g ) If it is raining, a home security system detects an intruder with probability 0.70. If it is NOT raining, the probability becomes 0.92. The probability of rain on any 2 given day is 0.25. To test the system on a randomly chosen day, the system technician pretends to be an intruder. Given that the technician will NOT be detected, what is the probability that it is NOT raining

Answers

Answer 1

Answer:

0.4444 = 44.44% probability that it is NOT raining

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: Technician not detected.

Event B: Not raining.

Probability the technician is not detected:

0.3 of 0.25(raining).

0.08 of 0.75(not raining). So

[tex]P(A) = 0.3*0.25 + 0.08*0.75 = 0.135[/tex]

Probability the technician is not detected and it is not raining:

0.08 of 0.75. So

[tex]P(A \cap B) = 0.08*0.75 = 0.06[/tex]

Given that the technician will NOT be detected, what is the probability that it is NOT raining?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.06}{0.135} = 0.4444[/tex]

0.4444 = 44.44% probability that it is NOT raining


Related Questions

round 32.68 to the nearest hundredth​

Answers

Answer:

32.70

Step-by-step explanation:

round up

The bar graph shows the z-score results of four students on two different mathematics tests. The students took Test 1 and then, a month later, took Test 2. Which student had the lowest score on Test 2? Euan Felicia Dave Carla

Answers

Answer:

euan had lowest score on test 2

The student with lowest score on test 2 is Euan.

What is bar graph ?

Bar graph is used for the graphical representation of data or quantities by using bars or strips.

Here,

The z-score results of four students on two different mathematics tests is represented by the given bar graph.

Calculating the scores of each students for the two tests respectively.

1) Carla

Test 1: 0.75

Test 2: -0.5

2) Dave

Test 1: -0.5

Test 2: 1

3) Euan

Test 1: 0.25

Test 2: -1

4) Felicia

Test 1: 1.25

Test 2: 1.5

Hence,

The student with lowest score on test 2 is Euan.

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What is the are of the polygon below!help please!

Answers

Answer:

Area= 525

Step-by-step explanation:

14x9=126

3x7=21

14x27=378

126+21+378=525

Average person who drives car in United States drives 15, 350 miles which is 50% more than an average driver in Europe. We assume that the number of yearly miles by U.S. drivers is approximately a normal random variable of standard deviation of 4200 miles. Calculate percent of drivers who traveled between 10,000 to 12,000 miles in a year.

Answers

Answer:

7,675

that is your answer

2^17+2^14 chia hết cho 9

Answers

Answer:

ABC

Step-by-step explanation:

= 2^14.2^3 +  2^14

= 2^14. (2^3 +1)

= 2^14 . 9  

Vì 2^14.9 chia hết cho 9 nên 2^17 + 2^14 chia hết cho 9

(. là dấu nhân)

Answer:

đúng

Step-by-step explanation:

A lawyer commutes daily from his suburban home to his midtown office. The average time for a one-way trip is 24 minutes, with a standard deviation of 3.8 minutes. Assume the distribution of trip times to be normally distributed.
(a) What is the probability that a trip will take at least ½ hour?
(b) If the office opens at 9:00 A.M. and he leaves his house at 8:45 A.M. daily, what percentage of the time is he late for work?
(c) If he leaves the house at 8:35 A.M. and coffee is served at the office from 8:50 A.M. until 9:00 A.M., what is the probability that he misses coffee?
​(d) Find the length of time above which we find the slowest 10​% of trips.
(e) Find the probability that 2 of the next 3 trips will take at least one half
1/2 hour.

Answers

Answer:

Step-by-step explanation:

a) Probability-Above 30 min = 5.72% = .0572

b) Probability-Above 15 min =  99.11% = .9911

c) *Probability-Between  1 - 59.49% = .4051

d) 19.136 minutes  z = -1.28

a) The probability that trip will take at least 1/2 hour will be 0.0606.

b) The percentage of time the lawyer is late for work will be 99.18%.

c) The probability that lawyer misses coffee will be 0.3659.

d) The length of time above which we find the slowest 10​% of trips will be 0.5438.

e) The probability that exactly 2 out of 3 trips will take at least one half

1/2 hour is 0.0103.

What do you mean by normal distribution ?

A probability distribution known as a "normal distribution" shows that data are more likely to occur when they are close to the mean than when they are far from the mean.

Let assume the time taken for a one way trip be x .

x ⇒ N( μ , σ ²)

x  ⇒ N( 24 , 3.8 ²)

a)

The probability that trip will take at least 1/2 hour or 30 minutes will be :

P ( x ≥ 30)

= P [ (x - μ) / σ ≥ (30 - μ) / σ ]

We know that , (x - μ) / σ = z.

= P [ z ≥ (30 - 24) / 3.8)]

= P [ z ≥ 1.578 ]

= 1 - P [  z ≤ 1.578 ]

Now , using the standard normal table :

P ( x ≥ 30)

= 1 - 0.9394

= 0.0606

b)

The percentage of the time the lawyer is late for work will be :

P ( x  ≥ 15)

= P [ z ≥ -2.368 ]

= P [  z ≤ 2.368]

= 0.9918

or

99.18%

c)

The probability that lawyer misses coffee :

P ( 15 < x < 25 ) = P ( x < 25 ) - P ( x < 15)

= P [  z < 0.263] - P ( z < -2.368)

or

= 0.3659

d)

The length of time above which we find the slowest 10​% of trips :

P( x ≥ X ) ≤ 0.10

=  0.5438

e)

Let's assume that y represents the number of trips that takes at least half hour.

y ⇒ B ( n , p)

y ⇒ B ( 3 , 0.0606)

So , the probability that exactly 2 out of 3 trips will take at least one half

1/2 hour is :

P ( Y = 2 )

= 3C2 × (0.0606)² × ( 1 - 0.0606)

= 0.0103

Therefore , the answers are :

a) The probability that trip will take at least 1/2 hour will be 0.0606.

b) The percentage of time the lawyer is late for work will be 99.18%.

c) The probability that lawyer misses coffee will be 0.3659.

d) The length of time above which we find the slowest 10​% of trips will be 0.5438.

e) The probability that exactly 2 out of 3 trips will take at least one half

1/2 hour is 0.0103.

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I need help this is confusing to me

Answers

Answer:i think it is b not really sure      

Step-by-step explanation:

Four randomly chosen Nevada students were asked how many times they drove to Arizona last year. Their replies were 4,5,6,7. The geometric mean is

Group of answer choices

5.31

5.38

4.98

3.95

Answers

The geometric mean of the numbers is 5.38

Given the values a, b, c and d

The geometric mean of the values will be expressed as:

[tex]GM = (abcd)^{1/4}[/tex]

Given the values 4, 5, 6, and 7, the geometric mean will be expressed as:

[tex]GM = (4\times5\times6\times7)^{1/4}\\[/tex]

[tex]GM = (840)^{1/4}\\GM=\sqrt[4]{840} \\GM = 5.38[/tex]

Hence the geometric mean of the numbers is 5.38.

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? Question
Use the drawing tools to form the correct answer on the graph.
Graph this step function:

Answers

Answer:

start on (0,1) and go up two and left three. keep going until you run out of room. then, draw a line through the points.

Step-by-step explanation:

Consider the graph below, and identify the piecewise function that describes it.

Answers

Answer:

f(x)=-x when x belongs to (-infinity, 3)

f(x)=-2 when x belongs to [3, 6]

f(x)=2x-7 when x belongs to (6, infinity)

3. In A PQR, MZP=(4x-5),
m2Q=(8x-50), and MZR=(3x+10).
Which of the following best describes
APQR?
® Right triangle
® Isosceles triangle
© Equlateral triangle
Scalene triangle

Answers

Answer:

B

Step-by-step explanation:

The sum of all of them will result in 180. 15x-45=180. x=15. P=55, Q=70 and R=55. It's an isosceles triangle

Answer:

b

Step-by-step explanation:

its b

explain how you determined which operation was needed to write the equation. 9 divided by 3/4

Answers

9/ (3/4)

= (9/1)/(3/4)

=(9x4)/(1x3)

=36/3

=12

Answer:

division:

divided means division (:)

9:3/4

And the answer is 12:))))))))))

Step-by-step explanation:

Help me with this please.

Answers

Answer:

the answer should be B

Step-by-step explanation:

take the total of people who got the flu(63) and the amount of them who were vaccinated(35) and write it as a fraction. 35/63 in its simplest form is 5/9

A nurse is preparing to administer cefaclor 40 mg/kg/day PO divided in equal doses every 8 hr to a child who weighs 48 lb. Available is cefactor
suspension 375 mg/5 ml. How many mL should the nurse administer per dose? (Round the answer to the nearest tenth. Use a leading zero if it
applies. Do not use a trailing zero.)

Answers

This question is solved by proportions.

Step 1:

A nurse is preparing to administer cefaclor 40 mg/kg/day.

This means that the first step is finding the baby's weight in kg.

The child weighs 48lb. Each lb has 0,453592kg.

So the child weighs 48*0.453592 = 21.7724kg.

Step 2:

Here, we find the daily dose.

For each kg, the baby is administered 40 mg.

Since the baby weighs 21.7724 kg, the daily dose is of 40*21.7724 = 870.896 mg.

Step 3:

Here, we find how many mL in a day.

For 375 mg, 5 mL are administered. How many mL for 870.896 mg?

375 mg - 5 mL

870.896 mg - x mL

Applying cross multiplication:

[tex]375x = 5*870.896[/tex]

[tex]x = \frac{5*870.896}{375}[/tex]

[tex]x = 11.6[/tex]

Step 4:

Here, we find how many mL per dose.

Equal doses every 8 hours, so 24/8 = 3 doses per day.

11.6/3 = 3.9

Thus, the nurse should administer 3.9 mL per dose.

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Answer:

x = 3.9 ml  quantity of ml / dose

Step-by-step explanation:

The child weighs 48 lbs.

Then the weigh in kgs is  48 * 0.454 = 21.792 kgs  (since 1000 lbs = 454 kgs)

If the nurse has to prepare doses according to 40 mg/kg/day then for a child of 21.792 kgs it is needed  21.792*40 mg or 871.68 mg/day, and the fact that he or (she) need to take three doses then each dose will be  of

871.68/3 = 290.56 mg

So far we know that each dose should contain 290.56 mg, now we have the cefactor in a suspension wich density is 375 mg/5 ml or 75 mg/ml

Then by rule of three

if              75  mg     ⇒   1 ml

        290.56 mg     ⇒     x (ml)

x = 290.56/75  ( mg*ml)/ mg

x = 3.87 ml round to the nearest tenth

x = 3.9 ml

Wesley is making a patio from stones of two sizes, 5 inch wide and 10 inch wide. He wants to begin and end his pattern with a 10 inch stone so there will be one more of the 10 inch stones than of 5inch stones. His patio will be 130 inches wide.

How many 10 inch stones will Wesley need for one row?

Answers

9514 1404 393

Answer:

  9

Step-by-step explanation:

If x is the number of 10-inch stones, then (x-1) is the number of 5-inch stones, and the total width is ...

  10x +5(x-1) = 130

  15x -5 = 130 . . . . . . . eliminate parentheses

  15x = 135 . . . . . . add 5

  x = 9 . . . . . . . divide by 15

Wesley will need 9 10-inch stones for one row.

if PQR measures 75° , what is the measure of SQR

Answers

Answer:

PQR+SQR=180°(angles in a triangle)

75°+SQR=180°

SQR=180°-75°

SQR=105°

Solve for the unknown variable
4y-2=8-2y+4y
y=?

Answers

Step-by-step explanation:

I hope it helped and it is easy to understand i hope it was helpful

1)4y-2=8-2y+4y

=4y-2y+4y=8-2

2y +4y=8-2

6y+6

12

Rotation 90° counterclockwise around the origin of the point (-8,1)​

Answers

(-1, -8). When we rotate to the fourth quadrant, we make both of the coordinate values negative.

The mean output of a certain type of amplifier is 102102 watts with a standard deviation of 1212 watts. If 6363 amplifiers are sampled, what is the probability that the mean of the sample would differ from the population mean by greater than 3.43.4 watts

Answers

Answer:

0.0244 = 2.44% probability that the mean of the sample would differ from the population mean by greater than 3.4 watts.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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 deviation [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.

Mean of 102, standard deviation of 12:

This means that [tex]\mu = 102, \sigma = 12[/tex]

Sample of 63:

This means that [tex]n = 63, s = \frac{12}{\sqrt{63}}[/tex]

What is the probability that the mean of the sample would differ from the population mean by greater than 3.4 watts?

Below 102 - 3.4 = 98.6 or above 102 + 3.4 = 105.4. Since the normal distribution is symmetric, these probabilities are equal, and thus, we find one of them and multiply by two.

Probability the mean is below 98.6.

p-value of Z when X = 98.6. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{98.6 - 102}{\frac{12}{\sqrt{63}}}[/tex]

[tex]Z = -2.25[/tex]

[tex]Z = -2.25[/tex] has a p-value of 0.0122.

2*0.0122 = 0.0244

0.0244 = 2.44% probability that the mean of the sample would differ from the population mean by greater than 3.4 watts.

Lydia has 955 in her account.she withdrew 245 and later 447.How many is left in her account.​

Answers

295 is left in her account.

Answer:

263

Step-by-step explanation:

with 955 in the account, you subtract all the amount withdrawed from the main money in the account.

955-245-447

=263

find the equation of the line

Answers

Y=(6/7)x - 1/2 (where 1/2 is the y intercept and 6/7 is the slope)

10. In a group of 50 people, there are two types of professionals, engineers and managers. If 36 of them are engineers and 24 of them are managers, how many persons are both managers and engineers?​

Answers

Step-by-step explanation:

The photo above is the Venn diagram

Now, the number of persons that are both managers and engineers= n

Since, Total number of persons is 50

Therefore, 50= M+n+E

M only = 36-n

E only = 24-n

Therefore, 50= 36 - n + n + 24 - n

50 = 36+24-n

50 = 60 - n

60 - n = 50

-n = 50 - 60

-n = - 10

Therefore, n = 10

Therefore, the number of persons that are both Managers and Engineers is 10persons.

find the volume of the following figure round your answer to the nearest tenth if necessary and make sure to use pi

Answers

Answer:

524cm^2

Step-by-step explanation:

Formula for Volume of sphere= 4/3 πr^2

We have,

r=5cm

Now,

Volume(v)=4/3 πr^2 = 4/3π 5^3= 4/3π 125 = 166.666666667π = 523.598775599

Rounding to the nearest tenth,

Volume=524cm^2


This semester, the tuition fee increased to $5,871. If this represents an increase by 14%, what was the original fee?

Answers

use a calculator its easy

Part C
Based on feedback from an independent research firm, the flashlight manufacturer has decided to change the design of the flashlight. The reflector now needs to extend 4 centimeters past the center of the bulb, as shown in the diagram. In the new design, how wide will the reflector (CD) be at its widest point? Show your work.

Answers

Answer:

The answer is "18".

Step-by-step explanation:

In the given graph by concluding we observe that  on the x-axis, one step is 2 units, and when we half each of the steps it will= 1 unit

[tex]\therefore\\\\CD = distance\ from\ -(8+1)\ to\ (8+1)\ = \text{distance between} -9 \ to\ 9\ = 18[/tex]

solve for x please help (show work)

Answers

Answer:

x=-2

Step-by-step explanation:

3x+8x - 3 = -25

Combine like terms

11x -3 = -25

Add 3 to each side

11x -3+3 = -25+3

11x = -22

Divide by 11

11x/11 = -22/11

x = -2

[tex]\large\bf{\pink{ \longrightarrow \: }} \tt \:3x \: + \: 8x \: - \: 3 \: = \: - 25[/tex]

[tex]\large\bf{\pink{ \longrightarrow \: }} \tt \:11x \: - \: 3 \: = \: - 25[/tex]

[tex]\large\bf{\pink{ \longrightarrow \: }} \tt \:11x \: = \: - 25 \: + \: 3[/tex]

[tex]\large\bf{\pink{ \longrightarrow \: }} \tt \:11x \: = \: - 22[/tex]

[tex]\large\bf{\pink{ \longrightarrow \: }} \tt \: x \: = \: {\cancel\frac{ {- 22} \:^{ - 2} }{11}} \\ [/tex]

[tex]\large\bf{\pink{ \longrightarrow \: }} \tt \:x \: = \: - 2[/tex]

A welding drawing shows that the​ weld-root reinforcement cannot exceed
​" in thickness. Your weld measurement tools are​ metric, so this value needs to be converted to millimeters. You know that one inch equals 2.54 centimeters. What is the maximum​ weld-root reinforcement allowed in​ millimeters? Round your answer to the nearest tenth of a millimeter.

Answers

Answer:

3.2 millimeters

Step-by-step explanation:

1/8*2.54 *10 = 3.175

= 3.2 millimeter. (rounded to nearest tenth)

Insurance companies are interested in knowing the population percentage of drivers who always buckle up before riding in a car. When designing a study to determine this population proportion, what is the minimum number of drivers you would need to survey to be 95% confident that the population proportion is estimated to within 0.04

Answers

Answer:

The minimum number of drivers you would need to survey is 601.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].  

What is the minimum number of drivers you would need to survey to be 95% confident that the population proportion is estimated to within 0.04?

The number is n for which M = 0.04.

We don't have an estimate for the proportion, so we use [tex]\pi = 0.5[/tex]. Then

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.04\sqrt{n} = 1.96*0.5[/tex]

[tex]\sqrt{n} = \frac{1.96*0.5}{0.04}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*0.5}{0.04})^2[/tex]

[tex]n = 600.25[/tex]

Rounding up:

The minimum number of drivers you would need to survey is 601.

The answer pl shhaoksngausinxbbs pls

Answers

Answer:

D. 3

Step-by-step explanation:

A triangle can be defined as a two-dimensional shape that comprises three (3) sides, three (3) vertices and three (3) angles.

Simply stated, any polygon with three (3) lengths of sides is a triangle.

In Geometry, a triangle is considered to be the most important shape.

Generally, there are three (3) main types of triangle based on the length of their sides and these include;

I. Equilateral triangle: it has all of its three (3) sides and interior angles equal.

II. Isosceles triangle: it has two (2) of its sides equal in length and two (2) equal angles.

III. Scalene triangle: it has all of its three (3) sides and interior angles different in length and size respectively.

In Geometry, an acute angle can be defined as any angle that has its size less than ninety (90) degrees.

Hence, we can deduce that the greatest number of acute angles that a triangle can contain is three (3) because the sum of all the interior angles of a triangle is 180 degrees.

Translate and solve: fife less than z is 4

Answers

Answer:

z=9

Step-by-step explanation:

z-5=4. /+5

z=4+5

z=9

Answer:

z<-1

Step-by-step explanation:

5<z=4

collect like terms

z=<4-5

z<-1

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