}[/tex] Fundamental trigonometric identity.
6) [tex]\frac{\sin x}{1-\cos x} = \frac{\sin x\cdot (1+\cos x)}{(1+\cos x)\cdot (1-\cos x)}[/tex] Factorization.
7) [tex]\frac{\sin x}{1-\cos x} = \frac{\sin x}{1-\cos x}[/tex] Existence of additive inverse/Modulative property/Result.
Match the Situation with an Inequality Statement Below
It cost $12 to attend a golf clinic with a pro. Practice golf balls cost $3 per bucket.
If you have $30 saved but don't want to spend it all, how many buckets of golf balls at most can you by for practice.
Group of answer choices
12 > 3x +30
3x -12 < 30
12 + 3x < 30
12 - 3x > 30
k/4 +3=14 What is the answer to this question?
Answer:
k=44
Step-by-step explanation:
Question 3
Which of the following can be formed when a plane intersects a cone? Select all that apply.
Answer:
in geometry nation, is circle, isosceles triangle and parabola.
Step-by-step explanation:
just did it.
Someone please help me answer this!!
Answer:
b = 9cm is the answer.
Step-by-step explanation:
a = 12cm
b = ?
c = 15cm
By using the Pythagoras theorem,
a² + b² = c²
12² + b² = 15²
144 + b² = 225
b² = 225 - 144
b² = 81
b = 9cm.
∴ b = 9cm is the length of the missing leg.
How do you add
2 2/3 + 6/7
Answer:
3 11/21
Step-by-step explanation:
2 2/3=(2*3+2)/3=8/3
8/3+6/7=56/21+18/21=74/21 or 3 11/21
What is the slope between (-4, 0) and (0, 2)?
Answer:0.5
Step-by-step explanation: y = 0.5x + 2
Evaluate x[tex]x^{2} \sqrt{(x^3+9)}[/tex]with subsititution using u=x^3+9
It sounds like you're talking about an integral, namely
[tex]\displaystyle\int x^2\sqrt{x^3+9}\,\mathrm dx[/tex]
Substitute u = x ³ + 9, so that du = 3x ² dx. Then
[tex]\displaystyle\int x^2\sqrt{x^3+9}\,\mathrm dx=\frac13\int\sqrt{u}\,\mathrm du=\frac13\times\frac23u^{\frac32}+C=\boxed{\frac29(x^3+9)^{\frac32}+C}[/tex]
pleasee help me i will give you brainliest
Answer:
40
Step-by-step explanation:
6=110 1=40 because it's not gonna be a higher character
Is 7/2 the same as 1/5
Answer:
No.
Step-by-step explanation:
Calculation: 2/4 + 3/4 - fraction calculator. Result: 5/4 = 1 1/4.
Arthur earned $22.50 last night delivering lunches for his family's restaurant. He puts 30% of his earnings into his savings account. he then bought a magazine for $3.95 and a CD for $11.49. of the amount earned last night, how much money does arthur have left that is not in his savings account
Answer:
$4.26
Step-by-step explanation:
New appliances for the kitchen will include a new refrigerator ($1,649.99), dishwasher ($369.99), and electric range ($1,146.99) which will be purchased at the local appliance store. Estimate the cost of the appliances to the nearest hundred dollars. Then calculate the actual total cost of the appliances. New appliances for the kitchen will include a new refrigerator ($1,649.99), dishwasher ($369.99), and electric range ($1,146.99) which will be purchased at the local appliance store. Estimate the cost of the appliances to the nearest hundred dollars. Then calculate the actual total cost of the appliances.
Answer:
estimated price is $3167 and actual price is $3166.97
What is the equation of the line that best fits the given data? A graph has points (negative 3, negative 3), (negative 2, negative 2), (1, 1.5), (2, 2), (3, 3), (4, 4). a. y = 2 x + 1 c. y = x + 1 b. y = x d. y = negative x Please select the best answer from the choices provided A B C D
Answer:
it's B on edge
Step-by-step explanation:
I took one for the team
Answer:
Step-by-step explanation:
Please help! Find the perimeter of Trapezoid ABCD. (round your answer to the nearest tenth.)
Answer + explanation please!
Answer:
19.8 units
Step-by-step explanation:
BC = 5
AD = 8
CD = 1²+3²=c²
1+9=c²
√10=c
c=3.1627766
AB = 2²+3²=c²
4+9=c²
√13=c
c=3.6
5+8+3.6+3.16=19.76
The area of a poster board is (x2 + 9x – 10) square inches. Find the dimensions of the
poster board if x = 16.
The dimensions of the poster board are
inches by
inches.
Answer:
Step-by-step explanation:
WILL GIVE BRAINLIEST TO BEST EXPLAINOR
how do you find and (draw) graph slope.
Answer:
y=-x+4
The equation is in the form y=mx+c, where m is the slope and c is the y-intercept, so we know that the slope (m) is -1, and the y-intercept (c) is 4.
The y-intercept is the value of y when x=0. So you can mark (0,4) as a point on the line.
The next thing I would do is take any value for x and find another point on the line. Let's let x=2:
y=-2+4
y=2
So now we know another point on the line (2,2). Mark this on the graph too.
Then connect these two points and extend to the line to finish off your graph, and you're done!
(PS: if the whole 'y-intercept' thing gives you a headache, you can just pick any two values for x, sub them in to find the points, mark those points and connect. There's also a method for graphing using just the slope and y-intercept, but the method above is usually what people prefer to do)
I've attached a sketch that corresponds to my answer to give you an idea:
Two hundred sixty students were surveyed on whether they prefer apple juice or orange juice. A table of relative frequencies is shown. How many more girls prefer apple juice than boys?
Answer:
91
Step-by-step explanation:
Can someone help with this, please? :)
Answer:
answer is D i believe
Step-by-step explanation:
(PART 2) Shout to the friend helping me
Answer:
6. 1351.92
7. -52
8.Bus Pass
9.448
10. No she of by two dollars
What is the area of the polygon below?
A. 120 square units
9
10
B. 174 square units
16
C. 66 square units
12
D. 84 square units
Answer:
D
Step-by-step explanation:
12-9 = 3 square unit
10 x 3 = 30 square unit
9×6 = 54 square unit
54+30 = 84 square units
and thats the answer
The area of the polygon is 84 square units, option D is correct.
What is Area of Rectangle?The area of Rectangle is length times of width.
The given polygon has two rectangles.
Area of rectangle with length 9 and width is 6 units
Area of rectangle 1 =9×6
=54 square inches
Now Area of rectangle with length 10 and width is 3 units
Area of rectangle 2 =10×3
=30 square inches
Total area = 54+30
=84 square units
Hence, the area of the polygon is 84 square units, option D is correct.
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A CD has a diamter of 4.75 inches, Find the circumference, Use calculator pi or 3.14. Round to the nearest hundredth, if necessary.
WILL GIVE BRAINLIEST!!!
Answer:
15 in.
Step-by-step explanation:
Solve the equation by completing the square. Round your solutions to the nearest hundredth if necessary. x^2+2x=5
Answer: The correct answers are -3.45 and 1.45
Step-by-step explanation: The only problem you had was you rounded it to the tenths place instead of the hundredths place.
Sorry for getting back to you late.
Pictures in order !
Answer:
Step-by-step explanation:
2XV=WY
2(2x+4)=7x-1
4x+8=7x-1
3x=9
x=3
XV=2x+4=10
WY=7x-1=20