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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 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]

Learn more about the topic of Probability:  brainly.com/question/26959834

Step-by-step explanation:

For example, the number 5 can be written as [tex]\frac{5}{1}[/tex] . And that [tex]\frac{5}{1}[/tex] can also be written as 5:1, which is a ratio. By converting the single number to a fraction, then converting the fraction into a ratio, you can turn a number into a ratio.

Hope this helps.

Answer:

The permiter is 22mm since its still  the same

Step-by-step explanation:

Answer:

b=24

Step-by-step explanation:

the sides are equal to each other so

b+24=2b

24+24=2 times 24

48=48

so b=24

The spider needs 15 hours to climb up the top of the wall.

A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

A spider is trying to climb a wall of height = 15 meters

In each hour, it climbs up 3 meters but falls back 2 meters,

⇒ [tex]+3-2=1[/tex]

Thus spider climbs 1 meter per hour.

For 15 meter wall, the spider needs 15 hours to climb up the wall.

Hence we can conclude that the spider needs 15 hours to climb up the top of the wall.

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Answer:

x=76

Step-by-step explanation:

The two marked angles are alternate angles, which means they're equal.

Answer

76%

Step-by-step explanation:

I think its defiantly not 104 because its smaller than 90% and not 41% because that's to small same with 67% so it is 76%

Step-by-step explanation:

Angle b + 100 = 180 (angles on the same straight line)

[tex]b + 100 = 180 \\ b = 180 - 100 \\ = 80[/tex]

Angle c = Angle b (Vertically opposite angles)

= 80 deg

270° → [tex] \frac{3π}{2} [/tex] ≈ 4.7

360° → [tex] 2π [/tex] ≈ 6.3

60° → [tex] \frac{π}{3} [/tex] ≈ 1.1

45° → [tex] \frac{π}{4} [/tex] ≈ 0.8

135° → [tex] \frac{3π}{4} [/tex] ≈ 2.4

225° → [tex] \frac{5π}{4} [/tex] ≈ 3.9

Answer:

A

Step-by-step explanation:

Answer:

E

Step-by-step explanation:

Answer:

Quadrilateral, square, rectangle

Step-by-step explanation:

An object have parallel sides if the sides have the same distance apart and they never meet.  

Quadrilaterals usually have parallel sides

Polygons including triangles and pentagons do not have parallel sides

the sides of a quadrilateral are also perpendicular. the sides form a 90 degree angle with each other

Opposite sides of a quadrilateral are usually equal. For example, the opposite lengths of a rectangle are equal. the four sides of a square are equal

Step-by-step explanation:

Answer:

1.) M=9,-9  2.) x=10,-10  3.) n=3,-3  4.) x=2,-2

Step-by-step explanation:

Answer:

42 + 6w

Step-by-step explanation:

Basically,

6(8+w) is 6 x (8+w)

OR 6(8) + 6(w)

Hence 42 + 6w

Answer:

y = 12

Step-by-step explanation:

y = 3x2+6

   = 6+6

   = 12

y = 12

Answer:

the smallest value of the sum is 7.65 cm.

Step-by-step explanation:

Given;

3.4 cm + 4.3 cm = 7.7 cm

To obtain the least value of the given result, we will apply the rounding-off method;

In the rounding-off method, digits between 0 to 4 will be rounded down to zero while digits between 5 and 9 will be rounded up to 1.

The smallest value of 7.7 cm = 7.65 cm (5 will be rounded up to 1 making 7.65 cm approximately 7.7 cm)

Also, other possible values of 7.7 cm include;

7.66 cm, 7.67 cm, 7.68 cm, 7.69 cm

Note :7.64 cm cannot be rounded up to 7.7 cm because 4 will be rounded down to zero making 7.64 cm approximately 7.6 cm.

Therefore, the smallest value of the sum is 7.65 cm.

Answer: The first and last options are correct.

f(x) = pi/4 cos (pix/5 - pi/2)

f(x) = pi/4 sin (pix/5)

Step-by-step explanation

The graph shows that A = pi/4.

B = 10, so the period = 2pi/10 = pi/5.

sin and cos are cofunctions, so a phase shift of -pi/2 makes the two functions equal to each other.

Hope this helps :)

The correct answer is f(x) = π/4 cos (πx/5 - π/2) and f(x) = π/4 sin (πx/5).

option (A) and (D) are correct.

It is given that height of 50 feet and graph is given.

It is to find f(x).

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The graph shows that A = π/4.

B = 10, so the period = 2π/10 = π/5.

sin and cos are co-functions, so a phase shift of -π/2 makes the two functions equal to each other.

So, the option are (A) and (D).

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Answer:

If the goal is to break the vases: 3/20 = 15.0% or 0.15

If the goal is to not break the vases: 17/20 = 85.0% or 0.85

Step-by-step explanation:

0/1 , 1/1

Multiply there denominators with any number...

0/1×60=0/60

1/1××60=60/60

Now,

You have many choices...

1/60,10/60,30/60,2/60,5/60........so on....

Answer:

d = 65

w = 55

Step-by-step explanation:

w + 90 + 35 = 180

w + 125 = 180

w = 55

35 + x = 60 (Vertical angle thm)

x = 25

d + x = 90

d + 25 = 90

d = 65

Answer:

the correct answer is b) 4

Answer:

33 cm

Step-by-step explanation:

volume of the under the pyramid Is 3×3×3=27

volume of pyramid is 3×3×2=18

divide 18 ÷3 =6

27+6=33

the reason why we divide by 3 because ti's is the formula

Answer:

1. B 130 2/3ft^3

2. B 226 in^3

3. B 33 cm^3

4. A 4 m

5. D 15m

Step-by-step explanation:

I got a 100! For connexus students, hope this helps!!

Answer:

The standard error of the sulfate in a collection of 10 water samples is of 0.506 mg/L.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard error [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Standard deviation of 1.60 mg/L.

This means that [tex]\sigma = 1.6[/tex]

Collection of 10 samples:

This means that [tex]n = 10, s = \frac{1.6}{\sqrt{10}} = 0.506[/tex]

The standard error of the sulfate in a collection of 10 water samples is of 0.506 mg/L.

Answer:

y=x+31.25

Because x stand for cauclator so 31.25 per x so it would end up being x+31.25

Step-by-step explanation:

Answer: b

Step-by-step explanation:

2x is x doubled

and then add 5 to the product